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http://ssa.gov/policy/docs/ssb/v67n2/v67n2p101.html | # PERSPECTIVES: How Postsecondary Education Improves Adult Outcomes for Supplemental Security Income Children with Severe Hearing Impairments
by Robert R. Weathers II, Gerard Walter, Sara Schley, John Hennessey, Jeffrey Hemmeter, and Richard V. Burkhauser
Social Security Bulletin, Vol. 67 No. 2, 2007
Robert R. Weathers II is with the Social Security Administration. Gerard Walter and Sara Schley are with the National Technical Institute for the Deaf. John Hennessey and Jeffrey Hemmeter are with the Social Security Administration. Richard V. Burkhauser is with Cornell University.
Acknowledgments: Partial funding for the work reported in this article came from the U.S. Department of Education, National Institute of Disability and Rehabilitation Research (NIDRR), cooperative agreement 1331390038, and the National Technical Institute for the Deaf (NTID). This work does not necessarily reflect the views of NIDRR, NTID, or the Social Security Administration (SSA). The matched administrative data files used here could not have been created without the help of several senior administrators at NTID and SSA. We thank them for their commitment to this project. We also thank Joyce Manchester, L. Scott Muller, and Kalman Rupp for comments and suggestions on earlier drafts of this article. The data extract for this project is restricted-use, and permission must be granted by NTID and SSA to use these data.
## Summary
The rapid growth in the number of children participating in the Supplemental Security Income (SSI) program before the age of 18 has led policymakers to consider new methods of assisting children with disabilities in their transition from school to work. Postsecondary education represents one path that SSI children may take to acquire the skills necessary to enter employment and reduce dependency on the SSI disability program as adults. Yet little is known about SSI children's experience with postsecondary education, let alone their ability to increase their labor market earnings and reduce their time on SSI as adults in the long term. This lack of information on long-term outcomes is due in part to a lack of longitudinal data.
This article uses a unique longitudinal data set to conduct a case study of SSI children who applied for postsecondary education at the National Technical Institute for the Deaf (NTID) within the Rochester Institute of Technology. The data set was created by merging NTID administrative data on the characteristics and experiences of its applicants to Social Security Administration (SSA) longitudinal data on earnings and program participation. We used this data file to estimate the likelihood that an SSI child will graduate from NTID relative to other hearing-impaired NTID applicants, and we estimated the influence of graduation from NTID on participation in the SSI adult program and later success in the labor market.
The results of our analysis show that the percentage of NTID applicants who were SSI children increased over time, from a low of 10 percent in 1982 to more than 41 percent in 2000. However, the differences in the probability of graduation from NTID between deaf SSI children and deaf applicants who were not SSI children did not change accordingly. The probability of graduation for SSI children who applied to NTID was 13.5 percentage points lower than for those who were not SSI children. The estimated disparity indicates that targeting college retention programs toward SSI children may be an effective way to improve overall graduation rates.
Our results also show that SSI children who graduated from NTID spent less time in the SSI adult program and had higher earnings than SSI children who did not graduate. Compared with SSI children who were accepted to NTID but chose not to attend, SSI children who graduated from NTID left the SSI program 19 months earlier, were less likely to reenter the program, and at age 30 had increased their earnings by an estimated 49 percent. Our findings demonstrate that SSI children need not be relegated to a lifetime of SSI participation as adults, despite the poor overall labor market experience of this population since the creation of the SSI program in 1974.
## Introduction
The Supplemental Security Income (SSI) program is the largest federal means-tested cash assistance program in the United States. It is administered by the Social Security Administration (SSA) and provides assistance to children with disabilities, working-age adults with disabilities, and the aged, as long as they meet the income and resource requirements necessary for eligibility.1 In 2005, approximately 1 million children under the age of 18 received disability payments through the SSI program. The number of children receiving SSI has tripled over the past 15 years, far outpacing the growth of working-age adults and the aged receiving it (Social Security Administration 2006). Many of these children are likely to participate in the SSI disability program for a majority of their lifetime (Rupp and Scott 1995) because they are unlikely to reach the income or resource levels, either through work or through other means, to make a long-term exit from the SSI program. The rapid growth in the number of children receiving disability payments and the evidence that suggests that many of them will depend on these benefits for most of their lives has prompted policymakers to consider new methods to assist children in the transition from school to work. SSA program administrators have referred to these efforts as "managing against the risk of disability."2
Postsecondary education represents one path that SSI children (that is, those who enter the SSI program before age 18) may take to acquire the skills necessary to enter employment and reduce dependency on the adult SSI disability program. Yet little is known about SSI children's experience with postsecondary education, let alone its ability to increase their labor market earnings and reduce their time on SSI as adults in the long term. This lack of information on the long-term outcomes is due in part to the absence of longitudinal data on them.3
The findings reported here are from a unique longitudinal data set we created. The data set consists of administrative records from the Rochester Institute of Technology's National Technical Institute for the Deaf (NTID) linked to data from SSA's Supplemental Security Record, the Master Earnings File, and the Numident file. We use these data to conduct a case study of the subsequent educational and labor market success of SSI children as well as their SSI program participation as adults, relative to other deaf children who apply for postsecondary education.
The case study followed persons with severe hearing impairments who applied to NTID, one of two federally supported postsecondary schools that serve the population with severe hearing impairments. The postsecondary education programs offered at NTID include vocational degree programs that provide specific training for particular occupations. They also include professional degree programs that may lead to an associate of science, bachelor of arts, or master of arts degree. Almost all NTID applicants have hearing impairments that meet the medical criteria used to determine eligibility for the Social Security disability programs, and so they also are eligible to receive SSI adult benefits if they meet the income and resource tests.
We found that SSI children who graduated from NTID spent less time in the SSI adult program and had higher earnings than SSI children who did not graduate. However, we also found that SSI children who applied to NTID had a greater risk of not graduating than their fellow deaf students who did not participate in the SSI program as children. Our findings suggest that greater effort may be necessary to prepare SSI children for postsecondary education and that the currently SSA-funded youth transition demonstration projects may contribute to our understanding of how such efforts can improve adult outcomes for SSI children with disabilities.
## Literature Review
There is a significant body of research on the transition from secondary school to postsecondary education and employment for youth with disabilities. (See Wittenburg and Maag [2002] for a review of this literature.) We contribute to this literature by examining a subgroup of SSI recipients—SSI children. We describe their experiences during the transition to postsecondary education and quantify their economic outcomes as young adults. Our study is unique in that the longitudinal data on Social Security participation and earnings allowed us to examine outcomes over a relatively long period after the completion of postsecondary education. Here we summarize research related to this study and describe its contribution to the larger body of research.
### Postsecondary Education for Youth with Disabilities
As of 2003, participation in postsecondary education among youth with disabilities was estimated to be about half of the participation rate for the general population of youth (Wagner and others 2005). This research, which used the National Longitudinal Transition Survey (NLTS) and the National Longitudinal Transition Survey 2 (NLTS–2), also showed increased participation in postsecondary education for youth with disabilities from 1987 to 2001 and that this increase was greater than the increase for the general population (Wagner and others 2005). This finding indicates that the gap between the two groups has declined over time and that the transition from secondary education to postsecondary education is becoming more prevalent among youth with disabilities.
Data on postsecondary education completion rates show that youth with disabilities are less likely to complete postsecondary education than other youth. Horn and Berktold (1999) used the Beginning Postsecondary Students Longitudinal Study (BPS: 90/94) to support this finding; the BPS: 90/94 was a survey of undergraduates who enrolled in postsecondary education for the first time in the 1989–1990 period and were interviewed for the last time in 1994. Their results show that, at the time of the last interview, 53 percent of students with disabilities had completed postsecondary education or were still enrolled, compared with 64 percent of those without disabilities. Horn and Berktold state that this difference may have been partly due to differences in attributes that correlate with lower completion rates. For example, persons with disabilities were more likely to have General Educational Development (GED) degrees rather than standard high school diplomas, and persons with GED degrees are less likely to complete postsecondary education.
Research on the benefits of postsecondary education is limited to outcomes immediately following completion of postsecondary education. Horn and Berktold (1999) used the BPS: 90/94 to show that the gap between postsecondary education graduates with and without disabilities is small in terms of postgraduation employment, participation in graduate school, and participation in employment related to their postsecondary degree. They concluded that postsecondary education graduates with disabilities fare relatively well when compared with those without disabilities. This finding is in stark contrast to the experience of the general population with disabilities, which does not fare nearly as well with respect to both employment and earnings compared with the general population. However, the postsecondary education outcomes considered by Horn and Berktold focused only on the year immediately following graduation; the study did not examine employment and earnings in subsequent years. Thus, these studies may have missed differences that arise in terms of earnings growth and long-term employment prospects.
The only study that examines long-term employment outcomes among persons with disabilities was performed by Walter, Clarcq, and Thompson (2002), who used data from a 1998 version of the NTID/SSA matched data to examine employment outcomes for all NTID applicants. Their analysis suggests that a postsecondary education from NTID yields significant economic gains for persons with severe hearing impairments. However, their analysis was based on a single cross section of data and hence did not follow the individuals over time; nor did it examine whether there are differences in these outcomes between those who are former SSI children and those who are not.
### SSI Children
Research on SSI children shows that they are likely to spend a significant portion of their adult life collecting SSI benefits and that they are less likely to enroll in postsecondary education compared with the general population.
Rupp and Scott (1995) provide evidence of the length of stay in the program for SSI children. The authors used sample cohorts of persons awarded SSI as children from 1974 through 1982 and examined a 10-year follow-up period using administrative records from 1974 through 1992. They found that the mean length of the first spell of SSI participation was 11.3 years for SSI children. By the time SSI children turn 65, it is estimated that more than half of them will have spent over 25 years in the program; the mean length of stay for all children was 26.7 years.4
The postsecondary education enrollment rates for former SSI children aged 19–23 are described in Loprest and Wittenburg (2005). To examine the transition process, they used data from the National Survey of SSI Children and Families (NSCF), an SSA-funded nationally representative survey of current and former SSI children, fielded from August 2001 through July 2002.5 Part of their study examined the educational attainment of a posttransition cohort of people who were aged 19–23 in 2000 and had received SSI payments as children in 1996. At the time of the interview, they found that an estimated 42.3 percent had graduated from secondary school but were not in postsecondary school, while 6.3 percent had graduated from secondary school and made the transition to postsecondary school.6 The 6.3 percent of SSI children who enrolled in postsecondary education provides some context for our study. Although the rate was not zero, it was small compared with the estimate of 35 percent enrollment rate for youth in the general population who were aged 18–24.7 The NSCF estimate of 42 percent of SSI children who completed secondary education but did not enroll in postsecondary education may point to additional SSI children who could benefit from postsecondary education.
### How the Current Study Contributes to the Literature
Our study builds on existing research by focusing on SSI children and examining postsecondary education completion rates, as well as on how postsecondary education can influence length of stay in the adult SSI program and long-term employment outcomes. No other study has examined either postsecondary education completion rates for SSI children or long-term outcomes, such as dependency on the adult SSI disability program or adult employment associated with postsecondary education for this population. The few studies that have considered long-term outcomes for youth with disabilities who participate in postsecondary education have not taken full advantage of the longitudinal data. Our analysis used a longitudinal database and used techniques that take advantage of the longitudinal nature of our data to characterize outcomes for SSI children.
## Data
A data file based on administrative data from NTID and SSA was used for the analyses. The data file was created under a Memorandum of Agreement (MOA) whereby NTID paid SSA to create the merged data file for the purpose of conducting research on outcomes for NTID applicants. The two organizations worked together with researchers at Cornell University to design a merged NTID/SSA event history data file that could be used to track NTID applicants' outcomes for Social Security program participation, employment, and labor earnings. SSA staff constructed the file, which is securely stored at SSA; only SSA employees are allowed to perform analysis on the individual records.8
The NTID data contain information on all persons who have applied to the school since it opened in 1968. The data allow NTID applicants to be disaggregated into four groups:
1. those who were not accepted,
2. those who were accepted but chose not to attend,
3. those who attended but withdrew before earning a degree, and
4. those who graduated.
Individual information is available on the age, sex, and race of all applicants. Additional data are collected for those who attended NTID, including information on the age at which the hearing impairment began, the severity of the person's hearing impairment, and family background.
Social Security Administration data come from the Supplemental Security Record, the Master Earnings File, and the Numident file.9 The Supplemental Security Record contains the complete history of SSI program participation since the program began in 1974. The file is used to identify childhood participation in the SSI program and to construct an event history file of SSI program participation in adulthood. The Master Earnings File contains information on annual earnings that are subject to Federal Insurance Contribution Act (FICA) taxes from 1981 through 2003.10 It is used to estimate labor earnings for the age/earnings profiles. The Numident file contains information on deaths that occurred before 2004.
The resulting NTID/SSA merged data file has several features that make it superior to all other data sets that describe postsecondary education experiences of and outcomes for persons with disabilities. First, it is the only data set able to track long-term outcomes for youth with disabilities, such as adult SSI participation, employment, and earnings. Second, the NTID data include three different groups of applicants who did not graduate from NTID—those who were not accepted, those who were accepted but chose not to attend, and those who attended but withdrew before earning a degree. By comparing NTID graduates with these applicant groups, we were able to reduce the influence of selection bias associated with comparing them with all other persons who had disabilities. Third, our data were administrative, so we were able to match almost all NTID applicants to their administrative records. In this way, we avoided the usual problems with survey data that rely on self-reporting and have low response rates, which can affect validity.
We focused on applicants born from 1965 through 1979 who were alive at the time we extracted their SSA administrative records.11 We restricted our sample to persons born after 1964 because a significant amount of data in the NTID database is missing for earlier cohorts and because by doing so we avoided complications associated with SSI rule changes that occurred in the early 1980s.12 We restricted our sample to persons born before 1980 to ensure that we would observe graduation from NTID.
A total of 5,638 applicants met our criteria for the analyses. We refer to this group as NTID applicants. In some of our analyses, we used the subset of 1,366 applicants who were SSI children. Finally, we drew a sample of 9,388 SSI children from SSA administrative data who met our selection criteria for the analyses. The latter group was used to show how program participation and earnings outcomes differ between SSI children in the four NTID applicant groups and all SSI children.
Table 1 describes the variables used in our analysis, organizing them by NTID applicant group, participation in the SSI program as a child, demographic characteristics, age at onset of hearing impairment, severity of impairment, and family background characteristics. The descriptive statistics in Table 2 show how the composition of characteristics differed across the four NTID groups.13 For example, there are differences in the percentage of each NTID applicant group who were SSI children—16 percent of graduates were SSI children compared with 29 percent of those who withdrew; 24 percent of those who were accepted but chose not to attend; and 32 percent of applicants who were not accepted. The lower percentage of NTID graduates who were SSI children suggests that the former SSI children who applied to NTID had a relatively lower chance of graduating than other NTID applicants. However, there also are sizable differences across the four groups in terms of other individual characteristics, and these differences may also explain differences in graduation probabilities. Below, we describe how we accounted for these differences in our analyses.
Table 1. Definition of variables
Variable Definition
Applicant group
Graduated Value equals 1 if person graduated from NTID; 0 otherwise.
Withdrew Value equals 1 if person withdrew from NTID; 0 otherwise.
Accepted, did not attend Value equals 1 if person was accepted but did not attend NTID; 0 otherwise.
Not accepted Value equals 1 if person was not accepted into NTID; 0 otherwise.
Received SSI as a child
SSI child Value equals 1 if person received SSI payments before age 18; 0 otherwise.
Not SSI child Value equals 1 if person did not receive SSI payments before age 18; 0 otherwise.
Sex and race
Female Value equals 1 if sex is female; 0 otherwise.
Nonwhite Value equals 1 if race is nonwhite; 0 otherwise.
Age at onset of hearing loss
Age Value equals age at deaf onset; 99 or "." if missing.
Birth Value equals 1 if age at hearing loss is birth; 0 otherwise.
Ages 0–5 Value equals 1 if age at hearing loss is 0–5; 0 otherwise.
Ages 6 or older Value equals 1 if age at hearing loss is 6 or older; 0 otherwise.
Missing Value equals 1 if age at hearing loss is missing; 0 otherwise.
Severity of hearing loss
Mild Value equals 1 if lowest PTA hearing score is between 0 and 60; 0 otherwise.
Severe Value equals 1 if lowest PTA hearing score is between 61 and 90; 0 otherwise.
Severe spline Is a continuous value that is the difference between the PTA score and the score of 60, which is the definition of a severe hearing impairment. It is equal to 0 for those with a PTA score above 89 and below 60.
Profound Value equals 1 if lowest PTA hearing score is greater than 90; 0 otherwise.
Profound spline Is a continuous value that is the difference between the PTA score and the score of 90, which is the definition of a profound hearing impairment. It is equal to 0 for those with a PTA score below 90.
Father's education
Elementary Value equals 1 if father's education is elementary school; 0 otherwise.
Secondary Value equals 1 if father's education is secondary school; 0 otherwise.
College
2 years Value equals 1 if father's education is 2 years of college; 0 otherwise.
4 years Value equals 1 if father's education is 4 years of college; 0 otherwise.
5 or more years Value equals 1 if father's education is postgraduate; 0 otherwise.
Missing Value equals 1 if father's education is missing; 0 otherwise.
Mother's education
Elementary Value equals 1 if mother's education is elementary school; 0 otherwise.
Secondary Value equals 1 if mother's education is secondary school; 0 otherwise.
College
2 years Value equals 1 if mother's education is 2 years of college; 0 otherwise.
4 years Value equals 1 if mother's education is 4 years of college; 0 otherwise.
5 or more years Value equals 1 if mother's education is 5 or more years of college; 0 otherwise.
Missing Value equals 1 if mother's education is missing; 0 otherwise.
Deaf parents
Neither Value equals 1 if neither parent is deaf; 0 otherwise.
One Value equals 1 if one parent is deaf; 0 otherwise.
Two Value equals 1 if two parents are deaf; 0 otherwise.
Missing Value equals 1 if parents' hearing status is missing; 0 otherwise.
Birth year Set of indicators equal to 1 for each birth year from 1965 to 1979; 0 otherwise.
SOURCES: Data file of administrative records from the National Technical Institute for the Deaf linked to data from the Social Security Administration's Supplemental Security Record, Master Earnings File, and Numident file.
NOTE: NTID = National Technical Institute for the Deaf; SSI = Supplemental Security Income; PTA = pure tone average hearing level.
## Methods
Our analyses focused on describing the following three outcomes for SSI children:
1. The probability that an SSI child who applied to NTID would graduate, compared with NTID applicants who did not participate in the SSI program in childhood;
2. Dependency on the SSI adult program for SSI children who graduated from NTID, compared with each of the three groups of SSI children who applied but did not graduate; and
3. Levels and growth of earnings for SSI children who graduated from NTID, compared with each of the three groups of SSI children who applied but did not graduate.
Different methods were required to describe each of the outcomes. Here, we provide an overview of the methods used. The technical details can be found in Appendix A.
### Educational Outcomes
The differences in the probability of graduation between SSI children and those who were not SSI children (outcome 1) were used to assess whether the differences between the two groups are large enough for policymakers to consider special programs that specifically target SSI children who apply for postsecondary education. If there are no differences in the probability of graduation between the two groups, then postsecondary education programs specifically targeting SSI children may have a smaller potential for affecting educational success. This information is important to policymakers interested in identifying which programs have the potential to help SSI children make the transition to adult life. We do not attribute the differences to the presence of the SSI program; that is, we do not conclude that if the SSI program did not exist there would be no difference in graduation rates. SSI eligibility is based on family income and resource tests, and in the absence of the SSI program these children might have experienced similar differences in the probability of graduation because their families had lower income and resources compared with NTID applicants who were not SSI children.
The method we used to estimate differences in the probability of graduation among all applicants is referred to as a sequential response model. This type of model disaggregates the probability of graduation into a sequence of three events and may be used to show how differences in the probability of graduation are related to the probability that each of the following events will occur:
• an NTID applicant will meet the school's admission criteria,
• an accepted applicant will choose to attend NTID, and
• for those who attend NTID, whether they will graduate.
Some of those who attend NTID will withdraw from the school before completing the requirements for graduation.
We used multivariate logit models to estimate how participation in the SSI program as a child is related to the probability that each of these events will occur; therefore, our model is referred to as a sequential logit.14 The motivation for using the sequential logit is based on the descriptive statistics in Table 2, which show substantial differences in sex and race for those who are admitted to NTID, those who choose to attend, and attendees who graduate from NTID. Therefore, differences between SSI children and those who are not SSI children could be driven by differences in sex or race.15 The sequential logit model allows us to estimate how the probability that a particular event will occur and differs for those who participate in the SSI program as children, compared with those who do not, after accounting for differences in sex, race, and birth year across the two groups. It also allows us to examine differences in graduation that may be related to sex or race.
Table 2. Descriptive statistics for NTID applicants, by outcome of application (in percent unless otherwise specified)
Variable Total Not accepted Accepted,
did not attend
Mean SE Mean SE Mean SE Mean SE Mean SE
Individual characteristics
Former SSI child 24.23 0.57 31.94 1.84 23.72 1.39 28.68 0.94 15.84 0.87
Female 44.75 0.66 49.61 1.97 53.51 1.63 38.90 1.02 45.93 1.19
Nonwhite 24.49 0.57 44.03 1.96 30.96 1.51 21.41 0.86 17.89 0.92
Age at onset of hearing loss
Mean age at onset (years) -- -- -- -- -- -- 10.80 0.64 9.65 0.69
Birth -- -- -- -- -- -- 75.15 0.90 76.52 1.01
Ages 1–5 -- -- -- -- -- -- 10.23 0.63 10.77 0.74
Ages 6 or older -- -- -- -- -- -- 1.00 0.21 0.68 0.20
Missing -- -- -- -- -- -- 13.62 0.72 12.02 0.78
Severity of hearing loss
Mean hearing loss -- -- -- -- -- -- 93.13 0.45 94.87 0.46
Missing -- -- -- -- -- -- 2.22 0.31 1.60 0.30
Mild -- -- -- -- -- -- 4.22 0.42 2.68 0.39
Severe -- -- -- -- -- -- 27.89 0.94 25.81 1.04
Severe spline (mean) -- -- -- -- -- -- 5.60 0.20 5.26 0.23
Profound -- -- -- -- -- -- 65.67 0.99 69.91 1.10
Profound spline (mean) -- -- -- -- -- -- 9.52 0.21 9.87 0.23
Father's education
Elementary -- -- -- -- -- -- 11.88 0.68 8.60 0.67
Secondary -- -- -- -- -- -- 32.94 0.98 30.71 1.10
College
2 years -- -- -- -- -- -- 17.15 0.79 15.67 0.87
4 years -- -- -- -- -- -- 17.93 0.80 22.22 0.99
5 or more years -- -- -- -- -- -- 9.27 0.61 14.07 0.83
Missing -- -- -- -- -- -- 10.84 0.65 8.72 0.67
Mother's education
Elementary -- -- -- -- -- -- 10.36 0.64 8.15 0.65
Secondary -- -- -- -- -- -- 39.51 1.02 35.84 1.14
College
2 years -- -- -- -- -- -- 22.32 0.87 21.20 0.98
4 years -- -- -- -- -- -- 16.45 0.77 20.97 0.97
5 or more years -- -- -- -- -- -- 5.09 0.46 7.29 0.62
Missing -- -- -- -- -- -- 6.27 0.51 6.55 0.59
Deaf parents
Neither -- -- -- -- -- -- 88.90 0.66 93.68 0.58
One -- -- -- -- -- -- 1.65 0.27 1.20 0.26
Two -- -- -- -- -- -- 8.18 0.57 4.90 0.52
Missing -- -- -- -- -- -- 1.26 0.23 0.23 0.11
Mean birth year 1970.9 0.1 1969.4 0.2 1970.1 0.1 1971.8 0.1 1970.6 0.1
Number of observations 5,638 645 940 2,298 1,755
SOURCES: Social Security Administration (SSA) calculations using the data file of administrative records from the National Technical Institute for the Deaf linked to data from SSA's Supplemental Security Record, Master Earnings File, and Numident file.
NOTE: NTID = National Technical Institute for the Deaf; SE = standard error; SSI = Supplemental Security Income; -- = not available.
The estimates from the sequential logit may be used to show how individual characteristics have different effects on the overall probability of graduation at each event within the sequence of events leading to graduation.16 This information is important because it can show policymakers how each of the three events—NTID admission among those who apply, NTID attendance among those accepted, and NTID graduation among those who attend—is related to differences in the probability of graduation for particular types of applicants. For example, if lower graduation rates among SSI children occur because they decide not to attend NTID, efforts to improve graduation rates might consist of providing better information on how SSI children can get financial assistance. However, other efforts would be called for—such as improvements to college retention programs—if lower graduation rates occur because SSI children are withdrawing from NTID before earning a degree.
### Program Dependency and Earnings Outcomes
SSI children who graduate from NTID (outcome 1) may experience reduced dependency on the adult program (outcome 2) and increased earnings (outcome 3). Our strategy for identifying the potential impact of NTID graduation was to compare these outcomes for SSI children who graduate from NTID with the outcomes for the following groups of applicants:
• SSI children who were accepted to NTID but chose not to attend, and
• SSI children who withdrew before earning a degree.
To attribute the entire difference in these outcomes to graduation from NTID, we need to assume that the NTID graduates would have experienced the same outcomes as the comparison groups if they had not graduated from NTID. We refer to our estimates as "potential impacts" because we are not able to verify that this assumption is valid.
We used two other comparison groups to provide further context to our estimates of these outcomes:
• SSI children who applied to NTID but who did not meet the admission standard. Our hypothesis is that this comparison group spent more time in the SSI program as adults and earned less than those who were accepted to NTID because they did not meet the NTID admission standard.
• former SSI children who qualified on the basis of a primary diagnosis of deafness and were similar in age to the NTID sample.
These comparison groups place our results in the context of the SSI program. We hypothesize that the full population of deaf SSI children spent the most time in the SSI program and had the lowest earnings.
We measured adult dependency on the SSI program using survival analysis, which provides estimates of the timing of exit from and reentry into the SSI program after reaching age 19. Survival analysis entails following individuals from one particular event (for example, entering the adult SSI program) to another (for example, exiting the adult SSI program), and comparing the amount of time between events across groups. We estimated the potential effect of NTID graduation by comparing SSI children who graduated from NTID with each of our comparison groups using the following measures:
• the estimated probability of remaining in the program for each year over a 10-year period,
• the probability of leaving the program at the end of the 10-year period, and
• the estimated median number of months spent in the adult SSI program.
Dependency on the SSI Program as an Adult. For this analysis, we confined our sample to NTID applicants who were SSI children receiving SSI adult benefits at age 19.17 The event history file contains the month that the person turns 19 and either the month that the person exits the adult SSI program or the last month available in our data. Months are a natural time unit for the measurement of SSI participation because an SSI recipient's payment status is determined on a monthly basis. For presentation purposes, we grouped months into yearly intervals. Some people in our data set were still participating in the SSI program as of the last time period we recorded; that is, we never observed a transition from the SSI program for some persons. These cases are referred to as censored cases, and we accounted for them by using standard statistical techniques (described in Appendix B).
We used a similar approach to examine the timing of reentry into the adult program after a first exit. In this case, the first event was the month that a person first exited the adult SSI program, and the second event was the month that a person first reentered the SSI program. Like the analysis of first exit from the adult SSI program, we grouped months into yearly intervals for presentation and used standard techniques to account for censored cases in the analysis. Because of data limitations, we focused on the probability of reentry into the program within 5 years of first exit as another measure of SSI dependency.
Earnings. To describe the third outcome, earnings, we used age/earnings profiles to examine differences in earnings from ages 18–30 across the four groups of NTID applicants. For each person in the data set, earnings were observed for each age up to 2002, the final year that annual earnings are available in our data. A data set that contains an observation for each person at each age was created, and the dollar values were adjusted to 2004 dollars using the consumer price index for all urban consumers (CPI-U). We used three key statistics to describe the age/earnings profiles:
• the percentage of persons with at least $1 of earnings at a particular age, • the mean earnings for those with at least$1 of earnings at a particular age, and
• the mean earnings for all persons at a particular age.
Appendix B contains data for each of the three statistics. Separate profiles were estimated for each of the four NTID applicant groups using mean earnings for all persons. Mean earnings for each age were plotted in an age/earnings graph, and a third-order polynomial trend line was fit to the means to illustrate the pattern for the various groups. The analysis allowed us to examine differences in both the level and growth in earnings from ages 18–30 and to describe the potential effects of an NTID education on earnings during this period.
## Results
From 1982 to 2000, the percentage of both NTID applicants and graduates who were SSI children steadily increased. These two trends are illustrated in Chart 1, which organizes NTID applicants and graduates by the year they first applied, so that there is a common basis of comparison. The chart shows that the percentage of all NTID applicants who were SSI children increased from 10 percent in 1983 to 43 percent in 1999. It also shows that the fraction of NTID graduates who were SSI children increased from 8 percent of those who applied in 1982 to 28 percent in 1999. These results indicate that SSI children with hearing impairments accounted for a significant share of applicants and graduates during this period and that they were willing and able to participate in postsecondary education.
Chart 1.
Time series of the percentage of NTID applicants and graduates who were SSI children, by year of application
SOURCES: Social Security Administration (SSA) calculations using the data file of administrative records from the National Technical Institute for the Deaf linked to data from SSA's Supplemental Security Record, Master Earnings File, and Numident file.
NOTE: NTID = National Technical Institute for the Deaf; SSI = Supplemental Security Income.
The position of the trend lines in Chart 1 also shows that, for each application year, the fraction of eventual graduates who were SSI children was smaller than the fraction of all applicants who were SSI children. For the 1999 application-year cohort, 42 percent of applicants were SSI children, compared with only 28 percent of eventual graduates. Overall, the percentage of those who graduated and were classified as SSI children was lower than the percentage who graduated and were not in the SSI program in childhood. Hence, SSI children who applied were less likely to graduate, compared with other applicants. The chart shows that this finding existed for almost every application year from 1982 to 1999.
Finally, the slopes of the two trend lines are different.18 This difference indicates that even though both trends increased, the fraction of NTID applicants who were SSI children increased at a faster rate. As a result, the likelihood that an SSI child who applies to NTID will eventually graduate has decreased over time. More SSI children are applying to NTID, but the rate of graduation among these applicants has declined slightly over time. The estimates below more precisely measure the exact relationship between participation in SSI as a child and educational success as an adult.
### Probability of Graduation
The results of our multivariate logit model show some substantial and statistically significant differences in the characteristics of applicants who were not admitted to NTID, were admitted and chose to attend NTID, and attended and completed degree requirements. Table 3 shows the differences in the probability for each of these events between SSI children and those who were not SSI children. Compared with non-SSI children, the probability that SSI children who applied to NTID would be admitted was 4.8 percentage points lower, the probability that SSI children who were admitted would attend NTID was not statistically different, and the probability that SSI children who attended NTID would graduate was 16 percentage points lower. The difference in the graduation rate among those who attend NTID is large; after adjusting for differences in sex and race, we estimate that 47 percent of NTID attendees who were not SSI children graduated compared with only 31 percent of those who were SSI children. The difference suggests that college preparation and retention programs that target SSI children may have the potential to substantially improve their graduation rates.
Table 3. Sequential logit model results of relationship between SSI participation as a child and graduation from NTID: Estimated impact on the probability that each event will occur (in percentage points)
Variable Difference in probability of being admitted to NTID among applicants Difference in probability of attending NTID among those admitted Difference in probability of graduation among those who attend NTID
Former SSI child -4.81***
[1.09]
-0.76
[1.34]
-16.07***
[1.81]
Female -1.93***
[0.83]
-7.27***
[1.11]
8.11***
[1.55]
Nonwhite -12.42***
[1.19]
-11.28***
[1.50]
-0.69
[1.98]
Birth year indicators Yes Yes Yes
Predicted probability (percent) 88.6 81.2 42.7
Number of observations 5,638 4,993 4,053
SOURCES: Social Security Administration (SSA) calculations using the data file of administrative records from the National Technical Institute for the Deaf linked to data from SSA's Supplemental Security Record, Master Earnings File, and Numident file.
NOTES: The sequential model is based on a sequential logit specification as described in Appendix A. Logit coefficients, odds ratios, and marginal effects for the entire model are in Table A-2.
Standard errors are in brackets.
SSI = Supplemental Security Income; NTID = National Technical Institute for the Deaf.
* significant at .10 level; ** significant at .05 level; *** significant at .01 level.
The results for females and nonwhite applicants are remarkably different from those described for SSI children. Females who applied were less likely to be admitted, and those who were admitted were less likely to attend. However, the probability of graduation for females who attended NTID was 8.1 percentage points higher than that of their male counterparts. Compared with whites, nonwhites were less likely to meet the admission criteria, and those who met the criteria were less likely to choose to attend NTID. However, the differences in graduation rates between whites and nonwhites who attended NTID were not statistically different.
We also looked at the relationship between individual characteristics and the overall probability of graduation among NTID applicants at each stage of the process.19 As shown in Table 4, the probability of graduation for all SSI children who applied to NTID was 13.5 percentage points lower than that for NTID applicants who were not SSI children. The lower probability was spread over the three separate events that lead to graduation for applicants—with 1.7 percentage points attributed to the admittance step, 0.3 percentage points attributed to the attendance step, and 11.5 percentage points attributed to the graduation step. Thus, the final step was responsible for most of the disparity in the overall graduation rates for SSI children who applied to NTID compared with the rate for those who were not SSI children.
Table 4. Sequential logit model results of relationship between SSI participation as a child and graduation from NTID: Decomposition of each event's impact on the overall probability of graduation among applicants (in percentage points)
Variable Difference in
probability of
among all NTID
applicants
Difference in
probability of
due to NTID
Difference in
probability of
due to decision
to attend NTID
Difference in
probability of
due to decision
to complete an
NTID degree
Former SSI child -13.5 -1.7 -0.3 -11.5
Female 2.4 -0.7 -2.7 5.8
Nonwhite -9.1 -4.3 -4.3 -0.5
SOURCES: Social Security Administration (SSA) calculations using the data file of administrative records from the National Technical Institute for the Deaf linked to data from SSA's Supplemental Security Record, Master Earnings File, and Numident file.
NOTES: The sequential model is based on a sequential logit specification as described in Appendix A. Logit coefficients, odds ratios, and marginal effects for the entire model are in Table A-2.
SSI = Supplemental Security Income; NTID = National Technical Institute for the Deaf.
Given the importance of the graduation step, we estimated a multivariate logit model of the probability of graduation for those who attended NTID that includes the additional characteristics available for those attendees. The results are in Table 5 and are comparable with those shown in Table 3. The inclusion of the additional characteristics slightly reduces the estimated difference in the probability of graduation between former SSI children and those who had not been in the SSI program as children. However, the difference is still large and statistically significant. The probability that former SSI children who attended NTID would graduate was 13.5 percentage points lower than for those who were not SSI children. To put this result in perspective, the probability of graduation for those who were not SSI children was 46 percent, compared with an estimated 32.5 percent for former SSI children. Thus, even after controlling for sex, race, severity of hearing impairment, family background characteristics, and birth cohort, former SSI children were significantly less likely to graduate than their non-SSI counterparts.
Table 5. Logit model results of the probability of graduation for NTID attendees
Variable Coefficient Effect on probability
(percentage points)
Individual characteristic
Former SSI child -0.5887***
[0.0873]
-13.5
[1.92]
Female 0.3653***
[0.0668]
8.5
[1.54]
Nonwhite -0.0158
[0.0873]
-0.4
[2.01]
Age at onset of hearing loss
Birth -0.0049
[0.1086]
-0.1
[2.52]
Ages 1–5 (reference) . . . . . .
Ages 6 or older -0.4722
[0.3797]
-10.7
[8.16]
Missing -0.2385
[0.1503]
-5.5
[3.4]
Severity of hearing loss
Mild 0.1989
[0.2492]
-4.5
[5.5]
Severe (reference) . . . . . .
Severe spline 0.0034
[0.0077]
0.1
[0.18]
Profound 0.2314
[0.1866]
5.4
[4.28]
Profound spline -0.0009
[0.0050]
0
[0.12]
Missing 0.5797*
[0.3399]
13.4
[7.84]
Father's education
Primary -0.0707
[0.1470]
-1.6
[3.3]
Secondary 0.0831
[0.1038]
1.9
[2.4]
College
2 years (reference) . . . . . .
4 years 0.2016*
[0.1113]
4.8
[2.65]
5 or more years 0.2923**
[0.1345]
7.0
[3.21]
Missing -0.3107
[0.1977]
-6.9
[4.29]
Mother's education
Primary 0.0741
[0.1467]
1.7
[3.35]
Secondary -0.0117
[0.0930]
-0.3
[2.14]
College
2 years (reference) . . . . . .
4 years 0.2*
[0.1072]
4.7
[2.53]
5 or more years 0.3513**
[0.1591]
8.3
[3.75]
Missing 0.6418***
[0.2372]
14.8
[5.42]
Deaf parents
Neither (reference) . . . . . .
One -0.1507
[0.2871]
-3.5
[6.59]
Two -0.3507**
[0.1409]
-8.0
[3.12]
Missing -1.9819***
[0.5822]
-34.0
[5.49]
Constant 0.4382*
[0.2350]
. . .
. . .
SOURCES: Social Security Administration (SSA) calculations using the data file of administrative records from the National Technical Institute for the Deaf linked to data from SSA's Supplemental Security Record, Master Earnings File, and Numident file.
NOTES: Birth cohort dummy variables are included. Number of observations was 4,053. Standard errors are in brackets.
NTID = National Technical Institute for the Deaf; SSI = Supplemental Security Income; . . . = not applicable.
* significant at .10 level; ** significant at .05 level; *** significant at .01 level.
In summary, the result of a lower probability of graduation for SSI children was partly due to the admission standard (that is, SSI children were less likely to be accepted to NTID), but most of it was due to the lower probability of graduation for SSI children who attended NTID. Devoting efforts to improving retention rates among SSI children who attend NTID appears to be necessary to reduce the differences in graduation rates.
### Relationship Between NTID Graduation and Participation in the Adult SSI Program
Almost all of the SSI children who applied to NTID participated in the SSI program when they turned 19. After age 19, the patterns of exiting the program differed substantially between NTID graduates and each of the comparison groups: SSI children who graduated were more likely to have left the program within 10 years following age 19 and were less likely to reenter the program.
Using the survival probability for each year following age 19 as a measure, we examined the changes in the probability of remaining on the SSI program for SSI children who graduated from NTID compared with each of our comparison groups. Chart 2 shows that SSI children who graduated were more likely to remain in the program during the first 4 years following their 19th birthday—the years that many of them were attending NTID—and that after the 4th year there was a relatively sharp decline in the probability of remaining in the SSI program. By the 10th year, there was only a 34 percent chance that they would remain in the SSI program, which was significantly lower than the probability for each of the other comparison groups.
Chart 2.
Probability that SSI children will remain in the adult SSI program for 1 10 years after age 19, by NTID status
SOURCES: Social Security Administration (SSA) calculations using the data file of administrative records from the National Technical Institute for the Deaf linked to data from SSA's Supplemental Security Record, Master Earnings File, and Numident file.
NOTE: SSI = Supplemental Security Income; NTID = National Technical Institute for the Deaf.
The potential impact of NTID graduation on the likelihood that SSI children will leave the program within 10 years following their 19th birthday and the median amount of time they spend in the program are shown in Table 6. We estimated that there was a 64.7 percent chance that SSI children who graduated from NTID would leave the program within 10 years, which was larger than and statistically different from the estimates of 52.2 percent for those who withdrew from NTID, 55.3 percent for those who did not attend, 51.6 percent for those who were not accepted, and 42.9 percent for the group of all SSI children with a primary diagnosis of deafness.
Table 6. Estimates of first exit from SSI program for children receiving SSI at age 19, by NTID status
NTID status Probability of leaving SSI program
within 10 years
Median number of months
to first exit from SSI
Estimate
(percent)
Potential impact of
(percentage points)
Estimate
(percent)
Potential impact of
(percentage points)
[3.29]
. . . 95
[1.44]
. . .
Withdrew 52.2
[2.28]
12.5*** 116
[3.34]
-21***
Accepted, did not attend 55.3
[3.71]
9.4* 114
[2.58]
-19***
Not accepted 51.6
[3.84]
13.1** 118
[2.61]
-23***
All SSI children awarded benefits on the basis of a hearing impairment a 42.9
[0.57]
21.8 145
[2.38]
-50
SOURCES: Social Security Administration (SSA) calculations using the data file of administrative records from the National Technical Institute for the Deaf linked to data from SSA's Supplemental Security Record, Master Earnings File, and Numident file.
NOTES: Standard errors are in brackets.
SSI = Supplemental Security Income; NTID = National Technical Institute for the Deaf; . . . = not applicable.
a. The group of all SSI children awarded benefits on the basis of a hearing impairment is not mutually exclusive from the group of NTID graduates, and we do not calculate statistical tests for this group.
* significant at .10 level; ** significant at .05 level; *** significant at .01 level.
We also found that NTID graduation may increase the probability of SSI children leaving the program within 10 years following their 19th birthday. That probability increased by 12.5 percentage points compared with SSI children who withdrew from NTID and by 9.4 percentage points compared with SSI children who were accepted but chose not to attend. SSI children who graduated from NTID fared even better when compared with each of the other two groups; the probability of leaving the program within 10 years was 13.1 percentage points higher for SSI children who were not admitted and 21.8 percentage points higher for the group of all SSI deaf children.
The potential impact measured as the difference in the median time spent in the SSI program before leaving is also shown in Table 6. For the group of NTID graduates, the median expected time spent in the SSI program before leaving it was 95 months—substantially less than the 116 months estimated for those who withdrew from NTID, 114 months for those who chose not to attend, 118 months for those who were not accepted, and 145 months for the group of all deaf SSI children. The potential impact for SSI children who graduated was a 21-month reduction in median months spent in the program before leaving when compared with those who withdrew from NTID and a 19-month reduction when compared with those who were accepted but chose not to attend. Again, SSI children who graduated fared even better when compared with the other two groups; the median time before leaving was 23 months less than for those who were not admitted and 50 months less than for the group of all SSI deaf children.
An examination of the first SSI episode does not fully measure the relationship between NTID graduation and dependency on the SSI program. If NTID graduates were less likely to reenter the program after their first exit, then our estimate may have understated the role of an NTID degree on reductions in dependency on the SSI program. Chart 3 shows that the probability that the person would remain off the program, or survive without the program, was higher for NTID graduates across the 5 years after first exit. The sample sizes declined dramatically after the 5th year (as shown in Table A–5), and our estimates for later years have larger standard errors.
Chart 3.
Probability that SSI children will remain off the adult program after first exit, by NTID status
SOURCES: Social Security Administration (SSA) calculations using the data file of administrative records from the National Technical Institute for the Deaf linked to data from SSA's Supplemental Security Record, Master Earnings File, and Numident file.
NOTE: NTID = National Technical Institute for the Deaf; SSI = Supplemental Security Income.
Table 7 shows the probability that an SSI child would reenter the SSI program within 5 and within 10 years following first exit from the program after reaching age 19, using the survival probability as a measure.20 The probability of reentry within 5 years after leaving the program was only 11.6 percent for SSI children who graduated from NTID, which was smaller than the 21.7 percent estimate for those who withdrew, the 17.9 percent estimate for those who were accepted but chose not to attend, the 24.1 percent for those who were not accepted, and the 23.2 percent for the group of all deaf SSI children. The potential impact of NTID graduation for SSI children was a drop of 10.1 percentage points in the probability of reentering the SSI program when compared with those who withdrew and a drop of 6.3 percentage points when compared with those who chose not to attend NTID (although the latter result is not statistically significant). The estimates for the other two groups show that the group of all deaf SSI children also fared better. The probability of reentering the program within 10 years shows that the potential impact of NTID graduation is also substantial and statistically significant.
Table 7. Probability that SSI children will reenter the SSI program within 5 or 10 years following first exit from the program after reaching age 19, by NTID status
NTID status Within 5 years Within 10 years
Estimate
(percent)
Potential impact of
(percentage points)
Estimate
(percent)
Potential impact of
(percentage points)
[2.84]
. . . 14.4
[3.38]
. . .
Withdrew 21.7
[2.86]
-10.1** 27.2
[3.67]
-12.8***
Accepted, did not attend 17.9
[3.99]
-6.3 33.1
[6.28]
-18.7***
Not accepted 24.1
[4.82]
-12.5** 26.1
[5.08]
-11.7*
All SSI children awarded benefits on the basis of a hearing impairment a 23.2
[0.88]
-11.6 32.2
[1.44]
-17.8
SOURCES: Social Security Administration (SSA) calculations using the data file of administrative records from the National Technical Institute for the Deaf linked to data from SSA's Supplemental Security Record, Master Earnings File, and Numident file.
NOTES: Standard errors are in brackets.
SSI = Supplemental Security Income; NTID = National Technical Institute for the Deaf; . . . = not applicable.
a. The group of all SSI children awarded benefits based on a hearing impairment is not mutually exclusive from the group of NTID graduates, and we do not calculate statistical tests for this group.
* significant at .10 level; ** significant at .05 level; *** significant at .01 level.
### Age/Earnings Profiles
To determine the potential impact of NTID graduation on the labor earnings of SSI children during the early portion of their adult life, we compared the age/earnings profile for SSI children who graduated from NTID with the profile for SSI children who withdrew from NTID (Chart 4).21 The results show that SSI children who graduated had a mean annual earnings level of less than $1,000 between the ages of 18 and 21, ages at which most graduates were attending NTID. The trend line shows that their mean annual earnings grew from about$1,000 at age 21 to $17,500 by age 30. SSI children who withdrew from NTID experienced very little earnings growth, and by age 30 the mean annual earnings level for the group was a little less than$11,600 per year. By age 30, the gap between the two groups was almost $6,000, with SSI children who graduated earning 51 percent more than those who withdrew. Chart 4. Age/earnings for SSI children who graduated from NTID compared with those who withdrew SOURCES: Social Security Administration (SSA) calculations using the data file of administrative records from the National Technical Institute for the Deaf linked to data from SSA's Supplemental Security Record, Master Earnings File, and Numident file. NOTES: Data include zero earners. SSI = Supplemental Security Income; NTID = National Technical Institute for the Deaf; Poly. = polynomial trend line. The potential earnings impact for SSI children who graduated from NTID compared with SSI children who were accepted to NTID but did not attend is shown in Chart 5. The earnings of SSI children who graduated exceeded the earnings of those who chose not to attend at every age after reaching age 24. The earnings of those who did not attend NTID grew to slightly more than$12,100 by the time they were age 30. By age 30, SSI children who graduated from NTID were earning about $5,400 (or 44 percent) more than SSI children who were accepted to NTID but chose not to attend. Chart 5. Age/earnings profiles for SSI children who graduated from NTID compared with those who were accepted but chose not to attend SOURCES: Social Security Administration (SSA) calculations using the data file of administrative records from the National Technical Institute for the Deaf linked to data from SSA's Supplemental Security Record, Master Earnings File, and Numident file. NOTES: Data include zero earners. SSI = Supplemental Security Income; NTID = National Technical Institute for the Deaf; Poly. = polynomial trend line. Comparisons between SSI children who graduated from NTID and those who were not admitted are shown in Chart 6. SSI children who were not accepted to NTID had modest growth in mean annual earnings from age 18 to age 30, with a mean level of earnings of about$8,800 at age 30. This level was well below the level for SSI children who graduated. At age 30, the earnings gap was about $8,700; SSI children who graduated from NTID earned about 99 percent more than those who were not accepted. Chart 6. Age/earnings for SSI children who graduated from NTID compared with those who were not accepted SOURCES: Social Security Administration (SSA) calculations using the data file of administrative records from the National Technical Institute for the Deaf linked to data from SSA's Supplemental Security Record, Master Earnings File, and Numident file. NOTES: Data include zero earners. SSI = Supplemental Security Income; NTID = National Technical Institute for the Deaf; Poly. = polynomial trend line. In Chart 7, the age/earnings profiles of the four groups of NTID applicants are compared with the broader population of SSI children with a primary diagnosis of deafness. Mean earnings among the group of former SSI children were lower than for all other groups from ages 25–30, and by age 30 their annual earnings were about$6,800, which was well below the earnings of each of the NTID applicant groups.
Chart 7.
Age/earnings for SSI children using polynomial trend lines, by NTID status
SOURCES: Social Security Administration (SSA) calculations using the data file of administrative records from the National Technical Institute for the Deaf linked to data from SSA's Supplemental Security Record, Master Earnings File, and Numident file.
NOTES: Data include zero earners.
SSI = Supplemental Security Income; NTID = National Technical Institute for the Deaf.
## Discussion of the Findings and Future Research
Our analysis focused on the relative success of former SSI children who applied to NTID. We found that the percentage of NTID applicants who were SSI children increased over time, from a low of 10 percent in 1982 to more than 41 percent in 2000. However, the differences in the probability of graduation from NTID between deaf SSI children and deaf NTID applicants who were not SSI children did not change accordingly. The probability of graduation for SSI children who applied to NTID was 13.5 percentage points lower than for those who were not SSI children. Finally, using our most credible comparison group—SSI children who were accepted to NTID but chose not to attend—we found that SSI children who graduated from NTID left the SSI program early in their adult life (19 months earlier), were less likely to reenter the SSI program, and at age 30 had increased their earnings by an estimated 49 percent. Our findings demonstrate that SSI children need not be relegated to a lifetime of SSI participation as adults, despite the poor overall experience of this population since the creation of the SSI program in 1974. Postsecondary education can increase their earnings and reduce their dependency on SSI as adults.
These key findings—the lower postsecondary graduation rates among deaf SSI children and the potential for successful adult outcomes for deaf SSI children who graduate—suggest that there is a need to carefully examine the current support services for SSI children and identify improvements or new support services that will increase postsecondary graduation rates for SSI children. The Social Security Administration's youth transition demonstration projects are beginning to address these issues, but to date they have not focused on specific support for postsecondary educational achievement.
Our analysis is a case study of deaf persons who apply to NTID, and there are limitations to generalizing our results to the broader population of SSI children with disabilities. Children who qualify for the SSI program on the basis of other types of disabilities may face different barriers to postsecondary education and to successful labor market outcomes. NTID is unique in that it is tailored to the needs of the deaf population. SSI children with other types of disabilities generally must rely on postsecondary educational institutions that are not specifically designed to meet their special needs. These children may face different challenges—such as an environment with physical barriers, an inaccessible commuting environment, or social isolation—that may reduce the likelihood of application to and graduation from postsecondary institutions.
To assess the potential for programs that promote postsecondary education to reach SSI children with different impairments, we used 2001–2002 data from the Office of Special Education Programs (OSEP) on high school graduation rates for all children with disabilities, by impairment type.22 According to OSEP data, 51 percent of children with disabilities graduated from high school. That percentage is similar to the estimate of 48 percent for SSI children reported by Loprest and Wittenburg (2005), which we used as an upper bound of SSI children who may benefit in the short run from such programs.23 The OSEP data showed substantial differences in high school graduation rates by impairment type: graduation rates were above average for children with visual impairments (71 percent), hearing impairments (67 percent), specific learning disabilities (57 percent), and orthopedic impairments (56 percent); graduation rates were below average for children with mental retardation (39 percent) and children with severe emotional disturbances (32 percent). These data suggest that programs that promote postsecondary education may be more accessible to SSI children with certain types of impairments than with others.
One area for further research is to examine specific barriers in completing postsecondary education for SSI children with different types of impairments and to estimate the impact that such barriers may have on program participation and labor market outcomes.24 Another area for future research is to extend our analysis by using data from the National Survey of Children and Families (NSCF) linked to Social Security administrative records for the broader population of SSI children who undertake postsecondary education. That study would be limited initially to a short postgraduation follow-up period and a smaller sample size, but over time the data may provide further evidence of the long-term effects of postsecondary education.
Our analysis has two other limitations that could be addressed in future research. First, our analysis does not examine entry and exits from the Social Security Disability Insurance (DI) program.25 Our analysis of the age earnings/profiles, as well as preliminary analysis of cross-sectional data on DI participation among NTID applicants, suggests that postsecondary education may have the added effect of reducing dependency on the DI program. We are currently constructing an event history file of DI participation, and future research will examine how postsecondary education is related to participation in this program.
Finally, our analysis is based on nonexperimental data, so it is possible that those who graduated from NTID may have experienced better adult outcomes, in part, because of unobserved attributes such as higher levels of motivation or ability. At the same time, our findings show that positive outcomes are possible and suggest that a more rigorous evaluation, such as a randomized experiment, may be worthwhile. In the future, it would be useful to consider a project that includes a rigorous test of interventions promoting postsecondary education and examines the effect of such interventions on postsecondary education outcomes, SSI program participation, and long-term earnings.
## Appendix A:Estimating the Probability of Graduation for SSI Children
The purpose of this section is to provide further details on the estimates and the statistical methodology used to estimate the probability of graduation. Table A–1 shows the time-series estimates used to create Chart 1. Table A–2 shows additional estimates used for the sequential logit model. Table A–3 shows additional logit model estimates of the probability of graduation. In the remainder of this section we provide further details on the statistical methodology used to estimate the probability of graduation.
Table A–1. Time series data on the composition of NTID applicants and graduates
Year of first
contact with NTID
Percentage of
applicants who
as a child
Percentage of
as a child
1982 18.07 8.33
1983 10.53 8.60
1984 13.29 6.45
1985 12.35 13.08
1986 14.15 7.14
1987 17.07 11.56
1988 19.76 16.67
1989 21.65 15.04
1990 29.05 20.95
1991 27.53 20.56
1992 27.81 17.58
1993 37.20 21.18
1994 32.22 18.85
1995 32.42 27.45
1996 36.47 29.90
1997 29.90 11.86
1998 36.41 17.24
1999 41.57 28.57
2000 43.59 0
SOURCES: Social Security Administration (SSA) calculations using the data file of administrative records from the National Technical Institute for the Deaf linked to data from SSA's Supplemental Security Record, Master Earnings File, and Numident file.
NOTE: NTID = National Technical Institute for the Deaf; SSI = Supplemental Security Income.
Equation A–1
$P ( Graduate | Applied = 1 , X ) = P ( Admitted = 1 | Applied = 1 , X ) ⋅ P ( Attend = 1 | Applied = 1 , Admitted = 1 , X ) ⋅ P ( Graduate = 1 | Applied = 1 , Admitted = 1 , Attended = 1 , X )$
In Equation A–1, X represents a vector of individual characteristics that includes an indicator variable for whether the person received SSI as a child, an indicator variable for nonwhite race, an indicator variable for female sex, and a set of indicator variables for year of birth. We estimate the conditional probability that each event will occur for the particular population of interest using logit models.27
To quantify how individual characteristics are associated with the likelihood of graduation at each point in the sequential process, we use the decomposition of the sequential logit proposed by Heckman and Smith (2004), shown in Equation A–2.
Equation A–2
$∂ P ( Graduate | Applied = 1 , X ) ∂ X = ∂ P ( Admitted = 1 | Applied = 1 , X ) ∂ X ⋅ P ( Attend = 1 | Applied = 1 , Admitted = 1 , X ) ⋅ P ( Graduate = 1 | Applied = 1 , Admitted = 1 , Attend e d = 1 , X ) + P ( Admitted = 1 | Applied = 1 , X ) ⋅ P ( Attend = 1 | Applied = 1 , Admitted = 1 , X ) ∂ X ⋅ P ( Graduate = 1 | Applied = 1 , Admitted = 1 , Attend e d = 1 , X ) + ∂ P ( Admitted = 1 | Applied = 1 , X ) ⋅ P ( Attend = 1 | Applied = 1 , Admitted = 1 , X ) ⋅ P ( Graduate = 1 | Applied = 1 , Admitted = 1 , Attend e d = 1 , X ) ∂ X$
This decomposition results from the application of the chain rule to Equation A–1. The first term on the right-hand side of Equation A–2 describes the relationship between the admittance step and the overall probability of graduation; the second term shows the relationship between the attendance step and the overall likelihood of graduation; and the third term shows the relationship between the graduation step and the overall likelihood of graduation.
The NTID/SSA matched data contain additional health and family background information for the two groups—those who graduate or withdraw—who choose to attend NTID. The additional information allows us to examine whether the inclusion of additional characteristics affects our estimate of the relationship between the receipt of SSI as a child and the conditional probability of graduation from NTID for those who choose to attend.
The estimates of the logit parameters do not provide a direct measure of the relationship between individual characteristics and the probability that each event in the graduation process will occur. We use the logit parameters to estimate how individual characteristics are related to the difference in the probability that each event within the sequential graduation process will occur, based on the mean of individual-level changes in the probability.28 For the sequential logit model, we also present the results of the decomposition that shows how individual-level characteristics contribute to the likelihood of graduation at each step in the process. The estimated logit parameters and odds ratios are reported in Tables A–2 and A–3.
Table A–2. Additional sequential logit results of the relationship between SSI participation as a child and the graduation process
Variable Accepted Attended Graduated
Coefficient Odds ratio Marginal
effects
Coefficient Odds ratio Marginal
effects
Coefficient Odds ratio Marginal
effects
Former SSI child -0.4645***
[0.0980]
0.6285***
[0.0616]
-0.0481***
[0.0109]
-0.0514
[0.0906]
0.9499
[0.0861]
-0.0076
[0.0134]
-0.6972***
[0.0831]
0.4980***
[0.0414]
-0.1607***
[0.0181]
Female -0.2006**
[0.0864]
0.8182**
[0.0707]
-0.0193**
[0.0083]
-0.4902***
[0.0744]
0.6125***
[0.0455]
-0.0727***
[0.0111]
0.3431***
[0.0659]
1.4092***
[0.0928]
0.0811***
[0.0155]
Nonwhite -1.0840***
[0.0904]
0.3382***
[0.0306]
-0.1242***
[0.0119]
-0.6931***
[0.0848]
0.5000***
[0.0424]
-0.1128***
[0.0150]
-0.0295
[0.0845]
0.9709
[0.0821]
-0.0069
[0.0198]
Birth year
1966 0.2658
[0.1692]
1.3044
[0.2207]
0.0357*
[0.0212]
0.0817
[0.1613]
1.0852
[0.1750]
0.0143
[0.0277]
0.1516
[0.1551]
1.1638
[0.1805]
0.0371
[0.0379]
1967 0.3797**
[0.1728]
1.4618**
[0.2526]
0.0494**
[0.0202]
0.1140
[0.1605]
1.1208
[0.1798]
0.0199
[0.0273]
0.0859
[0.1541]
1.0897
[0.1680]
0.0211
[0.0378]
1968 0.5901***
[0.1802]
1.8042***
[0.3251]
0.0728***
[0.0187]
0.1110
[0.1600]
1.1174
[0.1788]
0.0194
[0.0273]
0.0136
[0.1541]
1.0137
[0.1562]
0.0033
[0.0378]
1969 0.6125***
[0.1759]
1.8451***
[0.3246]
0.0749***
[0.0180]
0.5264***
[0.1674]
1.6928***
[0.2834]
0.0822***
[0.0228]
-0.0369
[0.1466]
0.9638
[0.1413]
-0.0090
[0.0359]
1970 0.6329***
[0.1837]
1.8831***
[0.3460]
0.0774***
[0.0186]
0.1960
[0.1637]
1.2166
[0.1991]
0.0336
[0.0268]
0.0398
[0.1549]
1.0406
[0.1612]
0.0097
[0.0379]
1971 0.7691***
[0.1897]
2.1579***
[0.4094]
0.0915***
[0.0178]
0.0930
[0.1628]
1.0974
[0.1786]
0.0164
[0.0281]
-0.0197
[0.1582]
0.9805
[0.1551]
-0.0048
[0.0386]
1972 0.7460***
[0.2115]
2.1085***
[0.4460]
0.0869***
[0.0194]
0.3340*
[0.1827]
1.3965*
[0.2551]
0.0551**
[0.0277]
-0.1330
[0.1664]
0.8754
[0.1457]
-0.0324
[0.0404]
1973 0.9294***
[0.2073]
2.5330***
[0.5251]
0.1065***
[0.0176]
0.5124***
[0.1840]
1.6693***
[0.3071]
0.0814***
[0.0255]
-0.2702
[0.1652]
0.7632
[0.1261]
-0.0649*
[0.0391]
1974 0.9625***
[0.2125]
2.6182***
[0.5563]
0.1088***
[0.0175]
0.0967
[0.1719]
1.1016
[0.1894]
0.0171
[0.0298]
-0.3212*
[0.1715]
0.7253*
[0.1244]
-0.0771*
[0.0403]
1975 1.5466***
[0.2822]
4.6953***
[1.3251]
0.1445***
[0.0144]
0.7759***
[0.2117]
2.1725***
[0.4599]
0.1141***
[0.0246]
-0.1904
[0.1736]
0.8266
[0.1435]
-0.0461
[0.0416]
1976 1.9192***
[0.3176]
6.8156***
[2.1648]
0.1632***
[0.0122]
1.2038***
[0.2381]
3.3328***
[0.7934]
0.1573***
[0.0206]
-0.1261
[0.1728]
0.8815
[0.1523]
-0.0305
[0.0416]
1977 1.9381***
[0.3281]
6.9458***
[2.2788]
0.1605***
[0.0120]
2.0937***
[0.3266]
8.1147***
[2.6505]
0.2081***
[0.0135]
-0.3876**
[0.1684]
0.6787**
[0.1143]
-0.0926**
[0.0391]
1978 1.7251***
[0.2972]
5.6129***
[1.6681]
0.1539***
[0.0133]
1.4081***
[0.2522]
4.0881***
[1.0309]
0.1726***
[0.0186]
-0.5450***
[0.1746]
0.5799***
[0.1012]
-0.1281***
[0.0390]
1979 1.3335***
[0.2544]
3.7942***
[0.9653]
0.1355***
[0.0159]
0.5186***
[0.1973]
1.6798***
[0.3314]
0.0830***
[0.0274]
-0.9355***
[0.1938]
0.3924***
[0.0760]
-0.2095***
[0.0377]
Constant 1.9054***
[0.1141]
. . .
. . .
. . .
. . .
1.5078***
[0.1103]
. . .
. . .
. . .
. . .
-0.1200
[0.1043]
. . .
. . .
. . .
. . .
Observations 5,638 5,638 5,638 4,993 4,993 4,993 4,053 4,053 4,053
SOURCES: Social Security Administration (SSA) calculations using the data file of administrative records from the National Technical Institute for the Deaf linked to data from SSA's Supplemental Security Record, Master Earnings File, and Numident file.
NOTES: Standard errors in brackets.
SSI = Supplemental Security Income; . . . = not applicable.
* significant at .10 level; ** significant at .05 level; *** significant at .01 level.
Table A–3. Additional logit model estimates of the probability of graduation
Variable Model with only
SSI child variable
Model with variables
available for all applicants
Model with full set
of variables for attendees
Coefficient Odds ratio Marginal effects
(percentage points)
Coefficient Odds ratio Marginal effects
(percentage points)
Coefficient Odds ratio Marginal effects
(percentage points)
Individual characteristics
Former SSI child 0.7590***
[0.0800]
2.1362***
[0.1709]
17.7***
[1.74]
0.7639***
[0.0814]
2.1467***
[0.1748]
17.7***
[1.76]
0.5887***
[0.0873]
1.8017***
[0.1574]
13.5***
[1.92]
Female . . .
. . .
. . .
. . .
. . .
. . .
-0.3224***
[0.0652]
0.7244***
[0.0472]
-7.7***
[1.56]
-0.3653***
[0.0668]
0.6940***
[0.0463]
-8.5***
[1.54]
Nonwhite . . .
. . .
. . .
. . .
. . .
. . .
0.0971
[0.0828]
1.1019
[0.0913]
2.3
[1.96]
0.0158
[0.0873]
1.0159
[0.0887]
0.4
[2.01]
Age at onset of hearing loss
Birth . . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
0.0049
[0.1086]
1.0049
[0.1091]
0.1
[2.52]
Ages 6 or older . . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
0.4722
[0.3797]
1.6036
[0.6089]
10.7
[8.16]
Missing . . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
0.2385
[0.1503]
1.2693
[0.1908]
5.5
[3.4]
Severity of hearing loss
Mild . . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
0.1989
[0.2492]
1.2201
[0.3040]
4.5
[5.5]
Spline severe . . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
-0.0034
[0.0077]
0.9966
[0.0077]
-0.1
[0.18]
Profound . . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
-0.2314
[0.1866]
0.7934
[0.1480]
-5.4
[4.28]
Profound spline . . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
0.0009
[0.0050]
1.0009
[0.0050]
0.0
[0.12]
Missing . . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
-0.5797*
[0.3399]
0.5600*
[0.1904]
-13.4*
[7.84]
Father's education
Primary . . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
0.0707
[0.1470]
1.0733
[0.1578]
1.6
[3.3]
Secondary . . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
-0.0831
[0.1038]
0.9203
[0.0955]
-1.9
[2.4]
College
4 years . . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
-0.2016*
[0.1113]
0.8174*
[0.0910]
-4.8*
[2.65]
5 years or more . . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
-0.2923**
[0.1345]
0.7466**
[0.1004]
-7.0**
[3.21]
Missing . . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
0.3107
[0.1977]
1.3643
[0.2698]
6.9
[4.29]
Mother's education
Primary . . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
-0.0741
[0.1467]
0.9286
[0.1362]
-1.7
[3.35]
Secondary . . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
0.0117
[0.0930]
1.0117
[0.0941]
0.3
[2.14]
College
4 years . . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
-0.2000*
[0.1072]
0.8187*
[0.0878]
-4.7*
[2.53]
5 years or more . . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
-0.3513**
[0.1591]
0.7038**
[0.1119]
-8.3**
[3.75]
Missing . . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
-0.6418***
[0.2372]
0.5263***
[0.1249]
-14.8***
[5.42]
Deaf parents
One . . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
0.1507
[0.2871]
1.1626
[0.3337]
3.5
[6.59]
Two . . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
0.3507**
[0.1409]
1.4201**
[0.2002]
8.0**
[3.12]
Missing . . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
1.9819***
[0.5822]
7.2564***
[4.2250]
34.0***
[5.49]
Inclusion of birth cohort dummy variables No No Yes
Constant 0.1041***
[0.0359]
. . .
. . .
. . .
. . .
0.2206***
[0.0468]
. . .
. . .
. . .
. . .
0.4382*
[0.2350]
. . .
. . .
. . .
. . .
Observations 4,053 4,053 4,053 4,053 4,053 4,053 4,053 4,053 4,053
SOURCES: Social Security Administration (SSA) calculations using the data file of administrative records from the National Technical Institute for the Deaf linked to data from SSA's Supplemental Security Record, Master Earnings File, and Numident file.
NOTES: Standard errors in brackets.
SSI = Supplemental Security Income; . . . = not applicable.
* significant at .10 level; ** significant at .05 level; *** significant at .01 level.
## Appendix B:Technical Description of Survival Analysis
The purpose of this section is to provide additional details on the estimates and methodology for the analysis of time spent in the SSI program, along with additional details on the estimates of age/earnings profiles. Table B–1 shows the estimates of the time to first exit from the SSI program that are used for Chart 2. Table B–2 shows the estimates of the time to reentry into the SSI program that are used for Chart 3. Table B–3 shows the data used to construct the age/earnings profiles that are used for Charts 4 through 7. In the remainder of this section we provide further details on survival analysis, which is the technique used to construct the estimates of the time spent in the SSI program.
Table B–1. Lifetable estimates of time to first exit from SSI for adults who received SSI as a child, by NTID status
Years
following
age 19
Graduated Withdrew Accepted, did not attend Not accepted All former SSI children with a
primary diagnosis of deafness
Number
eligible
Hazard
(multiplied
by 100)
Survival
(percent)
Number
eligible
Hazard
(multiplied
by 100)
Survival
(percent)
Number
eligible
Hazard
(multiplied
by 100)
Survival
(percent)
Number
eligible
Hazard
(multiplied
by 100)
Survival (percent) Number
eligible
Hazard
(multiplied
by 100)
Survival
(percent)
1 231 0.11 98.70 555 0.23 97.30 193 0.17 97.93 179 0.09 98.88 9,388 0.31 96.34
2 228 0.18 96.54 540 0.23 94.59 189 0.13 96.37 177 0.09 97.77 9,037 0.29 93.07
3 223 0.15 94.81 525 0.34 90.81 186 0.18 94.30 175 0.29 94.41 8,723 0.32 89.53
4 219 0.23 92.21 501 0.37 86.85 182 0.14 92.75 169 0.40 89.94 8,378 0.41 85.18
5 213 0.86 83.12 482 0.65 80.36 179 0.78 84.46 161 0.53 84.36 7,958 0.45 80.75
6 192 0.96 74.03 446 0.68 74.05 163 0.92 75.65 151 0.51 79.33 7,533 0.50 76.01
7 171 1.33 63.08 411 0.94 66.17 146 1.19 65.53 142 0.68 73.10 6,967 0.57 71.02
8 142 1.94 49.92 336 0.82 59.98 119 0.90 58.81 127 0.91 65.49 5,645 0.64 65.75
9 107 1.59 41.23 275 1.05 52.89 103 0.95 52.43 110 1.15 57.04 4,461 0.62 61.07
10 82 1.29 35.31 219 0.85 47.77 89 1.33 44.69 93 1.37 48.36 3,451 0.56 57.09
Cumulative
probability of
exit within
10 years
(percent)
64.7
[3.29]
52.2
2.28
55.3
3.71
51.6
3.84
42.9
0.57
Median
months to
SSI exit a
95
[1.44]
116
[3.34]
114
[2.58]
118
[2.61]
145
[2.38]
SOURCES: Social Security Administration (SSA) calculations using the data file of administrative records from the National Technical Institute for the Deaf linked to data from SSA's Supplemental Security Record, Master Earnings File, and Numident file.
NOTES: Standard errors are in brackets.
SSI = Supplemental Security Income; NTID = National Technical Institute for the Deaf.
a. Rounded to the nearest month.
Table B–2. Lifetable estimates of time to SSI reentry for adults who received SSI as a child, by NTID status
Years
following
first exit
Graduated Withdrew Accepted, did not attend Not accepted All former SSI children with a
primary diagnosis of deafness
Number
eligible
Hazard
(multiplied
by 100)
Survival
(percent)
Number
eligible
Hazard
(multiplied
by 100)
Survival
(percent)
Number
eligible
Hazard
(multiplied
by 100)
Survival
(percent)
Number
eligible
Hazard
(multiplied
by 100)
Survival
(percent)
Number
eligible
Hazard
(multiplied
by 100)
Survival
(percent)
1 157 0.29 96.63 295 0.62 92.82 115 0.46 94.59 104 0.62 92.82 3,315 0.69 92.07
2 135 0.20 94.39 242 0.34 89.15 101 0.18 92.62 84 0.53 87.09 2,619 0.52 86.53
3 120 0.29 91.12 205 0.36 85.39 89 0.30 89.35 73 0.36 83.36 2,122 0.33 83.17
4 107 0.25 88.41 166 0.39 81.52 78 0.70 82.11 64 0.43 79.12 1,764 0.40 79.28
5 92 0 88.41 136 0.34 78.26 64 0 82.11 51 0.35 75.86 1,371 0.26 76.84
6 79 0 88.41 109 0.17 76.68 51 0.35 78.72 44 0.22 73.91 994 0.22 74.88
7 71 0.27 85.58 87 0.21 74.74 44 0.42 74.84 33 0 73.91 710 0.22 72.96
8 52 0 85.58 69 0 74.74 35 0.56 70.01 23 0 73.91 520 0.17 71.51
9 45 0 85.58 54 0 74.74 25 0.38 66.90 17 0 73.91 376 0.10 70.64
10 36 0 85.58 44 0.22 72.82 19 0 66.90 15 0 73.91 280 0.34 67.80
Cumulative
probability
of reentry
within— a
5 years 11.60
[2.84]
21.70
[2.86]
17.90
[3.99]
24.10
[4.82]
23.16
[0.88]
10 years 14.40
[3.38]
27.20
[3.67]
33.10
[6.28]
26.10
[5.08]
32.2
[1.44]
SOURCES: Social Security Administration (SSA) calculations using the data file of administrative records from the National Technical Institute for the Deaf linked to data from SSA's Supplemental Security Record, Master Earnings File, and Numident file.
NOTES: Standard errors are in brackets.
SSI = Supplemental Security Income; NTID = National Technical Institute for the Deaf.
a. Median months to reentry not estimated.
Table B–3. Data used in age/earnings profiles for NTID applicants who received SSI as a child, by age and NTID status
Age Graduated Withdrew Accepted, did not attend Not accepted Graduated but not
a former SSI child
All former SSI children with
a primary diagnosis of deafness
Percentage
with earnings
Mean (dollars) Percentage
with earnings
Mean (dollars) Percentage
with earnings
Mean (dollars) Percentage
with earnings
Mean (dollars) Percentage
with earnings
Mean (dollars) Percentage
with earnings
Mean (dollars)
Earners Earners
and non-
earners
Earners Earners
and non-
earners
Earners Earners
and non-
earners
Earners Earners
and non-
earners
Earners Earners
and non-
earners
Earners Earners
and non-
earners
18 46.4 934 434 53.0 963 510 48.4 845 409 40.8 753 307 57.4 1,076 618 42.5 1,113 473
19 45.0 1,219 548 47.6 1,357 646 49.3 1,244 614 46.6 831 387 55.2 1,254 692 47.3 1,804 854
20 50.0 1,425 712 51.0 2,042 1,041 51.6 1,894 977 50.5 1,462 738 57.8 1,576 910 50.8 2,889 1,468
21 55.8 1,820 1,015 57.5 3,334 1,917 54.3 2,429 1,318 60.2 2,370 1,427 62.3 1,932 1,203 54.1 4,165 2,255
22 57.2 2,603 1,489 64.8 4,372 2,833 62.3 3,823 2,383 65.0 4,039 2,627 64.0 2,774 1,775 55.8 5,277 2,946
23 69.4 4,460 3,096 66.2 6,188 4,094 65.0 5,481 3,564 73.8 5,117 3,776 69.3 4,820 3,341 55.1 6,461 3,562
24 68.7 7,410 5,091 70.4 7,698 5,420 66.8 7,925 5,295 73.3 6,352 4,656 74.0 7,724 5,716 54.9 7,627 4,191
25 76.7 10,140 7,774 70.7 9,404 6,646 72.2 9,115 6,586 71.6 7,362 5,269 79.9 10,593 8,460 54.9 8,650 4,745
26 84.6 12,560 10,624 72.3 10,544 7,618 74.9 10,237 7,665 72.9 8,697 6,337 83.8 13,131 11,003 55.2 9,439 5,209
27 86.6 14,655 12,689 73.1 11,788 8,615 74.9 12,490 9,351 72.7 9,963 7,241 86.5 15,619 13,507 55.0 10,203 5,614
28 86.6 17,003 14,725 73.8 13,177 9,727 78.9 12,328 9,729 68.7 11,054 7,596 88.6 17,570 15,572 55.2 10,797 5,956
29 85.2 18,681 15,914 75.1 14,371 10,788 79.1 13,992 11,063 69.2 11,895 8,230 89.8 20,073 18,019 54.8 11,445 6,268
30 84.5 20,776 17,560 76.2 15,232 11,610 81.1 14,996 12,159 73.2 12,071 8,842 90.4 21,748 19,668 55.7 12,246 6,822
31 81.8 20,689 16,915 73.2 16,538 12,107 79.4 17,636 14,001 74.6 12,351 9,218 90.1 23,408 21,090 56.2 12,525 7,037
32 84.8 22,626 19,187 75.7 16,882 12,787 78.1 18,011 14,061 66.1 14,480 9,577 88.7 25,418 22,556 55.2 13,168 7,268
33 80.8 25,358 20,491 75.5 17,071 12,892 82.0 19,529 16,014 70.4 14,707 10,350 87.6 26,818 23,505 53.5 14,065 7,530
34 80.5 28,815 23,202 66.4 18,498 12,290 77.1 21,175 16,335 64.8 16,038 10,398 86.2 27,971 24,112 53.1 14,949 7,943
35 84.7 31,000 26,271 66.7 19,552 13,035 86.0 20,629 17,741 59.2 16,878 9,984 85.4 28,187 24,078 51.9 15,586 8,086
SOURCES: Social Security Administration (SSA) calculations using the data file of administrative records from the National Technical Institute for the Deaf linked to data from SSA's Supplemental Security Record, Master Earnings File, and Numident file.
NOTE: NTID = National Technical Institute for the Deaf; SSI = Supplemental Security Income.
The probability that an exit from the SSI program will occur within 1-year intervals beginning at age 19 may be described using a hazard function or a survival function. Both measures use the probability of failure, ft, in time interval t. The probability of failure is defined as the percentage of persons in the SSI program at the beginning of the time interval who are observed leaving the SSI program within the 12-month interval. The probability of failure is shown in Equation B–1.
Equation B–1
$f t = d t ( N t − m t 2 )$
In Equation B–1, dt is the number of people who leave the program in year t, Nt is the total number of persons observed at the beginning of the year, and mt is the number of censored observations within year t. Censored cases are those for which we do not have data on participation in the program within the time interval and so do not know whether the participants left the program.
The hazard at time t, λt, is the probability that a person will exit the SSI program within a 1-year interval, given that the person has not left the program at the beginning of the interval (shown in Equation B–2).
Equation B–2
$λ j = f j ( 1 − f j 2 ) ⋅ ( t j + 1 − t j )$
Where tj+1tj is the length of the interval in months—which is 12 in our case. The denominator is the standard adjustment for censored cases in the interval.29
The probability that a person remains on the SSI program until period j, referred to as survival (Sj), is the probability that a person has not left the SSI program within a particular interval (shown in Equation B–3).
Equation B–3
$S j = ∏ k = 1 j ( 1 − f k )$
Equation B–3 is simply the probability that failure will not occur in each time interval from 1 to j.
Equations B–1 through B–3 are modified to describe the hazard and the survival estimates for reentry into the SSI program within 1-year intervals, beginning at the point when applicants leave the SSI program. In this case, the hazard rate in Equation B–1 represents the probability that an applicant will reenter the program within a 1-year interval, given that he or she has not reentered the program before the interval. The survival rate in Equation B–3 represents the probability that an applicant has not reentered the SSI program within a particular interval.
## Notes
1 See Daly and Burkhauser (2003) for an overview of the SSI program.
2 The term "managing against the risk of disability" in the context of the children and youth remaining in the SSI disability program has been used by the former Deputy Commissioner for Disability and Income Support Programs at SSA (Gerry 2002).
3 Wittenburg and Maag (2002) identify the lack of data as a limitation to research on the relationship between children's participation in the SSI program and adult outcomes. The National Council on Disability (2003) also identifies limitations in the data available to examine postsecondary education for youth with disabilities.
4 Rupp and Scott (1995) do not disaggregate the length of stay in the program by the time spent on SSI as a child and the time spent in the program as an adult. Rather, for children, they estimate the total time spent in the program. Thus, one cannot use their estimates to identify the portion of time spent in the program as a child and the portion of time spent in the program as an adult.
5 See Davies and Rupp (2006) for further information on the NSCF data.
6 Of the remaining SSI children, 38.5 percent had dropped out of secondary school and 12.9 percent were still enrolled.
7 Estimates of enrollment rates vary across sources and subgroups. The 35 percent estimate is based on all persons aged 18–24. The rate is estimated from the Current Population Survey (CPS), as reported in Hurst and Hudson (2005). Estimates from other surveys range from 32 percent to almost 40 percent.
8 The data merge is possible under the authority of the Privacy Act of 1974 as amended by U.S.C. Section 552a (b) (5), which states, "disclosures may be made with advance adequate written assurance that the record will be used solely as a statistical and reporting record, and transferred in a form that is not individually identifiable."
9 The NTID/SSA merged data file contains information on a total of 13,863 persons who applied to NTID. Of these, 1,597 were not accepted to NTID, 2,068 were accepted but chose not to attend, 5,128 withdrew before completing a degree, and 5,070 graduated from NTID.
10 Although FICA earnings cover most workers, some persons may work in jobs not covered by FICA. Thus, our estimates must be interpreted as employment and earnings within the covered sector.
11 There were 66 deaths among the 5,704 sample members in our case study. The sample size is too small to treat these cases as separate outcomes in our analysis. We estimated the models with and without these cases. Although there was a slight difference in magnitude, it did not have a large impact on the results.
12 In particular, Public Law 96–265 (enacted in 1980) changed the rules regarding parental deeming. Children aged 18 or older were no longer subject to parental deeming for the purposes of program eligibility.
13 Note that Table 2 does not cover the SSA administrative sample of all former SSI children who had a primary diagnosis of deafness and who were born from 1964 through 1980. The reason is that NTID does not have data on those who do not apply for admission.
14 The technical details of the sequential logit model are given in Appendix A. It is important to emphasize that this is a reduced form model that describes the NTID graduation process, and not a formal structural model. Nonetheless, the descriptive results can be very informative to policymakers, as shown in Heckman and Smith (2004) and Ruiz-Quintanilla and others (2006).
15 To illustrate this point, the descriptive statistics show that former SSI children are less likely to graduate. They also show that nonwhites are less likely to graduate. Because SSI children tend to be nonwhite, it is possible that SSI children are less likely to graduate because they tend to be nonwhite, not because they participated in the program as children. Researchers have found lower college graduation rates among minority students and have attributed the findings to the low percentages of minority students on college campuses, which may lead to social isolation, lower social attachment, and, therefore, lower graduation rates (Scott and others 2006). At the same time, it is possible that nonwhites are less likely to graduate because they tend to participate in the SSI program as children. Research by Rupp and others (2006) show that 52.8 percent of all SSI children are nonwhite. The descriptive statistics cannot differentiate between these two alternative explanations. The multivariate models described below provide a measure of the influence of participation in the SSI program as a child, holding race and other characteristics constant.
16 See Appendix A for details.
17 We used age 19 because many SSI children have a short period of time around their 18th birthday when they are out of the program. As of their 19th birthday, 1,158 of the 1,366 SSI children were in the program. We also estimated the models for those who we observed collecting SSI adult benefits, beginning in the month they turned 18. The sample sizes were smaller for this analysis, but the results were similar to those described in this article. They are available on request from the corresponding author, [email protected].
18 We tested for the difference in slopes by estimating a regression that allowed for a separate intercept for each series but restricted the slopes to be equal (restricted model) and estimated a regression that allowed separate intercepts and slopes for each trend line (unrestricted model). We computed an F statistic as follows:
$F ( J , n − K ) = ( R u 2 − R r 2 ) / J ( 1 − R u 2 ) / ( n − K )$
Where J is the number of restrictions, which is equal to 1 in our case, n is the number of observations (which is equal to 36) and K is the number of independent variables in the unrestricted model (which is equal to four separate constants and slopes). The R-squared for the restricted model is 0.776487 and the R-squared for the unrestricted model is 0.810819. Thus, F (1,32) = 5.807 > 4.17, which is the 95th percentile of the corresponding F, and we can reject the hypothesis that the two slopes are the same.
19 The decomposition is based on estimates from Table 3. For example, the first term in decomposition shows the contribution of the admitted step to the overall probability of graduation. The first term in Equation A–2 in Appendix A shows that this can be estimated by multiplying the change in the probability of being admitted for SSI children by the conditional probability of attending and by the conditional probability of graduating given attendance. Using the values shown in Table 3, the first term of the decomposition is .0482 * 0.812 * .427 = -.017. We use the term "unconditional probability" to differentiate the probability of graduation among all applicants from the probability of graduation conditional on an applicant being admitted to and choosing to attend NTID.
20 We are unable to produce credible estimates of the median time to reentry because most of our sample does not reenter the SSI program.
21 In the comparisons that follow, we focused on former SSI children who graduated from NTID and compared them with SSI children who were in each of the three groups that did not graduate from NTID. As we showed earlier, SSI children are less likely to graduate from NTID compared with those who had not been on SSI as children. SSI children also had age/earnings profiles that were slightly lower than NTID graduates who were not SSI children. The results are available on request from the corresponding author, [email protected].
22 See Table 1–22 from Office of Special Education and Rehabilitative Services, Office of Special Education Programs (2005).
23 Loprest and Wittenburg (2005) do not disaggregate graduation rates by impairment type, which is why we use the OSEP data on graduation rates for all SSI children, by impairment type.
24 See Cornell University http://www.ilr.cornell.edu/edi/p-ccfid.cfm for a study that assesses the state of Web accessibility in the community college network for students with disabilities. The study focuses on examining problems that prospective students with disabilities may have with the online admissions application process, applying for financial aid via the Web, as well as finding important programmatic information on college Websites.
25 The DI program covered under Social Security is a social insurance program funded through payroll tax contributions to the Social Security trust funds, whereas the SSI program is a means-tested cash assistance program funded from general revenues. There are several important differences in these two programs that make separate analysis more practical than attempting to model the two together. We plan to conduct future research on the relationship between postsecondary education and dependency on the DI program.
26 See Madalla (1983) for more information on the sequential logit and Ruiz-Quintanilla and others (2006) for a recent application of the sequential logit to participation in SSA demonstration projects.
27 The logit for the first step was estimated by using the sample of all applicants to NTID. The logit for the second step used the subset of applicants who were admitted to NTID. The logit for the third step used the subset of applicants who were admitted and chose to attend NTID.
28 We used the Stata program written by Bartus (2004) to estimate the changes in the probability related to a change in each characteristic in our sequential logit model.
29 See Allison (1995, 46) for more details on the adjustment for censored observations.
## References
Allison, Paul D. 1995. Survival analysis using the SAS system: A practical guide. Cary, North Carolina: SAS Institute.
Bartus, Tamus. 2005. Estimation of marginal effects using Margeff. Stata Journal 5(3)309–329.
Burkhauser, Richard V., and Mary C. Daly. 2002. Policy watch: U.S. disability policy in a changing environment. Journal of Economic Perspectives 16(1)213–224.
Daly, Mary C., and Richard V. Burkhauser. 2003. The Supplemental Security Income program. In Means tested transfer programs in the United States, ed. Robert Moffitt, 79–140. Chicago: University of Chicago Press for the NBER.
Davies, Paul S., and Kalman Rupp. 2006. An overview of the National Survey of SSI Children and Families and related products. Social Security Bulletin 66(2)7–20.
Dowrick, Peter W., John Anderson, Katharina Heyer, and Joie Acosta. 2005. Postsecondary education across the U.S.A.: Experiences of adults with disabilities. Journal of Vocational Rehabilitation 22(1)41–47.
Gerry, Martin. 2002. Transcript from a public presentation at the 2002 National Workforce Inclusion Conference, March 13. (Accessed January 24, 2005.)
Heckman, James, and Jeffrey Smith. 2004. The determinants of participation in a social program: Evidence from the Job Training Partnership Act. Journal of Labor Economics 22(4): 243–298.
Horn, Laura, and Jennifer Berktold. 1999. Students with disabilities in postsecondary education: A profile of preparation, participation, and outcomes. Washington, DC: National Center for Education Statistics.
Hurst, David, and Lisa Hudson. 2005. Estimating undergraduate enrollment in postsecondary education using National Center for Education Statistics data (NCES 2005–063). U.S. Department of Education, National Center for Education Statistics. Washington, DC: Government Printing Office.
Lancaster, Tony. 1990. The econometric analysis of transition data. Cambridge University Press.
Loprest, Pamela, and David Wittenburg. 2005. Choices, challenges, and options: Child SSI recipients preparing for the transition to adult life. http://www.urban.org/url.cfm?ID=411168 (accessed May 5, 2006).
Madalla, G.S. 1982. Limited dependent and qualitative variables in econometrics. Cambridge University Press.
Office of Special Education and Rehabilitative Services, Office of Special Education Programs. 2005. 26th Annual (2004) report to Congress on the implementation of the Individuals with Disabilities Education Act, vol. 1, Washington, DC.
Ruiz-Quintanilla, Antonio, Robert R. Weathers II, Valerie Melburg, Kimberly Campbell, and Nawaf Madi. 2006. Participation in programs designed to improve employment outcomes for persons with psychiatric disabilities: Evidence from the New York WORKS demonstration project. Social Security Bulletin 66(2)49–79.
Rupp, Kalman, and Charlie Scott. 1995. Length of stay on the Supplemental Security Income Program. Social Security Bulletin 58(1)29–47.
Rupp, Kalman, Paul S. Davies, Chad Newcomb, Howard Iams, Carrie Becker, Shanti Mulpuru, Stephen Ressler, Kathleen Romig, and Baylor Miller. 2006. A profile of children with disabilities receiving SSI: Highlights from the National Survey of SSI Children and Families. Social Security Bulletin 66(2)21–48.
Scott, Marc, Thomas Bailey, and Greg Kienzl. 2006. Relative success? Determinants of college graduation rates in public and private colleges in the U.S. Research in Higher Education 47(3)249–279.
Social Security Administration. 2006. Children receiving SSI. Washington, DC: Social Security Administration.
Wagner, Mary, Lynn Newman, Renee Cameto, and Phyllis Levine. 2005. Changes over time in the early postschool outcomes of youth with disabilities: A report of findings from the National Longitudinal Transition Study (NLTS) and the National Longitudinal Transition Study-2 (NLTS2). Menlo Park, CA: SRI International.
Walter, Gerard G., Jack R. Clarcq, and Wendell S. Thompson. 2002. Effect of degree on improving the economic status of individuals who are deaf. Journal of the American Deafness and Rehabilitation Association 35(4)30–46.
Wittenburg, David C., and Elaine Maag. 2002. School to where? A literature review on economic outcomes of youth with disabilities. Journal of Vocational Rehabilitation 17(4)265–280. | 2015-03-31T00:17:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 6, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.30569931864738464, "perplexity": 2384.4619668510586}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-14/segments/1427131300031.99/warc/CC-MAIN-20150323172140-00099-ip-10-168-14-71.ec2.internal.warc.gz"} |
https://pdglive.lbl.gov/DataBlock.action?node=M013W1&home=sumtabM | #### PRODUCED BY PION BEAM
VALUE (MeV) DOCUMENT ID TECN COMMENT
$\bf{ 86.9 {}^{+2.3}_{-2.1}}$ OUR AVERAGE Error includes scale factor of 1.4. See the ideogram below.
• • We do not use the following data for averages, fits, limits, etc. • •
$102$ $\pm42$
2003
SPEC 40.0 ${{\mathit \pi}^{-}}$ ${}^{}\mathrm {C}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit K}_S^0}$ ${{\mathit K}_L^0}$ X
$108$ ${}^{+5}_{-2}$ 1
1986
MPS 22 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit K}_S^0}$ ${{\mathit n}}$
$69$ ${}^{+22}_{-16}$ 2
1981
ASPK 6 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit n}}$
$137$ ${}^{+23}_{-21}$
1981
ASPK 18.4 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit n}}$
$150$ ${}^{+83}_{-50}$
1980
ASPK 17 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ polarized $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit n}}$
$165$ $\pm42$ 3
1979
OMEG 12$-$15 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit n}}$
$92$ ${}^{+39}_{-22}$ 4
1979
STRC 7 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit n}}{{\mathit K}_S^0}$ ${{\mathit K}_S^0}$
1 From a partial-wave analysis of data using a K-matrix formalism with 5 poles.
2 CHABAUD 1981 is a reanalysis of PAWLICKI 1977 data.
3 From an amplitude analysis where the ${{\mathit f}_{{2}}^{\,'}{(1525)}}$ width and elasticity are in complete disagreement with the values obtained from ${{\mathit K}}{{\overline{\mathit K}}}$ channel, making the solution dubious.
4 From a fit to the ${{\mathit D}}$ with ${{\mathit f}_{{2}}{(1270)}}-{{\mathit f}_{{2}}^{\,'}{(1525)}}$ interference. Mass fixed at 1516 MeV.
${{\mathit f}_{{2}}^{\,'}{(1525)}}$ WIDTH (MeV)
References:
TIKHOMIROV 2003
PAN 66 828 Resonances in the ${{\mathit K}_S^0}$ ${{\mathit K}_S^0}$ ${{\mathit K}_L^0}$ System Produced in Collisions of Negative Pions with a Carbon Target at a Momentum of 40 GeV
LONGACRE 1986
PL B177 223 A Measurement of ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit K}_S^0}$ ${{\mathit n}}$ at 22 ${\mathrm {GeV/}}\mathit c$ and a Systematic Study of the $2+{}^{+}{}^{}$ Meson Spectrum
CHABAUD 1981
APP B12 575 A Study of the D-wave in the ${{\mathit K}^{+}}{{\mathit K}^{-}}$ System of the Reaction ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit n}}$ at 18 GeV
GORLICH 1980
NP B174 16 A Model Independent Partial Wave Analysis of the Reaction ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit n}}$ at $\sim{}$ 18 ${\mathrm {GeV/}}\mathit c$
CORDEN 1979
NP B157 250 An Amplitude Analysis of ${{\mathit \pi}}{{\mathit \pi}}$ Scattering from New Data on the Reaction ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit n}}$
POLYCHRONAKOS 1979
PR D19 1317 Study of the Reaction ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit n}}{{\mathit K}_S^0}$ ${{\mathit K}_S^0}$ at 6.0 and 7.0 ${\mathrm {GeV/}}\mathit c$ | 2022-08-20T05:25:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7993661761283875, "perplexity": 1760.9322397986155}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882573908.30/warc/CC-MAIN-20220820043108-20220820073108-00375.warc.gz"} |
https://par.nsf.gov/biblio/10384483-radio-pulse-profiles-polarization-terzan-pulsars | Radio Pulse Profiles and Polarization of the Terzan 5 Pulsars
Abstract
Terzan 5 is a rich globular cluster within the galactic bulge containing 39 known millisecond pulsars, the largest known population of any globular cluster. These faint pulsars do not have sufficient signal-to-noise ratio (S/N) to measure reliable flux density or polarization information from individual observations in general. We combined over 5.2 days of archival data, at 1500 and 2000 MHz, taken with the Green Bank Telescope over the past 12 years. We created high-S/N profiles for 32 of the pulsars and determined precise rotation measures (RMs) for 28. We used the RMs, pulsar positions, and dispersion measures to map the projected parallel component of the Galactic magnetic field toward the cluster. The 〈B∣∣〉 shows a rough gradient of ∼6 nG arcsec−1(∼160 nG pc−1) or, fractionally, a change of ∼20% in the R.A. direction across the cluster, implying Galactic magnetic field variability at sub-parsec scales. We also measured average flux densitiesSνfor the pulsars, ranging from ∼10μJy to ∼2 mJy, and an average spectral indexα= −1.35, whereSννα. This spectral index is flatter than most known pulsars, likely a selection effect due to the high frequencies used in pulsar searches to mitigate dispersion and scattering. We used flux densities from each observation more »
Authors:
; ; ; ; ; ; ; ;
Publication Date:
NSF-PAR ID:
10384483
Journal Name:
The Astrophysical Journal
Volume:
941
Issue:
1
Page Range or eLocation-ID:
Article No. 22
ISSN:
0004-637X
Publisher:
DOI PREFIX: 10.3847
National Science Foundation
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We present a toy model for the thermal optical/UV/X-ray emission from tidal disruption events (TDEs). Motivated by recent hydrodynamical simulations, we assume that the debris streams promptly and rapidly circularize (on the orbital period of the most tightly bound debris), generating a hot quasi-spherical pressure-supported envelope of radiusRv∼ 1014cm (photosphere radius ∼1015cm) surrounding the supermassive black hole (SMBH). As the envelope cools radiatively, it undergoes Kelvin–Helmholtz contractionRvt−1, its temperature risingTefft1/2while its total luminosity remains roughly constant; the optical luminosity decays as$νLν∝Rv2Teff∝t−3/2$. Despite this similarity to the mass fallback rate$Ṁfb∝t−5/3$, envelope heating from fallback accretion is subdominant compared to the envelope cooling luminosity except near optical peak (where they are comparable). Envelope contraction can be delayed by energy injection from accretion from the inner envelope onto the SMBH in a regulated manner, leading to a late-time flattening of the optical/X-ray light curves, similar to those observed in some TDEs. Eventually, as the envelope contracts to near the circularization radius, the SMBH accretion rate rises to its maximum, in tandem with the decreasing optical luminosity. This cooling-induced (rather than circularization-induced) delay of up to several hundred days may account for themore »
5. Abstract
We present a measurement of the intrinsic space density of intermediate-redshift (z∼ 0.5), massive (M*∼ 1011M), compact (Re∼ 100 pc) starburst (ΣSFR∼ 1000Myr−1kpc−1) galaxies with tidal features indicative of them having undergone recent major mergers. A subset of them host kiloparsec-scale, > 1000 km s−1outflows and have little indication of AGN activity, suggesting that extreme star formation can be a primary driver of large-scale feedback. The aim for this paper is to calculate their space density so we can place them in a better cosmological context. We do this by empirically modeling the stellar populations of massive, compact starburst galaxies. We determine the average timescale on which galaxies that have recently undergone an extreme nuclear starburst would be targeted and included in our spectroscopically selected sample. We find that massive, compact starburst galaxies targeted by our criteria would be selectable for$∼148−24+27$Myr and have an intrinsic space density$nCS∼(1.1−0.3+0.5)×10−6Mpc−3$. This space density is broadly consistent with ourz∼ 0.5 compact starbursts being the most extremely compact and star-forming low-redshift analogs of the compact star-forming galaxies in the early universe, as well as them being the progenitors to a fraction of intermediate-redshift, post-starburst, andmore » | 2023-02-01T06:17:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 15, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6140902042388916, "perplexity": 5174.613577102754}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499911.86/warc/CC-MAIN-20230201045500-20230201075500-00138.warc.gz"} |
https://dlmf.nist.gov/25.17 | # §25.17 Physical Applications
Analogies exist between the distribution of the zeros of $\zeta\left(s\right)$ on the critical line and of semiclassical quantum eigenvalues. This relates to a suggestion of Hilbert and Pólya that the zeros are eigenvalues of some operator, and the Riemann hypothesis is true if that operator is Hermitian. See Armitage (1989), Berry and Keating (1998, 1999), Keating (1993, 1999), and Sarnak (1999).
The zeta function arises in the calculation of the partition function of ideal quantum gases (both Bose–Einstein and Fermi–Dirac cases), and it determines the critical gas temperature and density for the Bose–Einstein condensation phase transition in a dilute gas (Lifshitz and Pitaevskiĭ (1980)). Quantum field theory often encounters formally divergent sums that need to be evaluated by a process of regularization: for example, the energy of the electromagnetic vacuum in a confined space (Casimir–Polder effect). It has been found possible to perform such regularizations by equating the divergent sums to zeta functions and associated functions (Elizalde (1995)). | 2018-06-20T20:56:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 1, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8397085070610046, "perplexity": 496.0459713841292}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267863886.72/warc/CC-MAIN-20180620202232-20180620222232-00379.warc.gz"} |
https://lammps.sandia.gov/doc/fix_nve_eff.html | # fix nve/eff command
## Syntax
fix ID group-ID nve/eff
• ID, group-ID are documented in fix command
• nve/eff = style name of this fix command
## Examples
fix 1 all nve/eff
## Description
Perform constant NVE integration to update position and velocity for nuclei and electrons in the group for the electron force field model. V is volume; E is energy. This creates a system trajectory consistent with the microcanonical ensemble.
The operation of this fix is exactly like that described by the fix nve command, except that the radius and radial velocity of electrons are also updated.
Restart, fix_modify, output, run start/stop, minimize info:
No information about this fix is written to binary restart files. None of the fix_modify options are relevant to this fix. No global or per-atom quantities are stored by this fix for access by various output commands. No parameter of this fix can be used with the start/stop keywords of the run command. This fix is not invoked during energy minimization.
## Restrictions
This fix is part of the USER-EFF package. It is only enabled if LAMMPS was built with that package. See the Build package doc page for more info. | 2019-04-18T10:35:09 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7696273922920227, "perplexity": 5280.339648256571}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578517558.8/warc/CC-MAIN-20190418101243-20190418123243-00484.warc.gz"} |
https://www.itl.nist.gov/div898/handbook/mpc/section4/mpc455.htm | 2. Measurement Process Characterization
2.4. Gauge R & R studies
2.4.5. Analysis of bias
Geometry/configuration differences
How to deal with configuration differences The mechanism for identifying and/or dealing with differences among geometries or configurations in an instrument is basically the same as dealing with differences among the gauges themselves.
Example of differences among wiring configurations An example is given of a study of configuration differences for a single gauge. The gauge, a 4-point probe for measuring resistivity of silicon wafers, can be wired in several ways. Because it was not possible to test all wiring configurations during the gauge study, measurements were made in only two configurations as a way of identifying possible problems.
Data on wiring configurations and a plot of differences between the 2 wiring configurations Measurements were made on six wafers over six days (except for 5 measurements on wafer 39) with probe #2062 wired in two configurations. This sequence of measurements was repeated after about a month resulting in two runs. Differences between measurements in the two configurations on the same day are shown in the following table.
Differences between wiring configurations
Wafer Day Probe Run 1 Run 2
17. 1 2062. -0.0108 0.0088
17. 2 2062. -0.0111 0.0062
17. 3 2062. -0.0062 0.0074
17. 4 2062. 0.0020 0.0047
17. 5 2062. 0.0018 0.0049
17. 6 2062. 0.0002 0.0000
39. 1 2062. -0.0089 0.0075
39. 3 2062. -0.0040 -0.0016
39. 4 2062. -0.0022 0.0052
39. 5 2062. -0.0012 0.0085
39. 6 2062. -0.0034 -0.0018
63. 1 2062. -0.0016 0.0092
63. 2 2062. -0.0111 0.0040
63. 3 2062. -0.0059 0.0067
63. 4 2062. -0.0078 0.0016
63. 5 2062. -0.0007 0.0020
63. 6 2062. 0.0006 0.0017
103. 1 2062. -0.0050 0.0076
103. 2 2062. -0.0140 0.0002
103. 3 2062. -0.0048 0.0025
103. 4 2062. 0.0018 0.0045
103. 5 2062. 0.0016 -0.0025
103. 6 2062. 0.0044 0.0035
125. 1 2062. -0.0056 0.0099
125. 2 2062. -0.0155 0.0123
125. 3 2062. -0.0010 0.0042
125. 4 2062. -0.0014 0.0098
125. 5 2062. 0.0003 0.0032
125. 6 2062. -0.0017 0.0115
Test of difference between configurations Because there are only two configurations, a t-test is used to decide if there is a difference. If $${\large t} = \left| \frac{\sqrt{N}}{{\large s}_{diff}} \mbox{Avg}_{\, diff} \right| > 2$$ the difference between the two configurations is statistically significant.
The average and standard deviation computed from the 29 differences in each run are shown in the table below along with the t-values which confirm that the differences are significant for both runs.
Average differences between wiring configurations
Run Probe Average Std dev N t
1 2062 - 0.00383 0.00514 29 -4.0
2 2062 + 0.00489 0.00400 29 +6.6
Unexpected result The data reveal a wiring bias for both runs that changes direction between runs. This is a somewhat disturbing finding, and further study of the gauges is needed. Because neither wiring configuration is preferred or known to give the 'correct' result, the differences are treated as a component of the measurement uncertainty. | 2018-06-22T03:24:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5249971151351929, "perplexity": 3855.4428887218446}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267864343.37/warc/CC-MAIN-20180622030142-20180622050142-00203.warc.gz"} |
https://par.nsf.gov/biblio/10347595-origin-weak-mg-ii-higher-ionization-absorption-lines-outflows-from-intermediate-redshift-dwarf-galaxies | Origin of Weak Mg ii and Higher-ionization Absorption Lines in Outflows from Intermediate-redshift Dwarf Galaxies
Abstract Observations at intermediate redshifts reveal the presence of numerous compact, weak Mg ii absorbers with near to supersolar metallicities, often surrounded by extended regions that produce C iv and/or O vi absorption, in the circumgalactic medium at large impact parameters from luminous galaxies. Their origin and nature remain unclear. We hypothesize that undetected satellite dwarf galaxies are responsible for producing some of these weak Mg ii absorbers. We test our hypothesis using gas dynamical simulations of galactic outflows from a dwarf galaxy with a halo mass of 5 × 10 9 M ⊙ , as might be falling into a larger L * halo at z = 2. We find that thin, filamentary, weak Mg ii absorbers (≲100 pc) are produced in two stages: (1) when shocked core-collapse supernova (SN II)–enriched gas descending in a galactic fountain gets shock compressed by upward flows driven by subsequent SN II and cools (phase 1) and, later, (2) during an outflow driven by Type Ia supernovae that shocks and sweeps up pervasive SN II–enriched gas, which then cools (phase 2). The Mg ii absorbers in our simulations are continuously generated by shocks and cooling with moderate metallicity ∼0.1–0.2 Z ⊙ but low more »
Authors:
; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10347595
Journal Name:
The Astrophysical Journal
Volume:
909
Issue:
2
Page Range or eLocation-ID:
157
ISSN:
0004-637X
1. ABSTRACT We present initial results from the Cosmic Ultraviolet Baryon Survey (CUBS). CUBS is designed to map diffuse baryonic structures at redshift z ≲ 1 using absorption-line spectroscopy of 15 UV-bright QSOs with matching deep galaxy survey data. CUBS QSOs are selected based on their NUV brightness to avoid biases against the presence of intervening Lyman limit systems (LLSs) at zabs < 1. We report five new LLSs of $\log \, N({\mathrm{ H} \,{\small I}})/{{\rm cm^{-2}}}\gtrsim 17.2$ over a total redshift survey path-length of $\Delta \, z_{\mathrm{ LL}}=9.3$, and a number density of $n(z)=0.43_{-0.18}^{+0.26}$. Considering all absorbers with $\log \, N({{\mathrm{ H} \,{\small I}}})/{{\rm cm^{-2}}}\gt 16.5$ leads to $n(z)=1.08_{-0.25}^{+0.31}$ at zabs < 1. All LLSs exhibit a multicomponent structure and associated metal transitions from multiple ionization states such as C ii, C iii, Mg ii, Si ii, Si iii, and O vi absorption. Differential chemical enrichment levels as well as ionization states are directly observed across individual components in three LLSs. We present deep galaxy survey data obtained using the VLT-MUSE integral field spectrograph and the Magellan Telescopes, reaching sensitivities necessary for detecting galaxies fainter than $0.1\, L_*$ at d ≲ 300 physical kpc (pkpc) in all five fields. A diverse range of galaxy properties ismore »
5. ABSTRACT We present a systematic investigation of physical conditions and elemental abundances in four optically thick Lyman-limit systems (LLSs) at z = 0.36–0.6 discovered within the cosmic ultraviolet baryon survey (CUBS). Because intervening LLSs at z < 1 suppress far-UV (ultraviolet) light from background QSOs, an unbiased search of these absorbers requires a near-UV-selected QSO sample, as achieved by CUBS. CUBS LLSs exhibit multicomponent kinematic structure and a complex mix of multiphase gas, with associated metal transitions from multiple ionization states such as C ii, C iii, N iii, Mg ii, Si ii, Si iii, O ii, O iii, O vi, and Fe ii absorption that span several hundred km s−1 in line-of-sight velocity. Specifically, higher column density components (log N(H i)/cm−2≳ 16) in all four absorbers comprise dynamically cool gas with $\langle T \rangle =(2\pm 1) \times 10^4\,$K and modest non-thermal broadening of $\langle b_\mathrm{nt} \rangle =5\pm 3\,$km s−1. The high quality of the QSO absorption spectra allows us to infer the physical conditions of the gas, using a detailed ionization modelling that takes into account the resolved component structures of H i and metal transitions. The range of inferred gas densities indicates that these absorbers consist of spatially compact clouds with a median line-of-sight thickness of $160^{+140}_{-50}$ pc. While obtaining robust metallicitymore » | 2022-12-03T05:56:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6853218078613281, "perplexity": 6439.696003553424}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710924.83/warc/CC-MAIN-20221203043643-20221203073643-00089.warc.gz"} |
http://dlmf.nist.gov/12.1 | # §12.1 Special Notation
(For other notation see Notation for the Special Functions.)
$x,y$ real variables. complex variable. nonnegative integers. real or complex parameters. arbitrary small positive constant.
Unless otherwise noted, primes indicate derivatives with respect to the variable, and fractional powers take their principal values.
The main functions treated in this chapter are the parabolic cylinder functions (PCFs), also known as Weber parabolic cylinder functions: $\mathop{U\/}\nolimits\!\left(a,z\right)$, $\mathop{V\/}\nolimits\!\left(a,z\right)$, $\mathop{\overline{U}\/}\nolimits\!\left(a,z\right)$, and $\mathop{W\/}\nolimits\!\left(a,z\right)$. These notations are due to Miller (1952, 1955). An older notation, due to Whittaker (1902), for $\mathop{U\/}\nolimits\!\left(a,z\right)$ is $\mathop{D_{\nu}\/}\nolimits\!\left(z\right)$. The notations are related by $\mathop{U\/}\nolimits\!\left(a,z\right)=\mathop{D_{-a-\frac{1}{2}}\/}\nolimits% \!\left(z\right)$. Whittaker’s notation $\mathop{D_{\nu}\/}\nolimits\!\left(z\right)$ is useful when $\nu$ is a nonnegative integer (Hermite polynomial case). | 2014-04-24T22:12:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 15, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9857264161109924, "perplexity": 1135.6321529014203}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1398223206770.7/warc/CC-MAIN-20140423032006-00523-ip-10-147-4-33.ec2.internal.warc.gz"} |
https://hit.lbl.gov/previous-seminars | # Previous HIT Seminars
### "Design Concept of Imaging Barrel Electromagnetic Calorimeter for the Electron-Ion Collider"
The Electron-Ion Collider (EIC) will be an experimental facility to explore the gluons in nucleons and nuclei, shedding light on their structure and the interactions within. Physics goals, detector requirements, and technologies at the EIC are outlined and discussed in the EIC community White Paper and Yellow Report. In particular, for the barrel electromagnetic calorimetry, the electron energy and shower profile measurements play a crucial role in the separation of electrons from background pions in deep inelastic scattering processes. Moreover, the calorimeter must measure the energy and position of photons, identify single photons originating from deeply virtual compton scattering process, and photon pairs from pi^0 decays. Based on detector requirements, we propose a design of the imaging barrel electromagnetic calorimeter. It is a hybrid design utilizing imaging calorimetry based on monolithic silicon sensors (AstroPix) and scintillating fibers embedded in Pb. We have studied the proposed calorimeter in detail through realistic simulations to test it against the requirements for the physics case described in the EIC community Yellow Report. In this talk, I will present the expected calorimeter performance based on simulations with 3T magnetic field and the outlook of the upcoming R&D program related to the imaging calorimetry will be also presented.
### "Conformal Colliders Meet the LHC"
Jets of hadrons produced at high-energy colliders provide experimental access to the dynamics of asymptotically free quarks and gluons and their confinement into hadrons. Motivated by recent developments in conformal field theory, we propose a reformulation of jet substructure as the study of correlation functions of a specific class of light-ray operators and their associated operator product expansion (OPE). We show that multi-point correlation functions of these operators can be measured in real LHC data, allowing us to experimentally verify properties of the light-ray OPE. We then discuss how this reformulation provides new ways of experimentally studying QCD at colliders, as well as new theoretical techniques for performing previously intractable calculations.
### "Exclusive hard processes for extracting Generalized Parton Distributions"
The Generalized Parton Distributions (GPDs) describe the distribution of quarks/gluons inside a colliding hadron in both longitudinal partonic momentum fraction $x$ and transverse space (“tomographic images”). Their moments of the momentum fraction $x$ provide critical information on partonic angular momentum contribution to the hadron spin and gravitational form factors of the hadron. Extracting GPDs reliably from experimental measurements has been a major science goal for studying QCD and hadron physics. However, conventional exclusive processes such as deeply-virtual Compton scattering (DVCS) cannot fully disentangle the longitudinal dependence and provide the tomographic images at fixed x. In this talk, I will introduce a class of exclusive hard processes, to be referred as single diffractive hard exclusive processes (SDHEP), for the extraction of GPDs. I will discuss the necessary and sufficient conditions for SDHEP to be factorized in terms of GPDs. I will also demonstrate that SDHEP is not only sufficiently generic to cover all known processes for extracting GPDs, but also well-motivated for the search of new processes for the study of GPDs. Finally, I will carefully examine the sensitivity of SDHEP to the parton momentum fraction $x$ dependence of GPDs.
### "Physics Program with SoLID"
The Solenoidal Large Intensity Device (SoLID) is a new experimental apparatus proposed for Hall A at the Thomas Jefferson National Accelerator Facility (JLab). SoLID will combine large angular and momentum acceptance with the capability to handle high data rates at large luminosity. As such SoLID will push JLab to a new limit at the QCD intensity frontier to exploit the full scientific potential of the 12-GeV CEBAF. The slate of approved high-impact experiments consists of the tomography of the nucleon in 3-D momentum space from Semi-Inclusive Deep Inelastic Scattering, expanding the phase space in the search for new physics and novel hadronic effects from parity-violating Deep Inelastic Scattering, a precision measurement of near-threshold J/psi production to probe the gluon field and its contribution to the proton mass, and more. In this talk, I will discuss the rich SoLID physics program and the proposed apparatus.
### "The equation of state of dense nuclear matter from heavy-ion collisions"
The equation of state (EOS) of dense nuclear matter can give insights into fundamental properties of QCD: among others, it can elucidate phases of matter in different regions of the QCD phase diagram, it can help explain the structure of both neutron stars and neutron-rich nuclei, and it can inform us about the nature of the underlying fundamental interactions. In experiments colliding heavy nuclei at relativistic velocities, the EOS is probed through observables describing the collective behavior of the produced matter, such as flow observables, the dependence of which on the EOS can be studied in simulations. In this talk, I will discuss recent progress on constraining the EOS with hadronic transport simulations, used to model heavy-ion collision experiments at intermediate energies. I will highlight results from a recent Bayesian analysis study using new data from RHIC, and I will discuss the findings in the context of other known constraints from heavy-ion collisions and neutron star studies. I will also outline developments in state-of-the-art hadronic transport codes necessary to fully utilize the potential of the forthcoming wealth of data from the BES-II FXT program at RHIC, from GSI and FAIR, as well as from FRIB and future FRIB400.
### "Overcoming exponential volume scaling in quantum simulations of lattice gauge theories"
Quantum computers hold the promise of overcoming the numerical sign problem and allowing for study of the dynamics of quantum field theories from first principles. Before performing such calculations, it is important to ensure that the quantum algorithms used do not have a cost that scales exponentially with the volume. In this talk, I will discuss an interesting test case: a formulation of compact U(1) gauge theory in 2+1 dimensions free of gauge redundancies. A naive implementation onto a quantum circuit has a gate count that scales exponentially with the volume. I will discuss how to break this exponential scaling by performing an operator redefinition that reduces the non-locality of the Hamiltonian. With the exponential volume scaling broken, I will then show how the gate count scaling with the volume can be further reduced by approximating the quantum circuit without introducing large errors.
### New Special time: Tuesday, February 14, 2023, 9:30 AM PST (Zoom)
Dr. Yousen Zhang (Rice University)
Host: Peter Jacobs and Farid Salazar
Slides and Recording available upon request to organizers
"Probing QCD matters using heavy flavor quarks at the LHC"
Quark gluon plasma created in relativistic heavy ion collisions is a novel state in which partons are deconfined from normal matter in the universe. It is characterized by the shocking collectivity of QGP and energy loss of high energy particles traversing through QGP. Recent measurements show that the collectivity can also emerge in high-multiplicity proton-proton and proton-nucleus collisions, which was originally believed to only exist in large ion collisions. However, the origin of these collective motions is still a puzzle in theoretical studies mainly debating on contributions from initial correlations and in-medium effects. Heavy flavor quarks are sensitive to both the initial stage conditions and the later-on in-medium effects of collisions, thus can provide important information for understanding the inner workings of QGP in large ion collisions and the origin of the collectivity in small systems. In this talk, I will present the recent progress of heavy flavor collectivity at the LHC from large to small colliding systems, and discuss the future opportunities with the high-luminosity LHC together with the CMS detector upgrades.
### Special time: Thursday, February 9, 2023, 2:00 PM PST (Zoom)
Dr. Nicole Lewis (Brookhaven)
Host: Peter Jacobs and Shujie Li
Slides
"Baryon Stopping in Photonuclear Collisions"
Photonuclear collisions are one of the simplest processes that can happen in a heavy-ion collision. They occur when one nucleus emits a quasi-real photon which interacts with the other colliding nucleus, similar to an electron-ion collision except that the photon tends to have a much smaller virtuality. Photonuclear collisions can be used to study bulk properties of the medium such as collectivity due to initial-state effects and hadron chemistry. In these photonuclear collisions we observed baryon stopping: more baryons that antibaryons even at midrapidity. This phenomenon is well documented in proton-proton and heavy-ion collisions, but it is not well understood and had never before been seen in photonuclear collisions. This could indicate the existence of a baryon junction within the nucleon, a nonperturbative Y-shaped configuration of gluons which carries the baryon number and is attached to all three valence quarks. These measurements will also inform future measurements using particle identification at the upcoming Electron Ion Collider.
### Tuesday, February 7th 2023, 3:30 PM PST (Zoom)
Dr. Xiaoxuan Chu (Brookhaven National Lab)
Host: Farid Salazar
"Probing nonlinear gluon dynamics at RHIC and the EIC"
The gluon distribution function grows with lower and lower momentum fraction very fast. As the total scattering cross section is bound by quantum mechanics, the raise of the gluon density has to be tamed, which is explained by gluon recombination under the color glass condensate (CGC) framework. A definitive discovery of nonlinear effects in QCD and as such the saturation regime would significantly improve our understanding of the nucleon structure and of nuclear interactions at high energy. Two particle azimuthal correlation is one of the most direct and sensitive channels to access the underlying nonlinear gluon dynamics. In this talk, we will present the recent results of forward di-hadron correlations measured at RHIC, together with the signatures of gluon saturation predicted by CGC. New opportunities for measurements with the STAR forward upgrade and future EIC to study the nonlinear effects in QCD will also be discussed.
### Special date & time: Thursday, February 2, 2023, 10:30 AM PST (Zoom)
Florian Jonas (University of Münster/ORNL)
Host: Peter Jacobs and Farid Salazar
Slides and Recording available upon request to organizers
"Prompt photon production: probing gluons in protons and nuclei at hadron colliders"
Measurements of prompt photons at hadron colliders offer unique insights into the substructure of the colliding projectiles, enabling constraints of so called Parton Distribution Functions (PDFs), which encode the inner structure of the hadron in a universal parametrization.
In particular, prompt photons are sensitive to the gluon distributions, which are one of the least constrained PDFs and not directly accessible via deep inelastic scattering.
Furthermore, studies of the gluon bound inside protons (and nuclei) are of key importance for the exploration of non-linear QCD, where in particular their low-x growth is expected to be tamed by gluon saturation.
Photons do not interact via the strong interaction, which makes them a particularly robust probe, carrying information from the initial hard scattering to the detector, unaffected by any final state effects commonly encountered in large collision system.
This talk outlines the key experimental techniques and challenges arising in isolated prompt photon measurements. An overview of the currently available experimental results at the LHC and their impact on the gluon PDF is followed by a look into the future, outlining how prompt photon measurements at hadron colliders with the ALICE Forward Calorimeter can play an important role in the search for gluon saturation and complement DIS measurements at the EIC.
### Wednesday, January 18th, 2023, 3:30 PM PST
Dr. Xiaohui Liu (Beijing)
Host: Jennifer Rittenhouse West
"Nucleon Energy Correlators for the Color Glass Condensate"
An invited talk and discussion on very recent work by Xiaohui Liu, Feng Yuan and collaborators on low-x physics, specifically a new method to access gluon saturation which is highly relevant for the future Electron-Ion Collider. All welcome, and please note this will be a pedagogical seminar with a combination of slides and whiteboard, particularly aimed toward early career people who might not be familiar with the physics.
### Tuesday, January 17th, 2023, 3:30 PM PST
Host: Jennifer Rittenhouse West
"Spatial distributions of energy and stresses in hadrons"
The Lorentz group of special relativity contains a Galilean subgroup, which manifests in the light front picture of spacetime. Light front coordinates thus allow a fully relativistic spatial description of the internal structure and dynamics of hadrons, specifically in the form of two-dimensional densities on the plane transverse to the observer's line of sight. The energy-momentum tensor allows distributions of energy, momentum, spin and stresses to be obtained. In this talk, I elaborate on the physical meaning of light front coordinates, and explain the formalism for determining internal distributions of hadrons. Concrete model examples for the internal structure of mesons are provided.
### Tuesday, January 10th, 2023, 3:30 PM PST (in-person & zoom)
Dr. Joao Barata (BNL)
Host: Farid Salazar/Xin-Nian Wang
Jet evolution in anisotropic plasmas
Over the last decades, the heavy-ion collisions at RHIC and the LHC allowed the exploration of QCD at high energies and densities. In these experiments, the nuclear matter is produced far from equilibrium, and undergoes a multiphase evolution until it thermalizes into a nearly ideal liquid: the quark-gluon plasma (QGP). The main effort of the heavy-ions community is focused in extracting the detailed properties of this phase of matter. Among the many probes used for this effect, QCD jets have proven to be able to explore the quark gluon plasma at different time and length scales, providing a differential and dynamical picture for the underlying matter. Nonetheless, a theoretical treatment of jet structure which is sensitive to the details of the QGP is still far from complete. In this talk, I will present some recent work on how to describe jet evolution in the presence of anisotropic matter. First, I will detail the basic modifications necessary to make to the standard jet quenching formalism. Afterwards, I will show that the QGP anisotropies can be taken into account to arbitrary order in a gradient expansion using an effective kinetic theory approach. Remarkably, at second order in the matter gradients, we find a novel master equation which generalizes the usual Boltzmann transport. Finally, I will discuss how such effects can be manifest at the level of jet observables.
### "Better parton showers for HL-LHC and beyond"
The Large Hadron Collider is currently running at its highest energy and luminosity. In order to maximally exploit the potential of this precise dataset to uncover physics beyond the Standard Model, it is of crucial importance to develop tools that faithfully characterise the QCD background. Parton showers lie at the core of general purpose Monte Carlo event generators. They aim at correctly describing the phase-space for QCD branchings across disparate energy scales. A natural question, largely overlooked in the literature, is up to which degree of logarithmic accuracy do parton showers meet this goal. In this talk, I will introduce recent efforts by the PanScales collaboration to establish the criteria that a parton shower should satisfy in order to reach a given logarithmic accuracy. Then, I will present the design and implementation of next-to-leading logarithmic accurate parton showers both in electron-positron annihilation and hadron collisions. I will conclude with some exploratory studies about the phenomenological impact of these highly-precise showers.
### "Achieving High Deuteron Tensor Polarization To Probe Nuclear Structure"
Advances in experimental technology have allowed for new high-luminosity scattering probes on highly spin polarized nuclear targets. These developments have made it possible to probe the structure of tensor-polarized deuterium with greater precision than ever before. Two experiments, approved to run in Jefferson Lab's experimental hall C will measure two deuteron tensor observables. The first experiment will probe the deuteron tensor structure function b1 in the x<1 deep inelastic region, and the second experiment will measure the deuteron tensor asymmetry Azz in the quasielastic region. In order to achieve a high tensor polarized deuteron target, developments are being made in nuclear polarization technology using the dynamic nuclear polarization (DNP) technique. DNP is used to enhance the nuclear spin polarization of materials. DNP works by using microwaves to continuously drive spin transitions in a material that is doped with free radicals and placed inside a 1 K environment in a high magnetic field. Further tensor polarization enhancement is achieved using additional RF saturation on the target magterial. Once enhanced, the nuclear polarization can be determined by analyzing the lineshape of the NMR absorption spectrum. This talk will describe the DNP system used at the University of New Hampshire, and explain novel techniques in inducing high tensor polarization in deuterium.
### "Physics Program and Detector Development with ALICE3"
ALICE 3 constitutes the next-generation upgrade for heavy-ion physics in LHC Runs 5 and 6. It addresses the questions about the quark-gluon plasma which remain inaccessible to other existing or planned experiments, e.g. on the transport properties and thermalisation in the QGP, the formation of hadrons, and the early stages of the plasma evolution. To this end, precise measurements of heavy-flavour probes as well as of electromagnetic radiation are key. The required pointing and tracking performance are achieved with a high-resolution vertex tracker, installed within the beam pipe, and a large-acceptance tracker, both based on monolithic silicon-pixel sensors. The particle identification relies on a combination of a silicon-based time-of-flight detector and a Ring-Imaging Cherenkov detector. In addition, an electromagnetic calorimeter, a muon identifier, and a dedicated forward detector for ultra-soft photons are foreseen. In this presentation, we will explain the detector concept and its physics reach as well as discuss the innovative R&D activities in areas of interest for HEP experiments in general.
### "Evidence for Intrinsic Charm Quarks in the Proton"
It has been argued for a long time that the proton could have a sizable intrinsic component of the charm quark.
I will discuss how to disentangle the intrinsic charm component from charm-anticharm pairs arising from high-energy radiation and present results providing evidence for intrinsic charm, by exploiting the NNPDF4.0 high-precision determination of proton Parton Distribution Functions. The existence of intrinsic charm is estabilished at the 3σ level, with a momentum distribution in remarkable agreement with model predictions. Finally I will discuss how these findings are supported by the very recent data on Z-boson production with charm jets from the LHCb experiment.
### Host: Nu Xu
"Predicting randomness in relativistic hydrodynamics"
We usually think of hydrodynamics as a deterministic description of fluid motion. The focus of this talk is on random fluctuations in fluids caused by thermal noise, inherent in systems with dissipation. The interest in this subject is driven by the progress of heavy-ion collision experiments towards the mapping of the QCD phase diagram. In particular, the search for the QCD critical point at RHIC requires quantitative understanding of fluctuations and their dynamics. I will discuss the role of the fluctuations in hydrodynamics and how we can predict their evolution using deterministic equations.
Photo credit: Jessica Rotkiewicz
### Tuesday, November 8th, 2022, 3:30 PM PDT (Zoom only)
Dr. Björn Schenke (BNL)
Host: Farid Salazar
"QCD at the Crossroads: Hot QCD Town Hall meeting summary"
In this talk, I will try to summarize the discussions/presentations at the QCD town meeting, Boston, September 23-25: https://indico.mit.edu/event/538/
### In-person (Theory Lounge 70-228) & Zoom
Dr. Feng Yuan (LBNL)
Host: Nu Xu/Farid Salazar
"QCD at the Crossroads: Cold QCD Town Hall meeting summary"
In this talk, I will try to summarize the discussions/presentations at the QCD town meeting, Boston, September 23-25: https://indico.mit.edu/event/538/
### In-person (Theory Lounge 70-228) & Zoom
Dr. Tyler Hague (LBNL)
Host: Shujie Li/Jennifer Rittenhouse West
"The EMC Effect: Light Nuclei are Weird"
In 1983, the European Muon Collaboration (EMC) recorded Deep-Inelastic Scattering data on Iron, Deuterium, and Hydrogen. Comparisons of the targets noted that the quark structure of nucleons is modified by the surrounding nuclear environment, dubbed the EMC Effect. Nearly 40 years later, the community is still working to understand the mechanism behind this. Initial studies of the EMC Effect on heavy nuclei were able to paint broad strokes pictures of how the effect scales across nuclei. However, later precision tests of light nuclei were found to be in tension with these previous understandings. Key missing pieces to understanding this are the free neutron structure function and nuclear effects. The MARATHON experiment used a novel technique to extract F2n/F2p by largely canceling nuclear effects in the A=3 mirror nuclei in the yield ratio. In this talk, I will give an overview of our current knowledge of the EMC Effect followed by a discussion of the MARATHON experimental results and recent work applying these to light nuclei to understand nuclear effects.
### Mr. Henry Klest (Stony Brook University) Host: Nu Xu
Teaching an Old Experiment New Tricks: Measuring Modern Jet Observables Using Archived H1 e+p DIS Data
A renaissance in jet physics is now underway, with novel, theoretically rigorous approaches to jet measurements being used to probe QCD in new ways using data from hadronic collisions at RHIC and the LHC. It is timely to explore these new techniques using data from high-energy collider experiments, which were recorded before these techniques were developed. In particular, colliders with leptons in the initial state provide a clean and complementary environment to study jets. The H1 experiment was a hermetic, general-purpose detector at the HERA electron-proton collider complex at DESY, which terminated data-taking in 2007. However, the H1 Collaboration continues to be active scientifically, preserving the data and updating analysis software. The H1 dataset therefore remains as accessible for high-quality analyses as that for currently running experiments, making it the ideal playground for testing modern QCD analysis approaches on DIS data before the EIC turns on. This talk will focus on the measurement of groomed event shapes in ep DIS collisions, using a set of novel inclusive observables which leverage recent advances such as the Centauro jet algorithm and precision jet grooming phenomenology. The advantages and challenges of the event-wide grooming technique will be discussed, as well as some lessons learned that are applicable to the EIC physics program.
### Host: Nu Xu
Quarkonium Production in Heavy-ion Collisions at the LHC
Measurements of J/ψ production have been a valuable probe to study the properties of the hot and dense medium created in heavy-ion collisions, also known as the quark-gluon plasma (QGP). Experimentally, the first glimpse of the QGP was provided by collisions of lead beams at the Super Proton Synchrotron (SPS) in the late 90s via the measurements of J/ψ production. The suppression of J/ψ production in Pb–Pb collisions with respect to p–A collisions was observed, which was proposed as a smoking gun of the QGP as a consequence of colour screening in the QGP medium keeping charmed quark-antiquark pairs from binding to each other.
The higher collision energy at the Large Hadron Collider (LHC) with respect to previous collision programs at SPS and RHIC opened new perspectives on quarkonium measurements due to the increased heavy quark production cross section. The large data samples collected at the LHC based on the excellent performance of the LHC and the four experiments provided precise measurements of charmonium and bottomonium production in a wide kinematic range. Moreover, a multitude of new observables including multi-differential measurements of various quarkonium states becomes accessible, which provided crucial inputs to disentangle various quarkonium in-medium effects in the presence of the QGP.
In this talk, a selection of recent quarkonium measurements at the LHC will be discussed.
### Tuesday, October 11th, 2022, 3:30 PM PDT (Zoom only)
Dr. Niklas Mueller (U. Washington)
Host: Farid Salazar
What can QIS do for high energy and nuclear physics?
Slides
The possibility to simulate quantum many-body systems with digital quantum computers and analog devices is an exciting opportunity for high energy and nuclear physics. I will present an overview over new directions in two old examples: understanding systems far-from-equilibrium, such as QCD in ultra-relativistic heavy ion collisions, and their approach to thermal equilibrium, and addressing thermal systems in regimes where Monte-Carlo importance sampling techniques face a sign problem. For those of you impatiently waiting for quantum computers to outrun classical computers, I will emphasize that QIS not only allows to make progress computationally, but more importantly conceptually, including previously unexplored aspects such as, e.g. entanglement. I will present a few relevant examples, still far from the ultimate goal QCD, but interesting because of their interdisciplinary relevance for high energy and nuclear physics, condensed matter theory and quantum information science.
### Tuesday, October 4th, 2022, 3:30 PM PDT (Zoom only)
Dr. Yoshitaka Hatta (BNL)
Host: Farid Salazar
Spin Physics Opportunities at the EIC
I give an overview of high energy QCD spin physics with particular emphasis on physics opportunities at the future Electron-Ion Collider. Topics will include longitudinal spin decomposition, orbital angular momentum, spin at small-x, Ji sum rule and the generalized parton distributions, and transverse single spin asymmetries. I review the recent developments in the field and identify what are the outstanding challenges at the EIC.
### Thursday, 08.11.2022, 2:30 PM PDT Special date and time! in the Theory Lounge (hybrid)
Dr. Raymond Ehlers (LBNL)
What can we learn about the quark-gluon plasma from reconstructed jets with Bayesian inference?
Bayesian inference provides an approach for constraining the parameters of complex models according to the available information. In particular, the wealth of information contained within multi-messenger experimental measurements provides the opportunity for detailed data-model comparison. The need for such rigorous comparison is pervasive throughout science. The JETSCAPE collaboration has now applied this Bayesian approach to the familiar problem of jet quenching. In this talk, I will discuss our recent results, in-progress analysis, and implications for the future of the field.
### Wednesday, 06.29.2022, 3:30 PM PDT
Joint Nuclear Theory/HIT seminar! Special date on Wednesday!
Dr. Jennifer Rittenhouse West (LBNL)
Host: Xin-Nian Wang
Diquark Formation as a Breakthrough of Fundamental QCD into Nuclear Physics
A diquark bond formed from valence quarks across a nucleon-nucleon pair has been proposed as the fundamental quantum chromodynamics (QCD) physics causing short-range correlations (SRC) in nuclei. Short-range correlated nucleon-nucleon pairs and the nucleon shell model are the basis for nuclear physics, with SRC accounting for 20% of the nucleons in a nucleus. While SRC have been extensively studied both experimentally and theoretically, notably by the CLAS collaboration in recent years, their underlying cause at the QCD level has remained a mystery. The diquark formation model, if shown to be the cause of SRC in nuclei, represents a breakdown of the assumption of scale separation in effective field theories. Rather than a boundary between scales, however fuzzy and broad, a case is made in this work for diquark formation as a direct breakthrough of the underlying theory, capturing 20% of the physics of nuclear structure.
### Tuesday, 06.21.2022, 3:30 PM PDT
Dr. Aihong Tang (BNL)
Host: Xin-Nian Wang
Global Spin Alignment in Relativistic Heavy Ion Collisions : A Progress Review
In relativistic heavy ion collisions, quarks can possess global spin polarization in a globally vortical system. Such process is initially induced by the spin-orbital coupling, and the evolution of polarized quarks and the subsequent formation of hadrons involves various interesting physics mechanisms. This phenomena can be studied either by global spin polarization of hyperons or global spin alignment of vector mesons. Recently the STAR collaboration released interesting results of global spin alignment for phi- and K*-mesons. It is found that the surprisingly large value of phi-meson global spin alignment cannot be explained by conventional mechanisms, but can be accommodated by a model invoking the strong force field. In this talk we will review the recent progress in the understanding of global spin alignment, and in particular we will discuss STAR's result and its implications.
### Monday, 06.13.2022, 3:00 PM PDT (Hybrid at Persevervance Hall, note special time and date!)
Prof. Ulrich Mosel (Giessen University)
Host: Jennifer Rittenhouse West
Neutrino-nucleus interactions in quantum-kinetic transport theory
The analysis of results from long-baseline experiments such as T2K, NOvA and DUNE requires knowledge of the incoming neutrino energy. The latter has to be reconstructed from only partially measured final states of the reaction. Any theory thus has to go beyond the calculation of inclusive cross sections and has to deliver the full final state of the reaction. Since all present experiments work with nuclear targets not only the initial, first interaction of the incoming neutrino plays a role. In addition, the final state interactions of the initially produced hadrons with the nuclear environment are important and determine the final state. The state-of-the-art method to treat such processes is quantum-kinetic transport theory which has been around since 50 years, but only over the last 20 years major numerical implementations to describe nuclear reactions have become available. In my talk I will illustrate some of the results obtained with such a theory, applied both to nuclear reactions and neutrino-nucleus reactions.
### Tuesday, 06.07.2022, 12 PM PDT - Special time!
Dr. Sergey Kulagin (Institute of Nuclear Research, RAS Moscow)
Host: Jennifer Rittenhouse West
What can we say about modification of the bound nucleon at the parton level from global QCD fits?
We briefly review available experimental observations on nuclear effects in deep-inelastic scattering (DIS). We then briefly discuss a few basic mechanisms responsible for nuclear corrections and review progress in understanding the observed phenomenon focusing on the valence quark region. We report the results of our global QCD analysis which includes a "standard" set of high-energy data for the proton target (DIS, DY production of lepton pair as well as W+- / Z boson production) and also nuclear 2H, 3H, and 3He DIS data. In this analysis we treat nuclear corrections in DIS in terms of a nuclear convolution approach with off-shell bound nucleon. The off-shell correction describes the modification of parton distributions in bound nucleons, which is determined along with the parton distribution functions (PDFs). A number of systematic studies have been performed aiming to estimate the uncertainties arising from the use of various deuterium data sets, from the model of high twist contributions to the structure functions, from the treatment of target mass corrections. We compare our predictions for the ratio F2n/F2p and the d/u ratio of the quark distributions with the results of other analyses as well as with the recent data from the MARATHON experiment.
### Tuesday, 05.31.2022, 3:30 PM PDT
Dr. Christopher McGinn (Univ of Colorado Boulder)
Inclusive and Electroweak Boson-tagged Jets as Probes of the Quark-Gluon Plasma and Medium Response
Jets, as proxy for hard scattered partons in initial collision of heavy and ultrarelativistic nuclei, are modified significantly relative their vacuum reference counterparts when traversing the subsequently formed hot-and-dense medium of deconfined quarks and gluons known as the Quark-Gluon Plasma (QGP). Specifically, a suppression in the overall production of jets is observed compared to vacuum expectation, as well as a modification to jet fragmentation patterns towards softer fragments. These phenomena are known collectively as 'jet-quenching'. Recently, much attention has been paid to the impact of jet-medium interactions on the medium itself, in searches for medium response and in searches for quenching in small systems (such as proton-nucleus collisions) in the context of observed high-pT v2. Using data taken with the ATLAS detector at the LHC, sqrt(sNN) = 5.02 TeV, jets produced with electroweak boson partners (unmodified by strong-force interactions in QGP) are studied to characterize both the jet production and fragmentation, with the latter providing insight into the necessity of incorporating medium response in theoretical model comparisons. Additionally, simultaneous studies of jet v2 and quenching in big-and-small systems reveals there may be more questions on the exact nature of the jet-medium interactions in both systems and how they lead to the physical final state observed.
### Tuesday, 05/24/2022,3:30 PM PDT
Prof. Mike Lisa (Ohio State University)
Host: Xin-Nian Wang
Subatomic Smoke Rings: Polarization and Toroidal Vorticity in the QGP
Since the discovery of global hyperon polarization in Au+Au collisions at RHIC about five years ago, there has been intense theoretical and experimental focus on the topic. After a brief review, I will discuss novel vortex structures that may be generated in two situations. The first is a p+A collision, which may produce droplets of QGP that develop toroidal vortex ("smoke ring") structure. Experimental observation of such a structure would provide compelling evidence supporting the hydrodynamic nature of this tiny system, a much-debated topic today. The other is an idealized "hot moving spot" that may result from thermalization of a jet in an expanding QGP; in this case, the "smoke ring" centers on the jet direction. In both cases, we suggest an experimental observable to measure the toroidal vortex structure, and present full hydrodynamical simulations to make quantitative predictions, including initial state fluctuation effects. I will mention prospects and challenges for observing this novel phenomenon in experiment.
### Tuesday, 05.17.2022, 3:30 PM PDT
Prof. Jorge Noronha (UIUC)
Host: Xin-Nian Wang
Hydrodynamic Frames: the Good, the Bad, and the Ugly
Three of the most cutting-edge experiments in modern science, RHIC, LHC, and LIGO are now producing data whose description requires a major overhaul of our current understanding of what constitutes fluid dynamic behavior in the relativistic regime. In this talk I will explain how the choice of hydrodynamic variables in a system out of equilibrium, i.e., our definition of the so-called hydrodynamic frame, affects the domain of applicability of relativistic viscous fluid dynamics formulations. I will also show how developments in relativistic viscous hydrodynamics obtained in heavy-ion collisions could be instrumental in determining the viscous properties of ultradense matter formed in neutron star mergers.
### Tuesday, 05.10.2022, 3:30 PM PDT
Prof. Kenji Fukushima (Univ. of Tokyo)
Host: Feng Yuan
Continuity or Discontinuity between Nuclear and Quark Matter and the Astrophysical Implications
In this talk I will review theoretical scenarios of quark matter at high density. Although a phase transition is not logically excluded, a crossover or weak first-order transition is likely to occur. I will explain how the equation of state is constrained by the neutron star observation and demonstrate that the future gravitational wave detection can identify the nature of the quatk matter onset.
### Wednesday, 05.04.2022, 3:30 PM PDT (Special date)
(Hybrid talk in the INPA room)
Prof. Carl Schroeder (LBNL/UCB)
Host: Peter Jacobs
Laser-Plasma Accelerators
Slides
Laser-driven plasma-based accelerators (LPAs) are able to sustain extremely large accelerating gradients, orders of magnitude larger than those achievable using conventional metallic accelerating structures. LPA experiments have demonstrated the generation of multi-GeV electron beams in cm-scale plasmas. These high gradients have attracted interest in LPA technology for high-energy collider applications. In this talk, I will review the basic physics of LPAs, LPA research in the BELLA Center at LBNL, and how LPAs can be developed for various applications. Employing LPAs as a linac for an e+e- collider is the most challenging application, and I will discuss the design considerations and expected performance for an LPA-based linear collider. .
### (This will be a hybrid seminar in theTheory Lounge)
Dr. Jan Steinheimer (FIAS)
Hyper-nuclei production in heavy-on collisions
Hypernuclei have been an interesting topic of study for more than half a century. Yet their properties are still not fully understood. In this talk, I will give a short introduction to hypernuclei and how they can be produced. Here, the production of nuclei with one or more units of strangeness from relativistic heavy ion collisions is of particular interest, due to the abundance of strange baryons created. While the absorption of hyperons offers a chance to create large hypercluster in the spectator fragments of nuclear collisions, also the observation of light hypernuclei from the central hot region is of interest. I will discuss how the production probability can be well described by a coalescence mechanism using the UrQMD model over a beam energy range of three orders of magnitude. In addition I will show how the measurement of different nuclei can be used to determine the size of the region of homogeneity from which baryons, that will eventually form (hyper-)nuclei, are emitted . Within this context I will discuss recent interpretations of the centrality dependence of (hyper-)nuclei production.
### Tuesday, 04.19.2022, 3:30 PM PDT
Dr. Brandon Kriesten (Center for Nuclear Femtography)
Host: Jennifer Rittenhouse West
Quark and Gluon Spatial Distributions in the Nucleon
Studying the role of gluonic observables in exclusive scattering processes is essential as new physics programs, such as an electron ion collider, are planned in unprecedented kinematic regimes. I will present a parameterization of quark and gluon generalized parton distributions (GPDs) calculated using a reggeized spectator model. This parameterization is constrained using a combination of lattice QCD form factor calculations and extracted deep inelastic parton distributions. We evolve our parameterization at leading order in Q2 to the scale of experimental data using a perturbative QCD evolution framework. We demonstrate expected spatial distributions under Fourier transformation using our parametrization. Understanding the behavior of gluon GPDs is a first step towards extracting the gluon contribution to deeply virtual Compton scattering (DVCS) and timelike Compton scattering (TCS) observables at the EIC.
### Tuesday, 04.12.2022, 3:30 PM PDT
Dr. Gunther M Roland (MIT)
Hot QCD with sPHENIX at RHIC
Over the last decades heavy-ion experiments at RHIC and LHC have demonstrated a range of novel QCD phenomena that emerge under conditions of extreme pressure and temperature. New efforts, sPHENIX at RHIC and the upgraded LHC experiments, will begin collecting high precision new data in the next year. These data will allow us to investigate the microscopic origins of observed phenomena in the produced Quark-Gluon Plasma (QGP). Of particular importance will be the complementarity of experiments in the two energy regimes, elucidating the temperature dependence of QGP properties. In this talk I will present the sPHENIX design, construction status and expected performance, and discuss case studies that illustrate key aspects of the sPHENIX physics program.
### Tuesday, 03.29.2022, 3:30 PM PST
Prof. MaElena Tejeda Yeomans (Universidad de Colima)
Host: Jennifer Rittenhouse West
Rise and Fall of Lambda and anti-Lambda Polarization from the Core-Corona Model
The polarization of particles produced in heavy-ion collisions provides the perfect arena to study amazing phenomena such as the collective rotation of the nuclear medium, the transference of global angular momenta to spin properties of certain particles, and the evolution of these properties when there are drastic changes in the properties of the hot and dense medium. Recently, measurements by STAR collaboration at RHIC and HADES collaboration at GSI show the rising of Lambda and anti-Lambda global polarization with decreasing collision energy. Many models predict the vanishing of global polarization due to the lack of system angular momentum, but the height and location of the expected peaks for both Lambda and anti-Lambda are still not well understood. In this talk I will report on recent work to study Lambda and anti-Lambda global polarization in heavy-ion collisions using the core-corona model, where the source of these hyperons is a high-density core and a less dense corona. I will show that the overall properties of the polarization excitation functions can be linked to the relative abundance of Lambdas and anti-Lambdas coming from the core versus those coming from the corona. We will see how the global polarization peak at the expected ranges of collision energies but, the exact positions and heights of these peaks depend on the centrality class, which is directly related to the QGP volume and lifetime, as well as on the relative abundances of Lambdas and anti-Lambdas in the core and corona regions. Finally, I will talk about the improvements we are making to this model to study polarization properties of other species, and as a probe of critical phenomena in the nuclear medium.
### Tuesday, 03.22.2022, 3:30 PM PST
Dr. Xiaojun Yao (MIT)
Host: Xin-Nian Wang
Pure quark and gluon jet observables
Disentangling quark- and gluon-initiated jets can help us to better understand fundamental interactions in QCD and use jets as probes of the quark-gluon plasma in heavy ion collisions. Many previous studies relied on the Sudakov factors of some jet substructure observables such as the soft drop jet mass in the tail region and failed to reach a 100% efficiency in the disentangling. In this talk, I will introduce novel jet observables that are made pure quark or gluon in a wide kinematic region. The construction is based on the collinear drop grooming technique and nonperturbative effects are taken into account. I will show both analytic and Monte Carlo results for these observables in proton-proton collisions and discuss the impact of initial-state radiation and multi-parton interaction. Finally, I will discuss the potential obstacles in applying these observables in heavy ion collisions.
### Tuesday, 03.15.2022, 2:00 PM PST (Special time)
Dr. You Zhou (NBI)
Host: Xin-Nian Wang
Multi-particle correlations for the new decade of QGP studies
Multi-particle correlations have been compelling tools to probe the properties of the Quark-Gluon Plasma (QGP) created in the ultra-relativistic heavy-ion collisions. In this seminar, I will present a generic recursive algorithm for multi-particle cumulants, which enables the calculation of arbitrary order multi-particle cumulants. Among them, I will emphasize a particular series of mixed harmonic multi-particle cumulants, which measures the general correlations between any moments of different flow coefficients. The study of these new multi-particle cumulants in heavy-ion collisions will significantly improve the understanding of the initial event-by-event geometry fluctuations and the hydrodynamic response in the final state. This will pave the way for more stringent constraints on the initial state and help extract more precise information on how the created hot and dense matter evolves. Last but not least, I will show the most recent study of correlations between anisotropic flow and mean transverse momentum in terms of multi-particle correlations/cumulants. I will show how we can directly access the initial conditions of heavy-ion collisions using the latest experimental measurements at the LHC and discuss the critical challenge of the state-of-the-art QGP studies via Bayesian analyses.
### Tuesday, 03.08.2022, 2:00 PM PST
Dr. Giuliano Giacalone (Heidelberg University)
Host: Xin-Nian Wang
The initial state of the quark-gluon plasma: status, prospects, interdisciplinary connections
The hydrodynamic model of the quark-gluon plasma (QGP) formed in relativistic nuclear collisions has permitted us over the years not only to obtain quantitative estimates of the transport properties of this medium from data, but also to establish a phenomenologically viable picture of its initial condition and how it emerges from the interaction of two ions at high energy. I review the current understanding of the initial condition of the QGP, emphasizing the outcome of state-of-the-art models and the overall picture that they yield. I discuss the progress made in the definition of observable quantities that offer a specific sensitivity to the physics of the initial state, with a focus on recent results (both theoretical and experimental) on mean transverse momentum-anisotropic flow correlations. Such observables pose unprecedented constraints on the parameters of state-of-the-art Monte Carlo generators for nuclear collisions, demonstrating, in particular, the importance of having an accurate implementation of the structure of the colliding ions, and the nucleons therein, in such frameworks. Consequently, the initial state of heavy-ion collisions provides fertile ground for new interdisciplinary connections involving different aspects of hadronic and nuclear physics across energy scales.
### Spin-momentum correlation in hot and dense QCD matter
The transport phenomena involving spin are instrumental in investigating quantum effects in many-body systems. In heavy-ion collisions, the recent measurement of spin polarization and spin alignment opens a new avenue to explore the properties of hot and dense QCD matter. Based on linear response theory and quantum kinetic equation, we have systematically studied spin-momentum correlation induced by hydrodynamic gradients [1]. In addition to the widely studied thermal vorticity effects, we identify an undiscovered contribution from the fluid shear [2]. This shear-induced polarization (SIP) can be viewed as the fluid analog of strain-induced polarization observed in elastic and nematic materials. The possible signature of SIP at RHIC and LHC will be elaborated. Then, I will present our prediction for the signature Spin Hall effect induced by baryon chemical gradient at RHIC beam scan energies [3,4]. If time permitted, I will briefly discuss the effect of SIP on vector mesons. .
### The End of the Proton Radius Puzzle?
For many years scientists believed that the proton radius was 0.877(6) fm based on a series of atomic Lamb shift and electron scattering measurements. In 2010, a new type of measurement, making use of muonic hydrogen, determined the radius to be 0.842(1) fm. The large systematic difference between muonic hydrogen measurements and the previous results became known as the proton radius puzzle. To solve this puzzle, a world-wide theoretical and experimental investigation has been undertaken. I will review the status of the puzzle with an emphasis on electron scattering results and the systematic differences between the different analysis techniques that led to disparate conclusions. I will leave it to the audience to decide if the puzzle is solved.
### Joint NT and HIT seminar (note special day and time)
Wednesday, 2022.02.02, 1:00 PM PST
### Host: Aaron Meyer
Lattice QCD Determination of the Bjorken-$x$ Dependence of PDFs at Next-to-next-to-leading Order
The large-momentum effective theory (LaMET) is a systematic approach to calculate parton physics from Euclidean approaches such as lattice QCD. With major progress in the lattice renormalization and perturbative matching, the lattice calculation of PDFs with LaMET is now entering the stage of precision control. In this talk, I will present a state-of-the-art lattice QCD calculation of pion valence quark distribution with next-to-next-to-leading order matching correction, which is done using two fine lattices with spacings $a=0.04$ fm and $0.06$ fm and valence pion mass $m_\pi=300$ MeV at boost momentum as large as 2.42 GeV. I will demonstrate that perturbative matching in Bjorken-$x$ space yields a reliable determination of the valence quark distribution for moderate x with a target precision, which shows considerably improved systematic uncertainty compared to a previous analysis of the same lattice data with a short-distance factorization approach in the coordinate space, and is in excellent agreement with the most recent global analyses.
### Tuesday, 2022.01.25, 3:30 PM PST
Prof. Rene Bellwied (University of Houston)
Matter under extreme conditions - Particle Collisions along the QCD Phase Diagram
Relativistic particle collisions have come a long way during the past two decades with the characterization of states of matter along the QCD phase transition line. I will try to show how these discoveries lead to significant multi-disciplinary efforts to understand the creation and evolution of matter under extreme conditions. Examples that will be highlighted are the connection of fundamental quantum theories to collective phenomena and particle production, as well as astrophysical measurements that link to interactions observed at RHIC and LHC.
### Tuesday, 2022.01.18, 3:30 PM PST
Prof. Tanja Horn (JLab & The Catholic University of America)
Host: Jennifer Rittenhouse West
PION AND KAON STRUCTURE FUNCTIONS | 2023-03-27T19:52:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.512108325958252, "perplexity": 1925.0210723274784}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948684.19/warc/CC-MAIN-20230327185741-20230327215741-00468.warc.gz"} |
https://quark.phy.bnl.gov/seminars/oldseminars.html | # Past Theoretical Physics Seminars at BNL
• ## Wednesday, October 31, 2018
2:30pm, Small Seminar Room
Unveiling New Physics Through Angular Distributions at the LHC
Rodolfo Capdevilla (Notre Dame)
HET Seminar
• ## Thursday, November 1, 2018
12:00pm, Room 2-160, Bldg. 510
DIS on "Nuclei" using holography
RIKEN Lunch Seminar
4:00pm, CFNS Seminar Room 2-38
TBA
Al Mueller (Columbia University)
CFNS Seminar
• ## Friday, November 2, 2018
2:00pm, CNFS Seminar Room 2-38
Diffractive Electron-Nucleus Scattering and Ancestry in Branching Random Walks
Al Mueller (Columbia)
Nuclear Theory / RIKEN seminar
• ## Friday, November 9, 2018
2:00pm, CNFS Seminar Room 2-38
TBA
Ajit Srivastava (Institute of Physics, Bhubaneswar)
Nuclear Theory/RIKEN seminar
• ## Wednesday, November 14, 2018
2:30pm, Small Seminar Room
TBA
Konstantinos Orginos (College of William and Mary)
HET Seminar
• ## Thursday, November 15, 2018
12:00pm, 2-160, Bldg. 510
Exclusive $\rho$ meson production in $eA$ collisions: collinear factorization and the CGC
Renaud Boussarie (Brookhaven National Laboratory)
We will focus on the theoretical description of exclusive ρ meson production in eA collisions, using a hybrid factorization scheme which involves Balitsky's shockwave description of the Color Glass Condensate in the t channel, and Distribution Amplitudes (DAs) in the s channel. We will first give a quick introduction to the shockwave framework and to collinear factorization up to twist 3 for DAs, then we will apply these framweworks to the production of a longitudinal meson at NLO accuracy, and to the production of a transverse meson at twist 3 accuracy. We will insist on the experimental applications, and on several theoretical questions raised by our results: the dilute BFKL limit at NLO for diffraction, and collinear factorization breaking at twist 3.
• ## Friday, November 16, 2018
2:00pm, CNFS Seminar Room 2-38
N/A
Dimitra Karabali (Lehman College CUNY)
Nuclear Theory/RIKEN
• ## Thursday, November 29, 2018
12:00pm, 2-160, Bldg. 510
TBA
Mario Mitter (Brookhaven National Laboratory)
• ## Friday, November 30, 2018
2:00pm, CNFS seminar room 2-38
TBA
Juan Rojo (VU University)
Nuclear Theory / RIKEN seminar
• ## Wednesday, December 5, 2018
2:30pm, YITP Stony Brook
TBA
Jiji Fan (Syracuse)
Joint YITP/HET Theory Seminar
• ## Thursday, December 6, 2018
12:00pm, Room 2-160, Bldg. 510
Proton decay
Jun-Sik Yoo (Stony Brook University)
RIKEN Lunch Seminar
12:00pm, 2-160, Bldg. 510
On QCD and its Phase Diagram from a Functional RG Perspective
Mario Mitter (BNL)
• ## Wednesday, December 12, 2018
2:30pm, YITP Stony Brook
TBA
TBA
Joint YITP/HET Theory Seminar
• ## Thursday, January 10, 2019
12:00pm, 2-160, Bldg. 510
A novel background subtraction method for jet studies in heavy ion collisions
Alba Soto Ontoso (BNL)
• ## Friday, January 18, 2019
2:00pm, CFNS seminar room 2-38
TBA
Nuclear Theory / RIKEN seminar
• ## Thursday, January 24, 2019
12:00pm, 1-224, Bldg. 510 (different from usual room)
In this talk, I will present a connection between two approaches of studying quarkonium dynamics inside quark-gluon plasma: the open quantum system formalism and the transport equation. I will discuss insights from the perspective of quantum information. I will show that under the weak coupling and Markovian approximations, the Lindblad equation turns to a Boltzmann transport equation after a Wigner transform is applied to the system density matrix. I will demonstrate how the separation of physical scales justifies the approximations, by using effective field theory of QCD. Finally, I will show some phenomenological results based on the derived transport equation.
Xiaojun Yao (Duke University)
In this talk, I will present a connection between two approaches of studying quarkonium dynamics inside quark-gluon plasma: the open quantum system formalism and the transport equation. I will discuss insights from the perspective of quantum information. I will show that under the weak coupling and Markovian approximations, the Lindblad equation turns to a Boltzmann transport equation after a Wigner transform is applied to the system density matrix. I will demonstrate how the separation of physical scales justifies the approximations, by using effective field theory of QCD. Finally, I will show some phenomenological results based on the derived transport equation.
• ## Friday, January 25, 2019
2:00pm, CNFS Seminar Room 2-38
TBA
Paolo Glorioso (Kadanoff Center for Theoretical Physics and Enrico Fermi Institute, University of Chicago)
Nuclear Theory/RIKEN seminar | 2021-01-27T03:55:23 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3040505051612854, "perplexity": 13496.867922732432}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610704820894.84/warc/CC-MAIN-20210127024104-20210127054104-00025.warc.gz"} |
https://math.wikia.org/wiki/Open | ## FANDOM
1,165 Pages
An open subset of a metric space is a set that contains only interior points.
In the text below, $(X, d)$ will always refer to a metric space.
## Definition: neighbourhood of a point
Let $x \in X$. By a neighbourhood of $x$ of radius $0 < r \in \mathbf R$ we mean the set $N_r(x) = \{ y \in X | d(x, y) < r \}$.
## Definition: interior point
Let $E$ be a nonempty subset of $X$. A point $x \in E$ is said to be an interior point of $E$ if and only if there exists a neighbourhood $N$ of $x$ such that $N \subset E$.
## Definition: open set
A nonempty subset $E$ of $X$ is said to be open if and only if every point of $E$ is an interior point of $E$.
The property of being open is related to the property of being closed by the following theorem.
## Theorem: relation between open and closed sets
A subset $E$ of $X$ is open if and only if its complement $E^c$ is a closed subset of $X$.
Proof. First suppose that $E^c$ is closed. We want to show that this implies that $E$ is open. Choose $x \in E$. Then $x$ is not a limit point of $E^c$ (if it was, then $x$ would be an element of $E^c$, by definition of being closed, which is absurd, since $x \in E$), and hence there exists a neighbourhood $N$ of $x$ such that $N \cap E^c$ is empty. But then $N \subset E$ so that $x$ is an interior point of $E$. Hence $E$ is open.
Now suppose that $E$ is open. We want to show that this implies that $E^c$ is closed. Let $x$ be a limit point of $E^c$. If no such $x$ exists, then $E^c$ contains all its limit points, and the proof is complete. If not, then every neighbourhood $N$ of $x$ is such that $N \cap E^c$ is not empty. But then $x$ is not an interior point of $E$. Since $E$ is open, we must have $x \in E^c$. But then $E^c$ is closed, and the proof is complete.
QED.
## References
• Rudin, Walter: Principles of Mathematical Analysis, 3rd edition, McGraw Hill, 1976.
Community content is available under CC-BY-SA unless otherwise noted. | 2019-07-22T01:26:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.953811526298523, "perplexity": 46.973346001093084}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195527458.86/warc/CC-MAIN-20190722010436-20190722032436-00203.warc.gz"} |
https://mgi.gov/content/center-theoretical-and-computational-materials-science-ctcms | # Center for Theoretical and Computational Materials Science (CTCMS)
### Mission
#### The Center's mission is to support the Material Measurement Laboratory's mission in materials measurement and data delivery by:
• developing, solving, and quantifying materials models using state-of-the-art computational approaches;
• creating opportunities for collaboration where CTCMS can make a positive difference by virtue of its structure, focus, and people;
• developing powerful new tools for materials theory and modeling and accelerating their integration into industrial research.
### Active Working Groups
• Diffusion Working Group on High Throughput Analysis of Multicomponent Multiphase Diffusion Data
• OOF: Object-Oriented Finite Element Analysis of Real Material Microstructures Working Group
• FiPy: A Finite Volume PDE Solver Using Python
• Interatomic Potential Repository Project
• Micromagnetic Modeling ($\mu$MAG) Working Group
• The Materials Digital Library
### Working Group Archives
• Solder Interconnect Geometry and Reactive Wetting code archive
• Phase Field Modeling Tools simulation archive
## Navigate to Other Activities by Strategic Goal
Data and Computational Tools for Advanced Materials Design: Structural Materials Applications - Cobalt Based Superalloys Innovation in High Energy Diffraction Microscopy Adds New Insights to Material Deformation and Failure Rational Design of Advanced Polymeric Capacitor Films Multidisciplinary University Research Initiative (MURI) The Nanoporous Materials Genome Center Center of Excellence on Integrated Materials Modeling (CEIMM) Center for Hierarchical Materials Design (CHiMaD) The Center for Materials in Extreme Dynamic Environments (CMEDE) Center of Materials in Extreme Dynamic Environments (CMEDE) QMCPACK PRedictive Integrated Structural Materials Science (PRISMS) Center DOE EERE Fuel Cell Technologies Office Database Multidisciplinary University Research Initiative: Managing the Mosaic of Microstructure
Innovation in High Energy Diffraction Microscopy Adds New Insights to Material Deformation and Failure Center of Materials in Extreme Dynamic Environments (CMEDE) Joint Center for Artificial Photosynthesis (JCAP) PRedictive Integrated Structural Materials Science (PRISMS) Center Materials Data Curation System Data and Computational Tools for Advanced Materials Design: Structural Materials Applications - Cobalt Based Superalloys DOE EERE Fuel Cell Technologies Office Database AFRL, NIST, and NSF Announce Materials Science and Engineering Data Challenge Awardees Center for Hierarchical Materials Design (CHiMaD) Automatic Flow for Materials Discovery (AFLOW) Development and application of innovative methods for quantification of hexavalent chromium in soils Center for Theoretical and Computational Materials Science (CTCMS) The Materials Project Innovative methods to identify critical and/or strategic elements from unconventional domestic sources
The Materials Project Center of Materials in Extreme Dynamic Environments (CMEDE) Center of Excellence on Integrated Materials Modeling (CEIMM) Multidisciplinary University Research Initiative: Managing the Mosaic of Microstructure Joint Center for Energy Storage Research (JCESR) QMCPACK AFRL, NIST, and NSF Announce Materials Science and Engineering Data Challenge Awardees The Brilliance of Diamonds PRedictive Integrated Structural Materials Science (PRISMS) Center Center for Hierarchical Materials Design (CHiMaD) The Center for Materials in Extreme Dynamic Environments (CMEDE) The Nanoporous Materials Genome Center
Center of Excellence on Integrated Materials Modeling (CEIMM) PRedictive Integrated Structural Materials Science (PRISMS) Center Multidisciplinary University Research Initiative: Managing the Mosaic of Microstructure Automatic Flow for Materials Discovery (AFLOW) Center for Hierarchical Materials Design (CHiMaD) Center of Materials in Extreme Dynamic Environments (CMEDE) Rational Design of Advanced Polymeric Capacitor Films Multidisciplinary University Research Initiative (MURI) Joint Center for Energy Storage Research (JCESR) The Materials Project | 2019-04-25T16:40:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.25125429034233093, "perplexity": 14118.937377669845}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578727587.83/warc/CC-MAIN-20190425154024-20190425180024-00198.warc.gz"} |
https://lammps.sandia.gov/doc/pair_thole.html | # pair_style lj/cut/thole/long/omp command
## Syntax
pair_style style args
• style = thole or lj/cut/thole/long or lj/cut/thole/long/omp
• args = list of arguments for a particular style
thole args = damp cutoff
damp = global damping parameter
cutoff = global cutoff (distance units)
lj/cut/thole/long or lj/cut/thole/long/omp args = damp cutoff (cutoff2)
damp = global damping parameter
cutoff = global cutoff for LJ (and Thole if only 1 arg) (distance units)
cutoff2 = global cutoff for Thole (optional) (distance units)
## Examples
pair_style hybrid/overlay ... thole 2.6 12.0
pair_coeff 1 1 thole 1.0
pair_coeff 1 2 thole 1.0 2.6 10.0
pair_coeff * 2 thole 1.0 2.6
pair_style lj/cut/thole/long 2.6 12.0
## Description
The thole pair styles are meant to be used with force fields that include explicit polarization through Drude dipoles. This link describes how to use the thermalized Drude oscillator model in LAMMPS and polarizable models in LAMMPS are discussed on the Howto polarizable doc page.
The thole pair style should be used as a sub-style within in the pair_hybrid/overlay command, in conjunction with a main pair style including Coulomb interactions, i.e. any pair style containing coul/cut or coul/long in its style name.
The lj/cut/thole/long pair style is equivalent to, but more convenient that the frequent combination hybrid/overlay lj/cut/coul/long cutoff thole damp cutoff2. It is not only a shorthand for this pair_style combination, but it also allows for mixing pair coefficients instead of listing them all. The lj/cut/thole/long pair style is also a bit faster because it avoids an overlay and can benefit from OMP acceleration. Moreover, it uses a more precise approximation of the direct Coulomb interaction at short range similar to coul/long/cs, which stabilizes the temperature of Drude particles.
The thole pair styles compute the Coulomb interaction damped at short distances by a function
$$$T_{ij}(r_{ij}) = 1 - \left( 1 + \frac{s_{ij} r_{ij} }{2} \right) \exp \left( - s_{ij} r_{ij} \right)$$$
This function results from an adaptation to point charges (Noskov) of the dipole screening scheme originally proposed by Thole. The scaling coefficient $$s_{ij}$$ is determined by the polarizability of the atoms, $$\alpha_i$$, and by a Thole damping parameter $$a$$. This Thole damping parameter usually takes a value of 2.6, but in certain force fields the value can depend upon the atom types. The mixing rule for Thole damping parameters is the arithmetic average, and for polarizabilities the geometric average between the atom-specific values.
$$$s_{ij} = \frac{ a_{ij} }{ (\alpha_{ij})^{1/3} } = \frac{ (a_i + a_j)/2 }{ [(\alpha_i\alpha_j)^{1/2}]^{1/3} }$$$
The damping function is only applied to the interactions between the point charges representing the induced dipoles on polarizable sites, that is, charges on Drude particles, $$q_{D,i}$$, and opposite charges, $$-q_{D,i}$$, located on the respective core particles (to which each Drude particle is bonded). Therefore, Thole screening is not applied to the full charge of the core particle $$q_i$$, but only to the $$-q_{D,i}$$ part of it.
The interactions between core charges are subject to the weighting factors set by the special_bonds command. The interactions between Drude particles and core charges or non-polarizable atoms are also subject to these weighting factors. The Drude particles inherit the 1-2, 1-3 and 1-4 neighbor relations from their respective cores.
For pair_style thole, the following coefficients must be defined for each pair of atoms types via the pair_coeff command as in the example above.
• alpha (distance units^3)
• damp
• cutoff (distance units)
The last two coefficients are optional. If not specified the global Thole damping parameter or global cutoff specified in the pair_style command are used. In order to specify a cutoff (third argument) a damp parameter (second argument) must also be specified.
For pair style lj/cut/thole/long, the following coefficients must be defined for each pair of atoms types via the pair_coeff command.
• epsilon (energy units)
• sigma (length units)
• alpha (distance units^3)
• damps
• LJ cutoff (distance units)
The last two coefficients are optional and default to the global values from the pair_style command line.
Styles with a gpu, intel, kk, omp, or opt suffix are functionally the same as the corresponding style without the suffix. They have been optimized to run faster, depending on your available hardware, as discussed on the Speed packages doc page. The accelerated styles take the same arguments and should produce the same results, except for round-off and precision issues.
These accelerated styles are part of the GPU, USER-INTEL, KOKKOS, USER-OMP and OPT packages, respectively. They are only enabled if LAMMPS was built with those packages. See the Build package doc page for more info.
You can specify the accelerated styles explicitly in your input script by including their suffix, or you can use the -suffix command-line switch when you invoke LAMMPS, or you can use the suffix command in your input script.
See the Speed packages doc page for more instructions on how to use the accelerated styles effectively.
Mixing:
The thole pair style does not support mixing. Thus, coefficients for all I,J pairs must be specified explicitly.
The lj/cut/thole/long pair style does support mixing. Mixed coefficients are defined using
$$$\alpha_{ij} = \sqrt{\alpha_i\alpha_j}$$$
$$$a_{ij} = \frac 1 2 (a_i + a_j)$$$
## Restrictions
These pair styles are part of the USER-DRUDE package. They are only enabled if LAMMPS was built with that package. See the Build package doc page for more info.
This pair_style should currently not be used with the charmm dihedral style if the latter has non-zero 1-4 weighting factors. This is because the thole pair style does not know which pairs are 1-4 partners of which dihedrals.
The lj/cut/thole/long pair style should be used with a Kspace solver like PPPM or Ewald, which is only enabled if LAMMPS was built with the kspace package. | 2019-06-27T04:18:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 4, "x-ck12": 0, "texerror": 0, "math_score": 0.3455137610435486, "perplexity": 9237.238399758056}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560628000613.45/warc/CC-MAIN-20190627035307-20190627061307-00486.warc.gz"} |
https://www.aimsciences.org/article/doi/10.3934/eect.2022003 | Article Contents
Article Contents
# A shape optimization problem constrained with the Stokes equations to address maximization of vortices
• *Corresponding author: John Sebastian Simon
• We study an optimization problem that aims to determine the shape of an obstacle that is submerged in a fluid governed by the Stokes equations. The mentioned flow takes place in a channel, which motivated the imposition of a Poiseuille-like input function on one end and a do-nothing boundary condition on the other. The maximization of the vorticity is addressed by the $L^2$-norm of the curl and the det-grad measure of the fluid. We impose a Tikhonov regularization in the form of a perimeter functional and a volume constraint to address the possibility of topological change. Having been able to establish the existence of an optimal shape, the first order necessary condition was formulated by utilizing the so-called rearrangement method. Finally, numerical examples are presented by utilizing a finite element method on the governing states, and a gradient descent method for the deformation of the domain. On the said gradient descent method, we use two approaches to address the volume constraint: one is by utilizing the augmented Lagrangian method; and the other one is by utilizing a class of divergence-free deformation fields.
Mathematics Subject Classification: Primary: 49Q10, 49J20, 49K20; Secondary: 35Q93.
Citation:
• Figure 1. Set up of the domain
Figure 2. Initial geometry of the domain with the refined mesh
Figure 3. From curlaL-problem, the figure features the following: (left) Evolution of the free-boundary $\Gamma_{\rm f}$, (upper right) Normalized trend of the objective functional, (lower right) Normalized trend of the volume
Figure 4. From detgradaL-problem, the figure features the following: (left) Evolution of the free-boundary $\Gamma_{\rm f}$, (upper right) Normalized trend of the objective functional, (lower right) Normalized trend of the volume
Figure 5. From curldF-problem, the figure features the following: (left) Evolution of the free-boundary $\Gamma_{\rm f}$, (upper right) Normalized trend of the objective functional, (lower right) Normalized trend of the volume
Figure 6. (left) Comparison of final shapes between aL-algorithm and dF-algorithm for the problem with the parameters $\gamma_1 = 1$, $\gamma_2 = 0$ and $\alpha = 5$, (upper right) Comparison of objective value trends between aL-algorithm and dF-algorithm, (lower right) Comparison of volume trends between aL-algorithm and dF-algorithm
Figure 7. From detgraddF-problem, the figure features the following: (left) Evolution of the free-boundary $\Gamma_{\rm f}$, (upper right) Normalized trend of the objective functional, (lower right) Normalized trend of the volume
Figure 8. (left) Comparison of final shapes between aL-algorithm and dF-algorithm with the parameters $\gamma_1 = 0$, $\gamma_2 = 1$, and $\alpha = 1$, (upper right) Comparison of objective value trends between aL-algorithm and dF-algorithm, (lower right) Comparison of volume trends between aL-algorithm and dF-algorithm
Figure 9. (left) Comparison of final shapes between aL-algorithm and dF-algorithm with the parameters $\gamma_1 = 0$, $\gamma_2 = 1$, and $\alpha = 1.2$, (upper right) Comparison of objective value trends between aL-algorithm and dF-algorithm, (lower right) Comparison of volume trends between aL-algorithm and dF-algorithm
Figure 10. From configuration 1 of mixeddF-problem, the figure features the following: (left) Evolution of the free-boundary $\Gamma_{\rm f}$, (upper right) Normalized trend of the objective functional, (lower right) Normalized trend of the volume
Figure 11. (left) Plots of the solutions of mixeddF-problem (using configuration 1), of curldF-problem and of detgraddF-problem generated boundaries, (upper right) Comparison of the objective function value of the curldf-problem and the curl part of the mixeddF-problem, (lower right) Comparison of the objective function value of the curldF-problem and the detgrad part of the mixeddf-problem
Figure 12. (left) Plots of the solutions of mixeddF-problem (using configuration 2), of curldF-problem and of detgraddF-problem generated boundaries, (upper right) Comparison of the objective function value of the curldF-problem and the detgrad part of the mixeddF-problem, (lower right) Comparison of the objective function value of the curldF-problem and the detgrad part of the mixeddF-problem
Figure 13. (left) Plots of the solutions of mixeddF-problem (using configuration 4), of curldF-problem and of detgraddF-problem generated boundaries, (upper right) Comparison of the objective function value of the curldF-problem and the detgrad part of the mixeddF-problem, (lower right) Comparison of the objective function value of the curldF-problem and the detgrad part of the mixeddF-problem
Figure 14. (left) Plots of the solutions of mixeddF-problem (configurations 1 and 10), of curldF-problem, and of detgraddF-problem, (upper right) Hausdorff distance between mixeddF-solution and curldF-solution on each configuration, (lower right) Hausdorff distance between mixeddF-solution and detgraddF-solution on each configuration
Figure 15. The figure shows the configurations for the two-obstacle experiment: (top) Set-up of the domain where the obstacles are placed parallel to the flow; (bottom) Set-up of the domain where the obstacles are placed perpendicular to the flow
Figure 16. From the first configuration of the two-obstacle experiment, the figure features the following: (left) Evolution of the free-boundary $\Gamma_{\rm f}$, (upper right) Normalized trend of the objective functional, (lower right) Normalized trend of the volume
Figure 17. From the second configuration of the two-obstacle experiment, the figure features the following: (left) Evolution of the free-boundary $\Gamma_{\rm f}$, (upper right) Normalized trend of the objective functional, (lower right) Normalized trend of the volume
Figure 18. The figure shows the comparison of the flows using the initial domain (lower part), and the final shape from curldf-problem (upper part)
Figure 19. The figure shows the comparison of the flows using the initial domain (lower part), and the final shape from detgraddf-problem (upper part)
Figure 20. The figure shows the comparison of the flows using the the final shape from curldf-problem (lower part), and the final shape from detgraddf-problem (upper part)
Table 1. Parameter values for curlaL-problem
Parameter Value Parameter Value $\alpha$ 6.0 $\ell_0$ 20 $b_0$ $1\times10^{-4}$ $\tau$ 1.05 $\overline{b}$ 10
Table 2. Parameter values for detgradaL-problem
Parameter Value Parameter Value $\alpha$ 1.3 $\ell_0$ .5 $b_0$ $1\times10^{-2}$ $\tau$ 1.05 $\overline{b}$ 10
Table 3. Parameter Values for mixeddF-problem
Configuration $\alpha$ $\gamma_1$ $\gamma_2$ 1 6.0 1.0 1.0 2 7.0 1.0 2.0 3 8.0 1.0 3.0 4 9.0 1.0 4.0 5 10.0 1.0 5.0 6 11.0 1.0 6.0 7 12.0 1.0 7.0 8 13.0 1.0 8.0 9 14.0 1.0 9.0 10 15.0 1.0 10.0
• [1] H. Azegami, Solution of shape optimization problem and its application to product design, In Mathematical Analysis of Continuum Mechanics and Industrial Applications, (eds. H. Itou, M. Kimura, V. Chalupecký, K. Ohtsuka, D. Tagami and A. Takada), Springer Singapore, Singapore, 26 (2017), 83–98. doi: 10.1007/978-981-10-2633-1_6. [2] J. Bacani and G. Peichl, On the first-order shape derivative of the Kohn–Vogelius cost functional of the Bernoulli problem, Abstr. Appl. Anal., 2013 (2013), Art. ID 384320, 19 pp. doi: 10.1155/2013/384320. [3] D. Chenais, On the existence of a solution in a domain identification problem, J. Math. Anal. Appl, 52 (1975), 189-219. doi: 10.1016/0022-247X(75)90091-8. [4] M. S. Chong, A. E. Perry and B. J. Cantwell, A general classification of three-dimensional flow fields, Phys. Fluids A, 2 (1990), 765-777. doi: 10.1063/1.857730. [5] C. Dapogny, P. Frey, F. Omnès and Y. Privat, Geometrical shape optimization in fluid mechanics using {F}ree{F}em++, Struct. Multidiscip. Optim., 58 (2018), 2761-2788. doi: 10.1007/s00158-018-2023-2. [6] M. Delfour and J.-P. Zolesio, Shapes and Geometries: Metrics, Analysis, Differential Calculus, and Optimization, 2$^{nd}$ edition, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2011. doi: 10.1137/1.9780898719826. [7] M. Desai and K. Ito, Optimal controls of Navier–Stokes equations, SIAM J. Control Optim., 32 (1994), 1428-1446. doi: 10.1137/S0363012992224972. [8] M. F. Eggl and P. J. Schmid, Mixing enhancement in binary fluids using optimised stirring strategies, J. Fluid Mech., 899 (2020), A24, 21 pp. doi: 10.1017/jfm.2020.448. [9] L. Evans, Partial Differential Equations, Graduate Studies in Mathematics, American Mathematical Society, 1998. [10] T. L. B. Flinois and T. Colonius, Optimal control of circular cylinder wakes using long control horizons, Physics of Fluids, 27 (2015), 087105. doi: 10.1063/1.4928896. [11] Z. M. Gao, Y. C. Ma and H. W. Zhuang, Shape optimization for Navier–Stokes flow, Inverse Probl. Sci. Eng., 16 (2008), 583-616. doi: 10.1080/17415970701743319. [12] V. Girault and P.-A. Raviart, Finite Element Methods for Navier–Stokes Equations: Theory and Algorithms, Springer Series in Computational Mathematics, 5. Springer-Verlag, Berlin, 1986. doi: 10.1007/978-3-642-61623-5. [13] K. Goto, K. Nakajima and H. Notsu, Twin vortex computer in fluid flow, New J. Phys., 23 (2021), 063051, 14 pp. doi: 10.1088/1367-2630/ac024d. [14] J. Haslinger, K. Ito, T. Kozubek, K. Kunisch and G. Peichl, On the shape derivative for problems of Bernoulli type, Interfaces Free Bound., 11 (2009), 317-330. doi: 10.4171/IFB/213. [15] J. Haslinger, J. Málek and J. Stebel, Shape optimization in problems governed by generalised Navier–Stokes equations: Existence analysis, Control Cybernet., 34 (2005), 283-303. [16] F. Hecht, New development in FreeFem++, J. Numer. Math., 20 (2012), 251-265. doi: 10.1515/jnum-2012-0013. [17] A. Henrot and M. Pierre, Shape Variation and Optimization: A Geometrical Analysis, EMS Tracts in Mathematics, 28. European Mathematical Society (EMS), Zürich, 2018. doi: 10.4171/178. [18] A. Henrot and Y. Privat, What is the optimal shape of a pipe?, Arch. Ration. Mech. Anal., 196 (2010), 281-302. doi: 10.1007/s00205-009-0243-8. [19] J. C. R. Hunt, A. A. Wray and P. Moin, Eddies, streams, and convergence zones in turbulent flows, In Proc. 1988 Summer Program of Center for Turbulence Research Program, (1998), 193–208. [20] K. Ito, K. Kunisch and G. H. Peichl, Variational approach to shape derivatives, ESAIM Control Optim. Calc. Var., 14 (2008), 517-539. doi: 10.1051/cocv:2008002. [21] Y. Iwata, H. Azegami, T. Aoyama and E. Katamine, Numerical solution to shape optimization problems for non-stationary Navier–Stokes problems, JSIAM Lett., 2 (2010), 37-40. doi: 10.14495/jsiaml.2.37. [22] J. Jeong and F. Hussain, On the identification of a vortex, J. Fluid Mech., 285 (1995), 69-94. doi: 10.1017/S0022112095000462. [23] H. Kasumba and K. Kunisch, Vortex control in channel flows using translational invariant cost functionals, Comput. Optim. Appl., 52 (2012), 691-717. doi: 10.1007/s10589-011-9434-y. [24] G. Mather, I. Mezić, S. Grivopoulos, U. Vaidya and L. Petzold, Optimal control of mixing in Stokes fluid flows, J. Fluid Mech., 580 (2007), 261-281. doi: 10.1017/S0022112007005332. [25] B. Mohammadi and O. Pironneau, Applied Shape Optimization for Fluids, 2$^{nd}$ edition, Numerical Mathematics and Scientific Computations, Oxford University Press, 2010. [26] P. Monk, Finite Element Methods for Maxwell's Equations, Oxford University Press, 2003. doi: 10.1093/acprof:oso/9780198508885.001.0001. [27] M. T. Nair, M. Hegland and R. S. Anderssen, The trade-off between regularity and stability in Tikhonov regularization, Math. Comp., 66 (1997), 193-206. doi: 10.1090/S0025-5718-97-00811-9. [28] J. Nocedal and S. Wright, Numerical Optimization, vol. 2 of Springer Series in Operations Research and Financial Engineering, 2$^{nd}$ edition, Springer, New York, 2006. [29] H. Notsu and M. Tabata, Error estimates of a stabilized Lagrange-Galerkin scheme for the Navier–Stokes equations, ESAIM Math. Model. Numer. Anal., 50 (2016), 361-380. doi: 10.1051/m2an/2015047. [30] M. Pošta and T. Roubíček, Optimal control of Navier–Stokes equations by Oseen approximation, Comput. Math. Appl., 53 (2007), 569-581. doi: 10.1016/j.camwa.2006.02.034. [31] J. F. T. Rabago and H. Azegami, An improved shape optimization formulation of the Bernoulli problem by tracking the Neumann data, J. Engrg. Math., 117 (2019), 1-29. doi: 10.1007/s10665-019-10005-x. [32] J. F. T. Rabago and H. Azegami, A second-order shape optimization algorithm for solving the exterior Bernoulli free boundary problem using a new boundary cost functional, Comput. Optim. Appl., 77 (2020), 251-305. doi: 10.1007/s10589-020-00199-7. [33] S. Schmidt and V. Schulz, Shape derivatives for general objective functions and the incompressible Navier–Stokes equations, Control Cybernet., 39 (2010), 677-713. [34] J. Sokolowski and J.-P. Zolesio, Introduction to Shape Optimization: Shape Sensitivity Analysis, 1$^{st}$ edition, Springer Series in Computational Mathematics, 16. Springer-Verlag Berlin, 1992. doi: 10.1007/978-3-642-58106-9.
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https://zbmath.org/authors/?q=ai%3Aluca.florian | # zbMATH — the first resource for mathematics
## Luca, Florian
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Author ID: luca.florian Published as: Luca, F.; Luca, Florian Homepage: https://www.wits.ac.za/staff/academic-a-z-listing/l/florianlucawitsacza/ External Links: MGP · Math-Net.Ru · Wikidata · ORCID · dblp · GND
Documents Indexed: 705 Publications since 1993, including 7 Books Reviewing Activity: 306 Reviews
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all top 5
#### Serials
50 Journal of Number Theory 42 Acta Arithmetica 27 The Fibonacci Quarterly 25 International Journal of Number Theory 21 Colloquium Mathematicum 21 Journal of Integer Sequences 18 Publicationes Mathematicae 18 Integers 14 Indagationes Mathematicae. New Series 13 Periodica Mathematica Hungarica 13 Monatshefte für Mathematik 13 Boletín de la Sociedad Matemática Mexicana. Third Series 12 Glasnik Matematički. Serija III 11 Bulletin of the Australian Mathematical Society 11 Annales Mathematicae et Informaticae 10 Rocky Mountain Journal of Mathematics 10 Proceedings of the American Mathematical Society 10 Journal de Théorie des Nombres de Bordeaux 9 Glasgow Mathematical Journal 8 Mathematics of Computation 8 Archiv der Mathematik 8 Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie. Nouvelle Série 8 The Ramanujan Journal 8 Uniform Distribution Theory 7 Mathematica Slovaca 6 Functiones et Approximatio. Commentarii Mathematici 6 Proceedings of the Edinburgh Mathematical Society. Series II 6 The New York Journal of Mathematics 6 Journal of Combinatorics and Number Theory 5 American Mathematical Monthly 5 Annales des Sciences Mathématiques du Québec 5 Canadian Mathematical Bulletin 5 Proceedings of the Japan Academy. Series A 5 Revista Colombiana de Matemáticas 5 Congressus Numerantium 5 Smarandache Notions Journal 4 Lithuanian Mathematical Journal 4 Bulletin of the London Mathematical Society 4 International Journal of Mathematics and Mathematical Sciences 4 Mathematika 4 Quaestiones Mathematicae 4 Mathematica Bohemica 4 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 4 Acta Academiae Paedagogicae Agriensis. Nova Series. Sectio Matematicae 4 Journal of the Australian Mathematical Society 4 Portugaliae Mathematica. Nova Série 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 3 Indian Journal of Mathematics 3 Journal für die Reine und Angewandte Mathematik 3 Studia Scientiarum Mathematicarum Hungarica 3 Transactions of the American Mathematical Society 3 Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio Computatorica 3 IMRN. International Mathematics Research Notices 3 Aequationes Mathematicae 3 Divulgaciones Matemáticas 3 Mathematical Communications 3 Revista Matemática Complutense 3 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 3 Communications in Mathematics 3 Moscow Journal of Combinatorics and Number Theory 3 Research in Number Theory 2 Houston Journal of Mathematics 2 Archivum Mathematicum 2 Journal of Algebra 2 Michigan Mathematical Journal 2 Publications de l’Institut Mathématique. Nouvelle Série 2 Results in Mathematics 2 Bulletin of the Greek Mathematical Society 2 Bulletin of the Korean Mathematical Society 2 Acta Mathematica Hungarica 2 Forum Mathematicum 2 Journal of the Ramanujan Mathematical Society 2 Elemente der Mathematik 2 Analele Ştiinţifice ale Universităţii Al. I. Cuza din Iaşi. Serie Nouă. Matematică 2 Applicable Algebra in Engineering, Communication and Computing 2 Experimental Mathematics 2 Bulletin of the Belgian Mathematical Society - Simon Stevin 2 Turkish Journal of Mathematics 2 Finite Fields and their Applications 2 Analele Ştiinţifice ale Universităţii “Ovidius” Constanţa. Seria: Matematică 2 Annals of Combinatorics 2 Acta Mathematica Sinica. English Series 2 The Quarterly Journal of Mathematics 2 La Gaceta de la Real Sociedad Matemática Española 2 Nieuw Archief voor Wiskunde. Vijfde Serie 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 JP Journal of Algebra, Number Theory and Applications 2 Missouri Journal of Mathematical Sciences 2 Mediterranean Journal of Mathematics 2 Algebra & Number Theory 2 Albanian Journal of Mathematics 2 Annales Mathématiques du Québec 1 Communications in Algebra 1 Discrete Mathematics 1 IEEE Transactions on Information Theory 1 Indian Journal of Pure & Applied Mathematics 1 Revue Roumaine de Mathématiques Pures et Appliquées 1 Acta Scientiarum Mathematicarum 1 Ars Combinatoria ...and 64 more Serials
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#### Fields
689 Number theory (11-XX) 25 Combinatorics (05-XX) 9 Field theory and polynomials (12-XX) 9 Group theory and generalizations (20-XX) 8 Algebraic geometry (14-XX) 5 Information and communication theory, circuits (94-XX) 4 General and overarching topics; collections (00-XX) 4 $$K$$-theory (19-XX) 3 History and biography (01-XX) 2 Functions of a complex variable (30-XX) 2 Sequences, series, summability (40-XX) 2 Geometry (51-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Commutative algebra (13-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Associative rings and algebras (16-XX) 1 Category theory; homological algebra (18-XX) 1 Real functions (26-XX) 1 Partial differential equations (35-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Difference and functional equations (39-XX) 1 Algebraic topology (55-XX) 1 Probability theory and stochastic processes (60-XX) 1 Systems theory; control (93-XX)
#### Citations contained in zbMATH Open
462 Publications have been cited 1,740 times in 927 Documents Cited by Year
On a conjecture about repdigits in $$k$$-generalized Fibonacci sequences. Zbl 1274.11035
Bravo, Jhon J.; Luca, Florian
2013
Powers of two in generalized Fibonacci sequences. Zbl 1353.11020
Bravo, Jhon J.; Luca, Florian
2012
On the complexity of algebraic numbers. Zbl 1119.11019
Adamczewski, Boris; Bugeaud, Yann; Luca, Florian
2004
Fibonacci and Lucas numbers with only one distinct digit. Zbl 0958.11007
Luca, F.
2000
Linear combinations of factorials and $$S$$-units in a binary recurrence sequence. Zbl 1361.11007
Sanchez, Sergio Guzmán; Luca, Florian
2014
Analytic number theory. Exploring the anatomy of integers. Zbl 1247.11001
De Koninck, Jean-Marie; Luca, Florian
2012
Fibonacci numbers at most one away from a perfect power. Zbl 1156.11008
Bugeaud, Yann; Luca, Florian; Mignotte, Maurice; Siksek, Samir
2008
Powers of two as sums of two $$k$$-Fibonacci numbers. Zbl 1389.11041
Bravo, Jhon J.; Gómez, Carlos A.; Luca, Florian
2016
On the equation $$x^2 + 2^a \cdot 3^b = y^n$$. Zbl 1085.11021
Luca, Florian
2002
Repdigits as sums of three Fibonacci numbers. Zbl 1305.11008
Luca, Florian
2012
On some problems of Mąkowski-Schinzel and Erdős concerning the arithmetical functions $$\varphi$$ and $$\sigma$$. Zbl 1027.11007
Luca, Florian; Pomerance, Carl
2002
17 lectures on Fermat numbers. From number theory to geometry. With a foreword by Alena Šolcová. Zbl 1010.11002
Křížek, Michal; Luca, Florian; Somer, Lawrence
2001
Distinct digits in base $$b$$ expansions of linear recurrence sequences. Zbl 1030.11004
Luca, Florian
2000
Coincidences in generalized Fibonacci sequences. Zbl 1272.11028
Bravo, Jhon J.; Luca, Florian
2013
On numbers $$n$$ dividing the $$n$$th term of a linear recurrence. Zbl 1262.11015
Alba González, Juan José; Luca, Florian; Pomerance, Carl; Shparlinski, Igor E.
2012
Fibonacci numbers which are sums of two repdigits. Zbl 1287.11021
2011
A generalization of a classical zero-sum problem. Zbl 1123.11012
Luca, Florian
2007
Some relationships between poly-Cauchy numbers and poly-Bernoulli numbers. Zbl 1289.11021
Komatsu, Takao; Luca, Florian
2013
On the largest prime factor of the $$k$$-Fibonacci numbers. Zbl 1292.11034
Bravo, Jhon J.; Luca, Florian
2013
Character sums and congruences with $$n!$$. Zbl 1060.11046
Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor E.
2004
On a Diophantine equation. Zbl 0997.11027
Luca, Florian
2000
On a problem of Pillai with Fibonacci numbers and powers of 2. Zbl 1421.11017
Ddamulira, Mahadi; Luca, Florian; Rakotomalala, Mihaja
2017
On the $$x$$-coordinates of Pell equations which are rep-digits. Zbl 1389.11076
Dossavi-Yovo, Appolinaire; Luca, Florian; Togbé, Alain
2016
On the Diophantine equation $$x^2+2^a\cdot 5^b=y^n$$. Zbl 1231.11041
Luca, Florian; Togbé, Alain
2008
Diophantine equations with products of consecutive terms in Lucas sequences. Zbl 1081.11023
Luca, F.; Shorey, T. N.
2005
Values of the Euler $$\varphi$$-function not divisible by a given odd prime, and the distribution of Euler-Kronecker constants for cyclotomic fields. Zbl 1294.11164
Ford, Kevin; Luca, Florian; Moree, Pieter
2014
Irreducible radical extensions and Euler-function chains. Zbl 1172.11029
Luca, Florian; Pomerance, Carl
2007
On $$X$$-coordinates of Pell equations that are repdigits. Zbl 1459.11082
2018
On the $$x$$-coordinates of Pell equations which are Fibonacci numbers. Zbl 1416.11027
Luca, Florian; Togbé, Alain
2018
On the $$X$$-coordinates of Pell equations which are Tribonacci numbers. Zbl 1410.11007
Luca, Florian; Montejano, Amanda; Szalay, Laszlo; Togbé, Alain
2017
Functional graphs of polynomials over finite fields. Zbl 1327.05323
Konyagin, Sergei V.; Luca, Florian; Mans, Bernard; Mathieson, Luke; Sha, Min; Shparlinski, Igor E.
2016
The distribution of self-Fibonacci divisors. Zbl 1390.11119
Luca, Florian; Tron, Emanuele
2015
On the exponential local-global principle. Zbl 1330.11019
Bartolome, Boris; Bilu, Yuri; Luca, Florian
2013
An exponential Diophantine equation related to powers of two consecutive Fibonacci numbers. Zbl 1253.11046
Luca, Florian; Oyono, Roger
2011
Almost powers in the Lucas sequence. Zbl 1204.11030
Bugeaud, Yann; Luca, Florian; Mignotte, Maurice; Siksek, Samir
2008
Fibonacci numbers of the form $$p^a\pm p^b+1$$. Zbl 1228.11021
Luca, Florian; Szalay, László
2007
On the lower bound of the linear complexity over $$\mathbb F_p$$ of Sidelnikov sequences. Zbl 1296.94073
Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor; Winterhof, Arne
2006
On Pillai’s Diophantine equation. Zbl 1136.11026
Bugeaud, Yann; Luca, Florian
2006
On the exponent of the group of points on elliptic curves in extension fields. Zbl 1082.11041
Luca, Florian; Shparlinski, Igor E.
2005
Divisibility of class numbers: enumerative approach. Zbl 1072.11084
Bilu, Yuri F.; Luca, Florian
2005
On Pillai’s problem with tribonacci numbers and powers of 2. Zbl 1379.11013
Bravo, Jhon J.; Luca, Florian; Yazán, Karina
2017
$$p$$-adic quotient sets. Zbl 1428.11023
Garcia, Stephan Ramon; Hong, Yu Xuan; Luca, Florian; Pinsker, Elena; Sanna, Carlo; Schechter, Evan; Starr, Adam
2017
Quotients of Fibonacci numbers. Zbl 1391.11027
Garcia, Stephan Ramon; Luca, Florian
2016
Rational products of singular moduli. Zbl 1400.11113
Bilu, Yuri; Luca, Florian; Pizarro-Madariaga, Amalia
2016
Pell and Pell-Lucas numbers with only one distinct digit. Zbl 1349.11023
2015
Generalized balancing numbers. Zbl 1239.11035
Liptai, Kálmán; Luca, Florian; Pintér, Ákos; Szalay, László
2009
Fibonacci Diophantine triples. Zbl 1218.11020
Luca, Florian; Szalay, László
2008
Catalan and Apéry numbers in residue classes. Zbl 1101.11010
Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor E.
2006
The Diophantine equation $$P(x)=n!$$ and a result of M. Overholt. Zbl 1085.11023
Luca, Florian
2002
On shifted primes with large prime factors and their products. Zbl 1370.11110
Luca, Florian; Menares, Ricardo; Pizarro-Madariaga, Amalia
2015
On stable quadratic polynomials. Zbl 1241.11027
Ahmadi, Omran; Luca, Florian; Ostafe, Alina; Shparlinski, Igor E.
2012
On composite integers $$n$$ for which $$\varphi(n)\mid n-1$$. Zbl 1294.11005
Luca, Florian; Pomerance, Carl
2011
Some additive combinatorics problems in matrix rings. Zbl 1208.11037
Ferguson, Ron; Hoffman, Corneliu; Luca, Florian; Ostafe, Alina; Shparlinski, Igor E.
2010
Common values of the arithmetic functions $$\varphi$$ and $$\sigma$$. Zbl 1205.11010
Ford, Kevin; Luca, Florian; Pomerance, Carl
2010
Some results on Oppenheim’s “factorisatio numerorum” function. Zbl 1213.11020
2010
On the Diophantine equation $$x^2 + 2^{\alpha}5^{\beta}13^{\gamma} = y^n$$. Zbl 1232.11130
Goins, Edray; Luca, Florian; Togbé, Alain
2008
On the Diophantine equation $$x^2 + 5^a 13^b = y^n$$. Zbl 1186.11016
Abu Muriefah, Fadwa S.; Luca, Florian; Togbé, Alain
2008
On a diophantine equation related to a conjecture of Erdös and Graham. Zbl 1132.11319
Luca, F.; Walsh, P. G.
2007
On factorials which are products of factorials. Zbl 1132.11017
Luca, Florian
2007
Fibonacci numbers with the Lehmer property. Zbl 1112.11007
Luca, Florian
2007
On the maximal order of numbers in the “factorisatio numerorum” problem. Zbl 1169.11043
Klazar, Martin; Luca, Florian
2007
Exponential sums and congruences with factorials. Zbl 1071.11051
Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor E.
2005
Average order in cyclic groups. Zbl 1079.11003
von zur Gathen, Joachim; Knopfmacher, Arnold; Luca, Florian; Lucht, Lutz G.; Shparlinski, Igor E.
2004
MOV attack in various subgroups on elliptic curves. Zbl 1072.11094
Luca, Florian; Mireles, David Jose; Shparlinski, Igor E.
2004
On the largest prime factor of $$(ab+1)(ac+1)(bc+1)$$. Zbl 1108.11030
Hernández, Santos; Luca, Florian
2003
The number of non-zero digits of $$n$$! Zbl 1043.11008
Luca, Florian
2002
Some remarks on Heron triangles. Zbl 1062.11019
Kramer, Alpar-Vajk; Luca, Florian
2000
On a problem of Pillai with $$k$$-generalized Fibonacci numbers and powers of 2. Zbl 1437.11051
Ddamulira, Mahadi; Gómez, Carlos A.; Luca, Florian
2018
On perfect powers that are sums of two Fibonacci numbers. Zbl 06865878
Luca, Florian; Patel, Vandita
2018
Powers of two as sums of three Pell numbers. Zbl 1433.11032
Bravo, Jhon J.; Faye, Bernadette; Luca, Florian
2017
On the $$x$$-coordinates of Pell equations which are Fibonacci numbers. II. Zbl 1420.11037
Kafle, Bir; Luca, Florian; Togbé, Alain
2017
Powers of two as sums of two Lucas numbers. Zbl 1358.11026
Bravo, Jhon J.; Luca, Florian
2014
Control of coupled parabolic systems and Diophantine approximations. Zbl 1272.93029
Luca, Florian; De Teresa, Luz
2013
On equal values of power sums of arithmetic progressions. Zbl 1330.11020
Bazsó, András; Kreso, Dijana; Luca, Florian; Pintér, Ákos
2012
On the number of isogeny classes of pairing-friendly elliptic curves and statistics of MNT curves. Zbl 1329.11063
Jiménez-Urroz, Jorge; Luca, Florian; Shparlinski, Igor E.
2012
On the number of factorizations of an integer. Zbl 1245.11100
Balasubramanian, Ramachandran; Luca, Florian
2011
Fibonacci numbers which are sums of three factorials. Zbl 1259.11038
Bollman, Mark; Hernández Hernández, Santos; Luca, Florian
2010
On factorials expressible as sums of at most three Fibonacci numbers. Zbl 1253.11048
Luca, Florian; Siksek, Samir
2010
Fibonacci numbers of the form $$p^a\pm p^b$$. Zbl 1273.11030
Luca, Florian; Stănică, Pantelimon
2009
Non-holonomicity of sequences defined via elementary functions. Zbl 1189.11007
Bell, Jason P.; Gerhold, Stefan; Klazar, Martin; Luca, Florian
2008
On the Diophantine equation $$x^2+7^{2k}=y^n$$. Zbl 1221.11091
Luca, Florian; Togbé, Alain
2007
Composite integers $$n$$ for which $$\varphi (n)\mid n-1$$. Zbl 1215.11094
Banks, William D.; Luca, Florian
2007
Perfect powers from products of terms in Lucas sequences. Zbl 1137.11011
Bugeaud, Yann; Luca, Florian; Mignotte, Maurice; Siksek, Samir
2007
Elliptic curves with low embedding degree. Zbl 1133.14303
Luca, Florian; Shparlinski, Igor E.
2006
Diophantine $$m$$-tuples for primes. Zbl 1085.11019
Dujella, Andrej; Luca, Florian
2005
On shifted products which are powers. Zbl 1123.11011
Luca, Florian
2005
Fibonacci numbers that are not sums of two prime powers. Zbl 1113.11011
Luca, Florian; Stănică, Pantelimon
2005
A quantitative lower bound for the greatest prime factor of $$(ab+1)(bc+1)(ca+1)$$. Zbl 1122.11060
Bugeaud, Yann; Luca, Florian
2004
The Diophantine equation $$x^2=p^a\pm p^b+1$$. Zbl 1067.11016
Luca, Florian
2004
On the prime power factorization of $$n$$! Zbl 1049.11092
Luca, Florian; Stănică, Pantelimon
2003
Palindromes in Lucas sequences. Zbl 1027.11012
Luca, Florian
2003
On the convergence of series of reciprocals of primes related to the Fermat numbers. Zbl 1026.11011
Křížek, Michal; Luca, Florian; Somer, Lawrence
2002
Squares in Lehmer sequences and some Diophantine applications. Zbl 1006.11011
Luca, Florian; Walsh, P. G.
2001
On the $$x$$-coordinates of Pell equations which are $$k$$-generalized Fibonacci numbers. Zbl 1447.11025
2020
Repdigits as sums of four Pell numbers. Zbl 1455.11019
Luca, Florian; Normenyo, Benedict Vasco; Togbé, Alain
2019
On cyclotomic factors of polynomials related to modular forms. Zbl 1450.11041
Heim, Bernhard; Luca, Florian; Neuhauser, Markus
2019
$$X$$-coordinates of Pell equations as sums of two tribonacci numbers. Zbl 1424.11036
Bravo, Eric F.; Gómez Ruiz, Carlos Alexis; Luca, Florian
2018
Repdigits as sums of three Pell numbers. Zbl 1413.11008
Normenyo, Benedict Vasco; Luca, Florian; Togbé, Alain
2018
Polynomial values of sums of products of consecutive integers. Zbl 1442.11055
Bazsó, A.; Bérczes, A.; Hajdu, L.; Luca, F.
2018
Every positive integer is a sum of three palindromes. Zbl 1441.11016
Cilleruelo, Javier; Luca, Florian; Baxter, Lewis
2018
On the $$x$$-coordinates of Pell equations which are $$k$$-generalized Fibonacci numbers. Zbl 1447.11025
2020
Zeckendorf representations with at most two terms to $$x$$-coordinates of Pell equations. Zbl 1455.11031
Gómez, Carlos A.; Luca, Florian
2020
Primitive root bias for twin primes. II: Schinzel-type theorems for totient quotients and the sum-of-divisors function. Zbl 1450.11002
Garcia, Stephan Ramon; Luca, Florian; Shi, Kye; Udell, Gabe
2020
Products of $$k$$-Fibonacci numbers which are rep-digits. Zbl 07287377
2020
Correction to: $$X$$-coordinates of Pell equations as sums of two tribonacci numbers. Zbl 1449.11051
Bravo, Eric F.; Gómez Ruiz, Carlos Alexis; Luca, Florian
2020
Trinomials with given roots. Zbl 07152833
Bilu, Yuri; Luca, Florian
2020
Multiplicative dependence between $$k$$-Fibonacci and $$k$$-Lucas numbers. Zbl 07301185
Gómez, Carlos A.; Gómez, Jhonny C.; Luca, Florian
2020
The $$x$$-coordinates of Pell equations and sums of two Fibonacci numbers. II. Zbl 07271355
2020
On members of Lucas sequences which are products of factorials. Zbl 07242544
Laishram, Shanta; Luca, Florian; Sias, Mark
2020
Lucas factoriangular numbers. Zbl 07217178
Kafle, Bir; Luca, Florian; Togbé, Alain
2020
On a Diophantine equation involving powers of Fibonacci numbers. Zbl 07192786
Gueth, Krisztián; Luca, Florian; Szalay, László
2020
Pell and Pell-Lucas numbers as sums of two repdigits. Zbl 1452.11020
Adegbindin, Chèfiath; Luca, Florian; Togbé, Alain
2020
On $$Y$$-coordinates of Pell equations which are members of a fixed binary recurrence. Zbl 07179055
2020
On certain sums concerning the gcd’s and lcm’s of $$k$$ positive integers. Zbl 1452.11007
Hilberdink, Titus; Luca, Florian; Tóth, László
2020
Repdigits as sums of four Pell numbers. Zbl 1455.11019
Luca, Florian; Normenyo, Benedict Vasco; Togbé, Alain
2019
On cyclotomic factors of polynomials related to modular forms. Zbl 1450.11041
Heim, Bernhard; Luca, Florian; Neuhauser, Markus
2019
$$X$$-coordinates of Pell equations which are Lucas numbers. Zbl 07137965
Kafle, Bir; Luca, Florian; Togbé, Alain
2019
Primitive root bias for twin primes. Zbl 1450.11001
Garcia, Stephan Ramon; Kahoro, Elvis; Luca, Florian
2019
Repdigits as sums of three Lucas numbers. Zbl 1459.11041
Luca, Florian; Normenyo, Benedict Vasco; Togbé, Alain
2019
$$x$$-Coordinates of Pell equations which are Tribonacci numbers. II. Zbl 1449.11030
Kafle, Bir; Luca, Florian; Togbé, Alain
2019
Lucas numbers as sums of two repdigits. Zbl 1427.11013
Adegbindin, Chèfiath; Luca, Florian; Togbé, Alain
2019
On Pillai’s problem with the Fibonacci and Pell sequences. Zbl 1440.11018
Hernández Hernández, Santos; Luca, Florian; Rivera, Luis Manuel
2019
On the $$x$$-coordinates of Pell equations which are products of two Fibonacci numbers. Zbl 1420.11061
Kafle, Bir; Luca, Florian; Montejano, Amanda; Szalay, László; Togbé, Alain
2019
On Pillai’s problem with $$X$$-coordinates of Pell equations and powers of 2. Zbl 07081797
Erazo, Harold S.; Gómez, Carlos A.; Luca, Florian
2019
Recurrence relations for polynomials obtained by arithmetic functions. Zbl 1435.11055
Heim, Bernhard; Luca, Florian; Neuhauser, Markus
2019
On the discriminator of Lucas sequences. Zbl 1456.11021
Faye, Bernadette; Luca, Florian; Moree, Pieter
2019
On the zero-multiplicity of a fifth-order linear recurrence. Zbl 1450.11009
Gómez Ruiz, Carlos Alexis; Luca, Florian
2019
An exponential Diophantine equation related to the difference between powers of two consecutive Balancing numbers. Zbl 1449.11036
Rihane, Salah Eddine; Faye, Bernadette; Luca, Florian; Togbé, Alain
2019
Product of consecutive tribonacci numbers with only one distinct digit. Zbl 1455.11027
Bravo, Eric F.; Gómez, Carlos A.; Luca, Florian
2019
Diophantine equations with the Ramanujan $$\tau$$ function of factorials, Fibonacci numbers, and Catalan numbers. Zbl 1456.11031
Luca, Florian; Mabaso, Sibusiso
2019
On the exponential Diophantine equation $$P_n^x+P_{n+1}^x=P_m$$. Zbl 1455.11056
Rihane, Salah Eddine; Faye, Bernadette; Luca, Florian; Togbé, Alain
2019
On the typical size and cancellations among the coefficients of some modular forms. Zbl 1450.11100
Luca, Florian; Radziwiłł, Maksym; Shparlinski, Igor E.
2019
Linear independence of powers of singular moduli of degree three. Zbl 1451.11069
Luca, Florian; Riffaut, Antonin
2019
On $$X$$-coordinates of Pell equations that are repdigits. Zbl 1459.11082
2018
On the $$x$$-coordinates of Pell equations which are Fibonacci numbers. Zbl 1416.11027
Luca, Florian; Togbé, Alain
2018
On a problem of Pillai with $$k$$-generalized Fibonacci numbers and powers of 2. Zbl 1437.11051
Ddamulira, Mahadi; Gómez, Carlos A.; Luca, Florian
2018
On perfect powers that are sums of two Fibonacci numbers. Zbl 06865878
Luca, Florian; Patel, Vandita
2018
$$X$$-coordinates of Pell equations as sums of two tribonacci numbers. Zbl 1424.11036
Bravo, Eric F.; Gómez Ruiz, Carlos Alexis; Luca, Florian
2018
Repdigits as sums of three Pell numbers. Zbl 1413.11008
Normenyo, Benedict Vasco; Luca, Florian; Togbé, Alain
2018
Polynomial values of sums of products of consecutive integers. Zbl 1442.11055
Bazsó, A.; Bérczes, A.; Hajdu, L.; Luca, F.
2018
Every positive integer is a sum of three palindromes. Zbl 1441.11016
Cilleruelo, Javier; Luca, Florian; Baxter, Lewis
2018
On the difference in values of the Euler totient function near prime arguments. Zbl 1455.11127
Garcia, Stephan Ramon; Luca, Florian
2018
Repdigits as sums of four Fibonacci or Lucas numbers. Zbl 1453.11006
Normenyo, Benedict Vasco; Luca, Florian; Togb, Alain
2018
Primitive root biases for prime pairs. I: Existence and non-totality of biases. Zbl 1431.11112
Garcia, Stephan Ramon; Luca, Florian; Schaaff, Timothy
2018
On Pillai’s problem with Pell numbers and powers of 2. Zbl 1448.11042
Ouamar Hernane, Mohand; Luca, Florian; Rihane, Salah; Togbé, Alain
2018
Diophantine triples and $$k$$-generalized Fibonacci sequences. Zbl 1447.11054
Fuchs, Clemens; Hutle, Christoph; Luca, Florian; Szalay, László
2018
Random ordering in modulus of consecutive Hecke eigenvalues of primitive forms. Zbl 1444.11071
Bilu, Yuri F.; Deshouillers, Jean-Marc; Gun, Sanoli; Luca, Florian
2018
Markov equation with Fibonacci components. Zbl 1458.11056
Luca, Florian; Srinivasan, Anitha
2018
A Diophantine equation in $$k$$-Fibonacci numbers and repdigits. Zbl 1407.11026
Bravo, Jhon J.; Gómez, Carlos A.; Luca, Florian
2018
Arithmetic properties of coefficients of $$L$$-functions of elliptic curves. Zbl 1423.11169
Güloğlu, Ahmet M.; Luca, Florian; Yalçiner, Aynur
2018
Denominators of Bernoulli polynomials. Zbl 1415.11121
Bordellès, Olivier; Luca, Florian; Moree, Pieter; Shparlinski, Igor E.
2018
A variation on the theme of Nicomachus. Zbl 1410.11079
Luca, Florian; Polanco, Geremías; Zudilin, Wadim
2018
On the error term of a lattice counting problem. Zbl 1380.11085
Bordellès, Olivier; Luca, Florian; Shparlinski, Igor E.
2018
On a problem of Pillai with Fibonacci numbers and powers of 2. Zbl 1421.11017
Ddamulira, Mahadi; Luca, Florian; Rakotomalala, Mihaja
2017
On the $$X$$-coordinates of Pell equations which are Tribonacci numbers. Zbl 1410.11007
Luca, Florian; Montejano, Amanda; Szalay, Laszlo; Togbé, Alain
2017
On Pillai’s problem with tribonacci numbers and powers of 2. Zbl 1379.11013
Bravo, Jhon J.; Luca, Florian; Yazán, Karina
2017
$$p$$-adic quotient sets. Zbl 1428.11023
Garcia, Stephan Ramon; Hong, Yu Xuan; Luca, Florian; Pinsker, Elena; Sanna, Carlo; Schechter, Evan; Starr, Adam
2017
Powers of two as sums of three Pell numbers. Zbl 1433.11032
Bravo, Jhon J.; Faye, Bernadette; Luca, Florian
2017
On the $$x$$-coordinates of Pell equations which are Fibonacci numbers. II. Zbl 1420.11037
Kafle, Bir; Luca, Florian; Togbé, Alain
2017
On Diophantine quadruples of Fibonacci numbers. Zbl 1386.11065
Fujita, Yasutsugu; Luca, Florian
2017
On arithmetic lattices in the plane. Zbl 1358.11074
Fukshansky, Lenny; Guerzhoy, Pavel; Luca, Florian
2017
Diversity in parametric families of number fields. Zbl 1414.11150
Bilu, Yuri; Luca, Florian
2017
Only finitely many Tribonacci Diophantine triples exist. Zbl 1440.11042
Fuchs, Clemens; Hutle, Christoph; Irmak, Nurettin; Luca, Florian; Szalay, László
2017
Fibonacci factoriangular numbers. Zbl 1373.11011
Gómez Ruiz, Carlos Alexis; Luca, Florian
2017
The $$r$$th moment of the divisor function: an elementary approach. Zbl 1366.11103
Luca, Florian; Tóth, László
2017
Palindromes in several sequences. Zbl 1429.11018
Luca, Florian
2017
On the number of non-zero digits of integers in multi-base representations. Zbl 1399.11027
Bertók, Cs.; Hajdu, L.; Luca, F.; Sharma, D.
2017
Generalized incomplete poly-Bernoulli polynomials and generalized incomplete poly-Cauchy polynomials. Zbl 1409.11015
Komatsu, Takao; Luca, Florian
2017
Counting terms $$U_n$$ of third order linear recurrences with $$u_n = u^2 + nv^2$$. Zbl 1425.11024
Ciolan, Alexandru; Luca, Florian; Moree, Pieter
2017
Local behavior of the composition of the aliquot and co-totient functions. Zbl 1421.11076
Luca, Florian; Pomerance, Carl
2017
Number fields in fibers: the geometrically abelian case with rational critical values. Zbl 1413.12001
Bilu, Yuri; Luca, Florian
2017
Diophantine triples with values in the sequences of Fibonacci and Lucas numbers. Zbl 1417.11011
Luca, Florian; Munagi, Augustine O.
2017
Corrigendum to “Positive integers divisible by the product of their nonzero digits”, portugaliae math. 64 (2007), 1: 75 – 85. Zbl 1434.11195
De Koninck, Jean-Marie; Luca, Florian
2017
Lucas numbers with the Lehmer property. Zbl 1389.11043
2017
On polynomials whose roots have rational quotient of differences. Zbl 1435.11061
Luca, Florian
2017
On two functions arising in the study of the Euler and Carmichael quotients. Zbl 1425.11009
Luca, Florian; Sha, Min; Shparlinski, Igor E.
2017
Collinear CM-points. Zbl 1432.11061
Bilu, Yuri; Luca, Florian; Masser, David
2017
Pell numbers with the Lehmer property. Zbl 1439.11015
2017
Monotonic phinomial coefficients. Zbl 1437.11006
Luca, Florian; Stănică, Pantelimon
2017
Powers of two as sums of two $$k$$-Fibonacci numbers. Zbl 1389.11041
Bravo, Jhon J.; Gómez, Carlos A.; Luca, Florian
2016
On the $$x$$-coordinates of Pell equations which are rep-digits. Zbl 1389.11076
Dossavi-Yovo, Appolinaire; Luca, Florian; Togbé, Alain
2016
Functional graphs of polynomials over finite fields. Zbl 1327.05323
Konyagin, Sergei V.; Luca, Florian; Mans, Bernard; Mathieson, Luke; Sha, Min; Shparlinski, Igor E.
2016
Quotients of Fibonacci numbers. Zbl 1391.11027
Garcia, Stephan Ramon; Luca, Florian
2016
Rational products of singular moduli. Zbl 1400.11113
Bilu, Yuri; Luca, Florian; Pizarro-Madariaga, Amalia
2016
Fibonacci numbers which are products of two Pell numbers. Zbl 1400.11040
Ddamulira, Mahadi; Luca, Florian; Rakotomalala, Mihaja
2016
An explicit bound for the number of partitions into roots. Zbl 1343.05031
Luca, Florian; Ralaivaosaona, Dimbinaina
2016
Visual properties of generalized Kloosterman sums. Zbl 1338.11077
Burkhardt, Paula; Chan, Alice Zhuo-Yu; Currier, Gabriel; Garcia, Stephan Ramon; Luca, Florian; Suh, Hong
2016
On the Diophantine equation $$F_n + F_m=2^a$$. Zbl 1419.11024
Bravo, Jhon J.; Luca, Florian
2016
Sylvester’s theorem and the non-integrality of a certain binomial sum. Zbl 1400.11061
López-Aguayo, Daniel; Luca, Florian
2016
Multiplicative independence in $$k$$-generalized Fibonacci sequences. Zbl 1355.11010
Gómez Ruiz, Carlos Alexis; Luca, Florian
2016
Diophantine triples of Fibonacci numbers. Zbl 1359.11028
He, Bo; Luca, Florian; Togbé, Alain
2016
Cyclotomic coefficients: gaps and jumps. Zbl 1405.11032
Camburu, Oana-Maria; Ciolan, Emil-Alexandru; Luca, Florian; Moree, Pieter; Shparlinski, Igor E.
2016
A note on odd perfect numbers. Zbl 1400.11010
Dris, Jose Arnaldo B.; Luca, Florian
2016
Repdigits as Euler functions of Lucas numbers. Zbl 1389.11040
Bravo, Jhon J.; Faye, Bernadette; Luca, Florian; Tall, Amandou
2016
An elliptic sequence is not a sampled linear recurrence sequence. Zbl 1367.11020
Luca, F.; Ward, T.
2016
On a divisibility relation for Lucas sequences. Zbl 1402.11023
Bilu, Yuri F.; Komatsu, Takao; Luca, Florian; Pizarro-Madariaga, Amalia; Stănică, Pantelimon
2016
Carmichael numbers in the sequence $$(2^{n} k+1)_{n\geq 1}$$. Zbl 1400.11017
Cilleruelo, Javier; Luca, Florian; Pizarro-Madariaga, Amalia
2016
The distribution of self-Fibonacci divisors. Zbl 1390.11119
Luca, Florian; Tron, Emanuele
2015
Pell and Pell-Lucas numbers with only one distinct digit. Zbl 1349.11023
2015
On shifted primes with large prime factors and their products. Zbl 1370.11110
Luca, Florian; Menares, Ricardo; Pizarro-Madariaga, Amalia
2015
...and 362 more Documents
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#### Cited by 878 Authors
210 Luca, Florian 46 Shparlinski, Igor E. 27 Togbé, Alain 22 Pollack, Paul 21 Hajdu, Lajos 19 Bugeaud, Yann 16 Sanna, Carlo 14 Bravo, Jhon Jairo 14 Marques, Diego 14 Pomerance, Carl Bernard 14 Szalay, László 13 Komatsu, Takao 12 De Koninck, Jean-Marie 12 Dubickas, Artūras 12 Dujella, Andrej 12 Gómez, Carlos Alexis 12 Stănică, Pantelimon 11 Chen, Yonggao 11 Garaev, Moubariz Z. 10 Adamczewski, Boris 10 Ddamulira, Mahadi 10 Keskin, Refik 10 Pink, István 10 Ziegler, Volker 9 Bennett, Michael A. 9 Bilu, Yuri F. 9 Cilleruelo, Javier 9 Gómez Ruiz, Carlos Alexis 9 Siksek, Samir 9 Soydan, Gokhan 8 Banks, William D. 8 Fuchs, Clemens 8 Garcia, Stephan Ramon 8 Moree, Pieter 8 Shorey, Tarlok Nath 7 Bérczes, Attila 7 Heim, Bernhard Ernst 7 Neuhauser, Markus 7 Sha, Min 7 Tengely, Szabolcs 7 Tijdeman, Robert 7 Ulas, Maciej 6 Bazsó, András 6 Faye, Bernadette 6 Ford, Kevin B. 6 Grau, José María 6 Laishram, Shanta 6 Mignotte, Maurice 6 Panda, Gopal Krishna 6 Somer, Lawrence E. 6 Winterhof, Arne 5 Adhikari, Sukumar Das 5 Broughan, Kevin A. 5 Erduvan, Fatih 5 Irmak, Nurettin 5 Kátai, Imre 5 Křížek, Michal 5 Le, Maohua 5 Leonetti, Paolo 5 Miska, Piotr 5 Pappalardi, Francesco 5 Rout, Sudhansu Sekhar 4 Abu Muriefah, Fadwa S. 4 Bell, Jason P. 4 Berrizbeitia, Pedro 4 Bertók, Csanád 4 Bordellès, Olivier 4 Chattopadhyay, Jaitra 4 Chim, Kwok Chi 4 Coons, Michael 4 Drungilas, Paulius 4 Elsholtz, Christian 4 Hernández Hernández, Santos 4 Hu, Su 4 Kafle, Bir 4 Kihel, Omar 4 Oller-Marcén, Antonio M. 4 Pizarro-Madariaga, Amalia 4 Raggi-Cárdenas, Alberto Gerardo 4 Rihane, Salah Eddine 4 Roy, Bidisha 4 Sarkar, Subha 4 Shallit, Jeffrey O. 4 Sun, Xuegong 4 Thangadurai, Ravindrananathan 4 Trojovský, Pavel 4 Wu, Jie 4 Zhu, Huilin 3 Altassan, Alaa 3 Balasubramanian, Ramachandran 3 Berend, Daniel 3 Brandstätter, Nina 3 Bridy, Andrew 3 Bubboloni, Daniela 3 Chakraborty, Kalyan 3 Dai, Lixia 3 Deshouillers, Jean-Marc 3 Freiberg, Tristan 3 Fu, Ruiqin 3 Fujita, Yasutsugu ...and 778 more Authors
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#### Cited in 190 Serials
126 Journal of Number Theory 56 International Journal of Number Theory 28 Proceedings of the American Mathematical Society 25 Periodica Mathematica Hungarica 24 Mathematics of Computation 24 Monatshefte für Mathematik 22 Journal de Théorie des Nombres de Bordeaux 22 Journal of Integer Sequences 21 Bulletin of the Australian Mathematical Society 21 Indagationes Mathematicae. New Series 20 Integers 19 The Ramanujan Journal 18 Acta Arithmetica 15 Rocky Mountain Journal of Mathematics 15 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 14 Boletín de la Sociedad Matemática Mexicana. Third Series 13 Archiv der Mathematik 11 Lithuanian Mathematical Journal 11 Functiones et Approximatio. Commentarii Mathematici 11 Transactions of the American Mathematical Society 11 Research in Number Theory 10 Finite Fields and their Applications 10 Comptes Rendus. Mathématique. Académie des Sciences, Paris 9 Acta Mathematica Hungarica 8 Turkish Journal of Mathematics 8 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 7 Mathematical Proceedings of the Cambridge Philosophical Society 7 Mathematica Slovaca 7 Experimental Mathematics 7 Science China. Mathematics 6 Colloquium Mathematicum 6 Journal of Algebra 6 Mathematika 6 Proceedings of the Japan Academy. Series A 6 Journal of the Australian Mathematical Society 6 Bulletin of the Brazilian Mathematical Society. New Series 5 Discrete Mathematics 5 Proceedings of the Edinburgh Mathematical Society. Series II 5 European Journal of Combinatorics 5 Communications in Mathematics 5 Research in the Mathematical Sciences 4 Information Processing Letters 4 Glasgow Mathematical Journal 4 Journal of Combinatorial Theory. Series A 4 Mathematische Zeitschrift 4 Quaestiones Mathematicae 4 Journal of Inequalities and Applications 3 Indian Journal of Pure & Applied Mathematics 3 Israel Journal of Mathematics 3 Mathematical Notes 3 Ukrainian Mathematical Journal 3 Chaos, Solitons and Fractals 3 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 3 Canadian Mathematical Bulletin 3 Czechoslovak Mathematical Journal 3 Manuscripta Mathematica 3 Revista Matemática Iberoamericana 3 Journal of the Ramanujan Mathematical Society 3 Elemente der Mathematik 3 Glasnik Matematički. Serija III 3 Abstract and Applied Analysis 3 Acta Mathematica Sinica. English Series 3 Portugaliae Mathematica. Nova Série 3 Mediterranean Journal of Mathematics 3 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 3 European Journal of Mathematics 2 Discrete Applied Mathematics 2 Journal of Mathematical Analysis and Applications 2 Applied Mathematics and Computation 2 Archivum Mathematicum 2 Bulletin of the London Mathematical Society 2 Illinois Journal of Mathematics 2 Inventiones Mathematicae 2 Mathematische Annalen 2 Rendiconti del Circolo Matemàtico di Palermo. Serie II 2 Results in Mathematics 2 Advances in Applied Mathematics 2 Constructive Approximation 2 Forum Mathematicum 2 International Journal of Foundations of Computer Science 2 Designs, Codes and Cryptography 2 Geometric and Functional Analysis. GAFA 2 Aequationes Mathematicae 2 Bulletin of the American Mathematical Society. New Series 2 Expositiones Mathematicae 2 Applicable Algebra in Engineering, Communication and Computing 2 The Electronic Journal of Combinatorics 2 The New York Journal of Mathematics 2 Integral Transforms and Special Functions 2 Journal of Difference Equations and Applications 2 Annals of Combinatorics 2 LMS Journal of Computation and Mathematics 2 Journal of the European Mathematical Society (JEMS) 2 Communications of the Korean Mathematical Society 2 RAIRO. Theoretical Informatics and Applications 2 Acta et Commentationes Universitatis Tartuensis de Mathematica 2 Journal of High Energy Physics 2 Journal of Mathematical Cryptology 2 Algebra & Number Theory 2 Afrika Matematika ...and 90 more Serials
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#### Cited in 38 Fields
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https://library.achievingthedream.org/austinccphysics2/chapter/21-6-dc-circuits-containing-resistors-and-capacitors/ | # 35 DC Circuits Containing Resistors and Capacitors
### Learning Objectives
By the end of this section, you will be able to:
• Explain the importance of the time constant, τ, and calculate the time constant for a given resistance and capacitance.
• Explain why batteries in a flashlight gradually lose power and the light dims over time.
• Describe what happens to a graph of the voltage across a capacitor over time as it charges.
• Explain how a timing circuit works and list some applications.
• Calculate the necessary speed of a strobe flash needed to “stop” the movement of an object over a particular length.
When you use a flash camera, it takes a few seconds to charge the capacitor that powers the flash. The light flash discharges the capacitor in a tiny fraction of a second. Why does charging take longer than discharging? This question and a number of other phenomena that involve charging and discharging capacitors are discussed in this module.
## RC Circuits
An RC circuit is one containing a resistor R and a capacitor C. The capacitor is an electrical component that stores electric charge.
Figure 1 shows a simple RC circuit that employs a DC (direct current) voltage source. The capacitor is initially uncharged. As soon as the switch is closed, current flows to and from the initially uncharged capacitor. As charge increases on the capacitor plates, there is increasing opposition to the flow of charge by the repulsion of like charges on each plate.
In terms of voltage, this is because voltage across the capacitor is given by VQ/C, where Q is the amount of charge stored on each plate and C is the capacitance. This voltage opposes the battery, growing from zero to the maximum emf when fully charged. The current thus decreases from its initial value of $I_{o}=\frac{\text{emf}}{R}\\$ to zero as the voltage on the capacitor reaches the same value as the emf. When there is no current, there is no IR drop, and so the voltage on the capacitor must then equal the emf of the voltage source. This can also be explained with Kirchhoff’s second rule (the loop rule), discussed in Kirchhoff’s Rules, which says that the algebraic sum of changes in potential around any closed loop must be zero.
The initial current is $I_{o} =\frac{\text{emf}}{R}\\$, because all of the IR drop is in the resistance. Therefore, the smaller the resistance, the faster a given capacitor will be charged. Note that the internal resistance of the voltage source is included in R, as are the resistances of the capacitor and the connecting wires. In the flash camera scenario above, when the batteries powering the camera begin to wear out, their internal resistance rises, reducing the current and lengthening the time it takes to get ready for the next flash.
Voltage on the capacitor is initially zero and rises rapidly at first, since the initial current is a maximum. Figure 1(b) shows a graph of capacitor voltage versus time (t) starting when the switch is closed at = 0. The voltage approaches emf asymptotically, since the closer it gets to emf the less current flows. The equation for voltage versus time when charging a capacitor C through a resistor R, derived using calculus, is
= emf(1 − et/RC) (charging),
where V is the voltage across the capacitor, emf is equal to the emf of the DC voltage source, and the exponential e = 2.718 … is the base of the natural logarithm. Note that the units of RC are seconds. We define
τ RC
where τ (the Greek letter tau) is called the time constant for an RC circuit. As noted before, a small resistance R allows the capacitor to charge faster. This is reasonable, since a larger current flows through a smaller resistance. It is also reasonable that the smaller the capacitor C, the less time needed to charge it. Both factors are contained in τ RC. More quantitatively, consider what happens when τ RC. Then the voltage on the capacitor is
= emf (1 − e−1) = emf (1 − 0.368) = 0.632 ⋅ emf.
This means that in the time τ RC, the voltage rises to 0.632 of its final value. The voltage will rise 0.632 of the remainder in the next time τ. It is a characteristic of the exponential function that the final value is never reached, but 0.632 of the remainder to that value is achieved in every time, τ. In just a few multiples of the time constant τ, then, the final value is very nearly achieved, as the graph in Figure 1(b) illustrates.
## Discharging a Capacitor
Discharging a capacitor through a resistor proceeds in a similar fashion, as Figure 2 illustrates. Initially, the current is ${I}_{0}=\frac{{V}_{0}}{R}\\$, driven by the initial voltage V0 on the capacitor. As the voltage decreases, the current and hence the rate of discharge decreases, implying another exponential formula for V. Using calculus, the voltage V on a capacitor C being discharged through a resistor R is found to be
V = V0e−t/RC(discharging).
The graph in Figure 2(b) is an example of this exponential decay. Again, the time constant is τ RC. A small resistance R allows the capacitor to discharge in a small time, since the current is larger. Similarly, a small capacitance requires less time to discharge, since less charge is stored. In the first time interval τ RC after the switch is closed, the voltage falls to 0.368 of its initial value, since V⋅ e−1 = 0.368V0.
During each successive time τ, the voltage falls to 0.368 of its preceding value. In a few multiples of τ, the voltage becomes very close to zero, as indicated by the graph in Figure 2(b). Now we can explain why the flash camera in our scenario takes so much longer to charge than discharge; the resistance while charging is significantly greater than while discharging. The internal resistance of the battery accounts for most of the resistance while charging. As the battery ages, the increasing internal resistance makes the charging process even slower. (You may have noticed this.)
The flash discharge is through a low-resistance ionized gas in the flash tube and proceeds very rapidly. Flash photographs, such as in Figure 3, can capture a brief instant of a rapid motion because the flash can be less than a microsecond in duration. Such flashes can be made extremely intense. During World War II, nighttime reconnaissance photographs were made from the air with a single flash illuminating more than a square kilometer of enemy territory. The brevity of the flash eliminated blurring due to the surveillance aircraft’s motion. Today, an important use of intense flash lamps is to pump energy into a laser. The short intense flash can rapidly energize a laser and allow it to reemit the energy in another form.
### Example 1. Integrated Concept Problem: Calculating Capacitor Size—Strobe Lights
High-speed flash photography was pioneered by Doc Edgerton in the 1930s, while he was a professor of electrical engineering at MIT. You might have seen examples of his work in the amazing shots of hummingbirds in motion, a drop of milk splattering on a table, or a bullet penetrating an apple (see Figure 3). To stop the motion and capture these pictures, one needs a high-intensity, very short pulsed flash, as mentioned earlier in this module.
Suppose one wished to capture the picture of a bullet (moving at 5.0 × 10m/s) that was passing through an apple. The duration of the flash is related to the RC time constant, τ. What size capacitor would one need in the RC circuit to succeed, if the resistance of the flash tube was 10.0 Ω? Assume the apple is a sphere with a diameter of 8.0 × 10–2m.
#### Strategy
We begin by identifying the physical principles involved. This example deals with the strobe light, as discussed above. Figure 2 shows the circuit for this probe. The characteristic time τ of the strobe is given as τ RC.
#### Solution
We wish to find C, but we don’t know τ. We want the flash to be on only while the bullet traverses the apple. So we need to use the kinematic equations that describe the relationship between distance x, velocity v, and time t:
x = vt or $t=\frac{x}{v}\\$.
The bullet’s velocity is given as 5.0 × 10m/s, and the distance x is 8.0 × 10–2 m The traverse time, then, is
$t=\frac{x}{v}=\frac{8.0\times {10}^{-2}\text{ m}}{5.0\times {10}^{2}\text{ m/s}}=1.6\times {\text{10}}^{-4}\text{ s}\\$.
We set this value for the crossing time t equal to τ. Therefore,
$C=\frac{t}{R}=\frac{1.6\times \text{10}^{-4}\text{ s}}{10.0\text{ }\Omega }=16\text{ }\mu\text{ F}\\$.
(Note: Capacitance C is typically measured in farads, F, defined as Coulombs per volt. From the equation, we see that C can also be stated in units of seconds per ohm.)
#### Discussion
The flash interval of 160 μs (the traverse time of the bullet) is relatively easy to obtain today. Strobe lights have opened up new worlds from science to entertainment. The information from the picture of the apple and bullet was used in the Warren Commission Report on the assassination of President John F. Kennedy in 1963 to confirm that only one bullet was fired.
## RC Circuits for Timing
RC circuits are commonly used for timing purposes. A mundane example of this is found in the ubiquitous intermittent wiper systems of modern cars. The time between wipes is varied by adjusting the resistance in an RC circuit. Another example of an RC circuit is found in novelty jewelry, Halloween costumes, and various toys that have battery-powered flashing lights. (See Figure 4 for a timing circuit.)
A more crucial use of RC circuits for timing purposes is in the artificial pacemaker, used to control heart rate. The heart rate is normally controlled by electrical signals generated by the sino-atrial (SA) node, which is on the wall of the right atrium chamber. This causes the muscles to contract and pump blood. Sometimes the heart rhythm is abnormal and the heartbeat is too high or too low. The artificial pacemaker is inserted near the heart to provide electrical signals to the heart when needed with the appropriate time constant. Pacemakers have sensors that detect body motion and breathing to increase the heart rate during exercise to meet the body’s increased needs for blood and oxygen.
### Example 2. Calculating Time: RC Circuit in a Heart Defibrillator
A heart defibrillator is used to resuscitate an accident victim by discharging a capacitor through the trunk of her body. A simplified version of the circuit is seen in Figure 2. (a) What is the time constant if an 8.00-μF capacitor is used and the path resistance through her body is 1.00 × 10Ω? (b) If the initial voltage is 10.0 kV, how long does it take to decline to 5.00 × 10V?
#### Strategy
Since the resistance and capacitance are given, it is straightforward to multiply them to give the time constant asked for in part (a). To find the time for the voltage to decline to 5.00 × 10V, we repeatedly multiply the initial voltage by 0.368 until a voltage less than or equal to 5.00 × 10V is obtained. Each multiplication corresponds to a time of τ seconds.
#### Solution for (a)
The time constant τ is given by the equation τ RC. Entering the given values for resistance and capacitance (and remembering that units for a farad can be expressed as s/Ω) gives
τ RC (1.00 × 10Ω(8.00 μF8.00 ms.
#### Solution for (b)
In the first 8.00 ms, the voltage (10.0 kV) declines to 0.368 of its initial value. That is:
V 0.368 V3.680 × 10V at t 8.00 ms.
(Notice that we carry an extra digit for each intermediate calculation.) After another 8.00 ms, we multiply by 0.368 again, and the voltage is
$\begin{array}{lll}V′ & =& 0.368\text{ V}\\ & =& \left(0.368\right)\left(3.680\times {10}^{3}\text{ V}\right)\\ & =& 1.354\times {10}^{3}\text{ V}\text{at }t=16.0\text{ ms}\end{array}\\$
Similarly, after another 8.00 ms, the voltage is
$\begin{array}{lll}V'' & =& 0.368\text{ }V' =\left(\text{0.368}\right)\left(\text{1.354}\times{10}^{3}\text{ V}\right)\\ & =& 498\text{ V at }t=24.0\text{ ms}\end{array}\\$.
#### Discussion
So after only 24.0 ms, the voltage is down to 498 V, or 4.98% of its original value.Such brief times are useful in heart defibrillation, because the brief but intense current causes a brief but effective contraction of the heart. The actual circuit in a heart defibrillator is slightly more complex than the one in Figure 2, to compensate for magnetic and AC effects that will be covered in Magnetism.
### Check Your Understanding
When is the potential difference across a capacitor an emf?
#### Solution
Only when the current being drawn from or put into the capacitor is zero. Capacitors, like batteries, have internal resistance, so their output voltage is not an emf unless current is zero. This is difficult to measure in practice so we refer to a capacitor’s voltage rather than its emf. But the source of potential difference in a capacitor is fundamental and it is an emf.
## PhET Explorations: Circuit Construction Kit (DC only)
An electronics kit in your computer! Build circuits with resistors, light bulbs, batteries, and switches. Take measurements with the realistic ammeter and voltmeter. View the circuit as a schematic diagram, or switch to a life-like view.
## Section Summary
• An RC circuit is one that has both a resistor and a capacitor.
• The time constant τ for an RC circuit is τ RC.
• When an initially uncharged (V= 0 at = 0) capacitor in series with a resistor is charged by a DC voltage source, the voltage rises, asymptotically approaching the emf of the voltage source; as a function of time,
= emf(1 − et/RC) (charging),
• Within the span of each time constant τ, the voltage rises by 0.632 of the remaining value, approaching the final voltage asymptotically.
• If a capacitor with an initial voltage V0 is discharged through a resistor starting at= 0, then its voltage decreases exponentially as given by
V = V0e−t/RC(discharging).
• In each time constant τ, the voltage falls by 0.368 of its remaining initial value, approaching zero asymptotically.
### Conceptual questions
1. Regarding the units involved in the relationship τ RC, verify that the units of resistance times capacitance are time, that is, Ω ⋅ F=s.
2. The RC time constant in heart defibrillation is crucial to limiting the time the current flows. If the capacitance in the defibrillation unit is fixed, how would you manipulate resistance in the circuit to adjust the RC constant τ? Would an adjustment of the applied voltage also be needed to ensure that the current delivered has an appropriate value?
3. When making an ECG measurement, it is important to measure voltage variations over small time intervals. The time is limited by the RC constant of the circuit—it is not possible to measure time variations shorter than RC. How would you manipulate and C in the circuit to allow the necessary measurements?
4. Draw two graphs of charge versus time on a capacitor. Draw one for charging an initially uncharged capacitor in series with a resistor, as in the circuit in Figure 1 (above), starting from t = 0. Draw the other for discharging a capacitor through a resistor, as in the circuit in Figure 2 (above), starting at t = 0, with an initial charge Qo. Show at least two intervals of τ.
5. When charging a capacitor, as discussed in conjunction with Figure 2, how long does it take for the voltage on the capacitor to reach emf? Is this a problem?
6. When discharging a capacitor, as discussed in conjunction with Figure 2, how long does it take for the voltage on the capacitor to reach zero? Is this a problem?
7. Referring to Figure 1, draw a graph of potential difference across the resistor versus time, showing at least two intervals of τ. Also draw a graph of current versus time for this situation.
8. A long, inexpensive extension cord is connected from inside the house to a refrigerator outside. The refrigerator doesn’t run as it should. What might be the problem?
9. In Figure 4 (above), does the graph indicate the time constant is shorter for discharging than for charging? Would you expect ionized gas to have low resistance? How would you adjust R to get a longer time between flashes? Would adjusting R affect the discharge time?
10. An electronic apparatus may have large capacitors at high voltage in the power supply section, presenting a shock hazard even when the apparatus is switched off. A “bleeder resistor” is therefore placed across such a capacitor, as shown schematically in Figure 6, to bleed the charge from it after the apparatus is off. Why must the bleeder resistance be much greater than the effective resistance of the rest of the circuit? How does this affect the time constant for discharging the capacitor?
### Problems & Exercises
1. The timing device in an automobile’s intermittent wiper system is based on an RC time constant and utilizes a 0.500-μF capacitor and a variable resistor. Over what range must R be made to vary to achieve time constants from 2.00 to 15.0 s?
2. A heart pacemaker fires 72 times a minute, each time a 25.0-nF capacitor is charged (by a battery in series with a resistor) to 0.632 of its full voltage. What is the value of the resistance?
3. The duration of a photographic flash is related to an RC time constant, which is 0.100 μs for a certain camera. (a) If the resistance of the flash lamp is 0.0400 Ω during discharge, what is the size of the capacitor supplying its energy? (b) What is the time constant for charging the capacitor, if the charging resistance is 800 ?
4. A 2.00- and a 7.50-μF capacitor can be connected in series or parallel, as can a 25.0- and a 100-kΩ resistor. Calculate the four RC time constants possible from connecting the resulting capacitance and resistance in series.
5. After two time constants, what percentage of the final voltage, emf, is on an initially uncharged capacitor C, charged through a resistance R?
6. A 500-Ω resistor, an uncharged 1.50-μF capacitor, and a 6.16-V emf are connected in series. (a) What is the initial current? (b) What is the RC time constant? (c) What is the current after one time constant? (d) What is the voltage on the capacitor after one time constant?
7. A heart defibrillator being used on a patient has an RC time constant of 10.0 ms due to the resistance of the patient and the capacitance of the defibrillator. (a) If the defibrillator has an 8.00-μF capacitance, what is the resistance of the path through the patient? (You may neglect the capacitance of the patient and the resistance of the defibrillator.) (b) If the initial voltage is 12.0 kV, how long does it take to decline to 6.00 × 10V?
8. An ECG monitor must have an RC time constant less than 1.00 × 102 μs to be able to measure variations in voltage over small time intervals. (a) If the resistance of the circuit (due mostly to that of the patient’s chest) is 1.00 kΩ, what is the maximum capacitance of the circuit? (b) Would it be difficult in practice to limit the capacitance to less than the value found in (a)?
9. Figure 7 shows how a bleeder resistor is used to discharge a capacitor after an electronic device is shut off, allowing a person to work on the electronics with less risk of shock. (a) What is the time constant? (b) How long will it take to reduce the voltage on the capacitor to 0.250% (5% of 5%) of its full value once discharge begins? (c) If the capacitor is charged to a voltage V0 through a 100-Ω resistance, calculate the time it takes to rise to 0.865 V0 (This is about two time constants.)
10. Using the exact exponential treatment, find how much time is required to discharge a 250-μF capacitor through a 500-Ω resistor down to 1.00% of its original voltage.
11. Using the exact exponential treatment, find how much time is required to charge an initially uncharged 100-pF capacitor through a 75.0-MΩ resistor to 90.0% of its final voltage.
12. Integrated Concepts If you wish to take a picture of a bullet traveling at 500 m/s, then a very brief flash of light produced by an RC discharge through a flash tube can limit blurring. Assuming 1.00 mm of motion during one RC constant is acceptable, and given that the flash is driven by a 600-μF capacitor, what is the resistance in the flash tube?
13. Integrated Concepts A flashing lamp in a Christmas earring is based on an RC discharge of a capacitor through its resistance. The effective duration of the flash is 0.250 s, during which it produces an average 0.500 W from an average 3.00 V. (a) What energy does it dissipate? (b) How much charge moves through the lamp? (c) Find the capacitance. (d) What is the resistance of the lamp?
14. Integrated Concepts A 160-μF capacitor charged to 450 V is discharged through a 31.2-kΩ resistor. (a) Find the time constant. (b) Calculate the temperature increase of the resistor, given that its mass is 2.50 g and its specific heat is$1.67\frac{\text{kJ}}{\text{kg}\cdotº\text{C}}\\$, noting that most of the thermal energy is retained in the short time of the discharge. (c) Calculate the new resistance, assuming it is pure carbon. (d) Does this change in resistance seem significant?
15. Unreasonable Results (a) Calculate the capacitance needed to get an RC time constant of 1.00 × 103 with a 0.100-Ω resistor. (b) What is unreasonable about this result? (c) Which assumptions are responsible?
16. Construct Your Own Problem Consider a camera’s flash unit. Construct a problem in which you calculate the size of the capacitor that stores energy for the flash lamp. Among the things to be considered are the voltage applied to the capacitor, the energy needed in the flash and the associated charge needed on the capacitor, the resistance of the flash lamp during discharge, and the desired RC time constant.
17. Construct Your Own Problem Consider a rechargeable lithium cell that is to be used to power a camcorder. Construct a problem in which you calculate the internal resistance of the cell during normal operation. Also, calculate the minimum voltage output of a battery charger to be used to recharge your lithium cell. Among the things to be considered are the emf and useful terminal voltage of a lithium cell and the current it should be able to supply to a camcorder.
## Glossary
RC circuit:
a circuit that contains both a resistor and a capacitor
capacitor:
an electrical component used to store energy by separating electric charge on two opposing plates
capacitance:
the maximum amount of electric potential energy that can be stored (or separated) for a given electric potential
### Selected Solutions to Problems & Exercises
1. range 4.00 to 30.0 MΩ
3. (a) 2.50 μF (b) 2.00 s
5. 86.5%
7. (a) 1.25 kΩ (b) 30.0 ms
9. (a) 20.0 s (b) 120 s (c) 16.0 ms
11. 1.73 × 10s
12. 3.33 × 10Ω
14. (a) 4.99 s (b) 3.87ºC (c) 31.1 kΩ (d) No
## License
Physics II by Lumen Learning is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted. | 2022-09-29T04:24:40 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5114509463310242, "perplexity": 760.4481143086489}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335304.71/warc/CC-MAIN-20220929034214-20220929064214-00492.warc.gz"} |
https://pdglive.lbl.gov/DataBlock.action?node=S032SP4&home=MXXX035 | # ${{\boldsymbol D}^{0}}$ $\rightarrow$ ${{\boldsymbol K}^{*}}{{\boldsymbol K}}$ AVERAGE RELATIVE STRONG PHASE $\delta {}^{ {{\boldsymbol K}^{*}} {{\boldsymbol K}} }$ INSPIRE search
The quoted value of $\delta$ is based on the same sign $\mathit CP$ phase of ${{\mathit D}^{0}}$ and ${{\overline{\mathit D}}^{0}}$ convention.
VALUE ($^\circ{}$) DOCUMENT ID TECN COMMENT
$-16.6$ $\pm18.4$ 1
2012
CLEO ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\overline{\mathit D}}^{0}}$ at 3.77 GeV
1 Uses quantum correlations in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\overline{\mathit D}}^{0}}$ at the ${{\mathit \psi}{(3770)}}$, where the signal side ${{\mathit D}}$ decays to ${{\mathit K}_S^0}$ ${{\mathit K}}{{\mathit \pi}}$ and the tag-side ${{\mathit D}}$ decays to ${{\mathit K}}{{\mathit \pi}}$ , ${{\mathit K}}{{\mathit \pi}}{{\mathit \pi}}{{\mathit \pi}}$ , ${{\mathit K}}{{\mathit \pi}}{{\mathit \pi}^{0}}$ , and 10 additional $\mathit CP$-even, $\mathit CP$-odd, and mixed $\mathit CP$ modes involving ${{\mathit K}_S^0}$ or ${{\mathit K}_L^0}$ .
References:
INSLER 2012
PR D85 092016 Studies of the Decays ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}$ and ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ | 2021-06-19T02:24:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9777678847312927, "perplexity": 853.6766754202444}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487643380.40/warc/CC-MAIN-20210619020602-20210619050602-00457.warc.gz"} |
http://dergipark.gov.tr/hujms/issue/38121/439936 | Yıl 2018, Cilt 47, Sayı 3, Sayfalar 567 - 578 2018-06-01
| | | |
## New upper bounds of Ostrowski type integral inequalities utilizing Taylor expansion
#### Hüseyin Budak [1] , Fuat Usta [2] , Mehmet Zeki Sarikaya [3]
##### 30 30
In this paper, we have been introduced and tested some significant new bounds of Ostrowski type integral inequalities. In accordance with this purpose we have taken advantageous of the Taylor expansion for functions. Some numerical experiments have been given to show the applicability and accuracy of the proposed method.
Ostrowski inequality, Taylor expansion
• G. A. Anastassiou and S. S. Dragomir, On some estimates of the remainder in Taylor's formula, J. Math. Anal. Appl. 263 (2001), no. 1, 246263.
• P. Cerone, S. S. Dragomir, J. Roumeliotis, An inequality of Ostrowski type for mappings whose second derivatives are bounded and applications, RGMIA Res. Rep. Coll., 1 (1998).
• X.-L. Cheng. Improvement of some Ostrowski-Grüss type inequalities, Computers & Mathematics with Applications, 42, 109114, 2001.
• S. S. Dragomir, S. Wang, An inequality of Ostrowski-Grüss type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules, Comput. Math. Appl., 33 (1997), 1520.
• S. S. Dragomir and S. Wang, An inequality of Ostrowski-Gruss type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules, Comput. Math. Appl. 33 (1997), no. 11, 1520.
• V. N. Huy and Q. A. Ngo, New bounds for the Ostrowski-like type inequalities, Bull. Korean Math. Soc. 48 (2011) 95-104.
• A. R. Kashif, , M. Shoaib, M. A. Latif, Improved version of perturbed Ostrowski type inequalities for n-times dierentiable mappings with three-step kernel and its application, J. Nonlinear Sci. Appl. 9 (2016), 33193332.
• M. E. Kiris and M. Z. Sarikaya, On Ostrowski type inequalities and Ceby²ev type inequalities, Filomat, 29:8 (2015), 16951713.
• Z. Liu, Some OstrowskiGrüss type inequalities and applications, Comput. Math. Appl. 53 (2007) 7379.
• Z. Liu, Some Ostrowski type inequalities, Math. Comput. Modelling 48 (2008) 949960.
• W. Liu, New bounds for the companion of Ostrowski's inequality and applications, Filomat, 28 (2014), 167178.
• A. M. Ostrowski, Über die absolutabweichung einer dierentiebaren funktion von ihrem integralmitelwert, Comment. Math. Helv. 10(1938), 226-227.
• M. Z. Sarikaya and H. Yaldiz, New generalization fractional inequalities of Ostrowski-Grüss type, Lobachevskii Journal of Math., 2013, Vol. 34, No. 4, pp. 326-331.
• A. Qayyum, S. Hussain, A new generalized Ostrowski Gruss type inequality and applications, Appl. Math. Lett., 25 (2012),1875-1880.
• N. Ujevi¢, New bounds for the rst inequality of Ostrowski-Grüss type and applications, Comput. Math. Appl., 46 (2003), 421427.
Birincil Dil en Matematik Matematik Yazar: Hüseyin Budak Yazar: Fuat Usta (Sorumlu Yazar) Yazar: Mehmet Zeki Sarikaya
Bibtex @araştırma makalesi { hujms439936, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {Hacettepe Üniversitesi}, year = {2018}, volume = {47}, pages = {567 - 578}, doi = {}, title = {New upper bounds of Ostrowski type integral inequalities utilizing Taylor expansion}, key = {cite}, author = {Sarikaya, Mehmet Zeki and Budak, Hüseyin and Usta, Fuat} } APA Budak, H , Usta, F , Sarikaya, M . (2018). New upper bounds of Ostrowski type integral inequalities utilizing Taylor expansion. Hacettepe Journal of Mathematics and Statistics, 47 (3), 567-578. Retrieved from http://dergipark.gov.tr/hujms/issue/38121/439936 MLA Budak, H , Usta, F , Sarikaya, M . "New upper bounds of Ostrowski type integral inequalities utilizing Taylor expansion". Hacettepe Journal of Mathematics and Statistics 47 (2018): 567-578 Chicago Budak, H , Usta, F , Sarikaya, M . "New upper bounds of Ostrowski type integral inequalities utilizing Taylor expansion". Hacettepe Journal of Mathematics and Statistics 47 (2018): 567-578 RIS TY - JOUR T1 - New upper bounds of Ostrowski type integral inequalities utilizing Taylor expansion AU - Hüseyin Budak , Fuat Usta , Mehmet Zeki Sarikaya Y1 - 2018 PY - 2018 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 567 EP - 578 VL - 47 IS - 3 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2017 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics New upper bounds of Ostrowski type integral inequalities utilizing Taylor expansion %A Hüseyin Budak , Fuat Usta , Mehmet Zeki Sarikaya %T New upper bounds of Ostrowski type integral inequalities utilizing Taylor expansion %D 2018 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 47 %N 3 %R %U ISNAD Budak, Hüseyin , Usta, Fuat , Sarikaya, Mehmet Zeki . "New upper bounds of Ostrowski type integral inequalities utilizing Taylor expansion". Hacettepe Journal of Mathematics and Statistics 47 / 3 (Haziran 2018): 567-578. | 2018-12-10T19:27:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5842781662940979, "perplexity": 8630.547344629325}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376823442.17/warc/CC-MAIN-20181210191406-20181210212906-00503.warc.gz"} |
https://wiki.bnl.gov/eic/index.php?title=Special:MobileDiff/3739 | # BEGIN ANSIBLE MANAGED BLOCK WIKIEDITOR #17.01.14-> wfLoadExtension( 'WikiEditor' ); # ## Enables/disables use of WikiEditor by default but still allow users to disable it in preferences #$wgDefaultUserOptions['usebetatoolbar'] = 1; #$wgDefaultUserOptions['usebetatoolbar-cgd'] = 1; # ## Displays the Preview and Changes tabs #$wgDefaultUserOptions['wikieditor-preview'] = 0; # ## Displays the Publish and Cancel buttons on the top right side #$wgDefaultUserOptions['wikieditor-publish'] = 0; #17.01.14<- # END ANSIBLE MANAGED BLOCK WIKIEDITOR Changes - EIC
# Changes
, 15:14, 3 August 2013
Line 32: Line 32:
These protons cannot be detected in the main detector. The standard detectors used to detect the scattered proton are roman pots placed at different distances from the IR.
These protons cannot be detected in the main detector. The standard detectors used to detect the scattered proton are roman pots placed at different distances from the IR.
Using this detector technology poses an other requirement on the machine performance. To reach as small scattering angles as possible a small emittance of the beam is crucial as there is also an additional requirement of 10 sigma clearance from the core of the beam.
Using this detector technology poses an other requirement on the machine performance. To reach as small scattering angles as possible a small emittance of the beam is crucial as there is also an additional requirement of 10 sigma clearance from the core of the beam.
+
To have good acceptance at low scattering angle the beam needs to be cooled and we need
== Detector Space and Magnetic Field ==
== Detector Space and Magnetic Field ==
2,105
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https://mooseframework.inl.gov/source/kernels/PorousFlowPreDis.html | # PorousFlow PreDis
Precipitation-dissolution of chemical species
This Kernel implements the residual In this equation, is the porosity (only the old value is used), is the aqueous saturation, the sum over is a sum over all the precipitated-or-dissolved (PreDis) mineral species, are stoichiometric coefficients, is the density of a solid lump of the mineral, and is the mineral reaction rate (m(precipitate)/m(solution).s) which is computed by PorousFlowAqueousPreDisChemistry.
Details concerning precipitation-dissolution kinetic chemistry may be found in the chemical reactions module.
warning
The numerical implementation of the chemical-reactions part of PorousFlow is quite simplistic, with very few guards against strange numerical behavior that might arise during the non-linear iterative process that MOOSE uses to find the solution. Therefore, care must be taken to define your chemical reactions so that the primary species concentrations remain small, but nonzero, and that mineralisation does not cause porosity to become negative or exceed unity.
This Kernel is usually added to a PorousFlowMassTimeDerivative Kernel to simulate precipitation-dissolution of a mineral from some primary chemical species. For instance in the case of just one precipitation-dissolution kinetic reaction (1) and including diffusion and dispersion, the Kernels block looks like
[Kernels]
[./mass_a]
type = PorousFlowMassTimeDerivative
fluid_component = 0
variable = a
[../]
[./diff_a]
type = PorousFlowDispersiveFlux
variable = a
fluid_component = 0
disp_trans = 0
disp_long = 0
[../]
[./predis_a]
type = PorousFlowPreDis
variable = a
mineral_density = 1000
stoichiometry = 1
[../]
[./mass_b]
type = PorousFlowMassTimeDerivative
fluid_component = 1
variable = b
[../]
[./diff_b]
type = PorousFlowDispersiveFlux
variable = b
fluid_component = 1
disp_trans = 0
disp_long = 0
[../]
[./predis_b]
type = PorousFlowPreDis
variable = b
mineral_density = 1000
stoichiometry = 1
[../]
(modules/porous_flow/test/tests/chemistry/2species_predis.i)
Appropriate stoichiometric coefficients must be supplied to this Kernel. Consider the reaction system (2)
Then the stoichiometric coefficients for the PorousFlowPreDis Kernels would be:
- stoichiometry = '1 4' for Variable a - stoichiometry = '2 -5' for Variable b - stoichiometry = '-3 6' for Variable c
note
This Kernel lumps the mineral masses to the nodes. It also only uses the old values of porosity, which is an approximation: see porosity for a discussion.
See mass lumping for details.
## Input Parameters
• variableThe name of the variable that this Kernel operates on
C++ Type:NonlinearVariableName
Options:
Description:The name of the variable that this Kernel operates on
• mineral_densityDensity (kg(precipitate)/m^3(precipitate)) of each secondary species in the aqueous precipitation-dissolution reaction system
C++ Type:std::vector
Options:
Description:Density (kg(precipitate)/m^3(precipitate)) of each secondary species in the aqueous precipitation-dissolution reaction system
• stoichiometryA vector of stoichiometric coefficients for the primary species that is the Variable of this Kernel: one for each precipitation-dissolution reaction (these are one columns of the 'reactions' matrix)
C++ Type:std::vector
Options:
Description:A vector of stoichiometric coefficients for the primary species that is the Variable of this Kernel: one for each precipitation-dissolution reaction (these are one columns of the 'reactions' matrix)
• PorousFlowDictatorThe UserObject that holds the list of PorousFlow variable names.
C++ Type:UserObjectName
Options:
Description:The UserObject that holds the list of PorousFlow variable names.
### Required Parameters
• displacementsThe displacements
C++ Type:std::vector
Options:
Description:The displacements
• blockThe list of block ids (SubdomainID) that this object will be applied
C++ Type:std::vector
Options:
Description:The list of block ids (SubdomainID) that this object will be applied
### Optional Parameters
• enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
Description:Set the enabled status of the MooseObject.
• save_inThe name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector
Options:
Description:The name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
• use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Options:
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
• control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
• seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Options:
Description:The seed for the master random number generator
• diag_save_inThe name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector
Options:
Description:The name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
• implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Options:
Description:Determines whether this object is calculated using an implicit or explicit form
• vector_tagstimeThe tag for the vectors this Kernel should fill
Default:time
C++ Type:MultiMooseEnum
Options:nontime time
Description:The tag for the vectors this Kernel should fill
• extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector
Options:
Description:The extra tags for the vectors this Kernel should fill
• matrix_tagssystem timeThe tag for the matrices this Kernel should fill
Default:system time
C++ Type:MultiMooseEnum
Options:nontime system time
Description:The tag for the matrices this Kernel should fill
• extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector
Options:
Description:The extra tags for the matrices this Kernel should fill | 2019-04-20T18:44:09 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.19307436048984528, "perplexity": 6662.19439848406}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578529962.12/warc/CC-MAIN-20190420180854-20190420202854-00160.warc.gz"} |
http://gams.cam.nist.gov/35.9 | # §35.9 Applications
In multivariate statistical analysis based on the multivariate normal distribution, the probability density functions of many random matrices are expressible in terms of generalized hypergeometric functions of matrix argument $\mathop{{{}_{p}F_{q}}\/}\nolimits$, with $p\leq 2$ and $q\leq 1$. See James (1964), Muirhead (1982), Takemura (1984), Farrell (1985), and Chikuse (2003) for extensive treatments.
For other statistical applications of $\mathop{{{}_{p}F_{q}}\/}\nolimits$ functions of matrix argument see Perlman and Olkin (1980), Groeneboom and Truax (2000), Bhaumik and Sarkar (2002), Richards (2004) (monotonicity of power functions of multivariate statistical test criteria), Bingham et al. (1992) (Procrustes analysis), and Phillips (1986) (exact distributions of statistical test criteria). These references all use results related to the integral formulas (35.4.7) and (35.5.8).
For applications of the integral representation (35.5.3) see McFarland and Richards (2001, 2002) (statistical estimation of misclassification probabilities for discriminating between multivariate normal populations). The asymptotic approximations of §35.7(iv) are applied in numerous statistical contexts in Butler and Wood (2002).
In chemistry, Wei and Eichinger (1993) expresses the probability density functions of macromolecules in terms of generalized hypergeometric functions of matrix argument, and develop asymptotic approximations for these density functions.
In the nascent area of applications of zonal polynomials to the limiting probability distributions of symmetric random matrices, one of the most comprehensive accounts is Rains (1998). | 2015-10-07T17:22:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 4, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9471422433853149, "perplexity": 1689.4820206674926}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-40/segments/1443737875203.46/warc/CC-MAIN-20151001221755-00068-ip-10-137-6-227.ec2.internal.warc.gz"} |
https://atap.gov.au/tools-techniques/distributional-effects/6-commentaries.aspx | # 6. Commentaries
## 6.1 Appendix A Equity analysis in transport practice
Many transport plans, strategies and policies articulate equity as a key issue to consider in transport infrastructure investments. Selected examples from different jurisdictions are presented below.
For example, in 2003, a draft transport plan from the South Australian Government (SA Government, 2003), noted ‘transport’s contribution to social inclusion through recognition that not all South Australians fare equally and some experience acute and disproportionate disadvantage’. The following groups and issues were identified:
• Age (specifically the mobility needs of older people and the young who are especially dependent on public transport and others for transport)
• Gender (specifically people who have particular travel needs regarding access to private transport and in patterns of commuting and employment)
• People with disabilities
• Other socially or economically disadvantaged groups such as indigenous people.
Western Australia’s sustainability framework (WA Government, 2003) presented a set of criteria that could be used in the process of sustainability assessment, one of which emphasises increasing ‘access, equity and human rights in the provision of material security and effective choices’.
The NSW Government (DIPNR, 2004) has used the objectives of social equity, economic development, environmental protection and financial management to guide transport planning. In relation to transport, these objectives were described as follows:
• Social equity reflects access to jobs and services, the affordability of housing and transport, and the provision of transport choice.
• Economic development includes creating sustainable jobs, supporting exports, developing regions and minimising the cost of congestion.
• Environmental protection includes minimising the environmental impacts of transport on air, water, soils, vegetation and noise.
• Financial management includes ensuring taxpayers receive value for money from public investment, and considering inter-generational equity issues such as not overburdening future generations with excessive debts or capital requirements.
All these Australian examples emphasise the consideration of equity impacts during strategic planning and decision-making levels. There is scope to further develop and refine methodologies, tools and techniques for equity assessment of transport initiatives. Some progress has been made overseas. The Applied Research Centre in California, for example, has developed guidance for policymakers on preparing an Equity Impact Statement (ARC, 2004). The approach includes identification of the following elements:
• Communities of concern (including, for example, gender, income, disability characteristics)
• adverse effects (including social, cultural, economic, environmental, individual and cumulative effects)
• Key questions that are integrated into the policy-making process that address specific issues such as compliance with legislation, access to livelihood, quality of life and the distribution of the costs and benefits.
In Europe, the German transport investment appraisal method is both detailed and explicit in its treatment of distributional effects on different regions within Germany (Bristow and Nellthorp, 2000). A unique feature of the approach is the flexibility to assign extra weight to employment impacts to reflect specific socio-economic conditions within specific regions (Bristow and Nellthorp, 2000). These same authors also report that in Finland, distributional effects are assessed and presented as part of a Supplementary Study that is made available to the decision-maker alongside the cost-benefit results and other findings. Bristow and Nellthorp (2000) conclude that in many other EU countries there is little evidence that equity and distributional impacts are given a significant role in the assessment of proposed initiatives and the reporting of results.
## 6.2 Appendix B Techniques to estimate distributional (equity) impacts on the community
There are various quantitative and qualitative techniques for considering equity impacts on the community. Some common techniques described in this section include equity indexes and weights, social impact assessment, stated preference surveys and spatial analysis techniques.
### 6.2.1 Equity weights
A number of indexes have been developed to measure equity or inequity between groups or populations. This type of analysis is mostly used to estimate income inequity in the population; however, it is also being applied to concepts such as accessibility. The choice of which index to use will depend on the decision-makers’ needs, data availability and the level of development within the community of interest.
#### Welfare index
Loeis and Richardson (1997) identified a welfare index for use in transport analysis and evaluation. Travel demand estimation and the evaluation of travel proposals often rely on personal or household income as one of the explanatory variables. However, the financial significance of a unit of income varies from person to person and household to household. For example, at the same income level, a small household can buy more for its individual members than a larger household. Consequently, it is by itself not an adequate economic explanatory variable for travel behaviour or evaluation.
Loeis and Richardson (1997) developed their ‘Welfare Index’ through practical application of the welfare economics concept of equivalence scales, used in classifying households based on the relative cumulative needs or living costs of their members. Applied in combination with after-tax income, it rates households on relatively uniform standards of financial or welfare capacity. The result is therefore a better explanatory variable for travel behaviour than personal or household income.
##### Equity weights
The text in this section is provided as information for the reader only. In line with the advice of the Department of Finance and Administration (2006), the use of equity weights is not recommended by the ATAP (see discussion in chapter 1).
Equity weights provide a method of explicitly incorporating concepts of fairness into an economic analysis. Weights express the extent society is prepared to sacrifice efficiency in pursuit of fairness. The greater the equity weight, the more efficiency gain a society is willing to trade-off to achieve improved fairness (Sassi et al, 2001).
The underlying assumption to the development and application of such weights is that the concepts of equity and efficiency can be traded off against each other. The application of weights is thus used to effect a balancing of conflicting, but commensurable objectives when making complex resource allocation decisions (Sassi et al, 2001). An example of how to apply equity weights is provided below.
Equity weights can be derived from two major sources: the view of a (representative) sample of the population and/or the views of decision-makers (Sassi et al, 2001).
It is important to note that the application of equity weighting can be controversial. Equity weights are subjective and a detailed description of the equity effects should be provided to the decision-maker who can assess the distributional effects of an initiative. For this reason, equity weights are not often used in practice.
Box 1 How to apply equity weights
Equity weighting is a simple concept. Say that a particular initiative provides benefits for two different population groups A and B. The net benefit is given by:
NetB = Wa ΔA + Wb ΔB, where Wa and Wb are the distributional (or equity) weights.
In situations where population groups are equal, the weights are set to one. If there are equity differences between population groups (involving, for example, different income distributions) then the ‘marginal utility of income’ will be different for these two groups. The net benefit in such cases may be defined as:
NetB = WH ΔH + WL ΔL, where WH is the marginal utility of income for the high income group and WL is the marginal utility of income for the low income group.
If we say that the marginal utility of income is 0.40 for the high income group (i.e. a $1 change in income for this group results in a 0.4 change in economic welfare) and 1.25 for the low income group (i.e. a$1 rise in income causes a 1.25 change in economic welfare), then the net benefit equation becomes:
NetB = 0.4 ΔH + 1.25 ΔL ·(example taken from Sassi et al, 2001).
### 6.2.2. Social Impact Assessment of transport initiatives
Social impacts are the likely consequences for individuals or a community of implementing a particular course of action. It is common practice (and often required by legislation) to undertake a Social Impact Assessment in conjunction with an Environmental Impact Assessment in the process of evaluating major transport initiatives.
Social Impact Assessment relates to the identification and assessment of potential impacts for an area and the community of an initiative. Sinclair Knight Merz (1998) state that a Social Impact Assessment requires:
• A description of the existing and likely future social characteristics of an area
• A description of proposed changes
• An analysis of how these changes will impact on the community at both a broad (regional level) and a local level
• An examination of measures available to ameliorate adverse impacts.
Assessment of social impacts relies on community input to gain an understanding of community concerns, values and aspirations. As such, Social Impact Assessment processes and community consultation are inextricably linked (Sinclair Knight Merz, 1998).
The range of social impacts that can result from a transport initiative can be very large. The table below provides some common social impacts of a freeway construction (or extension) initiative.
Table 3: Selection of social impacts to consider when undertaking a road development initiative
Social impactIssues to consider
Displacement or isolation of residents Adequacy of the compensation and the relocation process, reduced land value, emotional issues including grief
Displacement or isolation of commercial and community facilities Adequacy of the compensation and the relocation process, economic hardships for existing or new businesses, reduced land value, clientele cut off, inaccessibility of services or inconvenience for customers
Barrier effects: effects on social interaction Effects on community cohesion, disruption of friendships or family contact, changes in convenience and travel time
Barrier effects: effects on business, recreation or services Inconvenience, changes to accessibility and travel time
Noise effects Physiological, psychological and social changes due to increased noise levels
Safety Effects on personal, family or child safety on a localised scale i.e. dependent on proximity to freeway or changes to traffic conditions in surrounding area
Health effects Physiological changes resulting from air and water quality
Environmental quality effects Changes in air or water quality as they affect people’s lifestyle and enjoyment of their environment, recreation, indoor and outdoor living
Land use changes Changes in zoning from residential to commercial areas or development in a previously undeveloped area, loss of recreational or public space
Aesthetics Changes to visual landscape, physical intrusion, scale, loss of open space, changes in flora or fauna
Cultural heritage Disturbance or destruction of heritage sites
The data required to facilitate a Social Impact Assessment process are firmly based on community consultation campaigns. Community participation is a major component of Social Impact Assessment. It is useful to begin the participation process early in the planning process and carry on throughout the life of individual initiatives. In many transport agencies, community participation/consultation is also a legislative requirement, meaning that an initiative cannot proceed beyond the planning stage without adequate consultation with the community. The support of the community is also often needed to ensure successful implementation of a transport initiative.
An added complication to impact assessment is that social impacts are classified differently by different practitioners. For example, air pollution is classified as an environmental issue in an Environmental Impact Assessment. A Social Impact Assessment should also include air pollution as a social issue because of its consequences on the health of the community. Air pollution mitigation would also be included in a CBA due to the economic costs of pollution mitigation measures.
The practitioner is often faced with a series of complexities inherent in impact assessment statements, which can lead to serious double counting issues in the economic appraisal of initiatives. It is very important to remember that a thorough appraisal should take into account a broad range of social impacts, not just those that are easily quantifiable and monetised such as relocation, pollution mitigation measures and safety, but also those that are more difficult to monetise such as community severance or loss of character or open space.
### 6.2.3 Equity Impact Assessment
Social (equity) Impact Assessment statements consider the winners and losers of the particular initiative investment. As stated by Levinson (2002), a set of specified (winner and loser) population subgroups would be normally identified. Then the outcomes of the initiative (e.g. travel time and delay, accessibility, consumer surplus, air pollution, noise pollution, accidents) would be assessed for each of these population subgroups.
Levinson (2002) provides an Equity Impact Statement checklist as shown below. The checklist includes a range of stratification variables (for example population, gender or spatial extent), specific process requirements (such as the opportunity to participate in decision-making) as well as desired outcome areas (such as mobility, economic, environmental and health outcomes) for transport initiatives.
Process Outcomes Stratification Opportunity to engage in decision-making process Mobility Economic Environmental Health Other Population Spatial (or jurisdictional) Temporal Modal Generational Gender Racial Ability Cultural Income
Source: Levinson, 2002.
### 6.2.4 Assessing cumulative impacts
The distribution of effects can change over time and through the cumulative effects of successive initiative activities. Transport practitioners involved in equity analysis should therefore be aware of procedures for conducting Cumulative Effects Assessment (CEA) or Cumulative Impact Assessment (CIA).
A cumulative impact on a resource is one that results from the incremental impact of an action when added to other past, present and reasonably foreseeable future actions (see below). Cumulative impacts can result from individually minor but collectively significant actions taking place over a period of time. Cumulative impacts may also include the effects of natural processes and events, depending on the specific resource in question (FHWA, undated).
Cumulative impact analysis is resource-specific and generally performed for the environmental resources directly impacted by a government action under study, such as a transportation initiative. However, not all of the resources directly impacted by an initiative will require a cumulative impact analysis. The resources subject to a Cumulative Impact Assessment should be determined on a case-by-case basis early in the process, generally as part of early coordination or scoping (FHWA, undated).
It is generally recognised among practitioners that specific methodologies for the assessment of indirect and cumulative impacts, particularly for predicting reasonable foreseeable impacts, are not as well established or universally accepted as those associated with direct impacts, such as traffic noise analysis or wetland delineation. Determining the most appropriate technique for assessing indirect and cumulative impacts of a specific initiative should include communication with the cooperating agencies and community stakeholders (FHWA, undated).
Figure 2: Cumulative impactsSource: (FHWA, undated)
### 6.2.5 Stated preference surveys
Stated preference surveys are important community consultation tools that are used to inform equity evaluations (e.g. cost-utility analysis). They are particularly useful in situations where empirical information does not exist. For example, stated preference surveys might be used because no data has yet been generated on a new type of travel mode or a special type of pricing instrument with unique characteristics (US EPA, 1998).
In a stated preference approach, it is possible to derive statistical estimates of ‘trade-off’ rates between various alternatives or their attributes by making respondents choose from among them in measured ways that indicate the relative importance of key attributes. These rates can then be assessed in relation to each traveller and their circumstances (US EPA, 1998).
The validity of the derived statistical relationships relies on how well the alternatives are portrayed to (and understood by) the respondent, and their comparison with known ‘standards’. While stated preference surveys rely on hypothetical situations, comparison of ‘elasticity’ relationships derived from stated preference with more conventional revealed preference surveys or models have shown corroboration. The results from these surveys should be used with caution, but they offer an important interim tool for agencies to estimate relationships between pricing instruments and travel behaviour response, not just in mode choice but also in relation to destination, time of day, route choice, etc (US EPA, 1998).
Stated preference methods were developed by the private market research industry and have been used successfully for many years to aid companies in identifying the critical attributes of their product, and maximising those attributes to gain market share over competitors. Use of the techniques in transport is a fairly recent development; however, there are examples where they have been used to explore time of day choice or assist in the development of a route choice model (US EPA, 1998).
### 6.2.6 Spatial analysis techniques
This section discusses the potential of spatially based analysis and micro-simulation modelling to explore distributional or equity issues.
#### Spatially based analysis
Since transport infrastructure occurs on a spatial scale, it is usually the case that physical or social impacts resulting from transport impacts can also be quantified over a spatial scale. This is most commonly undertaken with Geographic Information Systems (GIS) technology which is now readily available and widely used to quantify various effects; for example, emission of environmental contaminants or noise modelling. Most transport impacts have a geographical component; for example, property prices can be easily represented in geographic form.
Once the distributional impact is defined over a geographical scale, relevant socio-economic characteristics need to be transposed onto the geographical representation of the impact. Some of these characteristics will be derived from a community social profile.
Due to the aggregate nature of common data sources on population characteristics (such as the census), Statistical Local Area or Local Government Area population characteristics are generally used as a proxy for specific groups being examined. For example, if concern is expressed over impacts on low income or minority populations, the impacts are measured for neighbourhoods that exceed a certain percentage of those population groups, rather than for specific minority persons or households. This provides the decision-maker with a representation of the distributional effects of initiatives on the communities of interest, i.e. the ‘winners’ and ‘losers’.
The biggest problem with spatial techniques is that some factors that affect impact distribution are difficult to determine. It is often difficult to identify the geographic location of a population class according to social characteristics. An additional complicating factor is that people’s decisions about where they live may be affected by transportation investments. For example, positive externalities such as good public transport or highway access can lead to higher property values and a migration of higher-income people to the area served (FHWA, 2003).
##### Micro-simulation
Micro-simulation modelling techniques forecast travel by modelling a set of actual or synthetic individuals or households that represent the population as the basic unit of analysis rather than dealing with population averages by postcode or statistical region. A ‘synthetic’ sample is composed of a hypothetical set of people or households with characteristics that as a whole match the overall population. Results are aggregated only after the individual or household analyses are completed, allowing the user great flexibility in specifying output categories. This is more commonly referred to as sample enumeration or discrete choice analysis. Sample enumeration relies on the modelling of behaviour for a representative sample of the population generally derived from a regional home interview survey or stated preference survey (FHWA, 2003).
The benefit of this modelling approach for analysing distribution of impacts is that travel patterns, and therefore the travel benefits of transportation improvements, can be tracked across any population characteristic that is included in the sample of persons modelled. Historically, this has been done by income level, since income is commonly used to predict travel behaviour. However the characteristics of the sample can be broadened to include other attributes (FHWA, 2003). An example of a micro-simulation program from the United States (STEP) program is presented below.
##### STEP: a micro-simulation program
STEP is a travel demand analysis package composed of an integrated set of travel demand and activity analysis models, supplemented by a variety of impact analysis capabilities and a simple model of transportation supply. STEP has been used by the US Department of Transport and the US Environmental Protection Authority to analyse travel impacts of pricing scenarios (with the intention to reduce transport emissions) by income group.
STEP program models are applied using actual or forecast data on household socioeconomic characteristics, the spatial distribution of population and employment (land use), and transportation system characteristics for the selected analysis year(s). STEP reads through the household sample, attaching level-of-service and land use data to each household record as necessary. For each household, STEP uses its models to predict a daily travel and activity pattern for each individual in the household. Finally, household travel is summed up and household totals are expanded to represent the population as a whole.
Testing the effect of a change in conditions or policies is a simple matter of re-analysing the household sample using the new data values, and comparing the results with previous outputs. For example, a new highway or new transit service can be represented by changed travel times and costs for the areas served; a parking price increase can be represented by an increase in out-of pocket costs; an increase in income in a particular area or for a particular population subgroup can be represented by editing the household file to incorporate the revised incomes.
The sampling framework preserves the richness of the underlying distribution of population characteristics and permits tabulation by any subgroup with sufficient observations to be statistically significant. For example, the results can be disaggregated by income level and age, which would allow an assessment of effects for, say, various income classes among the retired population. This is a significant advantage over an aggregate model, which uses zonal averages for most socioeconomic and economic data. A possible STEP model structure is illustrated below.
Figure 3: STEP model structureSource: US EPA, 1998
## 6.3 Appendix C Community participation processes
There are varying degrees of public participation; from information provision and consultation to substantial support for community initiatives (see figure below). Higher degrees of participation are not necessarily 'better' - different levels are appropriate for different situations and interests (Wilcox, 1994). The most commonly applied form of participation is community consultation.
Figure 4: Levels of community participationSource: Adapted from Wilcox, 1994
The desired level of participation needed for a initiative will inform the selection of participatory methods and techniques. Choice of method should directly reflect the type of information needed and the purpose for which it will be used. The following table provides common purposes for which community input is sought and the methods generally effective in achieving the task.
Table 5: Matching participatory instruments to purpose
Participatory approachCharacteristicsParticipants
Purpose: To gain ideas and input from the public
Public hearing/ community meeting A public hearing is often formal, with statements going into an official record of the meeting. A community meeting will often be an informal gathering where people come to share ideas with local officials. An open gathering of people from the community who wish to be heard about a topic or issue
Focus groups A small gathering of stakeholders who meet in a confidential setting to discuss an issue or react to a proposal. The assumption is that through discussion, new information will emerge that would not otherwise come to light from individual questioning. These meetings are often facilitated by a trained individual. Local officials may or may not actively participate in the discussion. Selected stakeholders
Purpose: To complete a specific task with citizen input
Workshop A meeting focused on a predetermined task to be accomplished. Rather than soliciting general opinion, workshops are intended to focus on specific concerns and produce a predetermined product. The benefit of such meetings is that those most directly affected by an issue are directly involved in addressing it. Primary stakeholders are often involved because of a high level of interest in the issue. To be most effective in addressing a public issue, the full range of interests should be represented in the workshop
Task force Purpose is to complete a clearly defined task in the planning process. A task force is often appointed to study a particular issue and offer a report of findings and recommendations to the policy-making body. A small (usually 8 to 20 people) ad hoc citizen committee
Purpose: To have a discussion about citizen priorities associated with community initiatives
Priority-setting committee Citizen group appointed to advise local officials regarding citizen ideas and concerns in planning community initiatives. Participants who are trusted to represent the concerns of citizens and sometimes function as a ‘go-between’ with residents and local government
Purpose: To discuss citizen priorities associated with community initiatives
Delphi procedure The objective is to work toward a consensus of opinion that can be used by policymakers for decision making. Successive rounds of presented arguments and counterpoints move the group toward consensus, or at least to clearly established positions and supporting arguments. A panel of citizens chosen for their knowledge about an issue
Purpose: To quickly and quietly ascertain public sentiment about an issue
Interviews, polls, and surveys Detailed information can be gathered. While confidential, the information can be informative both in content and overall emotional/political reaction to an issue. Interested citizens are given a chance to speak directly with someone about their views
Purpose: To gain input about the alternatives and consequences of an issue.
Media-based issue balloting Coupled with a media-based effort to discuss alternatives and consequences of potential solutions, letters to the editor or radio call-in shows are monitored to gain a sense of public reaction. Unscientific and not a reliable indicator of overall community sentiment, it can be a good way to gain a quick reaction to proposals by those most likely to be active on an issue. Citizens are asked to respond through the local media
Purpose: To give citizens broad decision-making powers
Citizen advisory boards or councils An advisory board studies an issue and makes recommendations to policy makers. The range of decision-making authority can vary and, in some cases, may be binding. Appointed representatives of one or more community interests
Referenda Direct and binding decision-making authority by the electorate. Protracted campaigning leading to a referendum can become a divisive force. All eligible voters
Purpose: To stay informed about the needs of certain neighbourhoods or interest groups
Group or neighbourhood planning council This council serves as advisory to policy makers. Such councils keep decision makers informed about neighbourhood or group concerns, formulate goals and priorities on behalf of the neighbourhood or group, and evaluate plans and programs affecting the neighbourhood or group. Organised by, and composed entirely of citizens
Source: Adapted from Leatherman and Howell, 2000
## 6.4 Appendix D A distributional rules approach
Khisty (1996) attempts to draw analytical conclusions about equity effects by using distributional rules or theories of justice that can be applied depending on the outcomes sought. In this approach, the analyst needs to determine which analytical framework is the most appropriate for the situation under investigation.
This involves the application of different equity principles or theories to determine the types of outcomes that are possible or desirable. Theories of justice are used as input in the development of decision-making procedures. There is no one single theory of justice that will satisfy everyone. For example, Khisty (1996) provides the following six theories of justice chosen because they represent ideas that are either commonly used, understood by society or are documented in the literature.
To illustrate how theories of justice can be applied, Khisty (1996) developed an example of a hypothetical city showing six alternative bus configurations (1-6) as illustrated below. The income distribution (expressed from ‘low’ to ‘high’) on the route alternatives is then overlaid on the area map. Each alternative satisfies the goals and objectives set forth by the citizens of the city, and in each case the aggregate benefits exceed the aggregate costs.
Figure 5: A hypothetical city showing six bus transit configurationsSource: Khisty (1996)
There are five major socio-economic groups in the city and their population percentages are indicated in the table below. It is assumed that each group contributes taxes to the city in proportion to their income. The amount indicated under each alternative (1-6) represents units of benefit that each individual would receive.
Alternatives 1 2 3 4 5 6 Total Net Benefits 920 1045 1825 1885 2200 2450 Income class % population High 5% 6 9 25 28 35 50 Medium high 10% 7 11 22 25 30 40 Medium 50% 9 11 19 20 25 30 Medium low 25% 10 10 16 15 15 10 Low 10% 12 9 13 12 10 6 Average net benefit 9.20 10.45 18.25 18.85 22.00 24.50 Floor 6 9 13 12 10 6 Range 6 2 12 16 25 44
Source: Khisty (1996)
Given the details of the initiative, the question is: which of the six alternatives is the most equitable? The answer to this question depends on which distributional rules or equity principles the decision-maker adopts. Khisty (1996) provides the implications for route selection based on each of the six equity principles:
• Equal share distribution (distribution based on an equal share - or as equal as possible - of the benefits among the socioeconomic groups). Alternative 2 is most consistent with this principle with the minimum range between the highest and the lowest benefit received being 2 units and an average net benefit received of 10.45 units.
• Utilitarian distribution (distribution based on maximising the benefits to the community as a whole). Alternative 6 is most consistent with this principle. While the disparity between high-income and low-income groups is glaring, this alternative has the highest net benefit among all the alternatives.
• Distribution based on maximising the average net benefit with a minimum floor benefit of 10 units (this principle ensures that an attempt to maximise the average benefit is constrained by a certain amount to ensure that certain individuals or groups, particularly those ‘at the bottom’, receive a certain minimum amount of benefit). Alternative 5 is consistent with this principle. The choice of a minimum floor is a decision that must be made in advance by the decision-maker. This principle also illustrates the nature of an efficiency-equity trade-off; the principle is achieved with a reduction in total net benefits of 250 units compared with the maximum efficiency alternative.
• Distribution based on maximising the average net benefit with a benefit range constraint not exceeding 16 units (this principle ensures that an attempt to maximise the average benefit does not allow differences in benefit between the rich and the poor segments of the society to exceed a certain amount). Alternative 4 is consistent with this principle. As above, an efficiency-equity trade-off is apparent. In this case, 565 units of net benefit need to be traded-off.
• Distribution based on the egalitarian principle (this principle of ethical conduct attempts to reduce any existing social or economic inequalities among individuals and groups in the community). Alternative 1 distributes higher benefits to the lower end of the income distribution and is therefore consistent with the egalitarian principle. Although this alternative has the lowest total benefit of all alternatives, it probably benefits income groups that are truly in need of public transportation.
• Rawls’ theory of justice (distribution based on maximising benefits to the lowest income group). Alternative 3 is consistent with this principle. It also has the highest floor among the alternatives, but indicates a need of 625 units of net benefit to be traded for the desired equity outcome.
Which distribution theory to use will depend on the policy-maker and the characteristics of the community that is represented. Invariably, when people are affected by the choice of distribution rules, or when they are offered several rules from which to choose, they tend to prefer the rule that favours them. Preferences are a function of culture, political affiliations, gender, economic standing and so forth (Khisty, 1996).
Khisty (1996) suggests that citizens are generally not bothered by ethical theories as much as they are concerned with their own welfare in terms of ‘quality of life’. Therefore, Khisty defines ‘quality of life’ as the essence of the collective economic, social and physical conditions of people in a community.
It is important to recognise that these are highly subjective choices. They involve trade-offs between, on the one hand, the efficiency focus of increasing the net benefits to society as a whole and, on the other hand, striving for more equitable outcomes. For transport and infrastructure planners and analysts, it is also essential to note that in Australia the taxation and welfare system is the prime policy tool for addressing issues of inequality.
## 6.5 Appendix E Equity Considerations in road pricing
This section provides a discussion of equity issues associated with road pricing. The purpose is to illustrate how equity considerations are a key component of transport policy decision making. An example of providing for equity in road pricing is provided from the European Communities’ AFFORD Project.
Over recent years, the concept of road pricing has been gaining momentum due to concerns about road capacity and congestion management. However, there is still a great deal of controversy surrounding the wider introduction and application of road pricing. As stated by Stough et al (2004), there are misunderstandings over what road pricing seeks to do, concerns over how the revenues will be spent and issues relating to welfare distribution (equity) consequences.
Road pricing is intended to improve transport efficiency by rationing road capacity. In terms of reducing travel demand and making traffic flow more efficient, it does not matter how road pricing revenue is allocated. From an overall economic perspective, the revenue must be used to benefit society and the greater the benefit the more economically efficient the program. There is no requirement, however that the money be allocated in any particular way (Litman, 1999).
The major equity consideration of road pricing concerns the distribution of road pricing revenue. Two components of equity that need to be considered regarding road pricing are horizontal equity and vertical equity. Many people instinctively feel that horizontal equity implies that revenues should be dedicated to road improvements or to provide other benefits to people who pay the fee. However, horizontal equity is complicated by the existence of external costs – those that are borne by non-vehicle users (see table below). So horizontal equity is only fulfilled when revenue is returned to vehicle users as a class, but only after external costs are compensated. Since most estimates of motor vehicle external costs are larger than the expected revenue of road pricing proposals, the horizontal equity justification of returning revenues to drivers is reduced or eliminated (Litman, 1999).
The vertical equity component is more complex. Vertical equity requires that disadvantaged people receive more public resources (per capita or unit of service) than those who have a relative advantage, to accommodate their greater need. So revenues must benefit low-income drivers as a class at least as much as the costs they bear, and disadvantaged residents (including non-drivers) must benefit overall. Litman (1999) explains that vertical equity can be defined with respect to the ability to drive. As a class, non-drivers tend to be economically or socially disadvantaged. Road pricing has the potential of benefiting non-drivers overall by increasing the use of alternative travel modes. Vertical equity considerations justify using road pricing revenue in a broad range of ways including the support of alternative transport programs, reduction in taxes, or funding of public services that benefit disadvantaged populations. The table below illustrates an approach developed by Litman (1999) to assess the distribution of road pricing revenues to four classes of people based on horizontal and vertical equity considerations.
Table 7: Road pricing revenue distribution equity analysis
ClassDescriptionHorizontal equityVertical equity
Non-drivers People who cannot drive, usually due to age, disability, or low income. Non-drivers use automobiles as passengers, but their overall use of congested roads is typically low. Although this group would pay little in road pricing, they deserve a share of revenue if it is considered compensation for existing external impacts of driving. Non-drivers include many people who are economically, physically and socially disadvantaged; therefore, maximum use of road pricing revenues to benefit this group is justified.
Low-income drivers People who can drive and have access to an automobile, but whose travel decisions are significantly affected by vehicle expenses. They will be frequently tolled off by road pricing. This group pays a relatively small share of road pricing fees, but incurs costs from travel charges that provide a large portion of congestion reduction benefits. They deserve a share of toll revenues in compensation. This group is, by definition, disadvantaged so use of road pricing revenues to benefit this group is justified.
Middle-income drivers People who can drive and have access to an automobile, but whose travel decisions are only moderately affected by vehicle expenses. They will sometimes be tolled off the roadway and their net benefits of travel are reduced by road pricing. These drivers pay a large portion of total road pricing and lose net benefits. They deserve to benefit from road pricing revenues on the basis of horizontal equity, but only after all external costs are compensated. Since this group is not disadvantaged there is no vertical equity justification for using road pricing revenue to benefit them.
Upper-income drivers People who can drive and have access to an automobile, but whose travel decisions are not affected by vehicle expenses. They benefit overall from road pricing due to reduced congestion. These people enjoy net benefits from reduced congestion. They deserve a share of the revenue only after external costs are compensated. Since this group is not disadvantaged, there is no vertical equity justification for using road pricing revenue to benefit them.
Source: Litman, 1999
### 6.5.1 Road use charges: an example from the AFFORD project
The European Commission undertook a study of marginal cost transport pricing in three European cities – Helsinki, Oslo and Edinburgh – as part of the ‘Acceptability of Fiscal and Financial Measures and Organisational Requirements for Demand Management’ (AFFORD) study (Fridstrom et al, 2000).
The study distinguished between ‘first-best’ and ‘second-best’ road pricing policy packages. The first-best solution involves charging the user the true cost, i.e. the marginal cost of road use determined by the level of congestion, environmental and accident costs. The second-best pricing package was based on the use of a package of policy instruments that are available for use by transport authorities (e.g. time differentiated cordon toll rates or time differentiated parking charges) (Fridstrom et al, 2000).
The study concluded that inequity within a population increased when road pricing is implemented (based on a Gini coefficient defined in terms of household income per consumption unit before and after revenue redistribution). However, in most cases the changes to income distribution appeared to be relatively moderate.
Fridstrom et al (2000) noted that if revenue is redistributed proportionately by personal income, which is given as a percentage point relief in the income tax rate, it does nothing to correct the initial, adverse equity effects between people in the different income brackets. It does, however, reverse the potentially unpopular transfer of funds from private consumers to the public treasury.
However, if the same, absolute amount of money is redistributed to each adult individual (a ‘poll transfer’ or ‘flat distribution’) income inequity in the population improves considerably. According to model simulations, this is because the out-of-pocket expenditure on road charges represents a higher share of the household income in low income groups than among the more affluent. Both of these scenarios represent clear trade-offs between equity and efficiency: equity can be improved by redistribution but only at the expense of the efficiency gains from the road pricing strategy.
Fridstrom et al (2000) suggest that in principle it is possible to conceive of a road-pricing scheme with revenue redistribution that enhances economic efficiency as well as equity. It will usually be sufficient to redistribute a certain component of the revenue generated in a progressive manner, in order to keep the less affluent households at least equally well off. The main reason why road pricing schemes do not lead to any deterioration in income distribution is that the more affluent people, exhibiting higher rates of car ownership and use, tend – in general – to incur higher road pricing expenditure.
### 6.5.2 Non-pricing mechanisms for providing equity in road use
While road pricing is one method of rationing road capacity, there are other transport demand management mechanisms that do not involve pricing. These include priority measures such as high occupancy vehicle lanes and alternative rationing schemes. Travel behaviour change initiatives are another non-pricing mechanism to improve equity by encouraging more efficient modes of transport and better access for people without a vehicle. These measures are aimed at reducing total vehicle traffic and encouraging the use of efficient modes. Many of these strategies support equity objectives by improving travel choices/alternatives or affordability, especially for low income or mobility-disadvantaged groups (Litman, 2000).
Australia currently has a number of high occupancy vehicle lanes, commonly referred to as ‘transit lanes’. Transit lanes provide travel priority by allowing specified users (usually two or more people per private vehicle and public transport vehicles) exclusive use of part of the roadway to travel through congested sections of road. Transit lanes provide a high degree of horizontal equity (because they do not discriminate in regard to who can participate). This option benefits all existing users, especially public transport users by reducing travel times.
Road rationing schemes designate a certain percentage of the travelling population to use a road link on certain days or times of day. Those who have not been designated to use the road link at a particular time may still do so upon payment of a toll. Rationing schemes have been applied in many countries, for example in Athens and several Brazilian cities, with varied results. In these cities, access prohibitions have led to increased multiple car ownership and average fleet age, and after some years they lose their effectiveness (Viegas, 2001). Because of these results Viegas (2001) suggests that the ‘ration’ should be attributed to individuals, not to vehicles, so it is useable for driving and for riding on public transport (this also serves as an incentive to shift to public transport). Attributing the ration to individuals instead of vehicles prevents misuse of the system by those who own more than one car (Viegas, 2001). Nevertheless, rationing schemes are associated with high administration costs and are open to abuse by both users and administrators.
These are ‘second-best’ options because of administrative, spatial or other deficiencies. However, under certain scenarios, they provide a valid response to tackling complex equity issues. | 2018-02-25T09:15:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2593521773815155, "perplexity": 2545.6558784235854}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891816351.97/warc/CC-MAIN-20180225090753-20180225110753-00410.warc.gz"} |
https://zbmath.org/authors/?q=ai%3Alandau.zeph-a | # zbMATH — the first resource for mathematics
## Landau, Zeph A.
Compute Distance To:
Author ID: landau.zeph-a Published as: Landau, Z.; Landau, Zeph; Landau, Zeph A. External Links: MGP · Math-Net.Ru · Wikidata
Documents Indexed: 32 Publications since 1995
all top 5
#### Co-Authors
2 single-authored 7 Balan, Radu V. 6 Aharonov, Dorit 6 Arad, Itai 6 Casazza, Peter George 6 Landau, Henry Jacob 5 Abrams, Aaron 5 Heil, Christopher E. 5 Pommersheim, James E. 4 Vazirani, Umesh V. 4 Zaslow, Eric 2 Jones, Vaughan Frederick Randal 2 Kempe, Julia 2 Lloyd, Seth 2 Regev, Oded 2 Sunder, Viakalathur S. 2 van Dam, Wim 2 Vidick, Thomas 1 Babson, Eric K. 1 Daubechies, Ingrid Chantal 1 Ganzell, Sandy 1 Gharibian, Sevag 1 Huang, Yichen 1 Kodiyalam, Vijay 1 Kuwahara, Tomotaka 1 Reid, O. 1 Russell, Alexander C. 1 Shin, Seung Woo 1 Su, Francis Edward 1 Yershov, I.
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#### Serials
3 The Journal of Fourier Analysis and Applications 2 Journal of Functional Analysis 2 SIAM Journal on Computing 1 Communications in Mathematical Physics 1 Israel Journal of Mathematics 1 Theory of Probability and its Applications 1 Geometriae Dedicata 1 Pacific Journal of Mathematics 1 Social Choice and Welfare 1 Algorithmica 1 Journal of Theoretical Probability 1 Random Structures & Algorithms 1 SIAM Review 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Indagationes Mathematicae. New Series 1 Applied and Computational Harmonic Analysis 1 Combinatorics, Probability and Computing 1 The Electronic Journal of Combinatorics 1 Advances in Computational Mathematics 1 Electronic Research Announcements of the American Mathematical Society 1 Journal of Statistical Mechanics: Theory and Experiment 1 Foundations and Trends in Theoretical Computer Science 1 Journal of Probability and Statistics
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#### Fields
9 Functional analysis (46-XX) 9 Computer science (68-XX) 8 Harmonic analysis on Euclidean spaces (42-XX) 8 Quantum theory (81-XX) 3 Probability theory and stochastic processes (60-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Combinatorics (05-XX) 2 Associative rings and algebras (16-XX) 2 Category theory; homological algebra (18-XX) 2 Manifolds and cell complexes (57-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Group theory and generalizations (20-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Operator theory (47-XX) 1 Statistics (62-XX) 1 Mechanics of particles and systems (70-XX) 1 Information and communication theory, circuits (94-XX)
#### Citations contained in zbMATH
26 Publications have been cited 412 times in 332 Documents Cited by Year
Gabor time-frequency lattices and the Wexler-Raz identity. Zbl 0888.47018
Daubechies, Ingrid; Landau, H. J.; Landau, Zeph
1995
Density, overcompleteness, and localization of frames. I: Theory. Zbl 1096.42014
Balan, Radu; Casazza, Peter G.; Heil, Christopher; Landau, Zeph
2006
Adiabatic quantum computation is equivalent to standard quantum computation. Zbl 1134.81009
Aharonov, Dorit; Van Dam, Wim; Kempe, Julia; Landau, Zeph; Lloyd, Seth; Regev, Oded
2007
Density, overcompleteness, and localization of frames. II: Gabor systems. Zbl 1097.42022
Balan, Radu; Casazza, Peter G.; Heil, Christopher; Landau, Zeph
2006
Deficits and excesses of frames. Zbl 1029.42030
Balan, Radu; Casazza, Peter G.; Heil, Christopher; Landau, Zeph
2003
Quantum Hamiltonian complexity. Zbl 1329.68117
Gharibian, Sevag; Huang, Yichen; Landau, Zeph; Shin, Seung Woo
2014
A polynomial quantum algorithm for approximating the Jones polynomial. Zbl 1301.68129
Aharonov, Dorit; Jones, Vaughan; Landau, Zeph
2006
Exchange relation planar algebras. Zbl 1022.46039
Landau, Zeph A.
2002
Adiabatic quantum computation is equivalent to standard quantum computation. Zbl 1152.81008
Aharonov, Dorit; van Dam, Wim; Kempe, Julia; Landau, Zeph; Lloyd, Seth; Regev, Oded
2008
The planar algebra associated to a Kac algebra. Zbl 1039.46049
Kodiyalam, Vijay; Landau, Zeph; Sunder, V. S.
2003
A polynomial quantum algorithm for approximating the Jones polynomial. Zbl 1191.68313
Aharonov, Dorit; Jones, Vaughan; Landau, Zeph
2009
Redundancy for localized frames. Zbl 1254.42037
Balan, Radu; Casazza, Pete; Landau, Zeph
2011
Random Cayley graphs are expanders: a simple proof of the Alon-Roichman theorem. Zbl 1053.05060
Landau, Zeph; Russell, Alexander
2004
Excesses of Gabor frames. Zbl 1028.42021
Balan, Radu; Casazza, Peter G.; Heil, Christopher; Landau, Zeph
2003
Quantum computation and the evaluation of tensor networks. Zbl 1209.68261
2010
The detectability lemma and quantum gap amplification. Zbl 1304.68049
Aharonov, Dorit; Arad, Itai; Landau, Zeph; Vazirani, Umesh
2009
Measure functions for frames. Zbl 1133.46012
2007
Density, overcompleteness, and localization of frames. Zbl 1142.42313
Balan, Radu; Casazza, Peter G.; Heil, Christopher; Landau, Zeph
2006
Fuss-Catalan algebras and chains of intermediate subfactors. Zbl 1055.46511
Landau, Zeph A.
2001
Rigorous RG algorithms and area laws for low energy eigenstates in 1D. Zbl 1376.81079
Arad, Itai; Landau, Zeph; Vazirani, Umesh; Vidick, Thomas
2017
Planar depth and planar subalgebras. Zbl 1030.46078
Landau, Zeph; Sunder, V. S.
2002
A fair division solution to the problem of redistricting. Zbl 1184.91189
Landau, Z.; Reid, O.; Yershov, I.
2009
On the trigonometric moment problem in two dimensions. Zbl 1258.42023
Landau, H. J.; Landau, Zeph
2012
Rigorous RG algorithms and area laws for low energy eigenstates in 1D. Zbl 1406.81101
Arad, Itai; Landau, Zeph; Vazirani, Umesh V.; Vidick, Thomas
2017
Fair division and redistricting. Zbl 1307.91156
Landau, Zeph; Su, Francis Edward
2014
The 1D area law and the complexity of quantum states: a combinatorial approach. Zbl 1292.81010
Aharonov, Dorit; Arad, Itai; Landau, Zeph; Vazirani, Umesh
2011
Rigorous RG algorithms and area laws for low energy eigenstates in 1D. Zbl 1376.81079
Arad, Itai; Landau, Zeph; Vazirani, Umesh; Vidick, Thomas
2017
Rigorous RG algorithms and area laws for low energy eigenstates in 1D. Zbl 1406.81101
Arad, Itai; Landau, Zeph; Vazirani, Umesh V.; Vidick, Thomas
2017
Quantum Hamiltonian complexity. Zbl 1329.68117
Gharibian, Sevag; Huang, Yichen; Landau, Zeph; Shin, Seung Woo
2014
Fair division and redistricting. Zbl 1307.91156
Landau, Zeph; Su, Francis Edward
2014
On the trigonometric moment problem in two dimensions. Zbl 1258.42023
Landau, H. J.; Landau, Zeph
2012
Redundancy for localized frames. Zbl 1254.42037
Balan, Radu; Casazza, Pete; Landau, Zeph
2011
The 1D area law and the complexity of quantum states: a combinatorial approach. Zbl 1292.81010
Aharonov, Dorit; Arad, Itai; Landau, Zeph; Vazirani, Umesh
2011
Quantum computation and the evaluation of tensor networks. Zbl 1209.68261
2010
A polynomial quantum algorithm for approximating the Jones polynomial. Zbl 1191.68313
Aharonov, Dorit; Jones, Vaughan; Landau, Zeph
2009
The detectability lemma and quantum gap amplification. Zbl 1304.68049
Aharonov, Dorit; Arad, Itai; Landau, Zeph; Vazirani, Umesh
2009
A fair division solution to the problem of redistricting. Zbl 1184.91189
Landau, Z.; Reid, O.; Yershov, I.
2009
Adiabatic quantum computation is equivalent to standard quantum computation. Zbl 1152.81008
Aharonov, Dorit; van Dam, Wim; Kempe, Julia; Landau, Zeph; Lloyd, Seth; Regev, Oded
2008
Adiabatic quantum computation is equivalent to standard quantum computation. Zbl 1134.81009
Aharonov, Dorit; Van Dam, Wim; Kempe, Julia; Landau, Zeph; Lloyd, Seth; Regev, Oded
2007
Measure functions for frames. Zbl 1133.46012
2007
Density, overcompleteness, and localization of frames. I: Theory. Zbl 1096.42014
Balan, Radu; Casazza, Peter G.; Heil, Christopher; Landau, Zeph
2006
Density, overcompleteness, and localization of frames. II: Gabor systems. Zbl 1097.42022
Balan, Radu; Casazza, Peter G.; Heil, Christopher; Landau, Zeph
2006
A polynomial quantum algorithm for approximating the Jones polynomial. Zbl 1301.68129
Aharonov, Dorit; Jones, Vaughan; Landau, Zeph
2006
Density, overcompleteness, and localization of frames. Zbl 1142.42313
Balan, Radu; Casazza, Peter G.; Heil, Christopher; Landau, Zeph
2006
Random Cayley graphs are expanders: a simple proof of the Alon-Roichman theorem. Zbl 1053.05060
Landau, Zeph; Russell, Alexander
2004
Deficits and excesses of frames. Zbl 1029.42030
Balan, Radu; Casazza, Peter G.; Heil, Christopher; Landau, Zeph
2003
The planar algebra associated to a Kac algebra. Zbl 1039.46049
Kodiyalam, Vijay; Landau, Zeph; Sunder, V. S.
2003
Excesses of Gabor frames. Zbl 1028.42021
Balan, Radu; Casazza, Peter G.; Heil, Christopher; Landau, Zeph
2003
Exchange relation planar algebras. Zbl 1022.46039
Landau, Zeph A.
2002
Planar depth and planar subalgebras. Zbl 1030.46078
Landau, Zeph; Sunder, V. S.
2002
Fuss-Catalan algebras and chains of intermediate subfactors. Zbl 1055.46511
Landau, Zeph A.
2001
Gabor time-frequency lattices and the Wexler-Raz identity. Zbl 0888.47018
Daubechies, Ingrid; Landau, H. J.; Landau, Zeph
1995
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#### Cited by 486 Authors
20 Gröchenig, Karlheinz 10 Han, Deguang 10 Lu, Songfeng 10 Sun, Jie 9 Sun, Wenchang 8 Casazza, Peter George 8 Heil, Christopher E. 8 Sun, Qiyu 7 Luef, Franz 7 Romero, José Luis 6 Balan, Radu V. 6 Christensen, Ole 6 Landau, Zeph A. 6 Liu, Fang 6 Shen, Zuowei 5 Feichtinger, Hans Georg 5 Kauffman, Louis Hirsch 5 Kodiyalam, Vijay 5 Koo, Yooyoung 5 Kutyniok, Gitta 5 Li, Yunzhang 5 Lim, Jae Kun 5 Liu, Zhengwei 5 Sunder, Viakalathur S. 4 Aharonov, Dorit 4 Gabardo, Jean-Pierre 4 Jakobsen, Mads Sielemann 4 Kashefi, Elham 4 Krishtal, Ilya Arkadievich 4 Li, Shidong 4 Pfander, Götz E. 3 Brandão, Fernando G. S. L. 3 Cirac, Juan Ignacio 3 Freedman, Michael Hartley 3 Grossman, Pinhas 3 Ji, Hui 3 Kaiblinger, Norbert 3 Lidar, Daniel A. 3 Lomonaco, Samuel J. jun. 3 Morrison, Scott 3 Myers, Robert C. 3 Strohmer, Thomas 2 Aldroubi, Akram 2 Antezana, Jorge 2 Arad, Itai 2 Bakshi, Keshab Chandra 2 Balazs, Peter 2 Baskakov, Anatoliĭ Grigor’evich 2 Bhattacharyya, Arpan 2 Bishop, Shannon 2 Bravyi, Sergey B. 2 Cabrelli, Carlos A. 2 Choi, Vicky Siu-Ngan 2 Corach, Gustavo 2 Cui, Shawn Xingshan 2 Das, Paramita 2 De, Sandipan 2 Dutkay, Dorin Ervin 2 Eldar, Lior 2 Fan, Zhitao 2 Futamura, Fumiko 2 Gao, Chao 2 Ge, Yimin 2 Geraci, Joseph 2 Geronimo, Jeffrey S. 2 Ghosh, Shamindra Kumar 2 Gosset, David 2 Grohs, Philipp 2 Gupta, Ved Prakash 2 Haimi, Antti 2 Janssen, Augustus Josephus Elizabeth Maria 2 Jones, Vaughan Frederick Randal 2 Kastoryano, Michael J. 2 Krovi, Hari 2 Kuperberg, Gregory John 2 Labate, Demetrio 2 Lammers, Mark C. 2 Larson, David Royal 2 Leinert, Michael 2 Lemm, Marius 2 Lemvig, Jakob 2 Liu, Bei 2 Matusiak, Ewa 2 Mitkovski, Mishko 2 Molter, Ursula Maria 2 Ogawa, Hidemitsu 2 Ortega-Cerdà, Joaquim 2 Palcoux, Sebastien 2 Pérez-García, David 2 Peters, Emily 2 Powell, Alexander M. 2 Ren, Yunxiang 2 Ron, Amos 2 Ruiz, Mariano A. 2 Rzeszotnik, Ziemowit 2 Severini, Simone 2 Snyder, Noah 2 Søndergaard, Peter L. 2 Stöckler, Joachim 2 Stoeva, Diana T. ...and 386 more Authors
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#### Cited in 106 Serials
24 Journal of Functional Analysis 24 The Journal of Fourier Analysis and Applications 22 Quantum Information Processing 18 Applied and Computational Harmonic Analysis 14 Journal of Mathematical Physics 11 Transactions of the American Mathematical Society 9 Journal of Mathematical Analysis and Applications 8 Communications in Mathematical Physics 8 Journal of High Energy Physics 7 Advances in Mathematics 6 Journal of Approximation Theory 6 Proceedings of the American Mathematical Society 6 Advances in Computational Mathematics 5 International Journal of Mathematics 5 International Journal of Quantum Information 4 International Journal of Theoretical Physics 4 Monatshefte für Mathematik 4 Numerical Functional Analysis and Optimization 4 Acta Applicandae Mathematicae 4 The Journal of Geometric Analysis 4 Linear Algebra and its Applications 4 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 4 New Journal of Physics 3 Journal of Statistical Physics 3 Integral Equations and Operator Theory 3 SIAM Journal on Computing 3 Theoretical Computer Science 3 MSCS. Mathematical Structures in Computer Science 3 Journal of Physics A: Mathematical and Theoretical 2 Letters in Mathematical Physics 2 Reviews of Modern Physics 2 Results in Mathematics 2 Advances in Applied Mathematics 2 Constructive Approximation 2 Journal of the American Mathematical Society 2 Random Structures & Algorithms 2 Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences 2 Annals of Physics 2 Electronic Research Announcements of the American Mathematical Society 2 Open Systems & Information Dynamics 2 Acta Mathematica Sinica. English Series 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Banach Journal of Mathematical Analysis 1 Computers & Mathematics with Applications 1 Israel Journal of Mathematics 1 Linear and Multilinear Algebra 1 Mathematical Notes 1 Physics Letters. A 1 Physics Reports 1 Theoretical and Mathematical Physics 1 Mathematics of Computation 1 Chaos, Solitons and Fractals 1 Annales de l’Institut Fourier 1 Applied Mathematics and Computation 1 Duke Mathematical Journal 1 Inventiones Mathematicae 1 Journal of Algebra 1 Journal of Computational and Applied Mathematics 1 Journal of Pure and Applied Algebra 1 Mathematische Nachrichten 1 Michigan Mathematical Journal 1 Osaka Journal of Mathematics 1 Pacific Journal of Mathematics 1 European Journal of Combinatorics 1 Combinatorica 1 Circuits, Systems, and Signal Processing 1 Physica D 1 Social Choice and Welfare 1 Statistical Science 1 Revista Matemática Iberoamericana 1 Mathematical and Computer Modelling 1 SIAM Journal on Discrete Mathematics 1 Journal of Scientific Computing 1 Machine Learning 1 Proceedings of the National Academy of Sciences of the United States of America 1 SIAM Review 1 Journal of Knot Theory and its Ramifications 1 Russian Journal of Mathematical Physics 1 Journal of Mathematical Sciences (New York) 1 Annales Mathématiques Blaise Pascal 1 Advances in Applied Clifford Algebras 1 Selecta Mathematica. New Series 1 Mathematical Communications 1 Theory of Computing Systems 1 Journal of Inequalities and Applications 1 Revista Matemática Complutense 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Annales Henri Poincaré 1 Algebraic & Geometric Topology 1 Journal of the Australian Mathematical Society 1 Journal of Systems Science and Complexity 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 Multiscale Modeling & Simulation 1 Sampling Theory in Signal and Image Processing 1 Analysis and Applications (Singapore) 1 International Journal of Wavelets, Multiresolution and Information Processing 1 Journal of Function Spaces and Applications 1 Complex Analysis and Operator Theory 1 Ars Mathematica Contemporanea 1 Physical Review A, Third Series ...and 6 more Serials
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#### Cited in 42 Fields
158 Harmonic analysis on Euclidean spaces (42-XX) 111 Quantum theory (81-XX) 78 Functional analysis (46-XX) 56 Computer science (68-XX) 42 Information and communication theory, circuits (94-XX) 39 Operator theory (47-XX) 23 Statistical mechanics, structure of matter (82-XX) 21 Approximations and expansions (41-XX) 16 Combinatorics (05-XX) 16 Manifolds and cell complexes (57-XX) 16 Numerical analysis (65-XX) 13 Abstract harmonic analysis (43-XX) 8 Category theory; homological algebra (18-XX) 7 Linear and multilinear algebra; matrix theory (15-XX) 7 Associative rings and algebras (16-XX) 7 Group theory and generalizations (20-XX) 7 Relativity and gravitational theory (83-XX) 6 Partial differential equations (35-XX) 6 Probability theory and stochastic processes (60-XX) 5 Number theory (11-XX) 5 Topological groups, Lie groups (22-XX) 4 Order, lattices, ordered algebraic structures (06-XX) 4 Operations research, mathematical programming (90-XX) 3 Algebraic geometry (14-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Mathematical logic and foundations (03-XX) 2 Functions of a complex variable (30-XX) 2 Special functions (33-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Integral transforms, operational calculus (44-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Statistics (62-XX) 2 Mechanics of particles and systems (70-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 History and biography (01-XX) 1 Nonassociative rings and algebras (17-XX) 1 $$K$$-theory (19-XX) 1 Potential theory (31-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Difference and functional equations (39-XX) 1 Sequences, series, summability (40-XX) 1 Biology and other natural sciences (92-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2021-01-20T18:07:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4152829051017761, "perplexity": 9347.359015512617}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703521139.30/warc/CC-MAIN-20210120151257-20210120181257-00582.warc.gz"} |
https://www.futurelearn.com/info/courses/python-in-hpc/0/steps/65109 | £199.99 £139.99 for one year of Unlimited learning. Offer ends on 28 February 2023 at 23:59 (UTC). T&Cs apply
Linear algebra and polynomials
In this article we briefly introduce some of NumPy's linear algebra and
polynomial functionality.
© CC-BY-NC-SA 4.0 by CSC - IT Center for Science Ltd.
Linear algebra
NumPy includes linear algebra routines that can be quite handy.
For example, NumPy can calculate matrix and vector products efficiently (dot,
vdot), solve eigenproblems (linalg.eig, linalg.eigvals), solve linear
systems (linalg.solve), and do matrix inversion (linalg.inv).
A = numpy.array(((2, 1), (1, 3)))B = numpy.array(((-2, 4.2), (4.2, 6)))C = numpy.dot(A, B)b = numpy.array((1, 2))print(C)# output:# [[ 0.2 14.4]# [ 10.6 22.2]]print(b)# output: [1 2]# solve C x = bx = numpy.linalg.solve(C, b)print(x)# output: [ 0.04453441 0.06882591]
Normally, NumPy utilises high performance numerical libraries in linear
algebra operations. This means that the performance of NumPy is actually quite
good and not far e.g. from the performance of a pure-C implementations using
the same libraries.
Polynomials
NumPy has also support for polynomials. One can for example do least square
fitting, find the roots of a polynomial, and evaluate a polynomial.
A polynomial f(x) is defined by an 1D array of coefficients (p) with
length N, such that (f(x) = p[0] x^{N-1} + p[1] x^{N-2} + … + p[N-1]).
# f(x) = x^2 + random noise (between 0,1)x = numpy.linspace(-4, 4, 7)f = x**2 + numpy.random.random(x.shape)p = numpy.polyfit(x, f, 2)print(p)# output: [ 0.96869003 -0.01157275 0.69352514]# f(x) = p[0] * x^2 + p[1] * x + p[2]
© CC-BY-NC-SA 4.0 by CSC - IT Center for Science Ltd. | 2023-01-27T04:37:24 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3870032727718353, "perplexity": 10451.75815172144}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764494936.89/warc/CC-MAIN-20230127033656-20230127063656-00787.warc.gz"} |
https://dergipark.org.tr/tr/pub/ujma | ISSN: 2619-9653
Başlangıç: 2018
Yayın Aralığı: 3 Ayda 1
Yayıncı: Emrah Evren KARA
### Hakkında
Universal Journal of Mathematics and Applications (UJMA) (Univers. J. Math. Appl.) is an international and peer-reviewed journal which publishes high quality papers on pure and applied mathematics. To be published in this journal, a paper must contain new ideas and be of interest to a wide range of readers. Survey papers are also welcome. Similarity percentage must be less than 30% without bibliography.
No submission or processing fees are required. The journal appears in 4 numbers per year (March, June, September and December) and has been published since 2018.
Coverage touches on a wide variety of topics, including but not limited to
• Functional analysis and operator theory
• Real and harmonic analysis
• Complex analysis
• Partial differential equations
• Control and Optimization
• Probability
• Applied mathematics
• Convex and Geometric Analysis
The average time during which the preliminary assessment of manuscripts is conducted: 3 days
The average time during which the reviews of manuscripts are conducted: 60 days
The average time in which the article is published: 90 days
Son Sayılar
### 2022 - Cilt: 5 Sayı: 4
Araştırma Makalesi
2. Singular Perturbations of Multibrot Set Polynomials
Araştırma Makalesi
3. On a Rational $(P+1)$th Order Difference Equation with Quadratic Term
Araştırma Makalesi
4. Binomial Transform for Quadra Fibona-Pell Sequence and Quadra Fibona-Pell Quaternion
Araştırma Makalesi
5. Periodic Korovkin Theorem via $P_{p}^{2}$-Statistical $\mathcal{A}$-Summation Process
The published articles in UJMA are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. | 2023-01-28T11:13:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1842675656080246, "perplexity": 9090.702816488678}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499541.63/warc/CC-MAIN-20230128090359-20230128120359-00262.warc.gz"} |
https://zims-en.kiwix.campusafrica.gos.orange.com/wikipedia_en_all_nopic/A/Numerical_methods_for_linear_least_squares | # Numerical methods for linear least squares
Numerical methods for linear least squares entails the numerical analysis of linear least squares problems.
## Introduction
A general approach to the least squares problem ${\displaystyle \operatorname {\,min} \,{\big \|}\mathbf {y} -X{\boldsymbol {\beta }}{\big \|}^{2}}$ can be described as follows. Suppose that we can find an n by m matrix S such that XS is an orthogonal projection onto the image of X. Then a solution to our minimization problem is given by
${\displaystyle {\boldsymbol {\beta }}=S\mathbf {y} }$
simply because
${\displaystyle X{\boldsymbol {\beta }}=X(S\mathbf {y} )=(XS)\mathbf {y} }$
is exactly a sought for orthogonal projection of ${\displaystyle \mathbf {y} }$ onto an image of X (see the picture below and note that as explained in the next section the image of X is just a subspace generated by column vectors of X). A few popular ways to find such a matrix S are described below.
## Inverting the matrix of the normal equations
The algebraic solution of the normal equations with a full-rank matrix XTX can be written as
${\displaystyle {\hat {\boldsymbol {\beta }}}=(\mathbf {X} ^{\rm {T}}\mathbf {X} )^{-1}\mathbf {X} ^{\rm {T}}\mathbf {y} =\mathbf {X} ^{+}\mathbf {y} }$
where X+ is the Moore–Penrose pseudoinverse of X. Although this equation is correct and can work in many applications, it is not computationally efficient to invert the normal-equations matrix (the Gramian matrix). An exception occurs in numerical smoothing and differentiation where an analytical expression is required.
If the matrix XTX is well-conditioned and positive definite, implying that it has full rank, the normal equations can be solved directly by using the Cholesky decomposition RTR, where R is an upper triangular matrix, giving:
${\displaystyle R^{\rm {T}}R{\hat {\boldsymbol {\beta }}}=X^{\rm {T}}\mathbf {y} .}$
The solution is obtained in two stages, a forward substitution step, solving for z:
${\displaystyle R^{\rm {T}}\mathbf {z} =X^{\rm {T}}\mathbf {y} ,}$
followed by a backward substitution, solving for ${\displaystyle {\hat {\boldsymbol {\beta }}}}$:
${\displaystyle R{\hat {\boldsymbol {\beta }}}=\mathbf {z} .}$
Both substitutions are facilitated by the triangular nature of R.
## Orthogonal decomposition methods
Orthogonal decomposition methods of solving the least squares problem are slower than the normal equations method but are more numerically stable because they avoid forming the product XTX.
The residuals are written in matrix notation as
${\displaystyle \mathbf {r} =\mathbf {y} -X{\hat {\boldsymbol {\beta }}}.}$
The matrix X is subjected to an orthogonal decomposition, e.g., the QR decomposition as follows.
${\displaystyle X=Q{\begin{pmatrix}R\\0\end{pmatrix}}\ }$,
where Q is an m×m orthogonal matrix (QTQ=I) and R is an n×n upper triangular matrix with ${\displaystyle r_{ii}>0}$.
The residual vector is left-multiplied by QT.
${\displaystyle Q^{\rm {T}}\mathbf {r} =Q^{\rm {T}}\mathbf {y} -\left(Q^{\rm {T}}Q\right){\begin{pmatrix}R\\0\end{pmatrix}}{\hat {\boldsymbol {\beta }}}={\begin{bmatrix}\left(Q^{\rm {T}}\mathbf {y} \right)_{n}-R{\hat {\boldsymbol {\beta }}}\\\left(Q^{\rm {T}}\mathbf {y} \right)_{m-n}\end{bmatrix}}={\begin{bmatrix}\mathbf {u} \\\mathbf {v} \end{bmatrix}}}$
Because Q is orthogonal, the sum of squares of the residuals, s, may be written as:
${\displaystyle s=\|\mathbf {r} \|^{2}=\mathbf {r} ^{\rm {T}}\mathbf {r} =\mathbf {r} ^{\rm {T}}QQ^{\rm {T}}\mathbf {r} =\mathbf {u} ^{\rm {T}}\mathbf {u} +\mathbf {v} ^{\rm {T}}\mathbf {v} }$
Since v doesn't depend on β, the minimum value of s is attained when the upper block, u, is zero. Therefore, the parameters are found by solving:
${\displaystyle R{\hat {\boldsymbol {\beta }}}=\left(Q^{\rm {T}}\mathbf {y} \right)_{n}.}$
These equations are easily solved as R is upper triangular.
An alternative decomposition of X is the singular value decomposition (SVD)[1]
${\displaystyle X=U\Sigma V^{\rm {T}}\ }$,
where U is m by m orthogonal matrix, V is n by n orthogonal matrix and ${\displaystyle \Sigma }$ is an m by n matrix with all its elements outside of the main diagonal equal to 0. The pseudoinverse of ${\displaystyle \Sigma }$ is easily obtained by inverting its non-zero diagonal elements and transposing. Hence,
${\displaystyle \mathbf {X} \mathbf {X} ^{+}=U\Sigma V^{\rm {T}}V\Sigma ^{+}U^{\rm {T}}=UPU^{\rm {T}},}$
where P is obtained from ${\displaystyle \Sigma }$ by replacing its non-zero diagonal elements with ones. Since ${\displaystyle (\mathbf {X} \mathbf {X} ^{+})^{*}=\mathbf {X} \mathbf {X} ^{+}}$ (the property of pseudoinverse), the matrix ${\displaystyle UPU^{\rm {T}}}$ is an orthogonal projection onto the image (column-space) of X. In accordance with a general approach described in the introduction above (find XS which is an orthogonal projection),
${\displaystyle S=\mathbf {X} ^{+}}$,
and thus,
${\displaystyle \beta =V\Sigma ^{+}U^{\rm {T}}\mathbf {y} }$
is a solution of a least squares problem. This method is the most computationally intensive, but is particularly useful if the normal equations matrix, XTX, is very ill-conditioned (i.e. if its condition number multiplied by the machine's relative round-off error is appreciably large). In that case, including the smallest singular values in the inversion merely adds numerical noise to the solution. This can be cured with the truncated SVD approach, giving a more stable and exact answer, by explicitly setting to zero all singular values below a certain threshold and so ignoring them, a process closely related to factor analysis.
## Discussion
The numerical methods for linear least squares are important because linear regression models are among the most important types of model, both as formal statistical models and for exploration of data-sets. The majority of statistical computer packages contain facilities for regression analysis that make use of linear least squares computations. Hence it is appropriate that considerable effort has been devoted to the task of ensuring that these computations are undertaken efficiently and with due regard to round-off error.
Individual statistical analyses are seldom undertaken in isolation, but rather are part of a sequence of investigatory steps. Some of the topics involved in considering numerical methods for linear least squares relate to this point. Thus important topics can be
• Computations where a number of similar, and often nested, models are considered for the same data-set. That is, where models with the same dependent variable but different sets of independent variables are to be considered, for essentially the same set of data-points.
• Computations for analyses that occur in a sequence, as the number of data-points increases.
• Special considerations for very extensive data-sets.
Fitting of linear models by least squares often, but not always, arise in the context of statistical analysis. It can therefore be important that considerations of computation efficiency for such problems extend to all of the auxiliary quantities required for such analyses, and are not restricted to the formal solution of the linear least squares problem.
Matrix calculations, like any other, are affected by rounding errors. An early summary of these effects, regarding the choice of computation methods for matrix inversion, was provided by Wilkinson.[2]
## References
1. Lawson, C. L.; Hanson, R. J. (1974). Solving Least Squares Problems. Englewood Cliffs, NJ: Prentice-Hall. ISBN 0-13-822585-0.
2. Wilkinson, J.H. (1963) "Chapter 3: Matrix Computations", Rounding Errors in Algebraic Processes, London: Her Majesty's Stationery Office (National Physical Laboratory, Notes in Applied Science, No.32)
• Ake Bjorck, Numerical Methods for Least Squares Problems, SIAM, 1996.
• R. W. Farebrother, Linear Least Squares Computations, CRC Press, 1988.
• Barlow, Jesse L. (1993), "Chapter 9: Numerical aspects of Solving Linear Least Squares Problems", in Rao, C. R. (ed.), Computational Statistics, Handbook of Statistics, 9, North-Holland, ISBN 0-444-88096-8
• Björck, Åke (1996). Numerical methods for least squares problems. Philadelphia: SIAM. ISBN 0-89871-360-9.
• Goodall, Colin R. (1993), "Chapter 13: Computation using the QR decomposition", in Rao, C. R. (ed.), Computational Statistics, Handbook of Statistics, 9, North-Holland, ISBN 0-444-88096-8
• National Physical Laboratory (1961), "Chapter 1: Linear Equations and Matrices: Direct Methods", Modern Computing Methods, Notes on Applied Science, 16 (2nd ed.), Her Majesty's Stationery Office
• National Physical Laboratory (1961), "Chapter 2: Linear Equations and Matrices: Direct Methods on Automatic Computers", Modern Computing Methods, Notes on Applied Science, 16 (2nd ed.), Her Majesty's Stationery Office
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files. | 2022-12-05T04:03:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 24, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7826239466667175, "perplexity": 752.7908611219123}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711003.56/warc/CC-MAIN-20221205032447-20221205062447-00007.warc.gz"} |
https://www.zbmath.org/authors/?q=ai%3Arhines.peter-b | # zbMATH — the first resource for mathematics
## Rhines, Peter B.
Compute Distance To:
Author ID: rhines.peter-b Published as: Rhines, P. B.; Rhines, Peter; Rhines, Peter B. External Links: MGP · Wikidata
Documents Indexed: 13 Publications since 1969
all top 5
#### Co-Authors
6 single-authored 3 Young, William R. 2 Lindahl, E. G. 1 Afanasyev, Yakov D. 1 Bretherton, Francis P. 1 Dewar, William K. 1 Méndez, Arturo J. 1 Thomas, Leif N.
#### Serials
7 Journal of Fluid Mechanics 2 Geophysical and Astrophysical Fluid Dynamics 1 Physics of Fluids
all top 5
#### Fields
12 Fluid mechanics (76-XX) 9 Geophysics (86-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Numerical analysis (65-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Astronomy and astrophysics (85-XX)
#### Citations contained in zbMATH Open
12 Publications have been cited 258 times in 244 Documents Cited by Year
How rapidly is a passive scalar mixed within closed streamlines. Zbl 0576.76088
Rhines, P. B.
1983
Waves and Turbulence on a beta-plane. Zbl 0366.76043
Rhines, Peter B.
1975
Homogenization of potential vorticity in planetary gyres. Zbl 0497.76032
Rhines, Peter B.; Young, William R.
1982
Slowoscillations in an ocean of varying depth. I: Abrupt topography. II: Islands and seamounts. Zbl 0175.52803
Rhines, P. B.
1969
Topographic Rossby waves in a rough-bottomed ocean. Zbl 0271.76017
Rhines, Peter; Bretherton, Francis
1973
Geostrophic turbulence. Zbl 0474.76054
Rhines, Peter B.
1979
Optical altimetry: a new method for observing rotating fluids with applications to Rossby and inertial waves on a polar beta-plane. Zbl 1106.76318
Rhines, P. B.; Lindahl, E. G.; Mendez, A. J.
2007
Lectures in geophysical fluid dynamics. Zbl 0543.76058
Rhines, Peter B.
1983
Vortices and rossby waves in cylinder wakes on a parabolic $$\beta$$-plane observed by altimetric imaging velocimetry. Zbl 1182.76005
Afanasyev, Y. D.; Rhines, P. B.; Lindahl, E. G.
2008
Nonlinear stratified spin-up. Zbl 1129.76373
Thomas, Leif N.; Rhines, Peter B.
2002
Vorticity dynamics of the oceanic general circulation. Zbl 0634.76020
Rhines, Peter B.
1986
The nonlinear spin-up of a stratified ocean. Zbl 0598.76046
Dewar, William K.; Rhines, Peter B.; Young, William R.
1984
Vortices and rossby waves in cylinder wakes on a parabolic $$\beta$$-plane observed by altimetric imaging velocimetry. Zbl 1182.76005
Afanasyev, Y. D.; Rhines, P. B.; Lindahl, E. G.
2008
Optical altimetry: a new method for observing rotating fluids with applications to Rossby and inertial waves on a polar beta-plane. Zbl 1106.76318
Rhines, P. B.; Lindahl, E. G.; Mendez, A. J.
2007
Nonlinear stratified spin-up. Zbl 1129.76373
Thomas, Leif N.; Rhines, Peter B.
2002
Vorticity dynamics of the oceanic general circulation. Zbl 0634.76020
Rhines, Peter B.
1986
The nonlinear spin-up of a stratified ocean. Zbl 0598.76046
Dewar, William K.; Rhines, Peter B.; Young, William R.
1984
How rapidly is a passive scalar mixed within closed streamlines. Zbl 0576.76088
Rhines, P. B.
1983
Lectures in geophysical fluid dynamics. Zbl 0543.76058
Rhines, Peter B.
1983
Homogenization of potential vorticity in planetary gyres. Zbl 0497.76032
Rhines, Peter B.; Young, William R.
1982
Geostrophic turbulence. Zbl 0474.76054
Rhines, Peter B.
1979
Waves and Turbulence on a beta-plane. Zbl 0366.76043
Rhines, Peter B.
1975
Topographic Rossby waves in a rough-bottomed ocean. Zbl 0271.76017
Rhines, Peter; Bretherton, Francis
1973
Slowoscillations in an ocean of varying depth. I: Abrupt topography. II: Islands and seamounts. Zbl 0175.52803
Rhines, P. B.
1969
all top 5
#### Cited by 387 Authors
12 Bedrossian, Jacob 8 Johnson, Edward Robert 6 Coti Zelati, Michele 5 Berloff, Pavel S. 5 Galperin, Boris 5 Gilbert, Andrew D. 5 Sukoriansky, Semion 4 Bernoff, Andrew J. 4 Carnevale, George F. 4 Dritschel, David Gerard 4 Flierl, Glenn R. 4 Holloway, Greg 4 Lingevitch, Joseph F. 4 Nazarenko, Sergeĭ Vital’evich 4 Scott, Richard K. 4 Smith, Leslie M. 3 Afanasyev, Yakov D. 3 Camassa, Roberto 3 Chini, Gregory P. 3 Connaughton, Colm P. 3 Haynes, Peter H. 3 Majda, Andrew J. 3 Masmoudi, Nader 3 McWilliams, James C. 3 Obuse, Kiori 3 Shepherd, Theodore G. 3 Swaters, Gordon E. 3 Takehiro, Shin-Ichi 3 Tran, Chuong V. 3 Turner, Matthew R. 3 Vicol, Vlad C. 3 Villermaux, Emmanuel 3 Yamada, Michio 3 Young, William R. 2 Alobaidi, Ghada 2 Bakas, Nikolaos A. 2 Balk, Alexander M. 2 Bar-Yoseph, Pinhas Z. 2 Carrière, Philippe 2 Caulfield, C. P. 2 Dellar, Paul J. 2 Duplat, Jérôme 2 Esler, J. G. 2 Fox-Kemper, Baylor 2 Gelfgat, Alexander Yu. 2 Germain, Pierre 2 Gurarie, David 2 He, Siming 2 Held, Isaac M. 2 Hendershott, Myrl C. 2 Huang, Huei-Ping 2 Ioannou, Petros J. 2 Iyer, Gautam 2 Izrailsky, Yu. G. 2 Jones, Stephen M. R. 2 Kamenkovich, I. 2 Kamm, Roger D. 2 Khatri, Hemant 2 Koshel, Konstantin V. 2 Kozlov, V. F. 2 Legras, Bernard 2 Maas, Leo R. M. 2 Mallier, Roland 2 McLaughlin, Richard M. 2 Mei, Chiang C. 2 Moffatt, Henry Keith 2 Moulton, Derek E. 2 Novikov, Alexei 2 Nozawa, Toru 2 Pierrehumbert, Raymond T. 2 Pomeau, Yves 2 Poulin, Francis J. 2 Prahalad, Y. S. 2 Pullin, Dale I. 2 Pumir, Alain 2 Qi, Di 2 Quinn, Brenda E. 2 Rhines, Peter B. 2 Ryzhik, Lenya 2 Salmon, Rick 2 Shao, Sally 2 Smith, Ronald B. 2 Staroselsky, Ilya 2 Swanson, Kyle L. 2 Turney, B. W. 2 Vallis, Geoffrey K. 2 Vanneste, Jacques 2 Viotti, Claudio 2 Wang, Fei 2 Warneford, Emma S. 2 Waters, Sarah Louise 2 Wordsworth, R. D. 2 Yarin, Alexander L. 2 Yoden, Shigeo 1 Afanas’ev, Ya. D. 1 Agrawal, Shobha 1 Ait-Chaalal, Farid 1 Arbic, Brian K. 1 Aubert, Julien 1 Auclair, Francis ...and 287 more Authors
all top 5
#### Cited in 53 Serials
90 Journal of Fluid Mechanics 49 Physics of Fluids 18 Geophysical and Astrophysical Fluid Dynamics 13 Physica D 3 Archive for Rational Mechanics and Analysis 3 Communications in Mathematical Physics 3 Journal of Computational Physics 3 Physics of Fluids, A 3 Chaos, Solitons and Fractals 3 Chaos 3 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 Journal of Engineering Mathematics 2 Journal of Statistical Physics 2 Physica A 2 Wave Motion 2 Applied Mathematics and Computation 2 Probability Theory and Related Fields 2 Journal of Nonlinear Science 2 European Journal of Mechanics. B. Fluids 2 Annals of PDE 2 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Acta Mechanica 1 Bulletin of the Australian Mathematical Society 1 Computers & Mathematics with Applications 1 Fluid Dynamics 1 International Journal for Numerical Methods in Fluids 1 Physics Reports 1 Journal of Differential Equations 1 Journal of Functional Analysis 1 Memoirs of the American Mathematical Society 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Studies in Applied Mathematics 1 Chinese Annals of Mathematics. Series B 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Applied Numerical Mathematics 1 Numerical Methods for Partial Differential Equations 1 Japan Journal of Industrial and Applied Mathematics 1 Applied Mathematical Modelling 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 SIAM Journal on Applied Mathematics 1 SIAM Journal on Mathematical Analysis 1 Bulletin of the American Mathematical Society. New Series 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Annales Mathématiques Blaise Pascal 1 Russian Journal of Numerical Analysis and Mathematical Modelling 1 Discrete and Continuous Dynamical Systems 1 Mathematical Problems in Engineering 1 New Journal of Physics 1 Regular and Chaotic Dynamics 1 Combustion Theory and Modelling 1 Nonlinear Analysis. Theory, Methods & Applications 1 Research in the Mathematical Sciences
all top 5
#### Cited in 14 Fields
224 Fluid mechanics (76-XX) 64 Geophysics (86-XX) 31 Partial differential equations (35-XX) 14 Dynamical systems and ergodic theory (37-XX) 9 Astronomy and astrophysics (85-XX) 8 Numerical analysis (65-XX) 8 Classical thermodynamics, heat transfer (80-XX) 4 Probability theory and stochastic processes (60-XX) 4 Biology and other natural sciences (92-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Integral equations (45-XX) 1 Differential geometry (53-XX) 1 Mechanics of deformable solids (74-XX) 1 Quantum theory (81-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2021-06-24T02:36:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2810673415660858, "perplexity": 11783.713490602257}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488550571.96/warc/CC-MAIN-20210624015641-20210624045641-00549.warc.gz"} |
https://dlmf.nist.gov/25.16 | # §25.16 Mathematical Applications
## §25.16(i) Distribution of Primes
In studying the distribution of primes $p\leq x$, Chebyshev (1851) introduced a function $\psi\left(x\right)$ (not to be confused with the digamma function used elsewhere in this chapter), given by
25.16.1 $\psi\left(x\right)=\sum_{m=1}^{\infty}\sum_{p^{m}\leq x}\ln p,$ ⓘ Defines: $\psi\left(\NVar{x}\right)$: Chebyshev $\psi$-function Symbols: $\ln\NVar{z}$: principal branch of logarithm function, $m$: nonnegative integer, $p$: prime number and $x$: real variable Permalink: http://dlmf.nist.gov/25.16.E1 Encodings: TeX, pMML, png See also: Annotations for 25.16(i), 25.16 and 25
which is related to the Riemann zeta function by
25.16.2 $\psi\left(x\right)=x-\frac{\zeta'\left(0\right)}{\zeta\left(0\right)}-\sum_{% \rho}\frac{x^{\rho}}{\rho}+o\left(1\right),$ $x\to\infty$,
where the sum is taken over the nontrivial zeros $\rho$ of $\zeta\left(s\right)$.
The prime number theorem (27.2.3) is equivalent to the statement
25.16.3 $\psi\left(x\right)=x+o\left(x\right),$ $x\to\infty$. ⓘ Symbols: $\psi\left(\NVar{x}\right)$: Chebyshev $\psi$-function, $o\left(\NVar{x}\right)$: order less than and $x$: real variable Referenced by: §25.10(i) Permalink: http://dlmf.nist.gov/25.16.E3 Encodings: TeX, pMML, png See also: Annotations for 25.16(i), 25.16 and 25
The Riemann hypothesis is equivalent to the statement
25.16.4 $\psi\left(x\right)=x+O\left(x^{\frac{1}{2}+\epsilon}\right),$ $x\to\infty$, ⓘ Symbols: $O\left(\NVar{x}\right)$: order not exceeding, $\psi\left(\NVar{x}\right)$: Chebyshev $\psi$-function and $x$: real variable Referenced by: §25.16(i) Permalink: http://dlmf.nist.gov/25.16.E4 Encodings: TeX, pMML, png See also: Annotations for 25.16(i), 25.16 and 25
for every $\epsilon>0$.
## §25.16(ii) Euler Sums
Euler sums have the form
25.16.5 $H\left(s\right)=\sum_{n=1}^{\infty}\frac{h(n)}{n^{s}},$ ⓘ Symbols: $H\left(\NVar{s}\right)$: Euler sums, $n$: nonnegative integer, $s$: complex variable and $h(n)$: sum Permalink: http://dlmf.nist.gov/25.16.E5 Encodings: TeX, pMML, png See also: Annotations for 25.16(ii), 25.16 and 25
where $h(n)$ is given by (25.11.33).
$H\left(s\right)$ is analytic for $\Re s>1$, and can be extended meromorphically into the half-plane $\Re s>-2k$ for every positive integer $k$ by use of the relations
25.16.6 $H\left(s\right)=-\zeta'\left(s\right)+\gamma\zeta\left(s\right)+\frac{1}{2}% \zeta\left(s+1\right)+\sum_{r=1}^{k}\zeta\left(1-2r\right)\zeta\left(s+2r% \right)+\sum_{n=1}^{\infty}\frac{1}{n^{s}}\int_{n}^{\infty}\frac{\widetilde{B}% _{2k+1}\left(x\right)}{x^{2k+2}}\mathrm{d}x,$
25.16.7 $H\left(s\right)=\frac{1}{2}\zeta\left(s+1\right)+\frac{\zeta\left(s\right)}{s-% 1}-\sum_{r=1}^{k}\genfrac{(}{)}{0.0pt}{}{s+2r-2}{2r-1}\zeta\left(1-2r\right)% \zeta\left(s+2r\right)-\genfrac{(}{)}{0.0pt}{}{s+2k}{2k+1}\sum_{n=1}^{\infty}% \frac{1}{n}\int_{n}^{\infty}\frac{\widetilde{B}_{2k+1}\left(x\right)}{x^{s+2k+% 1}}\mathrm{d}x.$
For integer $s$ ($\geq 2$), $H\left(s\right)$ can be evaluated in terms of the zeta function:
25.16.8 $\displaystyle H\left(2\right)$ $\displaystyle=2\zeta\left(3\right),$ $\displaystyle H\left(3\right)$ $\displaystyle=\tfrac{5}{4}\zeta\left(4\right),$ ⓘ Symbols: $H\left(\NVar{s}\right)$: Euler sums and $\zeta\left(\NVar{s}\right)$: Riemann zeta function Permalink: http://dlmf.nist.gov/25.16.E8 Encodings: TeX, TeX, pMML, pMML, png, png See also: Annotations for 25.16(ii), 25.16 and 25
25.16.9 $H\left(a\right)=\frac{a+2}{2}\zeta\left(a+1\right)-\frac{1}{2}\sum_{r=1}^{a-2}% \zeta\left(r+1\right)\zeta\left(a-r\right),$ $a=2,3,4,\dots$. ⓘ Symbols: $H\left(\NVar{s}\right)$: Euler sums, $\zeta\left(\NVar{s}\right)$: Riemann zeta function and $a$: real or complex parameter Permalink: http://dlmf.nist.gov/25.16.E9 Encodings: TeX, pMML, png See also: Annotations for 25.16(ii), 25.16 and 25
Also,
25.16.10 $H\left(-2a\right)=\frac{1}{2}\zeta\left(1-2a\right)=-\frac{B_{2a}}{4a},$ $a=1,2,3,\dots$.
$H\left(s\right)$ has a simple pole with residue $\zeta\left(1-2r\right)$ ($=-B_{2r}/(2r)$) at each odd negative integer $s=1-2r$, $r=1,2,3,\dots$.
$H\left(s\right)$ is the special case $H\left(s,1\right)$ of the function
25.16.11 $H\left(s,z\right)=\sum_{n=1}^{\infty}\frac{1}{n^{s}}\sum_{m=1}^{n}\frac{1}{m^{% z}},$ $\Re(s+z)>1$,
which satisfies the reciprocity law
25.16.12 $H\left(s,z\right)+H\left(z,s\right)=\zeta\left(s\right)\zeta\left(z\right)+% \zeta\left(s+z\right),$
when both $H\left(s,z\right)$ and $H\left(z,s\right)$ are finite.
For further properties of $H\left(s,z\right)$ see Apostol and Vu (1984). Related results are:
25.16.13 $\displaystyle\sum_{n=1}^{\infty}\left(\frac{h(n)}{n}\right)^{2}$ $\displaystyle=\frac{17}{4}\zeta\left(4\right),$ ⓘ Symbols: $\zeta\left(\NVar{s}\right)$: Riemann zeta function, $n$: nonnegative integer and $h(n)$: sum Permalink: http://dlmf.nist.gov/25.16.E13 Encodings: TeX, pMML, png See also: Annotations for 25.16(ii), 25.16 and 25 25.16.14 $\displaystyle\sum_{r=1}^{\infty}\sum_{k=1}^{r}\frac{1}{rk(r+k)}$ $\displaystyle=\frac{5}{4}\zeta\left(3\right),$ ⓘ Symbols: $\zeta\left(\NVar{s}\right)$: Riemann zeta function and $k$: nonnegative integer Permalink: http://dlmf.nist.gov/25.16.E14 Encodings: TeX, pMML, png See also: Annotations for 25.16(ii), 25.16 and 25 25.16.15 $\displaystyle\sum_{r=1}^{\infty}\sum_{k=1}^{r}\frac{1}{r^{2}(r+k)}$ $\displaystyle=\frac{3}{4}\zeta\left(3\right).$ ⓘ Symbols: $\zeta\left(\NVar{s}\right)$: Riemann zeta function and $k$: nonnegative integer Permalink: http://dlmf.nist.gov/25.16.E15 Encodings: TeX, pMML, png See also: Annotations for 25.16(ii), 25.16 and 25
For further generalizations, see Flajolet and Salvy (1998). | 2018-02-18T21:55:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 126, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9841585755348206, "perplexity": 7071.483280968933}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891812259.30/warc/CC-MAIN-20180218212626-20180218232626-00378.warc.gz"} |
https://xgc.pppl.gov/html/cmake_changes.html | # Adding a new source file¶
Whenever you create a new source file you need to tell CMake what target it belongs to. We maintain lists of source files that are compiled into each of our libraries and executables. For example, see the core_SRCS variable in CMakeLists.txt.
# Adding support for another HPC facility¶
• Create a file CMake/find_dependencies_<name>.cmake. This will contain the location of XGC’s dependencies at this HPC facility.
• Add the facility name to the list of possible values of XGC_PLATFORM in our top-level CMakeLists.txt file.
# Adding a new configuration option¶
• In our top-level CMakeLists.txt, use the option command to create a new boolean option in the XGC build system. | 2021-08-02T09:32:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1939586102962494, "perplexity": 3433.8376691167964}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154310.16/warc/CC-MAIN-20210802075003-20210802105003-00559.warc.gz"} |
https://ftp.mcs.anl.gov/pub/fathom/moab-docs/IdealElements_8hpp_source.html | MOAB: Mesh Oriented datABase (version 5.4.1)
IdealElements.hpp
Go to the documentation of this file.
00001 /* *****************************************************************
00002 MESQUITE -- The Mesh Quality Improvement Toolkit
00003
00004 Copyright 2006 Sandia National Laboratories. Developed at the
00005 University of Wisconsin--Madison under SNL contract number
00006 624796. The U.S. Government and the University of Wisconsin
00007 retain certain rights to this software.
00008
00009 This library is free software; you can redistribute it and/or
00010 modify it under the terms of the GNU Lesser General Public
00012 version 2.1 of the License, or (at your option) any later version.
00013
00014 This library is distributed in the hope that it will be useful,
00015 but WITHOUT ANY WARRANTY; without even the implied warranty of
00016 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
00017 Lesser General Public License for more details.
00018
00019 You should have received a copy of the GNU Lesser General Public License
00020 (lgpl.txt) along with this library; if not, write to the Free Software
00021 Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
00022
00023 (2006) [email protected]
00024
00025 ***************************************************************** */
00026
00027 /** \file IdealElements.hpp
00028 * \brief
00029 * \author Jason Kraftcheck
00030 */
00031
00032 #ifndef MSQ_IDEAL_ELEMENTS_HPP
00033 #define MSQ_IDEAL_ELEMENTS_HPP
00034
00035 #include "Mesquite.hpp"
00036
00037 namespace MBMesquite
00038 {
00039
00040 class Vector3D;
00041
00042 /**\brief Get ideal element with unit edge length
00043 *
00044 * Get list of vertex coordinates for an ideal element with it's
00045 * centroid at the origin and all edges of unit length. Surface
00046 * elements lie in the XY plane.
00047 *
00048 *\param type the type of the element to obtain.
00049 *\param unit_height_pyramid If true, ideal pyramid has it's height equal
00050 * to the length of an edge of the base, rather than the default
00051 * of equilateral triangular faces.
00052 *\return corner vertex coordinates in canonical order.
00053 */
00054 const Vector3D* unit_edge_element( EntityTopology type, bool unit_height_pyramid = false );
00055
00056 /**\brief Get ideal element with unit area or volume
00057 *
00058 * Get list of vertex coordinates for an ideal element with it's
00059 * centroid at the origin and unit area/volume. Surface
00060 * elements lie in the XY plane.
00061 *
00062 *\param type the type of the element to obtain.
00063 *\param unit_height_pyramid If true, ideal pyramid has it's height equal
00064 * to the length of an edge of the base, rather than the default
00065 * of equilateral triangular faces.
00066 *\return corner vertex coordinates in canonical order.
00067 */
00068 const Vector3D* unit_element( EntityTopology type, bool unit_height_pyramid = false );
00069
00070 } // namespace MBMesquite
00071
00072 #endif | 2023-01-30T01:27:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.366719126701355, "perplexity": 8918.117054445214}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499790.41/warc/CC-MAIN-20230130003215-20230130033215-00847.warc.gz"} |
http://dlmf.nist.gov/18.36 | §18.36(i) Jacobi-Type Polynomials
These are OP’s on the interval $(-1,1)$ with respect to an orthogonality measure obtained by adding constant multiples of “Dirac delta weights” at $-1$ and $1$ to the weight function for the Jacobi polynomials. For further information see Koornwinder (1984b) and Kwon et al. (2006).
Similar OP’s can also be constructed for the Laguerre polynomials; see Koornwinder (1984b, (4.8)).
§18.36(ii) Sobolev OP’s
Sobolev OP’s are orthogonal with respect to an inner product involving derivatives. For an introductory survey to this subject, see Marcellán et al. (1993). Other relevant references include Iserles et al. (1991) and Koekoek et al. (1998).
§18.36(iii) Multiple OP’s
These are polynomials in one variable that are orthogonal with respect to a number of different measures. They are related to Hermite-Padé approximation and can be used for proofs of irrationality or transcendence of interesting numbers. For further information see Ismail (2005, Chapter 23).
§18.36(iv) Orthogonal Matrix Polynomials
These are matrix-valued polynomials that are orthogonal with respect to a square matrix of measures on the real line. Classes of such polynomials have been found that generalize the classical OP’s in the sense that they satisfy second-order matrix differential equations with coefficients independent of the degree. For further information see Durán and Grünbaum (2005). | 2014-11-27T19:36:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 3, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9548451900482178, "perplexity": 524.9771258421434}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-49/segments/1416931009084.22/warc/CC-MAIN-20141125155649-00119-ip-10-235-23-156.ec2.internal.warc.gz"} |
https://www.giss.nasa.gov/tools/latex/ltx-229.html | This page's content is no longer actively maintained, but the material has been kept on-line for historical purposes.
The page may contain broken links or outdated information, and parts may not function in current web browsers.
## Hypertext Help with LaTeX
### flushright
\begin{flushright}
Text on line 1 \\
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The flushright environment allows you to create a paragraph consisting of lines that are flushed right to the right-hand margin. Each line must be terminated with a \\. | 2019-03-24T15:10:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5234313011169434, "perplexity": 3899.9301059907966}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912203462.50/warc/CC-MAIN-20190324145706-20190324171706-00423.warc.gz"} |
https://par.nsf.gov/biblio/10374238-measurement-inclusive-differential-wz-production-cross-sections-polarization-angles-triple-gauge-couplings-pp-collisions-sqrt-tev | This content will become publicly available on July 1, 2023
Measurement of the inclusive and differential WZ production cross sections, polarization angles, and triple gauge couplings in pp collisions at $$\sqrt{s}$$ = 13 TeV
A bstract The associated production of a W and a Z boson is studied in final states with multiple leptons produced in proton-proton (pp) collisions at a centre-of-mass energy of 13 TeV using 137 fb − 1 of data collected with the CMS detector at the LHC. A measurement of the total inclusive production cross section yields σ tot (pp → WZ) = 50 . 6 ± 0 . 8 (stat) ± 1 . 5 (syst) ± 1 . 1 (lumi) ± 0 . 5 (theo) pb. Measurements of the fiducial and differential cross sections for several key observables are also performed in all the final-state lepton flavour and charge compositions with a total of three charged leptons, which can be electrons or muons. All results are compared with theoretical predictions computed up to next-to-next-to-leading order in quantum chromodynamics plus next-to-leading or- der in electroweak theory and for various sets of parton distribution functions. The results include direct measurements of the charge asymmetry and the W and Z vector boson polarization. The first observation of longitudinally polarized W bosons in WZ production is reported. Anomalous gauge couplings are searched for, leading to new constraints on beyond-the-standard-model contributions to the WZ more »
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Award ID(s):
Publication Date:
NSF-PAR ID:
10374238
Journal Name:
Journal of High Energy Physics
Volume:
2022
Issue:
7
ISSN:
1029-8479
1. Abstract Measurements of the Standard Model Higgs boson decaying into a $$b\bar{b}$$ b b ¯ pair and produced in association with a W or Z boson decaying into leptons, using proton–proton collision data collected between 2015 and 2018 by the ATLAS detector, are presented. The measurements use collisions produced by the Large Hadron Collider at a centre-of-mass energy of $$\sqrt{s} = 13\,\text {Te}\text {V}$$ s = 13 Te , corresponding to an integrated luminosity of $$139\,\mathrm {fb}^{-1}$$ 139 fb - 1 . The production of a Higgs boson in association with a W or Z boson is established with observed (expected) significances of 4.0 (4.1) and 5.3 (5.1) standard deviations, respectively. Cross-sections of associated production of a Higgs boson decaying into bottom quark pairs with an electroweak gauge boson, W or Z , decaying into leptons are measured as a function of the gauge boson transverse momentum in kinematic fiducial volumes. The cross-section measurements are all consistent with the Standard Model expectations, and the total uncertainties vary from 30% in the high gauge boson transverse momentum regions to 85% in the low regions. Limits are subsequently set on the parameters of an effective Lagrangian sensitive to modifications of the WHmore »
2. A bstract Measurements are presented of differential cross sections for the production of Z bosons in association with at least one jet initiated by a charm quark in pp collisions at $$\sqrt{s}$$ s = 13 TeV. The data recorded by the CMS experiment at the LHC correspond to an integrated luminosity of 35.9 fb − 1 . The final states contain a pair of electrons or muons that are the decay products of a Z boson, and a jet consistent with being initiated by a charm quark produced in the hard interaction. Differential cross sections as a function of the transverse momentum p T of the Z boson and p T of the charm jet are compared with predictions from Monte Carlo event generators. The inclusive production cross section 405 . 4 ± 5 . 6 (stat) ± 24 . 3 (exp) ± 3 . 7 (theo) pb, is measured in a fiducial region requiring both leptons to have pseudorapidity |η| < 2 . 4 and p T > 10 GeV, at least one lepton with p T > 26 GeV, and a mass of the pair in the range 71–111 GeV, while the charm jet is requiredmore »
3. A bstract Measurements of the production cross-sections of the Standard Model (SM) Higgs boson ( H ) decaying into a pair of τ -leptons are presented. The measurements use data collected with the ATLAS detector from pp collisions produced at the Large Hadron Collider at a centre-of-mass energy of $$\sqrt{s}$$ s = 13 TeV, corresponding to an integrated luminosity of 139 fb − 1 . Leptonic ( τ → ℓν ℓ ν τ ) and hadronic ( τ → hadrons ν τ ) decays of the τ -lepton are considered. All measurements account for the branching ratio of H → ττ and are performed with a requirement |y H | < 2 . 5, where y H is the true Higgs boson rapidity. The cross-section of the pp → H → ττ process is measured to be 2 . 94 ± $$0.21{\left(\mathrm{stat}\right)}_{-0.32}^{+0.37}$$ 0.21 stat − 0.32 + 0.37 (syst) pb, in agreement with the SM prediction of 3 . 17 ± 0 . 09 pb. Inclusive cross-sections are determined separately for the four dominant production modes: 2 . 65 ± $$0.41{\left(\mathrm{stat}\right)}_{-0.67}^{+0.91}$$ 0.41 stat − 0.67 + 0.91 (syst) pb for gluon-gluon fusion, 0 .more »
4. Abstract This paper reports on a search for heavy resonances decaying into WW , ZZ or WZ using proton–proton collision data at a centre-of-mass energy of $$\sqrt{s}=13$$ s = 13 TeV. The data, corresponding to an integrated luminosity of 139 $$\mathrm{fb}^{1}$$ fb 1 , were recorded with the ATLAS detector from 2015 to 2018 at the Large Hadron Collider. The search is performed for final states in which one W or Z boson decays leptonically, and the other W boson or Z boson decays hadronically. The data are found to be described well by expected backgrounds. Upper bounds on the production cross sections of heavy scalar, vector or tensor resonances are derived in the mass range 300–5000 GeV within the context of Standard Model extensions with warped extra dimensions or including a heavy vector triplet. Production through gluon–gluon fusion, Drell–Yan or vector-boson fusion are considered, depending on the assumed model.
5. Abstract This paper presents a measurement of the electroweak production of two jets in association with a $$Z\gamma$$ Z γ pair, with the Z boson decaying into two neutrinos. It also presents a search for invisible or partially invisible decays of a Higgs boson with a mass of 125 $$\text {GeV}$$ GeV produced through vector-boson fusion with a photon in the final state. These results use data from LHC proton–proton collisions at $$\sqrt{s}$$ s = 13 $$\text {TeV}$$ TeV collected with the ATLAS detector and corresponding to an integrated luminosity of 139 $$\hbox {fb}^{-1}$$ fb - 1 . The event signature, shared by all benchmark processes considered for the measurements and searches, is characterized by a significant amount of unbalanced transverse momentum and a photon in the final state, in addition to a pair of forward jets. Electroweak $$Z\gamma$$ Z γ production in association with two jets is observed in this final state with a significance of 5.2 (5.1 expected) standard deviations. The measured fiducial cross-section for this process is $$1.31\pm 0.29$$ 1.31 ± 0.29 fb. An observed (expected) upper limit of 0.37 ( $$0.34^{+0.15}_{-0.10}$$ 0 . 34 - 0.10 + 0.15 ) at 95% confidence level ismore » | 2023-03-22T11:44:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8603495955467224, "perplexity": 1025.4077264796572}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943809.76/warc/CC-MAIN-20230322114226-20230322144226-00361.warc.gz"} |
https://www-cdf.fnal.gov/physics/new/top/2015/AFB_tt_CDF/index.html | # Combination of $$\afbtt$$ at CDF
### Lepton+Jets Final State
Dan Amidei, Myron Campbell, Ryan Edgar, Dave Mietlicki, Monica Tecchio, Jon S. Wilson, and Tom Wright
University of Michigan
Thomas A Schwarz
FNAL
Joey Huston
Michigan State University
### Dilepton Final State
Ziqing Hong, Dave Toback, and Jon S. Wilson
Texas A&M University
##### Public note: CDF11161
We present a combination of the measurements of the $$\afbtt$$ from CDF with lepton+jets and dilepton final states using the full dataset collected by the CDF II detector. The improved measurement is $$\afbtt = 0.160\pm0.045$$. The combined result is consistent with the NNLO SM calculation at $$\afbtt = 0.095 \pm 0.007$$. The differential $$\afbtt$$ as a function of $$|\dy|$$ in the two final states are also combined with a simultaneous fit, yielding a result of $$\alpha=0.227\pm0.057$$, which is $$2\sigma$$ higher than the NNLO SM calculation.
1 $\afbtt = \frac{N(\dy > 0) - N(\dy < 0)}{N(\dy > 0) + N(\dy < 0)}$ $\dy=y_{t}-y_{\bar{t}}$ $$\ttbar\rightarrow\ell\nu+jets$$: $$\ttbar\rightarrow\ell^{+}\ell^{-}+jets+\MET$$: Inclusive $$\afbtt$$ 2 Table of uncertainties of $$\afbtt$$ measurement with the lepton+jets and the dilepton final states. In the column of correlation, "0" indicates no correlation and "1" indicates fully positive correlation. 3 The combined $$\afbtt$$: $\afbtt = 0.160\pm0.045$ The weight of the lepton+jets result is 91%, and the weight of the dilepton result is 9%. The correlation between the two results is 10%. Differential $$\afbtt$$ vs. $$|\dy|$$ 4 The best fit of $$\afbtt=\alpha\cdot|\dy|$$ with measurements from both lepton+jets and dilepton final states. All correlations are taken into account. The bin centroids, differential $$\afbtt$$, as well as eigenvalues and eigenvectors of the covariance matrix is shown. 5 The best fit result is $\alpha = 0.227\pm0.057$ This result is $$2\sigma$$ larger than the NNLO SM calculation 6 Comparison of the slope $$\alpha$$ of $$\afbtt$$ vs. $$|\dy|$$ from various measurements.
Last updated : | 2020-02-17T10:14:35 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6531423330307007, "perplexity": 2020.347806938185}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875141806.26/warc/CC-MAIN-20200217085334-20200217115334-00543.warc.gz"} |
https://owly.wiki/en/Pohlig%E2%80%93Hellman_algorithm/ | # Pohlig–Hellman algorithm
Steps of the Pohlig–Hellman algorithm.
In group theory, the Pohlig–Hellman algorithm, sometimes credited as the Silver–Pohlig–Hellman algorithm,[1] is a special-purpose algorithm for computing discrete logarithms in a finite abelian group whose order is a smooth integer.
The algorithm was introduced by Roland Silver, but first published by Stephen Pohlig and Martin Hellman (independent of Silver).
### Groups of prime-power order
As an important special case, which is used as a subroutine in the general algorithm (see below), the Pohlig–Hellman algorithm applies to groups whose order is a prime power. The basic idea of this algorithm is to iteratively compute the -adic digits of the logarithm by repeatedly "shifting out" all but one unknown digit in the exponent, and computing that digit by elementary methods.
(Note that for readability, the algorithm is stated for cyclic groups — in general, must be replaced by the subgroup generated by , which is always cyclic.)
Input. A cyclic group of order with generator and an element .
Output. The unique integer such that .
1. Initialize
2. Compute . By Lagrange's theorem, this element has order .
3. For all , do:
1. Compute . By construction, the order of this element must divide , hence .
2. Using the baby-step giant-step algorithm, compute such that . It takes time .
3. Set .
4. Return .
Assuming is much smaller than , the algorithm computes discrete logarithms in time complexity , far better than the baby-step giant-step algorithm's .
### The general algorithm
In this section, we present the general case of the Pohlig–Hellman algorithm. The core ingredients are the algorithm from the previous section (to compute a logarithm modulo each prime power in the group order) and the Chinese remainder theorem (to combine these to a logarithm in the full group).
(Again, we assume the group to be cyclic, with the understanding that a non-cyclic group must be replaced by the subgroup generated by the logarithm's base element.)
Input. A cyclic group of order with generator , an element , and a prime factorization .
Output. The unique integer such that .
1. For each , do:
1. Compute . By Lagrange's theorem, this element has order .
2. Compute . By construction, .
3. Using the algorithm above in the group , compute such that .
2. Solve the simultaneous congruence
The Chinese remainder theorem guarantees there exists a unique solution .
3. Return .
The correctness of this algorithm can be verified via the classification of finite abelian groups: Raising and to the power of can be understood as the projection to the factor group of order .
### Complexity
The worst-case input for the Pohlig–Hellman algorithm is a group of prime order: In that case, it degrades to the baby-step giant-step algorithm, hence the worst-case time complexity is . However, it is much more efficient if the order is smooth: Specifically, if is the prime factorization of , then the algorithm's complexity is
group operations.[2]
### Notes
1. ^ Mollin 2006, pg. 344
2. ^ Menezes, et. al 1997, pg. 108
### References
• Mollin, Richard (2006-09-18). An Introduction To Cryptography (2nd ed.). Chapman and Hall/CRC. p. 344. ISBN 978-1-58488-618-1.
• S. Pohlig and M. Hellman (1978). "An Improved Algorithm for Computing Logarithms over GF(p) and its Cryptographic Significance" (PDF). IEEE Transactions on Information Theory (24): 106–110.CS1 maint: uses authors parameter (link)
• Menezes, Alfred J.; van Oorschot, Paul C.; Vanstone, Scott A. (1997). "Number-Theoretic Reference Problems" (PDF). Handbook of Applied Cryptography. CRC Press. pp. 107–109. ISBN 0-8493-8523-7.
Original content from Wikipedia, shared with licence Creative Commons By-Sa - Pohlig–Hellman algorithm | 2021-08-03T03:43:49 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9523478746414185, "perplexity": 1115.1354761956015}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154420.77/warc/CC-MAIN-20210803030201-20210803060201-00629.warc.gz"} |
http://pdglive.lbl.gov/DataBlock.action?node=S008FA&home=sumtabM | # $\boldsymbol F_{\boldsymbol A}$, AXIAL-VECTOR FORM FACTOR INSPIRE search
VALUE EVTS DOCUMENT ID TECN COMMENT
$0.0119$ $\pm0.0001$ 65k 1, 2
2009
PIBE ${{\mathit e}^{+}}{{\mathit \nu}}{{\mathit \gamma}}$ at rest
• • • We do not use the following data for averages, fits, limits, etc. • • •
$0.0115$ $\pm0.0004$ 41k 1, 3
2004
PIBE ${{\mathit \pi}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}}{{\mathit \gamma}}$ at rest
$0.0106$ $\pm0.0060$ 4, 1
1990 B
SPEC 17 GeV ${{\mathit \pi}^{-}}$ $\rightarrow$ ${{\mathit e}^{-}}{{\overline{\mathit \nu}}_{{e}}}{{\mathit \gamma}}$
$0.021$ ${}^{+0.011}_{-0.013}$ 98
1989
SPEC ${{\mathit \pi}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}_{{e}}}{{\mathit e}^{+}}{{\mathit e}^{-}}$
$0.0135$ $\pm0.0016$ 4, 1
1986
SPEC ${{\mathit \pi}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}}{{\mathit \gamma}}$
$0.006$ $\pm0.003$ 4, 1
1986
SPEC ${{\mathit \pi}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}}{{\mathit \gamma}}$
$0.011$ $\pm0.003$ 5, 4, 1
1978
SPEC ${{\mathit \pi}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}}{{\mathit \gamma}}$
1 These values come from fixing the vector form factor at the CVC prediction, ${{\mathit F}_{{V}}}$ = $0.0259$ $\pm0.0005$.
2 When $\mathit F_{V}$ is released, the BYCHKOV 2009 $\mathit F_{A}$ is $0.0117$ $\pm0.0017$, and $\mathit F_{A}$ and $\mathit F_{V}$ results are highly (anti-)correlated: $\mathit F_{A}$ + 1.0286 $\mathit F_{V}$ = $0.03853$ $\pm0.00014$.
3 The sign of ${{\mathit \gamma}}$ = ${{\mathit F}_{{A}}}$ /${{\mathit F}_{{V}}}$ is determined to be positive.
4 Only the absolute value of $\mathit F_{\mathit A}$ is determined.
5 The result of STETZ 1978 has a two-fold ambiguity. We take the solution compatible with later determinations.
References:
BYCHKOV 2009
PRL 103 051802 New Precise Measurement of the Pion Weak Form Factors in ${{\mathit \pi}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}}{{\mathit \gamma}}$ Decay
FRLEZ 2004
PRL 93 181804 Precise Measurement of the Pion Axial Form Factor in the ${{\mathit \pi}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}}{{\mathit \gamma}}$ Decay
BOLOTOV 1990B
PL B243 308 The Experimental Study of the ${{\mathit \pi}^{-}}$ $\rightarrow$ ${{\mathit e}^{-}}{{\overline{\mathit \nu}}_{{e}}}{{\mathit \gamma}}$ Decay in Flight
EGLI 1989
PL B222 533 Measurement of the Decay ${{\mathit \pi}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}_{{e}}}{{\mathit e}^{+}}{{\mathit e}^{-}}$ and Search for a Light Higgs Boson
BAY 1986
PL B174 445 Measurement of the Pion Axial Formfactor from Radiative Decay
PIILONEN 1986
PRL 57 1402 Unique Determination of the Formfactor Ratio in Radiative Pion Decay
STETZ 1978
NP B138 285 Determination of the Axial-Vector Formfactor in the Radiative Decay of the Pion | 2019-12-08T16:01:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8322098255157471, "perplexity": 3012.2199705106636}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540511946.30/warc/CC-MAIN-20191208150734-20191208174734-00373.warc.gz"} |
https://www.anl.gov/article/katie-martin-keeps-the-advanced-photon-source-upgrade-project-on-track | # Argonne National Laboratory
Article | Argonne National Laboratory
# Katie Martin keeps the Advanced Photon Source Upgrade project on track
As Project Controls manager, Katie Martin’s job is to account for the APS Upgrade’s schedule and its $815 million budget, down to the penny. Katie Martin knows the value of a long-term investment. As a Project Controls manager for the U.S. Department of Energy’s (DOE) Argonne National Laboratory, Martin’s job is to manage the cost and schedule for long-term construction projects, working with the scientists and engineers to keep things on time and within budget. Some of these projects can span years and cost hundreds of millions of dollars, and Martin keeps track of every day and every dime. She’s also living proof that long-term investments pay off. Martin began working as an administrative assistant at Argonne in 2007, as part of a co-op program in high school. She stayed with the laboratory and worked full time while attending DeVry University part time, and Argonne provided financial assistance for her college education. Getting to work with these scientists and engineers, some of the best in the world, is a privilege.” — Katie Martin, Project Management Office, Argonne National Laboratory. The lab invested in me,” she said. That is really comforting, and has kept me going. I was taking 20 credit hours a semester, juggling classes and full-time work. They saw something in me, and helped me to go to school so they could keep me on.” For most of that time Martin has been working in the Project Management Office, which serves as a conduit between project teams and the DOE. As part of this team, Martin has worked on several construction projects at the laboratory, including the Energy Sciences Building and the Advanced Protein Characterization Facility, helping the project teams deliver on timing and costs. After working on smaller efforts at the Advanced Photon Source (APS), a DOE Office of Science user facility at Argonne, Martin now leads a team that manages the cost and schedule for the massive ongoing upgrade to the facility. The APS Upgrade will see the current particle accelerator at the heart of the facility replaced with a state-of-the-art model, one that will increase the brightness of the X-ray beams by up to 500 times. New research stations will be built and existing stations modified or enhanced to make use of the new high-brightness light source. With a projected cost of$815 million and a year-long installation period required for the new accelerator (during which the X-ray beams will be shut down), the APS Upgrade has a lot of moving parts, and Martin’s job is to keep her eye on each one of them.
We work with all of the technical teams, the scientists and engineers designing and building each component,” Martin said. We ask them to explain components to us, so we can break it down into a manageable process — where they order it from, the cost, when they get it — and we report monthly to the DOE, so they can see we’re performing to their standards.”
Those reports from Martin’s team are vital to maintaining close coordination with DOE’s Office of Basic Energy Sciences, which funds the project. Her team also keeps the master schedule for the project, tracking the timeliness of hundreds of vendors delivering important, complicated parts to order. Every change to the cost or schedule, no matter how small, has to be accounted for, with the proper forms filled out and regulations followed.
All of this careful management means that Martin was among the first to realize the impact the COVID-19 pandemic would have on the APS Upgrade project. She tracked delays from the project’s vendors — 20,000 different activities, she said, linked to other supply lines around the world — and used that information to build a case to the DOE for a change in the upgrade’s schedule.
In May 2021, the project announced a new date for the start of the installation period: April 2023, a change of 10 months from the original schedule.
People were expecting it and glad to have a final decision,” Martin said. There were so many delays, this was our only choice. I’m relieved that the new schedule is better for the project as a whole.”
The APS Upgrade is the largest and most complicated project Martin has been a part of — I have a lot of balls in the air at all times,” she said — and she is grateful for the mentors who invested in her, sharing their knowledge of the job.
I could not have gotten this far without a lot of people teaching me a lot of things,” she said. There’s a lot I am now able to pass on to my team.”
And she has nothing but positive words to say about working with the APS Upgrade team, and playing a part in a project that she knows will lead to positive changes in the world, from new energy storage devices to new treatments and vaccines for diseases.
This has been one of the best projects I have worked on,” she said. Everyone is so passionate about the work they’re doing. The APS Upgrade will directly impact the future of science in our country and around the world, and everyone realizes that. Getting to work with these scientists and engineers, some of the best in the world, is a privilege.” | 2022-01-27T05:50:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.26060205698013306, "perplexity": 1581.7398076193967}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320305141.20/warc/CC-MAIN-20220127042833-20220127072833-00244.warc.gz"} |
http://www.strengejacke.de/sjPlot/sjp.int/ | # sjp.int {sjPlot}
This document shows examples for using the sjp.int function of the sjPlot package.
Ressources:
• Developer snapshot at GitHub
• Submission of bug reports and issues at GitHub
(back to table of content)
## Data initialization
library(sjPlot)
library(sjmisc)
data(efc)
# set basic theme options
sjp.setTheme(theme = "539",
axis.title.size = .85,
axis.textsize = .85,
legend.size = .8,
geom.label.size = 3.5)
## Plotting interactions of regression models
The sjp.int function plots regression (predicted values) or probability lines (predicted probabilities) of significant interaction terms of fitted models. This helps better understanding effects of moderations in regression models. The function accepts following fitted model classes:
• linear models (lm)
• generalized linear models (glm)
• linear mixed effects models (lme4::lmer)
• generalized linear mixed effects models (lme4::glmer)
• linear mixed effects models (nlme::lme, but only for type = "eff")
• generalized least squares models (nlme::gls, but only for type = "eff")
• panel data estimators (plm::plm)
Note that beside interaction terms, also the single predictors of each interaction (main effects) must be included in the fitted model as well. Thus, lm(dep ~ pred1 * pred2) will work, but lm(dep ~ pred1:pred2) won’t!
## Types of effect displays
The sjp.int function has three different types of interaction (or moderation) effects that can be displayed. Use the type argument to select the effect type.
### type = “cond”
Plots the effective change or impact (conditional effect) on a dependent variable of a moderation effect, as described in Grace-Martin K: Clarifications on Interpreting Interactions in Regression, i.e. the difference of the moderation effect on the dependent variable in presence and absence of the moderating effect (simple slope plot or conditional effect, see Hayes 2012). All remaining predictors are set to zero (i.e. ignored and not adjusted for). Hence, this plot type may be used especially for - but is of course not restricted to - binary or dummy coded moderator values. This type does not show the overall effect of interactions on the result of Y. Use type = "eff" for effect displays similar to the effect-function from the effects-package.
### type = “eff”
Plots the overall effects (marginal effects( of the interaction, with all remaining covariates set to the mean. Effects are calculated using the effect-function from the effects-package.
### type = “emm”
Plots the estimated marginal means of interactions with categorical variables (which was the former sjp.emm.int function that is now deprecated). This plot type plots estimated marginal means (also called least square means or marginal means) of (significant) interaction terms, e.g. in two-way repeated measure ANOVA or ANCOVA. This function may be used, for example, to plot differences in interventions between control and treatment groups over multiple time points, as described here.
## Example for type = “cond”
### Fitting a linear model
# Note that the data sets used in the following examples may
# not be perfectly suitable for fitting linear models.
# fit "dummy" model.
fit <- lm(weight ~ Diet * Time, data = ChickWeight)
Let’s take a look at the model summary to see the estimates of interactions:
# show summary to see significant interactions
summary(fit)
##
## Call:
## lm(formula = weight ~ Diet * Time, data = ChickWeight)
##
## Residuals:
## Min 1Q Median 3Q Max
## -135.425 -13.757 -1.311 11.069 130.391
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 30.9310 4.2468 7.283 1.09e-12 ***
## Diet2 -2.2974 7.2672 -0.316 0.75202
## Diet3 -12.6807 7.2672 -1.745 0.08154 .
## Diet4 -0.1389 7.2865 -0.019 0.98480
## Time 6.8418 0.3408 20.076 < 2e-16 ***
## Diet2:Time 1.7673 0.5717 3.092 0.00209 **
## Diet3:Time 4.5811 0.5717 8.014 6.33e-15 ***
## Diet4:Time 2.8726 0.5781 4.969 8.92e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 34.07 on 570 degrees of freedom
## Multiple R-squared: 0.773, Adjusted R-squared: 0.7702
## F-statistic: 277.3 on 7 and 570 DF, p-value: < 2.2e-16
### Plot conditional effects of interactions in linear regressions
The first example is quite simple. It produces three plots, because Diet, as factor, has three levels (plus one reference level), thus we have the interaction of Time and each of the three levels of Diet.
# plot regression line of interaction terms
sjp.int(fit, type = "cond")
### Explaining the output
By default, the function examines both interaction terms and checks, which term has a larger range.
The predictor with the larger range is plotted along the x-axis. In this example, Time ranges from 0 to 21, while Diet is dichotomous (since it is splitted into its factor levels).
The predictor with lower range is used as grouping variable, indicating the different lines. By default, the lowest value (labelled lower bound in the plot) of this predictor is used to compute the effect (or change, or impact) for the interaction, indicating the absence of interaction (no moderation effect from predictor 2 on predictor 1). This is the red line. Second, the highest value of this predictor is used to calculate effect (or change, or impact) for the interaction, indicating the presence of an interaction (or the highest moderation effect from predictor 2 on predictor one). This is the blue line. Hence, this plot type may be used especially for binary or dummy coded moderator values.
To better understand the formula behind this, please refer to these two blog posts from Karen Grace: Interpreting Interactions in Regression and Clarifications on Interpreting Interactions in Regression.
## Example for type = “eff”
### Effect plot of fitted model
Using type = "eff" computes the interaction effects based on the effect-function from the effects-package. Using this approach, all covariates are set to the mean, and both main effects of the interaction term are used to calculate the overall mean of the dependent variable.
# plot regression line of interaction terms
sjp.int(fit, type = "eff")
### Explaining the output
The eff-type produces one plot, where all factor levels of Diet (i.e., all interaction effects) are included (note that the effect-function uses the first interaction term (in this case, Diet) as moderater variable; if you want to swap the moderator with the predictor on the x-axis (the second interaction term), use the argument swap.pred).
Each line in the plot represents one factor level of the moderator variable (i.e., each line stands for one interaction effect).
To better understand the formula behind this, please refer to this paper: Fox J (2003) Effect displays in R for generalised linear models. Journal of Statistical Software 8:15, 1–27, http://www.jstatsoft.org/v08/i15/.
In short, you see the unadjusted relation between response and interaction term, in presence and absence of the moderating effect.
### Difference between type = “cond” and type = “eff”
Comparing the overall interaction effect on the dependent variable (type = "eff") and the mere impact of the moderation effect (type = "cond") show the same tendencies. It’s a simple variation in the regression slopes: type = "cond" shows the (mere) impact of the moderation effect. The differences between the slopes (indicated by the shaded areas) are related to the different slopes in the overall effect.
### One plot for each interaction term
Use facet.grid = TRUE to plot each interaction term in a new plot.
# plot regression line of interaction terms
sjp.int(fit, type = "eff", facet.grid = TRUE)
## Showing value labels in the plot
With the show.values argument, you can also show value labels of the predicted values.
sjp.int(fit, type = "cond", show.values = TRUE)
## Adding confidence regions to the plot
With the show.ci argument, you can add confidence intervals regions to the plots. However, this argument does not work for type = "cond".
sjp.int(fit, type = "eff", show.values = TRUE, show.ci = TRUE)
## Choose the values of continuous moderators intentionally
By default (see above), the lower and upper bound (lowest and highest value) of the moderator are used to plot interactions. If the moderator is a continuous variable, you may also use other values instead of lowest/highest. One suggestion is to use the mean as well as one standard deviation above and below the mean value.
You can do this with the mdrt.values paramter, with mdrt.values = "meansd".
First, we fit another dummy model.
mydf <- data.frame(usage = efc$tot_sc_e, sex = efc$c161sex,
education = efc$c172code, burden = efc$neg_c_7,
barthel = efc$barthtot) # convert gender predictor to factor mydf$sex <- relevel(factor(mydf$sex), ref = "2") # fit "dummy" model fit <- lm(usage ~ .*., data = mydf) # show model summary summary(fit) ## ## Call: ## lm(formula = usage ~ . * ., data = mydf) ## ## Residuals: ## Min 1Q Median 3Q Max ## -2.2364 -0.8478 -0.2685 0.3086 8.1836 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) -0.1118091 0.7567683 -0.148 0.8826 ## sex1 0.5583579 0.5725374 0.975 0.3297 ## education 0.2242707 0.3434615 0.653 0.5140 ## burden 0.0432757 0.0437340 0.990 0.3227 ## barthel 0.0097000 0.0072795 1.333 0.1831 ## sex1:education -0.0127309 0.1560235 -0.082 0.9350 ## sex1:burden -0.0236557 0.0290406 -0.815 0.4156 ## sex1:barthel -0.0035729 0.0038240 -0.934 0.3504 ## education:burden 0.0150701 0.0185970 0.810 0.4180 ## education:barthel -0.0026358 0.0026749 -0.985 0.3247 ## burden:barthel -0.0007119 0.0003969 -1.794 0.0732 . ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 1.232 on 804 degrees of freedom ## (93 observations deleted due to missingness) ## Multiple R-squared: 0.04751, Adjusted R-squared: 0.03567 ## F-statistic: 4.011 on 10 and 804 DF, p-value: 2.22e-05 As we can see, the interaction terms are not significant, the one closest to significance has a p-value of 0.0732. By default, only interaction terms with a p-value lower than or equal to 0.1 are plotted. However, we can change this by adjusting the p-level sensivity with the plevel argument. # show mean and standard deviation values for moderator effect # and show all interactions with p-values up to 0.1 sjp.int(fit, type = "cond", mdrt.values = "meansd") ## Following non-significant interaction terms were omitted from the output: ## sex1:education ## sex1:burden ## sex1:barthel ## education:burden ## education:barthel ## ## Use plevel to show more interaction terms. In the above figure we can see the moderation effect (interaction) of burden of care on Barthel index (functional dependency scale of people in need of care) toward usage of supporting services. In general, with increasing Barthel index (i.e. people in need of care are less dependent) and absence of moderating effect (i.e. lower sd of burden of care), service usage increases. If the moderation effect increases, i.e. we have higher burden of care, service usage decreases. In short, a) decreasing dependency (higher Barthel index), moderated by higher burden, has a stronger impact on decreasing service usage, while b) decreasing dependency (higher Barthel index), moderated by lower burden, has a weaker impact on decreasing service usage (or a stronger impact on increasing service usage). Looking at the overall interaction effect on the dependent variable (type = "eff", see next example) shows the same tendencies. It’s a simple variation in the regression slopes: type = "cond" shows the (isolated) impact of the moderation effect. The differences between the slopes (indicated by the shaded areas) are related to the different slopes in the overall effect (shown in the next example). ### Different moderator values for effect display plot type The argument options for the mdrt.values also apply to type = "eff". While the default effect-function from the effects-package automatically selects a pretty range for continuous variables, the sjp.int function sticks to the mdrt.values-options, i.e. using min/max values of the moderator, zero/max or mean/+-sd. The p-level sensivity (plevel) is not needed for type = "eff", as this option always plots all interactions found. By default, this behaviour would result in six plots. To select a specific plot only, use the int.plot.index argument and specify the plot number. # show mean and standard deviation values for moderator effect sjp.int(fit, type = "eff", mdrt.values = "meansd", int.plot.index = 6) ## Interaction terms in generalized linear models Interpreting interaction terms in generalized linear models is a bit tricky. Instead of working with, e.g. odds ratios, the sjp.int function transforms estimates into probabilities or incidents rates and plots the predicted values of the interaction effect. First create some sample data and fit a binary logistic regression model: # load library for sample data # and getting value labels library(sjmisc) # load sample data data(efc) # create binary response care.burden <- dicho(efc$neg_c_7)
# create data frame for fitted model
mydf <- data.frame(care.burden = care.burden,
sex = to_factor(efc$c161sex), barthel = efc$barthtot)
# fit model
fit <- glm(care.burden ~ sex * barthel,
data = mydf, family = binomial(link = "logit"))
# plot interaction, increase p-level sensivity
sjp.int(fit,
type = "cond",
legend.labels = get_labels(efc$c161sex), plevel = 1) What we see in the above figure are the predicted probabilities of the outcome (care burden) by Barthel index (predictor) with no moderating effect of sex (red line). And we can see the predicted probabilities of the outcome considering the interaction effect (moderation) of sex on Barthel index (blue line). In general, care burden decreases with increasing functional status (independecy of cared for person), however, male care givers tend to perceive a higher care burden than women. Another way to analyse the moderator effect of sex on function status and care burden is to use box plots. The following figures “validates” our results we got from the above figure. sjp.grpfrq(mydf$barthel,
mydf$care.burden, intr.var = mydf$sex,
legend.labels = c("low burden", "high burden"),
type = "box")
To investigate the overall effect on burden, use the type = "eff" argument again.
# plot overall effect on burden
sjp.int(fit, type = "eff")
## Examples for type = “emm” - plotting estimated marginal means
With the type = "emm" argument, you can plot estimated marginal means from the dependent variable distinguished by groups and group-levels. For instance, you can use this function to visualize a pre-post-comparison (first preditcor, independent variable) of an intervention (dependent variable) between a treatment and control group (second preditcor, independent variable). The estimated marginal means are also called “adjusted means”. The sjp.int function extracts all significant interactions and calculates least-squares means, which are plotted.
### Fitting a linear model
First, we need to create a data frame and fit a linear model.
# load sample data set
data(efc)
# create data frame with variables that should be
# included in the model
mydf <- data.frame(burden = efc$neg_c_7, sex = to_factor(efc$c161sex),
education = to_factor(efc$c172code)) # set variable label set_label(mydf$burden) <- "care burden"
# fit model, including interaction
fit <- lm(burden ~ .*., data = mydf)
### Plotting estimated marginal means
This first example is taken from the function’s online-help. It uses the plevel argument because all interactions’ p-values are above 0.05.
sjp.int(fit, type = "emm", plevel = 1)
### Another example
# create data frame. we want to see whether the relationship between
# cared-for person's dependency and negative impact of care is moderated
# by the carer's employment status (interaction between dependency and
# deployment).
mydf <- data.frame(negimp = efc$neg_c_7, dependency = to_factor(efc$e42dep),
employment = to_factor(efc$c175empl), hours = efc$c12hour,
sex = to_factor(efc$c161sex), age = efc$e17age)
# set variable label
set_label(mydf\$negimp) <- "negative impact of care"
# fit model
fit <- lm(negimp ~ dependency +
employment +
dependency:employment +
hours +
sex +
age, data = mydf)
# bad dataset for demonstration, again no significant interaction
summary(fit)
##
## Call:
## lm(formula = negimp ~ dependency + employment + dependency:employment +
## hours + sex + age, data = mydf)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.064 -2.425 -0.737 1.736 17.034
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.760486 1.322190 7.382 3.65e-13 ***
## dependency2 0.976546 0.755183 1.293 0.19631
## dependency3 2.342064 0.724655 3.232 0.00128 **
## dependency4 4.386289 0.741475 5.916 4.75e-09 ***
## employment1 0.085163 0.888775 0.096 0.92368
## hours 0.006895 0.002826 2.440 0.01490 *
## sex2 0.461571 0.284276 1.624 0.10481
## age -0.015132 0.015222 -0.994 0.32047
## dependency2:employment1 0.595547 1.009922 0.590 0.55555
## dependency3:employment1 0.659697 0.980491 0.673 0.50124
## dependency4:employment1 -0.834350 1.002996 -0.832 0.40572
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.555 on 868 degrees of freedom
## (29 observations deleted due to missingness)
## Multiple R-squared: 0.1591, Adjusted R-squared: 0.1494
## F-statistic: 16.43 on 10 and 868 DF, p-value: < 2.2e-16
Since there’s no significant interaction, we again adjust the plevel-argument to allow also non-significant interactions to be plotted.
sjp.int(fit, type = "emm", plevel = 1)
The above figure shows the “pre-post” comparison (non-employed/employed) of an “intervention” (negative impact of care) in different “treatment” and “control” groups (dependency levels).
If necessary, you can swap the variables for the x and y axis with the swap.pred argument.
sjp.int(fit,
type = "emm",
plevel = 1,
swap.pred = TRUE) | 2016-10-28T00:28:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5802910923957825, "perplexity": 5954.400743662018}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988721415.7/warc/CC-MAIN-20161020183841-00096-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://ftp.aimsciences.org/article/doi/10.3934/proc.2011.2011.963 | Article Contents
Article Contents
# Continuous maximal regularity and analytic semigroups
• In this paper we establish a result regarding the connection between continuous maximal regularity and generation of analytic semigroups on a pair of densely embedded Banach spaces. More precisely, we show that continuous maximal regularity for a closed operator $A$ : $E_1 \to E_0$ implies that $A$ generates a strongly continuous analytic semigroup on $E_0$ with domain equal $E_1$.
Mathematics Subject Classification: Primary: 35K90, 47D06; Secondary: 35K35.
Citation:
Open Access Under a Creative Commons license | 2023-03-21T17:24:50 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.3010075092315674, "perplexity": 439.41869746976454}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943704.21/warc/CC-MAIN-20230321162614-20230321192614-00578.warc.gz"} |
https://par.nsf.gov/biblio/10089798-zinc-finger-readers-methylated-dna | Zinc Finger Readers of Methylated DNA
DNA methylation is a prevalent epigenetic modification involved in regulating a number of essential cellular processes, including genomic accessibility and transcriptional outcomes. As such, aberrant alterations in global DNA methylation patterns have been associated with a growing number of disease conditions. Nevertheless, the full mechanisms by which DNA methylation information is interpreted and translated into genomic responses is not yet fully understood. Methyl-CpG binding proteins (MBPs) function as important mediators of this essential process by selectively reading DNA methylation signals and translating this information into down-stream cellular outcomes. The Cys2His2 zinc finger scaffold is one of the most abundant DNA binding motifs found within human transcription factors, yet only a few zinc finger containing proteins capable of conferring selectivity for mCpG over CpG sites have been characterized. This review summarizes our current structural understanding for the mechanisms by which the zinc finger MBPs evaluated to date read this essential epigenetic mark. Further, some of the biological implications for mCpG readout elicited by this family of MBPs are discussed.
Authors:
;
Award ID(s):
Publication Date:
NSF-PAR ID:
10089798
Journal Name:
Molecules
Volume:
23
Issue:
10
Page Range or eLocation-ID:
2555
ISSN:
1420-3049
National Science Foundation
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1. INTRODUCTION Transposable elements (TEs), repeat expansions, and repeat-mediated structural rearrangements play key roles in chromosome structure and species evolution, contribute to human genetic variation, and substantially influence human health through copy number variants, structural variants, insertions, deletions, and alterations to gene transcription and splicing. Despite their formative role in genome stability, repetitive regions have been relegated to gaps and collapsed regions in human genome reference GRCh38 owing to the technological limitations during its development. The lack of linear sequence in these regions, particularly in centromeres, resulted in the inability to fully explore the repeat content of the human genome in the context of both local and regional chromosomal environments. RATIONALE Long-read sequencing supported the complete, telomere-to-telomere (T2T) assembly of the pseudo-haploid human cell line CHM13. This resource affords a genome-scale assessment of all human repetitive sequences, including TEs and previously unknown repeats and satellites, both within and outside of gaps and collapsed regions. Additionally, a complete genome enables the opportunity to explore the epigenetic and transcriptional profiles of these elements that are fundamental to our understanding of chromosome structure, function, and evolution. Comparative analyses reveal modes of repeat divergence, evolution, and expansion or contraction with locus-level resolution. RESULTS We implementedmore »
2. INTRODUCTION To faithfully distribute genetic material to daughter cells during cell division, spindle fibers must couple to DNA by means of a structure called the kinetochore, which assembles at each chromosome’s centromere. Human centromeres are located within large arrays of tandemly repeated DNA sequences known as alpha satellite (αSat), which often span millions of base pairs on each chromosome. Arrays of αSat are frequently surrounded by other types of tandem satellite repeats, which have poorly understood functions, along with nonrepetitive sequences, including transcribed genes. Previous genome sequencing efforts have been unable to generate complete assemblies of satellite-rich regions because of their scale and repetitive nature, limiting the ability to study their organization, variation, and function. RATIONALE Pericentromeric and centromeric (peri/centromeric) satellite DNA sequences have remained almost entirely missing from the assembled human reference genome for the past 20 years. Using a complete, telomere-to-telomere (T2T) assembly of a human genome, we developed and deployed tailored computational approaches to reveal the organization and evolutionary patterns of these satellite arrays at both large and small length scales. We also performed experiments to map precisely which αSat repeats interact with kinetochore proteins. Last, we compared peri/centromeric regions among multiple individuals to understand how thesemore »
3. Abstract Polycomb repressive complex 2 (PRC2) is a histone methyltransferase that methylates histone H3 at Lysine 27. PRC2 is critical for epigenetic gene silencing, cellular differentiation and the formation of facultative heterochromatin. It can also promote or inhibit oncogenesis. Despite this importance, the molecular mechanisms by which PRC2 compacts chromatin are relatively understudied. Here, we visualized the binding of PRC2 to naked DNA in liquid at the single-molecule level using atomic force microscopy. Analysis of the resulting images showed PRC2, consisting of five subunits (EZH2, EED, SUZ12, AEBP2 and RBBP4), bound to a 2.5-kb DNA with an apparent dissociation constant ($K_{\rm{D}}^{{\rm{app}}}$) of 150 ± 12 nM. PRC2 did not show sequence-specific binding to a region of high GC content (76%) derived from a CpG island embedded in such a long DNA substrate. At higher concentrations, PRC2 compacted DNA by forming DNA loops typically anchored by two or more PRC2 molecules. Additionally, PRC2 binding led to a 3-fold increase in the local bending of DNA’s helical backbone without evidence of DNA wrapping around the protein. We suggest that the bending and looping of DNA by PRC2, independent of PRC2’s methylation activity, may contribute to heterochromatin formation and therefore epigenetic gene silencing.
4. (Ed.)
Abstract The methyltransferase like (METTL) proteins constitute a family of seven-beta-strand methyltransferases with S-adenosyl methionine binding domains that modify DNA, RNA, and proteins. Methylation by METTL proteins contributes to the epigenetic, and in the case of RNA modifications, epitranscriptomic regulation of a variety of biological processes. Despite their functional importance, most investigations of the substrates and functions of METTLs within metazoans have been restricted to model vertebrate taxa. In the present work, we explore the evolutionary mechanisms driving the diversification and functional differentiation of 33 individual METTL proteins across Metazoa. Our results show that METTLs are nearly ubiquitous across the animal kingdom, with most having arisen early in metazoan evolution (i.e., occur in basal metazoan phyla). Individual METTL lineages each originated from single independent ancestors, constituting monophyletic clades, which suggests that each METTL was subject to strong selective constraints driving its structural and/or functional specialization. Interestingly, a similar process did not extend to the differentiation of nucleoside-modifying and protein-modifying METTLs (i.e., each METTL type did not form a unique monophyletic clade). The members of these two types of METTLs also exhibited differences in their rates of evolution. Overall, we provide evidence that the long-term evolution of METTL family members wasmore »
5. Abstract Background
Environmental fluctuation during embryonic and fetal development can permanently alter an organism’s morphology, physiology, and behaviour. This phenomenon, known as developmental plasticity, is particularly relevant to reptiles that develop in subterranean nests with variable oxygen tensions. Previous work has shown hypoxia permanently alters the cardiovascular system of snapping turtles and may improve cardiac anoxia tolerance later in life. The mechanisms driving this process are unknown but may involve epigenetic regulation of gene expression via DNA methylation. To test this hypothesis, we assessed in situ cardiac performance during 2 h of acute anoxia in juvenile turtles previously exposed to normoxia (21% oxygen) or hypoxia (10% oxygen) during embryogenesis. Next, we analysed DNA methylation and gene expression patterns in turtles from the same cohorts using whole genome bisulfite sequencing, which represents the first high-resolution investigation of DNA methylation patterns in any reptilian species.
Results
Genome-wide correlations between CpG and CpG island methylation and gene expression patterns in the snapping turtle were consistent with patterns observed in mammals. As hypothesized, developmental hypoxia increased juvenile turtle cardiac anoxia tolerance and programmed DNA methylation and gene expression patterns. Programmed differences in expression of genes such asSCN5Amay account for differences in heart rate, while genes such asTNNT2andTPM3maymore »
Conclusions
Our data strongly suggests that DNA methylation plays a conserved role in the regulation of gene expression in reptiles. We also show that embryonic hypoxia programs DNA methylation and gene expression patterns and that these changes are associated with enhanced cardiac anoxia tolerance later in life. Programming of cardiac anoxia tolerance has major ecological implications for snapping turtles, because these animals regularly exploit anoxic environments throughout their lifespan. | 2023-03-29T22:05:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.29499247670173645, "perplexity": 9140.929748083872}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949035.66/warc/CC-MAIN-20230329213541-20230330003541-00303.warc.gz"} |
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Lecture 3: Informal Example
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Schedule :: Intro :: Informal Example :: Function Spaces
We briefly review the concept of a vector space. A vector space has the following key property: If then for any scalars and . That is, linear combinations of vectors give vectors.
Most of your background with vectors has been for vectors in . But: the signals that we deal with are also elements of a vector space , since linear combinations of signals also gives a signal. This is a very important and powerful idea.
Recall that in vector spaces we deal with concepts like the length of a vector, the angle between vectors, and the idea of orthogonal vectors. All of these concepts carry over, by suitable definitions, to vector spaces of signals.
This powerful idea captures most of the significant and interesting notions in signal processing, controls, and communications. This is really the reason why the study of linear algebra is so important.
In this lecture we will learn about geometric representations of signals via signal space (vector) concepts. This straightforward idea is the key to a variety of topics in signals and systems:
1. It provides a distance concept useful in many pattern recognition techniques.
2. It is used in statistical signal processing for the filtering, smoothing, and prediction of noisy signals.
3. It forms the heart and geometric framework for the tremendous advances that have been made in digital communications.
4. It is every waveform-based transform you ever wanted (Fourier series, FFT, DCT, wavelet, etc.)
5. It is also used in the solution of partial differential equations, etc.
6. It relies on our old friend, linearity. One might even say it is the reason that we care so much about linearity in the first place.
We will soon turn our attention to Fourier series, which are a way of analyzing and synthesizing signals.
Vectors will be written in bold font (like the ingredients above. Initially, we can think of a vector as an ordered set of numbers, written in a column:
Often to conserve writing, this will be written in transposed form,
While we have written a vector as an -tuple, that is not what defines a vector. A vector is an element of a vector space, which is to say, it satisfies the linearity property given above.
Scalar multiplication of vectors is in the usual fashion. Matrix multiplication is also taken in the traditional manner.
Let
and
be two vectors. The inner product (known to many of you as the dot product ) of the vectors and is written as
In words, multiply component by component, and add them up. Two vectors are said to be orthogonal or perpendicular if their inner product is zero:
If and are orthogonal, this is sometimes written
The inner product can be expanded using the following rules:
1. For a scalar ,
2.
3. For real vectors (which is all we will be concerned about for the moment)
The (Euclidean) norm of a vector is given by
The distance between two vectors is given by
The projection of a vector onto a vector is given by
Geometrically, this is the amount of the vector in the direction of . (Show a picture.) Obviously, if and are orthogonal, then the projection of onto is 0.
Now suppose that we have a vector (an ingredient'') and we have a vector and we want to make the best approximation to using some amount of our ingredient. Draw a picture. We can write
where is the amount of we want and is the error between the thing we want and our approximation of it. To get the best approximation we want to minimize the length of the error vector. Before we go through and do it the hard way, let us make a geometric observation. The length of the error is minimized when the error vector is orthogonal to our ingredient vector :
or
Giving us
Note that this is simply the projection of onto the vector .
Now let's do it the hard way: we want to find the amount of to minimize the (length of the) error. The squared length of the error is
To minimize this, take the derivative with respect to the coefficient and equate to zero:
Solving for the coefficient,
This is the same one we got before.
We may actually have more than one ingredient'' vector to deal with. Suppose we want to approximate with the vectors and . As before write
where is the error in the approximation. Note that we can write this in the following way:
using the usual matrix multiplication. We want to find the coefficients and to minimize the length of the error. We could to it the calculus way, or using our orthogonality idea. We will go for the latter: The error is orthogonal to the data means that
(that is, the error is orthogonal to each of the ingredient "data'' points). Expanding these out gives
This is two equations in two unknowns that we can write in the form
If we know and the ingredient vectors, we can solve for the coefficients.
Of course, what we can do for two ingredient vectors, we can do for ingredient vectors (and may be infinite). We want to approximate as
We can find the set of coefficients that minimize the length of the error using the orthogonality principle as before, applied times. This gives us equations in the unknowns which may be written as
This could be readily solved (say, using Matlab).
It would seem that if we take large enough, we should be able to represent any vector. without any error. (Analogy: given enough ingredients, we could make any cake. We might not be able to make everything, but we could make everything some class of objects.) If this is true, the set of ingredient vectors are said to be complete . A more formal name for the ingredient vectors is basis vectors .
Although we have come up with a way of doing the approximation, there is still a lot of work to solve for the coefficients, since we have to first find a matrix and then invert it. Something that is commonly done is to choose a set of basis vectors that is orthogonal . That is, if and are any pair of basis vectors, then
Let us return to the case of two basis vectors when the vectors are orthogonal. Then the equation for the coefficients becomes
or
so the coefficients are
So solving for the coefficients in this case is as easy as doing it for the case of a single vector, and the coefficient is simply the projection of onto its corresponding basis vector. This generalizes to basis vectors: If the basis vectors are orthogonal, then the coefficient is simply
Copyright 2008, by the Contributing Authors. Cite/attribute Resource . admin. (2006, May 22). Lecture 3: Informal Example. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Signals_and_Systems/3_2node2.html. This work is licensed under a Creative Commons License | 2017-09-19T22:38:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8557258248329163, "perplexity": 326.8822634873995}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818686043.16/warc/CC-MAIN-20170919221032-20170920001032-00475.warc.gz"} |
https://www.mcs.anl.gov/research/projects/otc/InteriorPoint/abstracts/Anstreicher-Wolkowicz-1.html | On Lagrangian Relaxation of Quadratic Matrix Constraints
Kurt Anstreicher and Henry Wolkowicz
Quadratically constrained quadratic programs (QQP) play an important modeling role for many diverse problems. These problems are in general NP hard, and numerically intractable. Lagrangian relaxations often provide good approximate solutions to these hard problems. Such relaxations are equivalent to semidefinite programming relaxations. For several special cases of QQP, e.g. convex programs and trust region subproblems, the Lagrangian relaxation provides the exact optimal value, i.e. there is a zero duality gap. However this is not true for the general QQP, or even the QQP with two convex constraints, but a nonconvex objective. In this paper we consider a certain QQP where the quadratic constraints correspond to the matrix orthogonality condition $X\tran X=I$. For this problem we show that the Lagrangian dual based on relaxing the constraints $X\tran X=I$, {\em and} the seemingly redundant constraints $X\tran X=I$, has a zero duality gap. This result has natural applications to quadratic assignment and graph partitioning problems, as well as the problem of minimizing the weighted sum of the largest eigenvalues of a matrix. We also show that the technique of relaxing quadratic matrix constraints can be used to obtain a strengthened semidefinite relaxation for the max-cut problem.
Research Report CORR 98-24 University of Waterloo Department of Combinatorics and Optimization Waterloo, Ontario N2L 3G1, Canada
Contact: [email protected] | 2019-09-22T23:15:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8790904879570007, "perplexity": 500.83698457436907}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514575751.84/warc/CC-MAIN-20190922221623-20190923003623-00142.warc.gz"} |
https://frommyslipbox.blogspot.com/2021/04/how-to-eliminate-confounding-in.html | ### How to eliminate confounding in multivariate regression
Great grey owl (Creative Commons).
### Preamble
For my previous post on causal diagrams, I made up a fake dataset relating the incidence of COVID-19 to the wearing of protective goggles for hypothetical individuals. The dataset included several related covariates, such as whether the person in question was worried about COVID-19.
The goal of the exercise was to (hypothetically!) determine whether protective glasses was an effective intervention for COVID-19, and to see how accidental associations due to other variables could mess up the analysis.
I faked the data so that COVID-19 incidence was independent of whether the person wore protective goggles. But then I demonstrated, using multivariate regressions, that it is easy to incorrectly conclude that protective glasses are significantly effective for reducing the risk of COVID-19. I also showed how a causal diagram relating the variables can be used to determine which variables to include and exclude from the analysis.
In this article, I'll explain how to recognize the patterns in causal diagrams that lead to statistical confounding, and show how to do a causal analysis yourself.
Here's the entire 'statistical confounding' series:
- Part 1: Statistical confounding: why it matters: on the many ways that confounding affects statistical analyses
- Part 2: Simpson's Paradox: extreme statistical confounding: understanding how statistical confounding can cause you to draw exactly the wrong conclusion
- Part 3: Linear regression is trickier than you think: a discussion of multivariate linear regression models
- Part 4: A gentle introduction to causal diagrams: a causal analysis of fake data relating COVID-19 incidence to wearing protective goggles
- Part 5: How to eliminate confounding in multivariate regression (this post): how to do a causal analysis to eliminate confounding in your regression analyses
-Part 6: A simple example of omitted variable bias: an example of statistical confounding that can't be fixed, using only 4 variables.
### Introduction
In A gentle introduction to causal diagrams, I introduced a fake dataset in which rows represented individuals, containing the following information:
- $C$: does the person test positive for COVID-19?
- $G$: does the person wear protective glasses in public?
- $W$: is the person worried about COVID-19?
- $S$: does the person avoid social contact?
- $V$: is the person vaccinated?
I then did some multivariate logistic regressions to answer the following question: does wearing protective goggles help reduce the likelihood of catching COVID-19?
In generating the dataset, I made the following assumptions:
- protective glasses have no direct effect on COVID-19 incidence;
- avoiding social contact has a significant negative effect on COVID-19 incidence;
- getting vaccinated has a very significant negative effect on COVID-19 incidence;
- being worried about COVID makes a person much more likely to get vaccinated, avoid social contact, and wear protective glasses;
- being vaccinated makes a person less likely to avoid social contact.
The causal diagram associated with these variables and assumptions is shown below. An arrow from one variable to another indicates that the value of the 'to' variable depends on the 'from' variable.
The exercise in the article was to determine which variables to include in a multivariate regression, in order to analyze whether protective glasses reduce the risk of catching COVID-19. The colored nodes are the ones that were ultimately included; only the $W$ (worried about COVID-19) variable was used as a covariate, in addition to the dependent and independent variables $G$ and $C$.
### Backdoor paths
In the diagram above, the causal relationship we want to assess (between $G$ and $C$) is represented by the gray dashed arrow. But there are a lot of other connections with intermediate variables, in the form of paths in the graph between $G$ and $C$, that can accidentally generate statistical associations between $G$ and $C$.
The first such path is shown below: it passes from $G$ to $W$ to $S$ to $C$. This is called a 'backdoor path' because arrow 1 points into $G$, rather than emitting from $G$. This path can be described in words as follows: if the person is worried about COVID-19, this makes her more likely to both wear protective glasses and socially distance. Since social distancing is an effective intervention against COVID-19, this sets up a negative correlation between wearing glasses and catching COVID-19; but the dataset was constructed so that protective glasses had no impact on COVID-19, so the effect is only due to correlation, not causation.
A second path is shown below: it passes from $G$ through $W$ to $V$ and then to $C$. In words: If a person is worried about COVID-19, he is more likely to both wear protective glasses and to get vaccinated. Since vaccination is an effective intervention against COVID-19, this again sets up a negative correlation between wearing glasses and catching COVID-19.
A third path is shown below: it passes from $G$ through $W$ to $V$, then to $S$ and finally $C$. In words: if a person is worried about COVID-19, she is more likely to get vaccinated, after which she may be less likely to socially distance. This is a problem in our analysis if we do not know the person's vaccination status, since the presence of a lot of people who do not socially distance, and yet do not catch COVID-19, will obscure the effectiveness of social distancing as an intervention. In the presence of enough vaccine-positive people, it might even appear that people who do not socially distance are *less* likely to get COVID-19 if we don't know people's vaccination status!
There is another type of backdoor path to consider, shown below. Backdoor path 4 passes from $G$ to $W$, through $S$ and $V$, to $C$. Backdoor path 4 will not cause confounding unless we make the mistake of conditioning on variable $S$. The variable $S$ is called a collider variable, because it has two arrows in the path pointing into it. We have to be careful not to condition on a collider variable, i.e., not to include it in the multivariable regression.
### Patterns of confounding
Each of the backdoor paths in any causal diagram can be broken down into a series of connections among three variables in the path. There are 3 relationships that can occur among these 3 variables: the 'fork' pattern, the 'pipe' pattern, and the 'collider' pattern.
Fork pattern
The image below shows the 'fork' pattern, which occurs in our example among the variables $G, W$, and $S$. The fork occurs when a single variable affects two 'child' variables; in this case, being worried makes a person both more likely to socially distance, and more likely to wear protective glasses.
If three variables are related by the fork pattern, then the two child variables will be marginally statistically dependent, but will be independent if we condition on the parent variable. Mathematically, the fork pattern says that:
$$p(G, W, S) = p(G|W)p(S|W)p(W).$$
Since $p(G,S)=\int p(G|V)p(S|V)p(V) dV$, it follows that $p(G,S)\ne p(G)\cdot p(S)$ in general. However, $p(G,S|V)=p(G|V)\cdot p(S|V)$; in this graph of 3 variables, $W$ and $S$ are conditionally independent given $V$.
In words, this says that if I know whether a person is worried about COVID-19, then knowing whether a person socially distances tells me nothing additional about whether they are likely to wear glasses.
Pipe pattern
The image below shows the 'pipe' pattern, which occurs in our example among the variables $W, S$, and $C$. The pipe occurs when a variable is causally 'in-between' two other variables. In this case, being worried causes a person to socially distance, which in turn reduces their chance of getting COVID-19.
If three variables are related by the pipe pattern, then the two outer variables will be marginally statistically dependent, but will be independent if we condition on the inner variable. Mathematically, $p(W,C)\ne p(W)\cdot p(C)$ in general, but $p(W,C|S)=p(W|S)p(C|S)$. The fork and pipe patterns are alike in this regard.
In words, this says that if I know whether a person is avoiding social contact, then knowing whether the person is worried about COVID-19 tells me nothing additional about whether they might have caught it.
Collider pattern
The collider pattern occurs when a single variable is dependent on two unrelated parent variables. There aren't any simple collider pattern examples in our example causal diagram -- for example, social distancing $S$ is dependent both on $V$ and $W$, but these two variables are also directly related to each other. So I've added an extra random variable in the diagram below: $N$, which is 1 if the person is nearsighted, and 0 otherwise. Clearly, being nearsighted is another reason why someone might wear glasses.
The collider pattern is different from the fork and pipe patterns. In the collider pattern, the two parents of the common child are marginally independent of each other. Mathematically, we have $p(N,W) = p(N)p(W)$ (it follows from the definition of the joint distribution, $p(N,W,G)=p(G|N,W)p(N)p(W)$), but $p(N,W|G)\ne p(N|G)\cdot p(W|G)$ in general. In other words, conditioning the regression on the 'collider variable' $G$ causes the parent variables $N,W$ to become associated. But the association is purely statistical; the two parent variables are still causally unrelated.
To see why this happens, imagine that you know nothing about whether a person wears glasses or not. Then knowing in addition that the person is nearsighted gives you no additional information about whether they are worried about COVID-19.
But suppose that you now know that the person is wearing glasses (i.e., you are conditioning on $G=1$). If you know in addition that the person is not nearsighted, then the odds are higher that they are wearing glasses because they are worried about COVID-19; and if you know that they are not worried about COVID-19, the odds increase that they are wearing glasses because they are nearsighted. So the parent variables become related. Collider bias is sometimes called 'explaining away'; knowing that a person is nearsighted 'explains away' their reason for wearing glasses.
Putting it together
This tells you everything you need to know in order to construct an unconfounded multivariate regression analysis, in order to determine whether one variable has a causal impact on another. The game is to 'block all the backdoor paths', to prevent them from causing accidental correlations between the dependent and independent variables.
For example, consider 'backdoor path 1' at the beginning of the article. This path contains a fork pattern (the variable $W$, pointing to $G$ and $S$) and a pipe pattern (the variable $S$, which is pointed to by $W$, and which points to $C$). If we don't condition on $W$ or $S$, then these variables will set up associations between $G$ and $S$, and between $W$ and $C$; the unbroken line of associations sets up a relationship between $G$ and $C$ that is only a correlation, not causal.
In order to prevent this from happening, we need to condition on either $W$ or $S$. We must choose one of them; conditioning on either one of them will break that chain of association. This is called 'blocking the backdoor path'. But blocking one backdoor path isn't enough; we must block all of them.
Consider backdoor path 2 from $G$ to $C$; it contains a fork variable, $W$, and a pipe variable, $V$. Conditioning on either $V$ or $W$ will block backdoor path 2. Note that conditioning on $W$ will block both backdoor paths 1 and 2, but conditioning on $V$ or $S$ will leave one of the paths unblocked.
Now consider backdoor path 3. Backdoor path 3 contains a fork variable, $W$; a pipe variable, $V$; and another pipe variable, $S$. Conditioning on any of these will block this backdoor path, so again, $W$ will work for this path.
Finally, looking at backdoor path 4, we see that $S$ is a collider variable in this path. Looking at this path in isolation, $W$ and $V$ will be marginally independent of each other. But if we condition on the variable $S$, that will set up an association between $W$ and $V$, which will connect all the variables in backdoor path 4, and cause confounding.
The following shows how the association between $W$ and $V$ can occur, as a result of knowing the value of $S$. Suppose we know for sure that a person is not avoiding social contact (i.e., we have conditioned on $S$). Suppose we also know that this person is worried about COVID-19; then this makes it highly likely that the person is vaccinated, since they would otherwise be avoiding people. Conversely, if we know that a person is not avoiding social contact, and we also know that the person is not vaccinated, then it is highly likely that they just aren't worried about COVID-19.
The fact that $S$ is a collider in this path means that we have to avoid conditioning on $S$ (including it in the regression). Conditioning on it will open backdoor path 4, which would otherwise be blocked.
To summarize, there are 5 total backdoor paths in this diagram -- the four we have discussed, and one other that also contains the variable $S$ as a collider (see if you can find it). Conditioning on $W$ will block the first 3 backdoor paths, and will not accidentally unblock the two paths that contain $S$ as a collider variable. Therefore, a multivariate regression that contains only $W$ as a covariate, $G$ as the independent variable, and $C$ as the dependent variable, will correctly show that wearing glasses has no effect on COVID-19 incidence. | 2021-06-13T01:28:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6565737128257751, "perplexity": 705.3394217583655}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487598213.5/warc/CC-MAIN-20210613012009-20210613042009-00241.warc.gz"} |
https://studenttheses.uu.nl/handle/20.500.12932/10231?show=full | dc.rights.license CC-BY-NC-ND dc.contributor.advisor Bisseling, Prof. dr. R.H. dc.contributor.author Bleichrodt, F. dc.date.accessioned 2012-03-27T17:00:55Z dc.date.available 2012-03-27 dc.date.available 2012-03-27T17:00:55Z dc.date.issued 2012 dc.identifier.uri https://studenttheses.uu.nl/handle/20.500.12932/10231 dc.description.abstract The two-dimensional barotropic vorticity equation is one of basic equations of ocean dynamics. It is important to have efficient numerical solution techniques to solve this equation. In this paper, we present an implementation of a numerical solution of this equation using a Graphics Processing Unit (GPU). The speed-up of the calculation on the GPU with respect to that on a CPU depends on the grid size but reaches a factor 50 for the highest resolution cases ($4800 \times 4800$) tested. It may therefore be efficient to use GPU's in future high-resolution ocean modeling studies. dc.description.sponsorship Utrecht University dc.format.extent 590822 bytes dc.format.mimetype application/pdf dc.language.iso en dc.title Accelerating finite differences for solving a barotropic ocean model on the GPU dc.type.content Master Thesis dc.rights.accessrights Open Access dc.subject.courseuu Scientific Computing
| 2022-12-09T08:15:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.28419381380081177, "perplexity": 4268.514931603823}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711394.73/warc/CC-MAIN-20221209080025-20221209110025-00257.warc.gz"} |
https://pages.nist.gov/feasst/plugin/confinement/doc/ModelTableCart1DHard.html | # ModelTableCart1DHard¶
class ModelTableCart1DHard : public feasst::ModelOneBody
A tabular potential based on cartesian coordinates. Assumes symmetry along the x plane and that the Domain has no tilt.
Public Functions
void compute_table(Shape *shape, Domain *domain, Random *random, const argtype &args = argtype(), const int site_type = 0)
Generate the table by finding where the point is inside the shape and the nearest distance to the surface is half of the diameter. The initial bounds are [0, L/2] inclusive, assuming a plane (or line) of symmetry at origin perpendicular to y axis.
args:
• diameter: diameter of the sphere (default: 1)
double energy(const Position &wrapped_site, const Site &site, const Configuration &config, const ModelParams &model_params)
Return the energy given the wrapped coordinates, site, config and params.
void serialize(std::ostream &ostr) const
Output a serialized version of the existing model.
class ModelTableCart2DIntegr : public feasst::ModelOneBody
A tabular potential based on cartesian coordinates. Assumes symmetry along the x, y planes and that the Domain has no tilt. Integration of material does not take periodicity into account. E.g., the shapes extend forever and are not periodic in the domain.
Public Functions
void compute_table(Shape *shape, Domain *domain, Random *random, const argtype &integration_args, const int site_type = 0)
Parameters
• integration_args: See Shape for documentation of integration_args.
Generate the table by integration of the shape of the confinement over the entire and domain.
void compute_table_omp(Shape *shape, Domain *domain, Random *random, const argtype &integration_args, const int site_type = 0, const int node = 0, const int num_node = 1)
Same as above, but parallelize the task with OMP.
Parameters
• node: See Thread for documentation of these two arguments.
double energy(const Position &wrapped_site, const Site &site, const Configuration &config, const ModelParams &model_params)
Return the energy given the wrapped coordinates, site, config and params.
void serialize(std::ostream &ostr) const
Output a serialized version of the existing model.
class ModelTableCart3DIntegr : public feasst::ModelOneBody
A tabular potential based on cartesian coordinates. Assumes symmetry along the x, y and z planes and that the Domain has no tilt. Integration of material does not take periodicity into account. E.g., the shapes extend forever and are not periodic in the domain.
Public Functions
const Table3D &table(const int site_type = 0) const
Return the table for a given site type.
void compute_table(Shape *shape, Domain *domain, Random *random, const argtype &integration_args, const int site_type = 0)
Parameters
• integration_args: See Shape for documentation of integration_args.
Generate the table by integration of a shape, which represents a continuous medium, over the entire domain.
void compute_table_omp(Shape *shape, Domain *domain, Random *random, const argtype &integration_args, const int site_type = 0, const int node = 0, const int num_nodes = 1)
Same as above, but parallelize the task with OMP.
Parameters
• node: See Thread for documentation of these two arguments.
void compute_table(System *system, Select *select, const int site_type = 0)
Generate the table by computing the energy of interaction of the select with the rest of the system. The select is assumed to be a single site, so that tables can be generated for each site type.
void compute_table_omp(System *system, Select *select, const int site_type = 0, const int node = 0, const int num_node = 1)
Same as above, but parallelize the task with OMP.
Parameters
• node: See Thread for documentation of these two arguments.
double energy(const Position &wrapped_site, const Site &site, const Configuration &config, const ModelParams &model_params)
Return the energy given the wrapped coordinates, site, config and params.
void serialize(std::ostream &ostr) const
Output a serialized version of the existing model. | 2021-03-05T08:17:50 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.32330772280693054, "perplexity": 12143.700420775971}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178370239.72/warc/CC-MAIN-20210305060756-20210305090756-00210.warc.gz"} |
https://zbmath.org/authors/?q=ai%3Ashintani.takuro | # zbMATH — the first resource for mathematics
## Shintani, Takuro
Compute Distance To:
Author ID: shintani.takuro Published as: Shintani, T.; Shintani, Takuro External Links: MGP · Wikidata
Documents Indexed: 27 Publications since 1967 Biographic References: 1 Publication
#### Co-Authors
23 single-authored 4 Sato, Mikio 2 Muro, Masakazu
all top 5
#### Serials
6 Journal of the Mathematical Society of Japan 6 Proceedings of the Japan Academy 3 Journal of the Faculty of Science. Section I A 2 Nagoya Mathematical Journal 1 Tokyo Journal of Mathematics 1 Proceedings of the National Academy of Sciences of the United States of America 1 Annals of Mathematics. Second Series
all top 5
#### Fields
21 Number theory (11-XX) 5 Algebraic geometry (14-XX) 4 Topological groups, Lie groups (22-XX) 3 Special functions (33-XX) 3 Abstract harmonic analysis (43-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 Group theory and generalizations (20-XX)
#### Citations contained in zbMATH Open
24 Publications have been cited 746 times in 610 Documents Cited by Year
On construction of holomorphic cusp forms of half integral weight. Zbl 0316.10016
Shintani, Takuro
1975
On evaluation of zeta functions of totally real algebraic number fields at non-positive integers. Zbl 0349.12007
Shintani, Takuro
1976
On zeta functions associated with prehomogeneous vector spaces. Zbl 0309.10014
Sato, Mikio; Shintani, Takuro
1974
On a Kronecker limit formula for real quadratic fields. Zbl 0364.12012
Shintani, Takuro
1977
On zeta-functions associated with the vector space of quadratic forms. Zbl 0313.10041
Shintani, Takuro
1975
On an explicit formula for class-1 ”Whittaker functions” on $$GL_n$$ over $$\mathfrak p$$ -adic fields. Zbl 0387.43002
Shintani, Takuro
1976
On Dirichlet series whose coefficients are class numbers of integral binary cubic forms. Zbl 0227.10031
Shintani, Takuro
1972
Theory of prehomogeneous vector spaces. (Algebraic part). - The English translation of Sato’s lecture from Shintani’s note. Zbl 0715.22014
Sato, Mikio; Shintani, Takuro; Muro, Masakazu
1990
Two remarks on irreducible characters of finite general linear groups. Zbl 0323.20041
Shintani, T.
1976
A proof of the classical Kronecker limit formula. Zbl 0462.10014
Shintani, Takuro
1980
On certain ray class invariants of real quadratic fields. Zbl 0392.12009
Shintani, Takuro
1978
On Dirichlet series whose coefficients are class numbers of integral binary cubic forms. Zbl 0223.10032
Shintani, T.
1972
On certain square-integrable irreducible unitary representations of some p-adic linear groups. Zbl 0194.05602
Shintani, T.
1968
On zeta functions associated with prehomogeneous vector spaces (algebraic groups/gamma function/Dirichlet series). Zbl 0249.10034
Sato, Mikio; Shintani, Takuro
1972
On Kronecker limit formula for real quadratic fields. Zbl 0359.12004
Shintani, Takuro
1976
On special values of zeta functions of totally real algebraic number fields. Zbl 0426.12008
Shintani, Takuro
1980
On values at $$s=1$$ of certain $$L$$ functions of totally real algebraic number fields. Zbl 0363.12013
Shintani, Takuro
1977
On liftings of holomorphic cusp forms. Zbl 0415.10019
Shintani, Takuro
1979
On the decomposition of regular representation of the Lorentz group on a hyperboloid of one sheet. Zbl 0184.17403
Shintani, T.
1967
A remark on zeta functions of algebraic number fields. Zbl 0503.12006
Shintani, Takuro
1981
On irreducible unitary characters of a certain group extension of $$\text{GL}(2,\mathbb C)$$. Zbl 0342.20021
Shintani, T.
1977
On certain ray class invariants of real quadratic fields. Zbl 0377.12008
Shintani, Takuro
1977
On zeta-functions associated with the lattice of Hermitian forms with Gaussian integral coefficients. Zbl 0309.10015
Shintani, Takuro
1971
On certain square integrable irreducible unitary representations of some P-adic linear groups. Zbl 0265.22023
Shintani, Takuro
1968
Theory of prehomogeneous vector spaces. (Algebraic part). - The English translation of Sato’s lecture from Shintani’s note. Zbl 0715.22014
Sato, Mikio; Shintani, Takuro; Muro, Masakazu
1990
A remark on zeta functions of algebraic number fields. Zbl 0503.12006
Shintani, Takuro
1981
A proof of the classical Kronecker limit formula. Zbl 0462.10014
Shintani, Takuro
1980
On special values of zeta functions of totally real algebraic number fields. Zbl 0426.12008
Shintani, Takuro
1980
On liftings of holomorphic cusp forms. Zbl 0415.10019
Shintani, Takuro
1979
On certain ray class invariants of real quadratic fields. Zbl 0392.12009
Shintani, Takuro
1978
On a Kronecker limit formula for real quadratic fields. Zbl 0364.12012
Shintani, Takuro
1977
On values at $$s=1$$ of certain $$L$$ functions of totally real algebraic number fields. Zbl 0363.12013
Shintani, Takuro
1977
On irreducible unitary characters of a certain group extension of $$\text{GL}(2,\mathbb C)$$. Zbl 0342.20021
Shintani, T.
1977
On certain ray class invariants of real quadratic fields. Zbl 0377.12008
Shintani, Takuro
1977
On evaluation of zeta functions of totally real algebraic number fields at non-positive integers. Zbl 0349.12007
Shintani, Takuro
1976
On an explicit formula for class-1 ”Whittaker functions” on $$GL_n$$ over $$\mathfrak p$$ -adic fields. Zbl 0387.43002
Shintani, Takuro
1976
Two remarks on irreducible characters of finite general linear groups. Zbl 0323.20041
Shintani, T.
1976
On Kronecker limit formula for real quadratic fields. Zbl 0359.12004
Shintani, Takuro
1976
On construction of holomorphic cusp forms of half integral weight. Zbl 0316.10016
Shintani, Takuro
1975
On zeta-functions associated with the vector space of quadratic forms. Zbl 0313.10041
Shintani, Takuro
1975
On zeta functions associated with prehomogeneous vector spaces. Zbl 0309.10014
Sato, Mikio; Shintani, Takuro
1974
On Dirichlet series whose coefficients are class numbers of integral binary cubic forms. Zbl 0227.10031
Shintani, Takuro
1972
On Dirichlet series whose coefficients are class numbers of integral binary cubic forms. Zbl 0223.10032
Shintani, T.
1972
On zeta functions associated with prehomogeneous vector spaces (algebraic groups/gamma function/Dirichlet series). Zbl 0249.10034
Sato, Mikio; Shintani, Takuro
1972
On zeta-functions associated with the lattice of Hermitian forms with Gaussian integral coefficients. Zbl 0309.10015
Shintani, Takuro
1971
On certain square-integrable irreducible unitary representations of some p-adic linear groups. Zbl 0194.05602
Shintani, T.
1968
On certain square integrable irreducible unitary representations of some P-adic linear groups. Zbl 0265.22023
Shintani, Takuro
1968
On the decomposition of regular representation of the Lorentz group on a hyperboloid of one sheet. Zbl 0184.17403
Shintani, T.
1967
all top 5
#### Cited by 568 Authors
11 Yukie, Akihiko 10 Kohnen, Winfried 10 Kurokawa, Nobushige 10 Sato, Fumihiro 9 Friedberg, Solomon 9 Kudla, Stephen S. 8 Choi, Junesang 8 Muro, Masakazu 7 Eie, Minking 7 Rubenthaler, Hubert 6 Bringmann, Kathrin 6 Funke, Jens 6 Gerasimov, Anton A. 6 Kimura, Tatsuo 6 Lebedev, Dimitri R. 6 Lee, Jungyun 6 Millson, John J. 6 Oblezin, Sergey 6 Srivastava, Hari Mohan 5 Flicker, Yuval Z. 5 Kane, Ben 5 Kojima, Hisashi 5 Murase, Atsushi 5 Tangedal, Brett A. 5 Taniguchi, Takashi 4 Abramov, Sergeĭ Aleksandrovich 4 Bhargava, Manjul 4 Bump, Daniel 4 Duke, William Drexel 4 Gelbart, Stephen S. 4 Halbritter, Ulrich 4 Imamoḡlu, Özlem 4 Kable, Anthony C. 4 Mizuno, Yoshinori 4 Oda, Takayuki 4 Piatetski-Shapiro, Ilya 4 Shintani, Takuro 4 Solomon, David R. 4 Stasinski, Alexander 4 Sugano, Takashi 4 Tsuzuki, Masao 4 Wang, Shuping 4 Wright, David J. 3 Asai, Teruaki 3 Belabas, Karim 3 Brown, Jim L. 3 Cassou-Noguès, Pierrette 3 Chen, Shaoshi 3 Colmez, Pierre 3 Đoković, Dragomir Ž. 3 Espinoza, Milton 3 Friedman, Eduardo C. 3 Ginzburg, David 3 Hirose, Minoru 3 Hoffmann, Werner 3 Jun, Byungheup 3 Li, Yingkun 3 Lőrincz, András Cristian 3 Manickam, Murugesan 3 Mao, Zhengyu 3 Matringe, Nadir 3 Nishizawa, Michitomo 3 Niwa, Shinji 3 Petkovšek, Marko 3 Ramakrishnan, Balakrishnan 3 Raulf, Nicole 3 Rubin, Boris 3 Sadykov, Timur Mradovich 3 Sands, Jonathan W. 3 Sato, Mikio 3 Schiffmann, Gérard 3 Schwagenscheidt, Markus 3 Sczech, Robert 3 Strömberg, Fredrik 3 Tanaka, Hidekazu 3 Tong, Yue Lin Lawrence 3 Wakatsuki, Satoshi 3 Wakayama, Masato 3 Zemel, Shaul 2 Adler, Jeffrey D. 2 Agarwal, Mahesh 2 Alfes-Neumann, Claudia 2 Anandavardhanan, U. K. 2 Aomoto, Kazuhiko 2 Barquero-Sanchez, Adrian 2 Bennett, Michael A. 2 Bertolini, Massimo 2 Blind, Bruno 2 Böcherer, Siegfried 2 Brubaker, Ben 2 Bruinier, Jan Hendrik 2 Byeon, Dongho 2 Bykovskiĭ, Viktor Alekseevich 2 Choie, YoungJu 2 Cipra, Barry A. 2 Clozel, Laurent 2 Damon, James Norman 2 Darmon, Henri René 2 Dasgupta, Samit 2 Datskovsky, Boris A. ...and 468 more Authors
all top 5
#### Cited in 122 Serials
63 Journal of Number Theory 34 Mathematische Annalen 33 Inventiones Mathematicae 26 Transactions of the American Mathematical Society 24 Journal of Algebra 22 Nagoya Mathematical Journal 20 Duke Mathematical Journal 19 Advances in Mathematics 18 Tohoku Mathematical Journal. Second Series 16 Compositio Mathematica 16 Proceedings of the Japan Academy. Series A 14 Mathematische Zeitschrift 14 Proceedings of the American Mathematical Society 12 Annales de l’Institut Fourier 10 Mathematics of Computation 10 Journal of Functional Analysis 9 The Ramanujan Journal 8 Communications in Mathematical Physics 8 Israel Journal of Mathematics 8 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 7 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 7 Journal of Soviet Mathematics 6 Publications of the Research Institute for Mathematical Sciences, Kyoto University 6 Bulletin of the American Mathematical Society. New Series 6 Annals of Mathematics. Second Series 6 Journal of High Energy Physics 6 International Journal of Number Theory 6 Research in the Mathematical Sciences 5 Journal of Mathematical Analysis and Applications 5 Manuscripta Mathematica 5 Journal de Théorie des Nombres de Bordeaux 5 Selecta Mathematica. New Series 4 Letters in Mathematical Physics 4 Applied Mathematics and Computation 4 Journal of the Mathematical Society of Japan 4 Journal of Symbolic Computation 4 Bulletin of the American Mathematical Society 4 Proceedings of the Japan Academy 3 Communications in Algebra 3 Bulletin de la Société Mathématique de France 3 Publications Mathématiques 3 Journal of Pure and Applied Algebra 3 Journal für die Reine und Angewandte Mathematik 3 Memoirs of the American Mathematical Society 3 Advances in Applied Mathematics 3 Journal of the American Mathematical Society 3 Forum Mathematicum 3 Representation Theory 3 Research in Number Theory 2 Journal of Mathematical Physics 2 Theoretical and Mathematical Physics 2 Acta Arithmetica 2 Glasgow Mathematical Journal 2 Journal of Combinatorial Theory. Series A 2 Mathematika 2 Michigan Mathematical Journal 2 Monatshefte für Mathematik 2 Neural Computation 2 The Journal of Geometric Analysis 2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 2 Indagationes Mathematicae. New Series 2 Kyushu Journal of Mathematics 2 The Journal of Fourier Analysis and Applications 2 Journal of Topology 2 Kyoto Journal of Mathematics 2 Annales Mathématiques du Québec 2 Journal of Siberian Federal University. Mathematics & Physics 1 Bulletin of the Australian Mathematical Society 1 Computer Physics Communications 1 Journal d’Analyse Mathématique 1 Journal of Statistical Physics 1 Mathematical Notes 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Nuclear Physics. B 1 Periodica Mathematica Hungarica 1 Rocky Mountain Journal of Mathematics 1 Reviews in Mathematical Physics 1 Journal of Geometry and Physics 1 Archiv der Mathematik 1 Canadian Mathematical Bulletin 1 Functiones et Approximatio. Commentarii Mathematici 1 International Journal of Mathematics and Mathematical Sciences 1 Journal of Approximation Theory 1 Journal of Computational and Applied Mathematics 1 Programming and Computer Software 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Rendiconti del Seminario Matematico della Università di Padova 1 Acta Applicandae Mathematicae 1 Journal of Automated Reasoning 1 Science in China. Series A 1 Neural Networks 1 Geometric and Functional Analysis. GAFA 1 Mémoires de la Société Mathématique de France. Nouvelle Série 1 Journal of Algebraic Geometry 1 Bulletin des Sciences Mathématiques 1 Integral Transforms and Special Functions 1 Documenta Mathematica 1 Transformation Groups 1 Doklady Mathematics 1 Journal of Group Theory ...and 22 more Serials
all top 5
#### Cited in 39 Fields
449 Number theory (11-XX) 94 Topological groups, Lie groups (22-XX) 92 Algebraic geometry (14-XX) 67 Special functions (33-XX) 66 Group theory and generalizations (20-XX) 34 Several complex variables and analytic spaces (32-XX) 27 Nonassociative rings and algebras (17-XX) 21 Global analysis, analysis on manifolds (58-XX) 21 Quantum theory (81-XX) 15 Abstract harmonic analysis (43-XX) 11 Functions of a complex variable (30-XX) 10 Functional analysis (46-XX) 9 Manifolds and cell complexes (57-XX) 7 Associative rings and algebras (16-XX) 7 Difference and functional equations (39-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 5 Field theory and polynomials (12-XX) 5 Commutative algebra (13-XX) 5 Probability theory and stochastic processes (60-XX) 5 Computer science (68-XX) 4 Combinatorics (05-XX) 4 Dynamical systems and ergodic theory (37-XX) 3 Partial differential equations (35-XX) 3 Integral transforms, operational calculus (44-XX) 3 Operator theory (47-XX) 3 Differential geometry (53-XX) 2 $$K$$-theory (19-XX) 2 Measure and integration (28-XX) 2 Approximations and expansions (41-XX) 2 Algebraic topology (55-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Relativity and gravitational theory (83-XX) 1 Category theory; homological algebra (18-XX) 1 Real functions (26-XX) 1 Sequences, series, summability (40-XX) 1 Geometry (51-XX) 1 Convex and discrete geometry (52-XX) 1 Statistics (62-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2021-05-07T02:37:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4636654853820801, "perplexity": 3168.9214564712925}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988774.18/warc/CC-MAIN-20210506235514-20210507025514-00352.warc.gz"} |
http://popflock.com/learn?s=Dextrorotation_and_levorotation | Dextrorotation and Levorotation
Get Dextrorotation and Levorotation essential facts below. View Videos or join the Dextrorotation and Levorotation discussion. Add Dextrorotation and Levorotation to your PopFlock.com topic list for future reference or share this resource on social media.
Dextrorotation and Levorotation
A chemical compound showing dextrorotation in a polarimeter. From the perspective of the observer, the plane is rotated to the right (clockwise).
Dextrorotation and levorotation (also spelled laevorotation)[1] are terms used in chemistry and physics to describe the optical rotation of plane-polarized light. From the point of view of the observer, dextrorotation refers to clockwise or right-handed rotation, and levorotation refers to counterclockwise or left-handed rotation.[2][3]
A chemical compound that causes dextrorotation is called dextrorotatory or dextrorotary, while a compound that causes levorotation is called levorotatory or levorotary.[4] Compounds with these properties consist of chiral molecules and are said to have optical activity. If a chiral molecule is dextrorotary, its enantiomer (geometric mirror image) will be levorotary, and vice versa. Enantiomers rotate plane-polarized light the same number of degrees, but in opposite directions.
## Chirality prefixes
### (+)-, (-)-, d-, l-, D-, and L-
A dextrorotary compound is often prefixed with "(+)-" or "d-". Likewise, a levorotary compound is often prefixed with "(-)-" or "l-". These lowercase "d-" and "l-" prefixes are distinct from the SMALL CAPS "D-" and "L-" prefixes, which are most often used to distinguish chiral organic compounds in biochemistry and are based on the compound's absolute configuration relative to (+)-glyceraldehyde, which is the D-form by definition. The prefix used to indicate absolute configuration does not necessarily imply the prefix used to indicate chirality in the same molecule. For example, nine of the nineteen L-amino acids naturally occurring in proteins are, despite the L- prefix, actually dextrorotary (at a wavelength of 589 nm), and D-fructose is sometimes called "levulose" because it is levorotary.
### (R)- and (S)-
The (R)- and (S)- prefixes from the Cahn-Ingold-Prelog priority rules are different from the preceding ones in that the R and S labels characterize the absolute configuration of a specific stereocenter, rather than of a whole molecule. A molecule with just one stereocenter can be labeled R or S, but a molecule with multiple stereocenters needs more than one label, for example (2R,3S).
If there is a pair of enantiomers, each with one stereocenter, then one enantiomer is R and the other is S; one enantiomer is levorotary and the other is dextrorotary. However, there is no general correlation between these two labels. In some cases the (R)-enantiomer is the dextrorotary enantiomer, and in other cases the (R)-enantiomer is the levorotary enantiomer. The relationship can only be determined on a case-by-case basis with experimental measurements or detailed computer modeling.[5]
## Specific rotation
A standard measure of the degree to which a compound is dextrorotary or levorotary is the quantity [?], known as the specific rotation. Dextrorotary compounds have a positive specific rotation, while levorotary compounds have a negative specific rotation. Any pair of enantiomers have equal but opposite specific rotations.
The formula for specific rotation, [?], is
${\displaystyle [\alpha ]={\frac {\alpha }{c\cdot l}},}$
where:
? = observed rotation (in degrees),
c = concentration of the solution of an enantiomer (in g/ml),
l = length of the polarimeter tube (in decimeters).
The degree of rotation of plane-polarized light depends on the number of chiral molecules that it encounters on its way through the tube of the polarimeter (thus, the length of the tube and concentration of the enantiomer). In many cases, it also depends on the temperature and the wavelength of light that is employed.
## Other terminology
The equivalent French terms are dextrogyre and levogyre. These are used infrequently in English.[6]
## References
1. ^ The first word component dextro- comes from the Latin word dexter, meaning "right" (as opposed to left). Laevo- or levo- comes from the Latin laevus, meaning "left side".
2. ^ LibreTexts Chemistry - Polarimetry
3. ^ "Determination of optical rotation and specific rotation" (PDF). The International Pharmacopoeia. World Health Organization. 2017. ISBN 9789241550031.
4. ^ Solomons, T.W. Graham; Fryhle, Graig B. (2004). Organic Chemistry (8th ed.). Hoboken: John Wiley & Sons, Inc.
5. ^ See, for example,Stephens, P. J.; Devlin, F. J.; Cheeseman, J. R.; Frisch, M. J.; Bortolini, O.; Besse, P. (2003). "Determination of absolute configuration using calculation of optical rotation". Chirality. 15: S57-64. doi:10.1002/chir.10270. PMID 12884375.
6. ^ For example: Sebti; Hamilton, eds. (2001). Farnesyltransferase inhibitors in cancer therapy. p. 126. ISBN 9780896036291. Retrieved .
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https://publons.com/publon/546458/#review-502770 | 5 pre-pub reviews
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Abstract
Background: Collective animal behavior, such as the flocking of birds or the shoaling of fish, has inspired a class of algorithms designed to optimize distance-based clusters in various applications, including document analysis and DNA microarrays. In a flocking model, individual agents respond only to their immediate environment and move according to a few simple rules. After several iterations the agents self-organize, and clusters emerge without the need for partitional seeds. In addition to its unsupervised nature, flocking offers several computational advantages, including the potential to reduce the number of required comparisons.Findings: In the tool presented here, Clusterflock, we have implemented a flocking algorithm designed to locate groups (flocks) of orthologous gene families (OGFs) that share an evolutionary history. Pairwise distances that measure phylogenetic incongruence between OGFs guide flock formation. We tested this approach on several simulated datasets by varying the number of underlying topologies, the proportion of missing data, and evolutionary rates, and show that in datasets containing high levels of missing data and rate heterogeneity, Clusterflock outperforms other well-established clustering techniques. We also verified its utility on a known, large-scale recombination event in Staphylococcus aureus. By isolating sets of OGFs with divergent phylogenetic signals, we were able to pinpoint the recombined region without forcing a pre-determined number of groupings or defining a pre-determined incongruence threshold.Conclusions: Clusterflock is an open-source tool that can be used to discover horizontally transferred genes, recombined areas of chromosomes, and the phylogenetic 'core' of a genome. Although we used it here in an evolutionary context, it is generalizable to any clustering problem. Users can write extensions to calculate any distance metric on the unit interval, and can use these distances to 'flock' any type of data.
Authors
Narechania, Apurva; Baker, Richard; DeSalle, Rob; Mathema, Barun; Kolokotronis, Sergios-Orestis; Kreiswirth, Barry; Planet, Paul J.
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Clusterflock: a flocking algorithm for isolating congruent phylogenomic datasets
Reviewer #1 reported problems with using the Clusterflock tool due to the complexity with installing the software and its dependencies. In response, the authors of Clusterflock have provided a Docker container which ships all of the code and associated software libraries in a standalone package ready for use.
I have tested the clusterflock-0.1 Docker container and can report that I have successfully executed the clusterflock.pl and clusterflock_simulations.pl scripts to completion using the instructions available from https://github.com/narechan/clusterflock/blob/master/MANUAL. This involved:
1. Deploying an Ubuntu-14.04 EC2 virtual server as a t2.medium instance on the AWS cloud and installing the Docker software on it.
3. The Clusterflock scripts can then be executed by running the clusterflock-0.1 Docker container with this command on the host server:
$docker run -v /mount/path/on/host:/home/test -it narechan/clusterflock-0.1 The following two commands can then be executed using clusterflock-0.1 Docker image:$ clusterflock.pl -i test_data/4/fastas/ -c config.boids.simulations -l test_data/4/4.lds -s all -b 1 -d -x -o /home/test/4_out
\$ clusterflock_simulations.pl -c config.boids.simulations -r 10 -p 10 -o /home/test/4_sim/ -i test_data/4/fastas/ -l test_data/4/4.lds -j /home/clusterflock/dependencies/elki-bundle- 0.6.5~20141030.jar -k 4 -f 500 > /home/test/4_sim.avg_jaccard
Both of the above commands generated outputs as described in https://github.com/narechan/clusterflock/blob/master/MANUAL.
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Clusterflock: a flocking algorithm for isolating congruent phylogenomic datasets
The authors propose a method that uses a modified flocking algorithm figure out how many trees are needed to represent a set of alignments of the same taxa. This is an interesting problem, and the proposed solution is a valuable contribution. Nevertheless, there were a number of places in which I thought the study could and perhaps should be improved. I split them into two below: those to do with the software, and those to do with the manuscript.
1. Only a passing mention is given to previous solutions to this problem. Given that there are various previous solutions, it would be useful for the reader to be given some comparison of the relative merits and shortcomings of the solutions, to motivate the current study. It would also be worth noting in the discussion whether and how this new method overcomes the limitations of previous methods. This seems like an important point for readers who areconsidering which tool to use.
2. There are no simulations. This seems like an important omission to me, because without simulations it's impossible to know when the method works well, and when it doesn't. Although the authors present an analysis of one empirical dataset in which the algorithm appears to do roughly what it should, this is not sufficient to make robust judgements as to the general performance of the algorithm. Thus, without simulations I would argue that the conclusions of the paper are not supported by the data, specifically it is not possible claim that 'we show that [clusterflock] is particularly well suited to isolating genes into discrete flocks that share a unique phylogenetic history'. Simulations could obviously take many forms, but a simple approach would be to consider 100 datasets with 1-100 trees underlying them. 100 loci could then be sampled across these trees, and fed into the algorithm.
Repeating each simulation 10 times would require only 1000 analyses, and could give a quite detailed picture of the method's performance. Specific questions to ask would be: what is the false positive rate (i.e. how often do you detect more than one cluster when there is only a single underlying tree)? What is the false negative rate (i.e. how often do you cluster together genes with different underlying trees)? What are the detection limits (e.g. how much data and how different do two trees have to be before you can detect the differences)? What aspects of sequence evolution can mislead the algorithm (e.g. rates of evolution, see below)? How does the ratio of the number of loci to the number of trees affect performance (this seems like a particularly important point to address in a flocking algorithm - it's not obvious to me what will happen to trees that are represented by a single locus, and particularly in the case where most trees are represented by a very small number of loci)?
3. The design choices are described relatively thoroughly in the paper, but very few motivations for these choices are given. Thus, while I might be able to re-implement a similar algorithm by reading the paper, I have no idea why most of the choices were made. It would be nice to include the background to the decisions made when implementing the algorithms, because this would facilitate progress in this area.
4. The use of LD seems reasonable here, but it seems like it could also be misled by genes evolving at different rates. This is because higher rates will tend to exacerbate problems like long-branch attraction. Thus, under parsimony, a slow gene and a fast gene may have quite different most-parsimonious topologies. Given the vast differences in rates between many genes, this seems like a potential issue that could at the very least be explored with simulation, e.g. by simulating 100 genes on the same tree, where 50 evolve slowly and 50 evolve more quickly. By varying the rate ratio of the two genes, one could determine whether this is an issue, and at what kinds of scales it manifests itself.
5. A simple question - could the authors include some information on the relative proportion of the runtimes that are associated with different parts of the algorithm. I ask this because it's easy to think of other options (like calculating ML or NJ trees, and then using any of a number of metrics of tree distances) which might improve accuracy but increase runtimes. However, without knowing what the rate-limiting steps of the algorithm are, it's not possible to know whether such improvements are worth even thinking about.
6. Following from point 5: given that you have to run the algorithm 100 times to get some idea of the robustness of the flocking, how does the aggregated runtime compare to other approaches to this problem? E.g. what about software such as concaterpillar or conclustador? The latter states that it is specifically designed to solve the same problem as clusterflock, so it seems worth comparing the two here. Note that I don't think it's necessary to do better than any other software - this is a very interesting approach that should be described regardless of whether it's better on any particular metric - but it does seem important to make some attempt to compare performance in terms of accuracy and speed.
1. The way that github has been used is unconventional, and inconvenient. The only way I could download the software was to download a whole collection of other pieces of software along with it. Please give this software its own repository. This will also facilitate future collaboration and development, since github works fundamentally at the level of the single repository.
2. Please mint a DOI for the released version of the software with Zenodo or some other service. This ensures that the software will stay around if the github repo is deleted, and it also ensures that the ms refers to a persistent and tagged version of the software even if the repo stays around and the software continues to be developed.
3. There are no tests in the software. In this case, tests seem rather vital. The paper describes clusterflock 'an open source tool', so presumably the intention is that many others will use it. Simulations will form a useful set of tests on their own, and should be included in the repository with a script to run all tests and check that they produce the expected results. (note - the results don't have to be correct, but there should be some checking to make sure that they are expected). Given that the algorithm is stochastic, it might be useful to include an option to provide a random number seed in the code, in particular to facilitate testing. Unit tests would also be useful, to ensure that key functions are behaving as expected. As it stands, software with no tests does not inspire a great deal of confidence.
4. More documentation is needed. I suspect this is particularly the case here, since the vast majority of the end-users of the tool will not know Perl. It would be worth putting together a comprehensive manual, and in particular providing detailed installation instructions and a quickstart guide. For example, although I am quite proficient in a couple of languages I do not use Perl. Even if I had access to a linux machine to test the software (sadly, I don't, but I hope at least one reviewer does), I'm guessing that getting it up an running would have taken me some time.
5. I searched for a license, and found one in the script. But I am confused. The license states that the work is copyright of the AMNH, but also that it is released under the same terms as Perl itself. These seem incompatible, and also perhaps incompatible with the three dependencies that are packaged in the repo. Can the authors double check this, and when they are sure they have a valid license, include it somewhere obvious in the repository and the manual.
6. Just an observation: 'Clusterflock' is a very popular name for many things, and that makes this tool very hard to find on google. Even typing 'clusterflock phylogenetics github' does not produce a link to the tool. It might be worth considering a name that makes the tool easier to find.
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Clusterflock: a flocking algorithm for isolating congruent phylogenomic datasets
The manuscript present a method to identify phylogenetically-congruent genes through an agentbased modelling approach originally designed to model bird flocking. The method is concisely presented and applied to a set Staphylococcus aureus genomes known to have evolved via large hybridisation events.
The problem is relevant and the idea has merit, but as I elaborate below, I am concerned that no efforts were done to compare the approach to standard clustering approaches or to existing methods for the same problem. I am also concerned that the authors only provide results for a single dataset. The minimum standard in the field is to validate one's approach on a variety of simulated data, showing that the method performs well under these ideal conditions at least.
Major points:
1. Method only validated on a single problem instance. This is inadequate for a new method. Instead, the authors should at least show on simulated datasets covering a variety of scenarios that the algorithm is able to cluster the data correctly.
2. No comparison with other methods: As the authors correctly point out, their approach boils down to a clustering method. There are many such methods, so why should the proposed approach be preferred? Contrary to the claim two paragraphs prior to the conclusions (please number your ms pages), there are other clustering methods that do not require specifying the number of clusters. Even for those that do, there are heuristics available (elbow, silhouette, etc.). At the very least, it seems that embedding the genes in a space using a standard multidimensional scaling procedure followed by clustering (e.g. using the OPTICS algorithm used by the authors) would provide a reasonable baseline to gauge how useful the flocking approach is.
Minor Points:
3. What genomes were used as input? (accession number/date)
4. How were the orthologous groups computed? 5. How were the single-gene trees computed?
5. How were the single-gene trees computed?
6. Given that orthologous groups were inferred, why did the authors need to map genes to USA300/TCH1516 via profile HMM? In any case, this needs to be described.
7. Paragraph right before conclusions: "The LDs of these genes with respect...". The authors probably mean ILD here. In the context of recombination, LD usually means linkage disequilibrium, which could be confusing.
8. Same sentence: the conjecture that genes that are both in the "core cluster" and hybridisation region could have *reverted back* to the core phylogeny seems highly improbable to me. Assuming these indeed follow the core phylogeny, it seems more likely that they were translocated to that region *after* the hybridisation event.
9. The labels on Fig. 3 are illegible.
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By way of full disclosure, I am the senior author of a loosely related manuscript submitted to
another journal. However, the two manuscripts use different approaches, and have very different
focuses, so they are not in competition.
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Clusterflock: a flocking algorithm for isolating congruent phylogenomic datasets
I have a few remaining comments:
1. Usability
While I think the method is interesting, the implementation remains very difficult to use. After two hours of attempting to install and run the software (I am a proficient programmer in python and R, but have zero Perl experience) I gave up. The installation remains complex for non-perl experts, and the sparsity of the documentation does not help (the documentation has been expanded somewhat, but it remains far too sparse to be useful to non-perl programmers). Because of that, the utility of the tool for the end-users (presumably, biologists with multi-locus datasets) is questionable. This is not something I see as a barrier to publication of the method - which itself is interesting - but since the primary focus of this paper is the software itself, this does seem to me to be an issue.
2. DOI
The authors provide no cogent reason not to provide a DOI for their software. I don't know what the issue is here. By not providing a DOI (e.g. through Zenodo), there is no guarantee that the software will stay around. This is a problem for reproducibility and for the general utility of the work. Given that link rot, and lost/broken software in general is such a huge problem in our field, and given that the primary focus of this paper is the provision of 'an open-source tool' I think it's important to properly archive a version of the software with a DOI here. Neither tagging versions in github nor making a copy of the repo on bitbucket guarantees persistence. But the ~10 minutes it takes to provide a DOI through Zenodo does guarantee persistence. It means that, no matter what the authors decide to do with their github repository, the copy of the code used for this ms will be around and will be discoverable from the manuscript itself.
A side note: the authors state that they have tagged the current version of the software as 0.1. However, there are no tags or releases on their github repository. Tags and releases are specific things designed to help people get to particular versions of software: https://help.github.com/articles/creating-releases/ . Minting a DOI with Zenodo would solve this problem too - Zenodo works with tagged versions of the repository only.
3. Simulations
Can the authors please provide data (in a figure) on the number of clusters returned by clusterflock in each of the simulated datasets, versus the number of underlying topologies that were simulated. It's not possible to get this from the currently-presented data, and this is an important part of assessing the accuracy of the algorithm on the simulated datasets.
4. Data availability
Please provide the output data from the simulations: specifically, the data that could be used to recalculate figures 3 and 4 on the identity of the simulated topology versus the topology to which clusterflock assigned that locus.
5. Discussion of performance
Figures 3 and 4 would benefit from having the expected jacard index with random assignment of trees to loci plotted. This way we could see which methods do no better than randomly assigning trees to groups. As far as I can tell, clusterflock with 50% missing data tracks the random expectation very closely (JI = 0.5 with 2 trees; 0.1 with 10 trees; 0.04 with 25 trees). This in itself is interesting - even with data for 50% of the species, clusterflock does not appear to gain any benefit over randomly assigning trees to groups. Can comment on this particular case? It seems counterintuitive to me that with data for 50% of the species at each locus, the method gains no benefit over randomly assigning trees.
More generally, can the authors comment on the meaning (for biologists) of the fact that clusterflock gets a JI of ~0.4 when there are 25 simulated topologies. If the algorithm correctly assigns loci to topologies less than half of the time in these simulations, what does this mean for biological inferences from the data? For example, it seems from the simulated and empirical data that while clusterflock might be useful when the number of clusters is very small (e.g. <10) it might be much less useful with >10 clusters. For example, while the empirical test presented in the paper is compelling, it seems likely that the algorithm may be much less useful if there had been a lot of recombination events (as might be the case in many empirical datasets, such as the analysis of whole-bird genomes from across the avian tree of life).
As above, some comparison with existing approaches to this problem is warranted here: if clusterflock does better than existing approaches (i.e. Concaterpillar, conclustador, etc), then that's great even if the absolute performance remains less than ideal. In this case, biologists should prefer clusterflock because it makes the best inferences. However, if clusterflock is consistently worse than other methods, then we know that it is a neat method that requires additional development before it is useful. In my opinion, knowing which of these situations is the case would vastly strengthen the paper.
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Clusterflock: a flocking algorithm for isolating congruent phylogenomic datasets
My authors have satisfactorily addressed my remarks. I only have two small comments on the new analyses:
1) The comparison with other clustering methods is good addition. The fragility of hierarchical methods and "partitioning around medoid" with respect to missing data is surprising. The authors should make data and scripts available.
2) The legend of new figures 3 and 4 should be clearer. As it stands, one needs to read the main text to understand that "zero, ten, twenty" refers to percentages of missing data.
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I agree to the open peer review policy of the journal. I understand that my name will be included
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including any attachments I upload will be posted on the website along with the authors'
responses. I agree for my report to be made available under an Open Access Creative Commons | 2021-09-28T23:16:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4289627969264984, "perplexity": 1263.831828182424}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780060908.47/warc/CC-MAIN-20210928214438-20210929004438-00432.warc.gz"} |
https://www.usgs.gov/media/files/1970-comparison-basic-modes-imaging-earth-paper | # 1970 Comparison of Basic Modes for Imaging the Earth Paper
1970 Comparison of Basic Modes for Imaging the Earth Paper
## Detailed Description
1970 Comparison of Basic Modes for Imaging the Earth Paper - EROS HIstory Project | 2019-09-17T01:39:15 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8187608122825623, "perplexity": 8693.350423277247}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514572980.56/warc/CC-MAIN-20190917000820-20190917022820-00047.warc.gz"} |
https://tjyj.stats.gov.cn/CN/10.19343/j.cnki.11-1302/c.2019.02.008 | • •
环境规制的经济效应：“减排”还是“增效”
• 出版日期:2019-02-25 发布日期:2019-03-07
Economic Effects of Environmental Regulations: “Emission Reduction” or “Efficiency Enhancement”
Yu Binbin et al.
• Online:2019-02-25 Published:2019-03-07
Abstract: This paper constructs a theoretical and analytical framework for the economic effects of environmental regulations, and tests the "emission reduction" and "efficiency enhancement" effects of environmental regulations by applying the Chinese urban panel data and the dynamic spatial panel model. It is found that the environmental regulations in China has the economic and spatial spillover effects of "emission reductions only without economic efficiency", and the conclusion is still unchanged with a series of robustness tests. A further heterogeneity study reveals that the environmental effects of "emission reductions only without economic efficiency" are validated in those three parts of China, i.e., East, Central and West. After the international financial crisis, the "emission reductions" effects brought about by the environmental regulations have significantly intensified, but only with an increased "compliance cost", and no "innovation effects". The effects of "emission reductions only without economic efficiency" can only be improved efficiently through speeding up the restructuring of industries. The relationship between economic development and energy efficiency presents a trend of U shape, and China is on the left side of the "U", and so far the Kuznets environmental curve has not been confirmed by Chinese city data yet. | 2022-07-02T09:07:50 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.31025415658950806, "perplexity": 5055.460097934011}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103989282.58/warc/CC-MAIN-20220702071223-20220702101223-00696.warc.gz"} |
https://zbmath.org/authors/?q=ai%3Asmith.james-e | # zbMATH — the first resource for mathematics
## Smith, James E.
Compute Distance To:
Author ID: smith.james-e Published as: Smith, J.; Smith, J. E.; Smith, James; Smith, James E. External Links: MGP · Wikidata
Documents Indexed: 58 Publications since 1970, including 6 Books
all top 5
#### Co-Authors
9 single-authored 3 Brown, David B. 3 McCardle, Kevin F. 3 Ulu, Canan 2 Eiben, Ágoston Endre 2 Holt, Craig S. 1 Caleb-Solly, Praminda 1 Craven, Robert P. M. 1 Krasnogor, Natalio 1 Lam, Paklin 1 Metze, Gernot 1 Nair, Ravi 1 Nau, Robert F. 1 Pauplin, Olivier 1 Preece, William K. 1 Sun, Peng 1 Tahir, Muhammad Atif 1 Weiss, Shlomo
all top 5
#### Serials
10 Operations Research 9 IEEE Transactions on Computers 3 Management Science 2 Natural Computing Series 1 ACM Transactions on Mathematical Software 1 Pattern Recognition 1 Mathematical Modelling and Scientific Computing 1 JMMA. Journal of Mathematical Modelling and Algorithms
#### Fields
13 Operations research, mathematical programming (90-XX) 9 Computer science (68-XX) 9 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 8 Information and communication theory, circuits (94-XX) 1 Statistics (62-XX)
#### Citations contained in zbMATH
37 Publications have been cited 477 times in 429 Documents Cited by Year
Introduction to evolutionary computing. Zbl 1028.68022
Eiben, A. E.; Smith, J. E.
2003
Information relaxations and duality in stochastic dynamic programs. Zbl 1228.90062
Brown, David B.; Smith, James E.; Sun, Peng
2010
Valuing risky projects: Option pricing theory and decision analysis. Zbl 0843.90015
Smith, James E.; Nau, Robert F.
1995
Asymptotic dimension of discrete groups. Zbl 1100.20034
Dranishnikov, A.; Smith, J.
2006
$$L^p$$-$$L^q$$ estimate for wave equation with bounded time dependent coefficient. Zbl 1090.35046
Reissig, Michael; Smith, James
2005
Generalized Chebychev inequalities: theory and applications in decision analysis. Zbl 0842.90002
Smith, James E.
1995
On asymptotic dimension of countable Abelian groups. Zbl 1144.20024
Smith, J.
2006
Structural properties of stochastic dynamic programs. Zbl 1163.90685
Smith, James E.; Mccardle, Kevin F.
2002
Moment methods for decision analysis. Zbl 0825.90622
Smith, James E.
1993
On asymptotic Assouad-Nagata dimension. Zbl 1116.54020
Dranishnikov, A. N.; Smith, J.
2007
Dispersive and Strichartz estimates for hyperbolic equations with constant coefficients. Zbl 1191.35006
Ruzhansky, Michael; Smith, James
2010
Evaluating income streams: A decision analysis approach. Zbl 0989.90529
Smith, James E.
1998
Valuing oil properties: Integrating option pricing and decision analysis approaches. Zbl 1032.91631
Smith, James E.; McCardle, Kevin F.
1998
Uncertainty, information acquisition, and technology adoption. Zbl 1226.90127
Ulu, Canan; Smith, James E.
2009
Options in the real world: lessons learned in evaluating oil and gas investments. Zbl 1035.91503
Smith, James E.; McCardle, Kevin F.
1999
Introduction to evolutionary computing. 2nd edition. Zbl 1327.68003
Eiben, A. E.; Smith, James E.
2015
Coherent imaging spectroscopy of a quantum many-body spin system. Zbl 1355.81191
Senko, C.; Smith, J.; Richerme, P.; Lee, A.; Campbell, W. C.; Monroe, C.
2014
Technology adoption with uncertain future costs and quality. Zbl 1248.91031
Smith, James E.; Ulu, Canan
2012
Information relaxations, duality, and convex stochastic dynamic programs. Zbl 1327.90149
Brown, David B.; Smith, James E.
2014
Risk aversion, information acquisition, and technology adoption. Zbl 1405.91128
Smith, James E.; Ulu, Canan
2017
Two-loop corrections to Higgs boson production. Zbl 1119.81403
Ravindran, V.; Smith, J.; Van Neerven, W. L.
2005
Measures of the effectiveness of fault signature analysis. Zbl 0436.94036
Smith, James E.
1980
Alfred Tarski. Early work in Poland – geometry and teaching. With a bibliographic supplement. With a foreword by Ivor Grattan-Guinness. Zbl 1310.01002
McFarland, Andrew (ed.); McFarland, Joanna (ed.); Smith, James (ed.)
2014
Optimal sequential exploration: bandits, clairvoyants, and wildcats. Zbl 1273.90255
Brown, David B.; Smith, James E.
2013
A new family of l-group varieties. Zbl 0503.06017
Smith, J. E.
1981
The lattice of l-group varieties. Zbl 0459.06007
Smith, J. E.
1980
Discontinuity in decision-making when objectives conflict: a military command decision case study. Zbl 1121.90349
Dodd, L.; Moffat, J.; Smith, J.
2006
Solvable and $$\ell$$-solvable $$\ell$$-groups. Zbl 0543.06006
Smith, J. E.
1984
Diagnosis of systems with asymmetric invalidation. Zbl 0463.94020
Holt, Craig S.; Smith, James E.
1981
Detection of faults in programmable logic arrays. Zbl 0422.94057
Smith, James E.
1979
Optimal rocket trajectories in a general force-field. Zbl 0263.70033
Brookes, C. J.; Smith, J.
1970
On the chromatic number of subsets of the Euclidean plane. Zbl 1292.05096
Axenovich, M.; Choi, J.; Lastrina, M.; McKay, T.; Smith, J.; Stanton, B.
2014
Memetic algorithms: The polynomial local search complexity theory perspective. Zbl 1135.68630
Krasnogor, Natalio; Smith, James E.
2008
Global time estimates for solutions to equations of dissipative type. Zbl 1172.35011
Ruzhansky, Michael; Smith, James
2005
New methods for tunable, random landscapes. Zbl 0987.68026
Smith, R. E.; Smith, J. E.
2002
Strongly fault secure logic networks. Zbl 0388.94026
Smith, James E.; Metze, Gernot
1978
A computer simulation of a neuron net model as a self-organizing system. Zbl 0256.92006
Kuijpers, K.; Smith, J.
1973
Risk aversion, information acquisition, and technology adoption. Zbl 1405.91128
Smith, James E.; Ulu, Canan
2017
Introduction to evolutionary computing. 2nd edition. Zbl 1327.68003
Eiben, A. E.; Smith, James E.
2015
Coherent imaging spectroscopy of a quantum many-body spin system. Zbl 1355.81191
Senko, C.; Smith, J.; Richerme, P.; Lee, A.; Campbell, W. C.; Monroe, C.
2014
Information relaxations, duality, and convex stochastic dynamic programs. Zbl 1327.90149
Brown, David B.; Smith, James E.
2014
Alfred Tarski. Early work in Poland – geometry and teaching. With a bibliographic supplement. With a foreword by Ivor Grattan-Guinness. Zbl 1310.01002
McFarland, Andrew (ed.); McFarland, Joanna (ed.); Smith, James (ed.)
2014
On the chromatic number of subsets of the Euclidean plane. Zbl 1292.05096
Axenovich, M.; Choi, J.; Lastrina, M.; McKay, T.; Smith, J.; Stanton, B.
2014
Optimal sequential exploration: bandits, clairvoyants, and wildcats. Zbl 1273.90255
Brown, David B.; Smith, James E.
2013
Technology adoption with uncertain future costs and quality. Zbl 1248.91031
Smith, James E.; Ulu, Canan
2012
Information relaxations and duality in stochastic dynamic programs. Zbl 1228.90062
Brown, David B.; Smith, James E.; Sun, Peng
2010
Dispersive and Strichartz estimates for hyperbolic equations with constant coefficients. Zbl 1191.35006
Ruzhansky, Michael; Smith, James
2010
Uncertainty, information acquisition, and technology adoption. Zbl 1226.90127
Ulu, Canan; Smith, James E.
2009
Memetic algorithms: The polynomial local search complexity theory perspective. Zbl 1135.68630
Krasnogor, Natalio; Smith, James E.
2008
On asymptotic Assouad-Nagata dimension. Zbl 1116.54020
Dranishnikov, A. N.; Smith, J.
2007
Asymptotic dimension of discrete groups. Zbl 1100.20034
Dranishnikov, A.; Smith, J.
2006
On asymptotic dimension of countable Abelian groups. Zbl 1144.20024
Smith, J.
2006
Discontinuity in decision-making when objectives conflict: a military command decision case study. Zbl 1121.90349
Dodd, L.; Moffat, J.; Smith, J.
2006
$$L^p$$-$$L^q$$ estimate for wave equation with bounded time dependent coefficient. Zbl 1090.35046
Reissig, Michael; Smith, James
2005
Two-loop corrections to Higgs boson production. Zbl 1119.81403
Ravindran, V.; Smith, J.; Van Neerven, W. L.
2005
Global time estimates for solutions to equations of dissipative type. Zbl 1172.35011
Ruzhansky, Michael; Smith, James
2005
Introduction to evolutionary computing. Zbl 1028.68022
Eiben, A. E.; Smith, J. E.
2003
Structural properties of stochastic dynamic programs. Zbl 1163.90685
Smith, James E.; Mccardle, Kevin F.
2002
New methods for tunable, random landscapes. Zbl 0987.68026
Smith, R. E.; Smith, J. E.
2002
Options in the real world: lessons learned in evaluating oil and gas investments. Zbl 1035.91503
Smith, James E.; McCardle, Kevin F.
1999
Evaluating income streams: A decision analysis approach. Zbl 0989.90529
Smith, James E.
1998
Valuing oil properties: Integrating option pricing and decision analysis approaches. Zbl 1032.91631
Smith, James E.; McCardle, Kevin F.
1998
Valuing risky projects: Option pricing theory and decision analysis. Zbl 0843.90015
Smith, James E.; Nau, Robert F.
1995
Generalized Chebychev inequalities: theory and applications in decision analysis. Zbl 0842.90002
Smith, James E.
1995
Moment methods for decision analysis. Zbl 0825.90622
Smith, James E.
1993
Solvable and $$\ell$$-solvable $$\ell$$-groups. Zbl 0543.06006
Smith, J. E.
1984
A new family of l-group varieties. Zbl 0503.06017
Smith, J. E.
1981
Diagnosis of systems with asymmetric invalidation. Zbl 0463.94020
Holt, Craig S.; Smith, James E.
1981
Measures of the effectiveness of fault signature analysis. Zbl 0436.94036
Smith, James E.
1980
The lattice of l-group varieties. Zbl 0459.06007
Smith, J. E.
1980
Detection of faults in programmable logic arrays. Zbl 0422.94057
Smith, James E.
1979
Strongly fault secure logic networks. Zbl 0388.94026
Smith, James E.; Metze, Gernot
1978
A computer simulation of a neuron net model as a self-organizing system. Zbl 0256.92006
Kuijpers, K.; Smith, J.
1973
Optimal rocket trajectories in a general force-field. Zbl 0263.70033
Brookes, C. J.; Smith, J.
1970
all top 5
#### Cited by 901 Authors
8 Hirosawa, Fumihiko 7 Reissig, Michael 7 Ruzhansky, Michael V. 6 Bender, Christian 6 Dydak, Jerzy 6 Higes, J. 5 D’Abbicco, Marcello 5 Ebert, Marcelo Rempel 5 Wirth, Jens 4 Dranishnikov, Alexander Nikolaevich 4 Fister, Iztok 4 Haugh, Martin B. 4 Neumann, Frank 4 Segura, Carlos 4 Sudholt, Dirk 3 Al-Betar, Mohammed Azmi 3 Bell, Gregory C. 3 Bickel, J. Eric 3 Branke, Jürgen 3 Coello Coello, Carlos A. 3 Darnel, Michael R. 3 Di Caprio, Debora 3 Dikranjan, Dikran N. 3 Doerr, Benjamin 3 Dokuchaev, Nikolai G. 3 Dyer, James S. 3 Eidsvik, Jo 3 Khader, Ahamad Tajudin 3 Lam, Henry 3 Lu, Xiaojun 3 Luenberger, David G. 3 Matsuyama, Tokio 3 Mernik, Marjan 3 Powell, Warren Buckler 3 Santos-Arteaga, Francisco J. 3 Schweizer, Nikolaus 3 Tavana, Madjid 3 Tsetlin, Ilia 3 Zava, Nicolò 2 Akhavan-Tabatabaei, Raha 2 Arlotto, Alessandro 2 Awadallah, Mohammed A. 2 Balseiro, Santiago R. 2 Banakh, Taras Onufrievich 2 Barashko, A. S. 2 Berrones, Arturo 2 Betrò, Bruno 2 Birge, John R. 2 Blanchet, Jose H. 2 Brown, David B. 2 Chandramouli, Shyam Sundar 2 Clark, David Michael 2 Črepinšek, Matej 2 Date, Prasanna 2 Doerr, Carola 2 Doush, Iyad Abu 2 Fister, Iztok jun. 2 Garcia, Salvador G. 2 Garetto, Claudia 2 Gärtner, Christian 2 Gehrmann, Thomas 2 Graf, Peter A. 2 Guentner, Erik Paul 2 Hahn, Warren J. 2 Hammond, Robert K. 2 Hauge, Ragnar 2 Herrera, Francisco 2 Hu, Xiaobing 2 Jannelli, Enrico 2 Ji, Mingjun 2 Jones, Wesley B. 2 Joshi, Mark S. 2 Kalantari, Sh. 2 Karaboga, Dervis 2 Karaesmen, Fikri 2 Karlaftis, Matthew G. 2 Kepaptsoglou, Konstantinos 2 Kim, Kwiseon 2 Kozine, Igor O. 2 Krymsky, Victor G. 2 Kucab, Jacek 2 Kuhn, Daniel 2 Leeson, Mark S. 2 Leon, Coromoto 2 Li, Michael Z. F. 2 Lilleborge, Marie 2 Mezura-Montes, Efrén 2 Min, Yinghua 2 Musiela, Marek 2 Nagórko, Andrzej 2 Nau, Robert F. 2 Owhadi, Houman 2 Pajoohesh, Homeira 2 Ravindran, Varadarajan 2 Sakawa, Masatoshi 2 Sapir, Mark Valentinovich 2 Schosser, Josef 2 Secomandi, Nicola 2 Steele, J. Michael 2 Tessera, Romain ...and 801 more Authors
all top 5
#### Cited in 164 Serials
40 European Journal of Operational Research 22 Operations Research 20 Topology and its Applications 14 Computers & Operations Research 13 Annals of Operations Research 11 Applied Mathematics and Computation 10 Decision Analysis 9 Information Sciences 7 Journal of Mathematical Analysis and Applications 7 Operations Research Letters 6 Journal of Optimization Theory and Applications 6 Theoretical Computer Science 6 Quantitative Finance 5 Algebra Universalis 5 Journal of Differential Equations 5 Algorithmica 5 Mathematical Problems in Engineering 5 Mathematical Finance 5 Journal of High Energy Physics 4 Proceedings of the American Mathematical Society 4 Journal of Computer Science and Technology 4 Journal of Economic Dynamics & Control 4 Pattern Recognition 4 Journal of Heuristics 4 International Journal of Applied Mathematics and Computer Science 4 Algebraic & Geometric Topology 4 Natural Computing 3 Computer Methods in Applied Mechanics and Engineering 3 International Journal of Theoretical Physics 3 Information Processing Letters 3 Journal of Computational Physics 3 Mathematical Methods in the Applied Sciences 3 Mathematical Notes 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Osaka Journal of Mathematics 3 Order 3 International Journal of Approximate Reasoning 3 Journal of Global Optimization 3 Annals of Mathematics and Artificial Intelligence 3 Soft Computing 3 Probability in the Engineering and Informational Sciences 3 Algorithms 2 Artificial Intelligence 2 Biological Cybernetics 2 The Annals of Statistics 2 Automatica 2 Geometriae Dedicata 2 Journal of Economic Theory 2 Mathematische Annalen 2 Mathematics of Operations Research 2 International Journal of Production Research 2 International Journal of Algebra and Computation 2 Applied Mathematical Modelling 2 Mathematical Programming. Series A. Series B 2 SIAM Journal on Optimization 2 Computational Optimization and Applications 2 Journal of Applied Mathematics and Decision Sciences 2 OR Spectrum 2 Journal of Hyperbolic Differential Equations 2 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche 2 Optimization Letters 2 Statistics and Computing 1 Acta Informatica 1 Communications in Mathematical Physics 1 Discrete Mathematics 1 International Journal of General Systems 1 International Journal of Systems Science 1 Journal of Mathematical Biology 1 Physica A 1 Problems of Information Transmission 1 Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 1 Annals of the Institute of Statistical Mathematics 1 Applied Mathematics and Optimization 1 Archiv der Mathematik 1 BIT 1 Computing 1 Functional Analysis and its Applications 1 Funkcialaj Ekvacioj. Serio Internacia 1 Fuzzy Sets and Systems 1 Inventiones Mathematicae 1 Journal of Algebra 1 Journal of Applied Probability 1 Journal of Functional Analysis 1 Journal of the London Mathematical Society. Second Series 1 Journal für die Reine und Angewandte Mathematik 1 Journal of Statistical Planning and Inference 1 Mathematische Nachrichten 1 Mathematische Zeitschrift 1 Mathematika 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Numerical Functional Analysis and Optimization 1 SIAM Journal on Control and Optimization 1 SIAM Journal on Numerical Analysis 1 Theory and Decision 1 Transactions of the American Mathematical Society 1 Cybernetics 1 Mathematical Social Sciences 1 Insurance Mathematics & Economics 1 Statistics & Probability Letters 1 Optimization ...and 64 more Serials
all top 5
#### Cited in 46 Fields
180 Operations research, mathematical programming (90-XX) 98 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 60 Computer science (68-XX) 36 Group theory and generalizations (20-XX) 36 General topology (54-XX) 35 Statistics (62-XX) 34 Partial differential equations (35-XX) 32 Numerical analysis (65-XX) 28 Probability theory and stochastic processes (60-XX) 23 Systems theory; control (93-XX) 14 Quantum theory (81-XX) 14 Information and communication theory, circuits (94-XX) 12 Biology and other natural sciences (92-XX) 11 Algebraic topology (55-XX) 10 Category theory; homological algebra (18-XX) 9 Order, lattices, ordered algebraic structures (06-XX) 8 General algebraic systems (08-XX) 8 Calculus of variations and optimal control; optimization (49-XX) 8 Manifolds and cell complexes (57-XX) 7 Topological groups, Lie groups (22-XX) 7 Functional analysis (46-XX) 5 Combinatorics (05-XX) 5 Geometry (51-XX) 5 Differential geometry (53-XX) 4 Mechanics of particles and systems (70-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Mechanics of deformable solids (74-XX) 2 History and biography (01-XX) 2 Mathematical logic and foundations (03-XX) 2 Real functions (26-XX) 2 Abstract harmonic analysis (43-XX) 2 Convex and discrete geometry (52-XX) 2 Fluid mechanics (76-XX) 2 Optics, electromagnetic theory (78-XX) 1 General and overarching topics; collections (00-XX) 1 $$K$$-theory (19-XX) 1 Functions of a complex variable (30-XX) 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Approximations and expansions (41-XX) 1 Operator theory (47-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2021-01-20T17:56:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5966466069221497, "perplexity": 10228.531158841939}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703521139.30/warc/CC-MAIN-20210120151257-20210120181257-00305.warc.gz"} |
http://pdglive.lbl.gov/DataBlock.action?node=M200M&home=MXXX030 | # ${{\boldsymbol \eta}_{{b}}{(2S)}}$ MASS INSPIRE search
VALUE (MeV) EVTS DOCUMENT ID TECN COMMENT
$9999.0$ $\pm3.5$ ${}^{+2.8}_{-1.9}$ 26k 1
2012
BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ + hadrons
• • • We do not use the following data for averages, fits, limits, etc. • • •
$9974.6$ $\pm2.3$ $\pm2.1$ $11$ $\pm4$ 2, 3
2012
${{\mathit \Upsilon}{(2S)}}$ $\rightarrow$ ${{\mathit \gamma}}$ hadrons
1 Assuming ${\Gamma}_{{\mathit \eta}_{{b}}{(2S)}}$ = 4.9 MeV. Not independent of the corresponding mass difference measurement.
2 Obtained by analyzing CLEO III data but not authored by the CLEO Collaboration.
3 Assuming ${\Gamma}_{{\mathit \eta}_{{b}}{(2S)}}$ = 5 MeV. Not independent of the corresponding mass difference measurement.
References:
DOBBS 2012
PRL 109 082001 Observation of the ${{\mathit \eta}_{{b}}{(2S)}}$ Meson in ${{\mathit \Upsilon}{(2S)}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \eta}_{{b}}{(2S)}}$ , ${{\mathit \eta}_{{b}}{(2S)}}$ $\rightarrow$ Hadrons and Confirmation of the ${{\mathit \eta}_{{b}}{(1S)}}$ Meson
MIZUK 2012
PRL 109 232002 Evidence for the ${{\mathit \eta}_{{b}}{(2S)}}$ and Observation of ${{\mathit h}_{{b}}{(1P)}}$ $\rightarrow$ ${{\mathit \eta}_{{b}}{(1S)}}{{\mathit \gamma}}$ and ${{\mathit h}_{{b}}{(2P)}}$ $\rightarrow$ ${{\mathit \eta}_{{b}}{(1S)}}{{\mathit \gamma}}$ | 2019-12-16T04:51:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8823788166046143, "perplexity": 2476.524299697366}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575541317967.94/warc/CC-MAIN-20191216041840-20191216065840-00408.warc.gz"} |
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