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2307.11455v1_train__37db8cfe-8f77-41dc-bf8f-70ede422e80e
2307.11455v1
\begin{tabular}{lllllll} \hline & Type & Host galaxy & t$_{\rm{exp}}$ (MJD) & Redshift & $\mu$ (mag) & $A_{V}$ (mag) \\ \hline \hline SN~2017gmr & IIP & NGC~988 & 57999.09 & 0.005037 & 31.46 $\pm$ 0.15 & 1.14\\ \hline SN~2017ahn & IIL & NGC~3318 & 57791.76 & 0.009255 & 32.59 $\pm$ 0.43 & 0.82\\ \hline SN~2013ej & IIL & M~74 & 56496.90 & 0.002192 & 29.91 $\pm$ 0.16 & 0.19\\ \hline SN~2012ec & IIP & NGC~1084 & 56143.00 & 0.004693 & 31.10 $\pm$ 0.06 & 0.45\\ \hline SN~2012dh & IIL & ESO~443-G80 & 56104.98 & 0.007055 & 31.85 $\pm$ 0.45 & 0.20\\ \hline SN~2012aw & IIP & M~95 & 56002.10 & 0.002595 & 30.01 $\pm$ 0.09 & 0.23\\ \hline SN~2010hv & II & 2MASX~J23242536-1902139 & 55418.20 $\pm$ 8.00 & 0.024280 & - & - \\ \hline SN~2010co & II & NGC6862 & 55310.60 $\pm$ 11.50 & 0.014026 & - & - \\ \hline SN~2008bk & IIP & NGC~7793 & 54549.50 & 0.000767 & 27.66 $\pm$ 0.04 & 0.07\\ \hline SN~2007aa & IIP & NGC~4030 & 54126.70 & 0.004887 & 32.38 $\pm$ 0.20 & 0.06\\ \hline SN~2006ov & IIP & NGC~4303 & 53974.00 & 0.005224 & 30.5 $\pm$ 0.4 & 0.06\\ \hline SN~2004dj & IIP & NGC~2403 & 53186.50 & 0.000445 & 27.70 $\pm$ 0.19 & 0.22\\ \hline SN~2001du & II & NGC~1365 & 52145.20 $\pm$ 0.50 & 0.005457 & - & - \\ \hline SN~2001dh & II & ESO~340-G9 & 52099.50 $\pm$ 13.40 & 0.008700 & - & - \\ \hline SN~1999em & IIP & NGC~1637 & 51475.10 & 0.002392 & 30.34 $\pm$ 0.24 & 0.31\\ \hline \end{tabular}
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Details of the SNe
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2307.11455v1_train__764cbf39-4246-4474-999c-a5a1734097da
2307.11455v1
\begin{tabular}{cccc}\hline \noalign{\smallskip}Date (UT) & MJD & Telescope & Instrument\\ \noalign{\smallskip}\hline \noalign{\smallskip}2007 March 03.13 & 54162.13 & Calar Alto 2.2m telescope & CAFOS\\ 2007 March 11.05 & 54170.05 & Calar Alto 2.2m telescope & CAFOS\\ 2007 March 18.93 & 54177.93 & Calar Alto 2.2m telescope & CAFOS\\ 2007 March 31.01 & 54190.01 & Calar Alto 2.2m telescope & CAFOS\\ 2007 April 03.97 & 54193.97 & Calar Alto 2.2m telescope & CAFOS\\ 2007 April 23.94 & 54213.94 & Calar Alto 2.2m telescope & CAFOS\\ 2007 May 06.96 & 54226.96 & Calar Alto 2.2m telescope & CAFOS\\ 2007 May 14.89 & 54234.89 & Calar Alto 2.2m telescope & CAFOS\\ 2007 May 17.89 & 54237.89 & Calar Alto 2.2m telescope & CAFOS\\ 2007 May 19.87 & 54239.87 & Calar Alto 2.2m telescope & CAFOS\\ 2007 June 12.90 & 54263.90 & Calar Alto 2.2m telescope & CAFOS\\ 2007 June 13.90 & 54264.90 & Calar Alto 2.2m telescope & CAFOS\\ \noalign{\smallskip}\hline \end{tabular}
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Log of the spectroscopy of SN~2007aa.
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2308.11527v1_train__862d80e7-bbf4-41cd-a73a-a6c10c331c8a
2308.11527v1
\begin{tabular}{|c|c|c|c|}\hline & Impressions & Clicks & CTR \\ \hline Training Data & 216,038,149 & 7,550,609 & 0.0349 \\ \hline Validation Data & 19,544,730 & 667,024 & 0.0341 \\ \hline \end{tabular}
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Statistics for KDD CUP 2012 data set
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2210.09184v3_train__61aa7d4a-ea15-42d9-b4ed-d473f0c268f2
2210.09184v3
\begin{tabular}{clccccc}\toprule\textbf{OOD eval} & \textbf{Criterion} & $\alpha=2$, $\gamma=1$ $M=4$ & $\alpha=3$, $\gamma=1$ $M=8$ & $\alpha=4$, $\gamma=2$ $M=8$ & $\alpha=6$, $\gamma=4$ $M=8$ & $\alpha=8$, $\gamma=1$ $M=16$\\ \midrule\multirow{5}{*}{AUPR ($\uparrow$)} & \textbf{MSP} & 0.8952 $\pm$ 0.0132 & 0.9055 $\pm$ 0.0034 & 0.9153 $\pm$ 0.0012 & 0.9149 $\pm$ 0.0071 & 0.9141 $\pm$ 0.0057 \\ & \textbf{ML} & \textbf{0.9183 $\pm$ 0.0098} & \textbf{0.9175 $\pm$ 0.0044} & \textbf{0.9285 $\pm$ 0.0012} & \textbf{0.9265 $\pm$ 0.0070} & \textbf{0.9268 $\pm$ 0.0068} \\ & \textbf{Ent. } & \textbf{0.9105 $\pm$ 0.0138} & \textbf{0.9152 $\pm$ 0.0035} & \textbf{0.9260 $\pm$ 0.0016} & \textbf{0.9237 $\pm$ 0.0066} & \textbf{0.9252 $\pm$ 0.0060} \\ & \textbf{MI } & \textbf{0.8649 $\pm$ 0.0061} & \textbf{0.9139 $\pm$ 0.0077} & \textbf{0.9157 $\pm$ 0.0072} & \textbf{0.9196 $\pm$ 0.0109} & \textbf{0.9245 $\pm$ 0.0091} \\ & \textbf{v} & 0.8404 $\pm$ 0.0071 & 0.8746 $\pm$ 0.0056 & 0.8827 $\pm$ 0.0033 & 0.8842 $\pm$ 0.0102 & 0.8931 $\pm$ 0.0072 \\ \midrule\multirow{5}{*}{AUC ($\uparrow$)} & \textbf{MSP} & 0.8056 $\pm$ 0.0260 & 0.8204 $\pm$ 0.0101 & 0.8408 $\pm$ 0.0033 & 0.8432 $\pm$ 0.0134 & 0.8387 $\pm$ 0.0094 \\ & \textbf{ML} & \textbf{0.8562 $\pm$ 0.0194} & \textbf{0.8421 $\pm$ 0.0115} & \textbf{0.8665 $\pm$ 0.0027} & \textbf{0.8621 $\pm$ 0.0144} & \textbf{0.8607 $\pm$ 0.0114} \\ & \textbf{Ent. } & \textbf{0.8361 $\pm$ 0.0271} & \textbf{0.8427 $\pm$ 0.0095} & \textbf{0.8662 $\pm$ 0.0027} & \textbf{0.8617 $\pm$ 0.0136} & \textbf{0.8614 $\pm$ 0.0096} \\ & \textbf{MI } & \textbf{0.7711 $\pm$ 0.0064} & \textbf{0.8312 $\pm$ 0.0135} & \textbf{0.8402 $\pm$ 0.0116} & \textbf{0.8468 $\pm$ 0.0163} & \textbf{0.8513 $\pm$ 0.0120} \\ & \textbf{v} & 0.7305 $\pm$ 0.0153 & 0.7799 $\pm$ 0.0129 & 0.7943 $\pm$ 0.0082 & 0.7999 $\pm$ 0.0166 & 0.8092 $\pm$ 0.0113\\ \bottomrule\end{tabular}
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Comparison of the effect of the different uncertainty criteria for OOD on CIFAR-100 with different sets of parameters for Packed-Ensembles.
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2210.09184v3_train__51ea3bc5-48ed-4c51-a691-2a63b241958a
2210.09184v3
\begin{tabular}{cccccccccc}\hline Network & Acc & NLL & ECE & AUPR & AUC & FPR95 & Params (M) \\ \hline PE ResNet-50 & \textbf{96.0} & \textbf{0.1367} & \textbf{0.0087} & \textbf{97.1} & \textbf{94.9} & \textbf{14.5} & 23.6 \\ ResNeXt-50 & 90.4 & 0.4604 & 0.0709 & 90.4 & 82.5 & 63.4 & \textbf{23.0} \\ \hline \end{tabular}
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\textbf{Comparison between the results obtained with Packed-Ensembles and a similar ResNeXt-50
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2210.09184v3_train__0c0464f0-93a5-4677-9ad8-458d1cf5e557
2210.09184v3
\begin{tabular}{l|cc|cc}\hline \multirow{2}{*}{Datasets} & \multicolumn{2}{c|}{RMSE} & \multicolumn{2}{c}{NLL} \\ &\multicolumn{1}{c}{Packed-Ensembles} &\multicolumn{1}{c|}{Deep Ensembles} &\multicolumn{1}{c}{Packed-Ensembles} &\multicolumn{1}{c}{Deep Ensembles} \\ \hline Boston housing &\textbf{2.218 $\pm$ 0.099} & \textbf{2.219 $\pm$ 0.098} & \textbf{2.028 $\pm$ 0.034} & 2.047 $\pm$ 0.028 \\ Concrete &\textbf{5.092 $\pm$ 0.225 } & 5.167 $\pm$ 0.234 & \textbf{2.854 $\pm$ 0.028} & 2.885 $\pm$ 0.032 \\ Energy & \textbf{1.675 $\pm$ 0.085 }& 1.712 $\pm$ 0.067 &\textbf{ 1.543 $\pm$ 0.072} & \textbf{1.553 $\pm$ 0.060 }\\ Kin8nm & \textbf{0.058 $\pm$ 0.003} & \textbf{0.058 $\pm$ 0.003} & -1.442 $\pm$ 0.010 & \textbf{-1.452 $\pm$ 0.010 } \\ Naval Propulsion Plant &\textbf{0.002 $\pm$ 0.000} &\textbf{ 0.002 $\pm$ 0.000} & \textbf{-4.835 $\pm$ 0.066} & -4.833 $\pm$ 0.097 \\ Power Plant & 3.127 $\pm$ 0.018 & \textbf{3.097} $\pm$ \textbf{0.020} & 2.607 $\pm$ 0.007 & \textbf{2.600 $\pm$ 0.007 } \\ Protein & 3.476 $\pm$ 0.030 & \textbf{3.412 $\pm$ 0.017} & 2.472 $\pm$ 0.033 & \textbf{2.442 $\pm$ 0.015 } \\ Wine &\textbf{ 0.482 $\pm$ 0.006} & \textbf{0.483 $\pm$ 0.006} & 0.622 $\pm$ 0.014 & \textbf{0.611 $\pm$ 0.013 } \\ Yacht & \textbf{1.949} $\pm$ \textbf{0.215} & 2.511 $\pm$ 0.283 & 2\textbf{.023 $\pm$ 0.075 } & \textbf{2.023 $\pm$ 0.074} \\ \hline \end{tabular}
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\textbf{Comparison of the results obtained with Packed-Ensembles and Deep Ensembles on regression tasks.
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2302.10810v1_train__e077080b-c87e-41b3-a52b-ed8879061207
2302.10810v1
\begin{tabular}{lcccccccc}\hline %& \multicolumn{2}{c}{ Success Rate}\\ Algorithm & Floor hit rate & Mean positioning error (m)\\ \hline TNN &90.64\% & 12.35\\ TSNN &94.48\% &9.81\\ SCNN &95.52\% & 9.68\\ \hline \end{tabular}
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Localization results on UJIIndoorLoc validation dataset (1111 observations) using neural network algorithms
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2302.10810v1_train__f271b9ec-bbd4-4d5d-8352-a8b3586e3d21
2302.10810v1
\begin{tabular}{lcccccccc}\hline %& \multicolumn{2}{c}{ Success Rate}\\ Building ID &0 & 1 & 2 & Overall \\ (\# of obs.) & (536) & (307) & (268) & (1111)\\ \hline % \# of obs. &536 &307& 268& 1111\\ \hline %Algorithm: \\ \ \ \ \ TNN & 12.65 & 12.52 & 12.04 &12.35\\ \ \ \ \ TSNN &8.18 & 11.97 & 10.61 &9.81\\ \ \ \ \ SCNN &7.94 & 12.07 & 10.44 & 9.68\\ \hline \end{tabular}
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Building-wise mean positioning error (m)
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2102.08896v1_train__e6f4c3a5-d843-491b-84d9-a71fbb1add19
2102.08896v1
\begin{tabular}{|p{0.25in}|p{1.5in}|p{2.75in}|}\hline Sr. & Application Domains & Security Requirements \\ \hline 1 & Urban Surveillance and Public Safety & Privacy and Autonomy \cite{elmaghraby2014cyber}, Panoptic Systems \cite{van2011policing,xu2019blendmas}\\ \hline 2 & Smart Power Grid & Denial of Service Attacks \cite{bou2013communication}, Integrity Attacks \cite{metke2010security}, Malware attacks, Power thefts, Billing Manipulations \cite{aloul2012smart} \\ \hline 3 & Geospatial Data Analysis (UAV) & Secured Communication \cite{javaid2012cyber,he2016communication}, Man in the Middle attack, Privacy \cite{rodday2016exploring} \\ \hline 4 & Intelligent Transportation Systems (ITS) and Connected Vehicles & Authentication, Availability, Non-Repudiation, Integrity \cite{siegel2017survey},Denial of Service, Sybil, Black-hole attack \cite{sakiz2017survey}\\ \hline 5 & Smart Healthcare & Data Confidentiality, Data Authentication, Data Integrity, Availability for wireless body network \cite{saleem2009security} \\ \hline 6 & Industry 4.0 & Enterprise Cyber-Espionage,denial of service attacks, and phishing attacks \cite{pereira2017network} \\ \hline \end{tabular}
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Security Requirements for Fog Computing Use-cases
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2208.00362v1_train__f6921760-fdc2-40be-82ab-df995ed6d760
2208.00362v1
\begin{tabular}{|l|l|l|l|l|l|l|l|}\hline \hfil Name &\hfil Mag Range &\hfil Obs Num &\hfil Exp Time (s) &\hfil Distance (pc) &\hfil $E$($B$-$V$)&\hfil $m_{V1}$ &\hfil $M_{V1}$\\ A0821 & \hfil 11.85 - 12.15 (V) &\hfil 257 & \hfil 30 &\hfil $342.9\pm12.1$&\hfil0.063&12.12&$4.64\pm0.08$ \\ & \hfil 11.56 - 11.85 (R) &\hfil250 &\hfil 25 &\hfil &\hfil&& \\ & \hfil 12.26 - 12.58 (B) &\hfil 255 &\hfil 50 &\hfil &\hfil&& \\ \hline T7281 & \hfil 12.08 - 12.40 (V) &\hfil 160 &\hfil 20 &\hfil $426.4\pm11.0$&\hfil0.059&12.37&$4.40\pm0.06$ \\ & \hfil 11.78 - 12.08 (R) &\hfil 239&\hfil 20 &\hfil &\hfil&& \\ \hline T7275 & \hfil 11.47 - 11.71 (V) &\hfil 154 & \hfil 25 &\hfil $326.7\pm60$&\hfil0.059&11.67&$4.28\pm0.44$ \\ \hline \end{tabular}
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Basic Catalogue and Light Curve Parameters for the Three Systems. $m_{V1
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2208.10907v1_train__3422293b-fd71-4e7a-957d-ce95355449e8
2208.10907v1
\begin{tabular}{c|c|c|c}Low-rank structure & Basis & Admissibility & Complexity\\ \hline BLR~\cite{amestoyImprovingMultifrontalMethods2015} & Independent & Strong or weak & $O(N^2)$ \\ $\mathrm{BLR}^2$~\cite{ashcraftBlockLowRankMatrices2021} & Shared & Strong or weak & $O(N^{1.8})$ \\ HODLR~\cite{ambikasaranFastAlgorithmsDense2013} & Independent & Weak & $O(N\log^2 N)$ \\ $\mathcal{H}$-matrix~\cite{hackbuschSparseMatrixArithmetic1999} & Independent & Strong & $O(N\log^2 N)$ \\ HSS~\cite{chandrasekaranFastSolverHSS2006} & Shared & Weak & $O(N)$ \\ $\mathcal{H}^2$-matrix~\cite{hackbuschMatrices2000} & Shared & Strong & $O(N)$ \\ \end{tabular}
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List of Different Low-rank Structures
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2201.08335v2_train__8ddc1c80-aafd-4131-a716-9e20190b7e7f
2201.08335v2
\begin{tabular}{c || cccc}\hline \hline Filter & Accessible Sky-Coverage & $N_\text{lightcurves}$ & $N_\text{lightcurves}$ with $N_{obs} \ge 20$ \\ \hline g-band & 97.66\% & 1,226,245,416 & 582,677,216 \\ r-band & 98.31\% & 1,987,065,715 & 1,107,250,253 \\ i-band & 51.88\% & 346,398,848 & 78,425,164 \\ \end{tabular}
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Object Statistics for Public Data Release 5. Additional details can be found at \href{https://www.ztf.caltech.edu/page/dr5
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2201.08335v2_train__ce204483-d1e3-4e1e-b70b-32d4903f86dc
2201.08335v2
\begin{tabular}{c|cccc}& $t_0$ (hmjd) & $t_\text{eff}$ (days) & $f_0$ (flux) & $f_1$ (flux)\\ \hline Low Bound & min($t$) - 50 & 0.01 & $-\infty$ & 0 \\ High Bound & max($t$) + 50 & 5000 & $\infty$ & $\infty$ \\ \end{tabular}
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Boundaries for four-parameter microlensing model.
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2201.08335v2_train__9b09ba0d-9115-4ff1-8207-90279d2590d5
2201.08335v2
\begin{tabular}{ccc}\hline \hline Column Name & Datatype & Unit \\ \hline id & string & - \\ ra & float & degrees \\ dec & float & degrees \\ t0 & float & hmjd \\ t0\_err & float & hmjd \\ tE & float & days \\ tE\_err & float & days \\ u0\_amp & float & - \\ u0\_amp\_err & float & - \\ piE\_E & float & - \\ piE\_E\_err & float & - \\ piE\_N & float & - \\ piE\_N\_err & float & - \\ mag\_base\_r & float & magnitude \\ mag\_base\_err\_r & float & magnitude \\ mag\_base\_g & float & magnitude \\ mag\_base\_err\_g & float & magnitude \\ mag\_base\_i & float & magnitude \\ mag\_base\_err\_i & float & magnitude \\ b\_sff\_r & float & - \\ b\_sff\_err\_r & float & - \\ b\_sff\_g & float & - \\ b\_sff\_err\_g & float & - \\ b\_sff\_i & float & - \\ b\_sff\_err\_i & float & - \\ \end{tabular}
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Exported Candidate Schema. Exported data have been posted online for public use \citep{puzle_microlensing_catalogs
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2204.02010v1_train__6fe01863-ada1-4028-b214-94bdc99935cb
2204.02010v1
\begin{tabular}{|c|c|c|}\hline Method & K & Test error (↓)\\ \hline InfoGAN & 10 & 5 ± 0.01 \\ AAE & 32 & 4.10 ± 1.13 \\ \textbf{ours} & 10 & \textbf{2.38 ± 0.38} \\ \hline \end{tabular}
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MNIST Unsupervised Classification test error.
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2204.02010v1_train__0505f466-f604-4670-9677-9b07680ce364
2204.02010v1
\begin{tabular}{|c|c|c|c|}\hline Encoder $Enc$ & Decoder $Dec$ & Discriminator $D$ / $Q$ & Generator $G$\\ \hline Input(1X32x32) & Input $\in R^{64}$ & Input $\in R^{64}$ & Input $\in R^{76}$ \\ \hline c4-o16-s2-r & r-u4-c3-o128-p1-bn128-r & fc-o1000-r & fc-o1000-r \\ \hline c4-o32-s2-r & u2-c3-o64-p1-bn64-r & fc-o1000-r & fc-o1000-r \\ \hline c4-o64-s2-r & u2-c3-o32-p1-bn32-r & fc-o512-r & fc-o1000-r \\ \hline c4-o128-s2-r & u2-c3-o3-p1-tanh & fc-o1-sig,fc-o2,fc-o10 & fc-o64 \\ \hline c4-o128-s2-r & - & - & - \\ \hline fc-o64 & - & - & - \\ \hline \end{tabular}
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MNIST Network Architecture
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2204.02010v1_train__1ee44b14-eeda-4757-90c7-0d605dbf5820
2204.02010v1
\begin{tabular}{|c|c|c|c|}\hline Encoder $Enc$ & Decoder $Dec$ & Discriminator $D$ / $Q$ & Generator $G$\\ \hline Input(1X64x64) & Input $\in R^{128}$ & Input $\in R^{128}$ & Input $\in R^{190}$ \\ \hline c4-o64-s2-r & r-u4-c3-o512-p1-bn128-r & fc-o3000-r & fc-o3000-r \\ \hline c4-o128-s2-r & u2-c3-o256-p1-bn64-r & fc-o3000-r & fc-o3000-r \\ \hline c4-o256-s2-r & u2-c3-o128-p1-bn32-r & fc-o3000-r & fc-o3000-r \\ \hline c4-o512-s2-r & u2-c3-o64-p1-bn32-r & fc-o512-r & fc-o3000-r \\ \hline c4-o1024-s2-r & u2-c3-o1-p1-tanh& fc-o1-sig,(fc-o2),3x(fc-o20) & fc-o128\\ \hline c4-o128-s2-r & - & - & \\ \hline fc-o128 & - & - & - \\ \hline \end{tabular}
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3D Chair Network Architecture
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2204.02010v1_train__c24be00c-8196-4415-89e2-d7587c068e9d
2204.02010v1
\begin{tabular}{|c|c|c|c|}\hline Encoder $Enc$ & Decoder $Dec$ & Discriminator $D$ / $Q$ & Generator $G$\\ \hline Input(3X32x32) & Input $\in R^{128}$ & Input $\in R^{128}$ & Input $\in R^{228}$ \\ \hline c4-o64-s2-r & r-u4-c3-o512-p1-bn128-r & fc-o3000-r & fc-o3000-r \\ \hline c4-o128-s2-r & u2-c3-o256-p1-bn64-r & fc-o3000-r & fc-o3000-r \\ \hline c4-o256-s2-r & u2-c3-o128-p1-bn32-r & fc-o3000-r & fc-o3000-r \\ \hline c4-o512-s2-r & u2-c3-o3-p1-tanh & fc-o512-r & fc-o3000-r \\ \hline c4-o128-s2-r & - & fc-o1-sig,10x(fc-o10) & fc-o128\\ \hline fc-o128 & - & - & - \\ \hline \end{tabular}
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CelebA Network Architecture
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2209.12210v1_train__03e0d97d-4cb0-4d75-bdbd-b5e1cbb3b772
2209.12210v1
\begin{tabular}{|c|c|c|c|c|}\hline \textbf{Study} & \textbf{Data Type} & \textbf{Noise Type} & \textbf{\% Active Pixels} & \textbf{Neighborhood Radius} \\ \hline Krull et al., 2019 & Natural Images & i.i.d. & 0.2 - 2 & 5 \\ \hline Birnie et al., 2021 & Seismic & WGN & 0.2 & 5 \\ \hline Birnie et al., 2021 & Seismic & Bandpassed & 25 & 15 \\ \hline Birnie et al., 2021 & Seismic & Field Data & 33 & 15 \\ \hline This study & Seismic & Field Data & 33 & 15 \\ \hline \end{tabular}
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Blind-spot network parameters for different data and noise types.
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2209.12210v1_train__76a839e5-fee9-4cf5-9ffc-3890e954cbaf
2209.12210v1
\begin{tabular}{|c|c|c|c|}\hline \textbf{NN Architecture} & \textbf{\# Layers} & \textbf{\# Initial Filters} & \textbf{Kernel Size} \\ \hline UNet & 2 & 32 & 3x3 \\ \hline \textbf{Loss Function} & \textbf{Batch Size} & \textbf{Optimiser} & \textbf{Initial LR} \\ \hline MAE & 32 & Adam & 1e-4 \\ \hline \end{tabular}
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The neural network architecture and training parameters.
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2207.03919v2_train__c02d5753-0338-41c9-b902-2cd23a8c1603
2207.03919v2
\begin{tabular}{c|cc|c}\hline \hline & \multicolumn{2}{c|}{Si} & NaCl \\ & indirect & \ \ \ direct at $\Gamma$ & direct at $\Gamma$\\ \hline QMC derived& 0.69 & 2.72&5.25\\ PBE & 0.66 & 2.60 &5.08\\ % Connector & 0.86 \\ LDA & 0.49 &2.55 &4.59\\ TBmBJ & 1.19& 3.09 & 8.93\\ \hline Exp. & 1.17 \cite{silicon-gap} & 3.05\cite{Ortega1993} & 8.5\cite{nacl-gap} \\ & & 3.40\cite{silicon-gap} & \\ \hline \hline \end{tabular}
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KS minimum band gaps and direct band gaps at $\Gamma$ (eV) in comparison with experimental photoemission gaps from Refs. \cite{silicon-gap,Ortega1993,nacl-gap
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2203.08391v2_train__b6fd43eb-1a5b-4338-8c6d-696faf8b160f
2203.08391v2
\begin{tabular}{c|c|c|c}\hline $n$ & $M_{2n}^\pi$ & $E_{2n}^\pi$ & Singular Value Distribution\\ \hline 1 & 0.25 & 0.5 & $1\times 0.5$\\ 2 & 0.01928711 & 0.94882494 & $3\times0.282788+1\times 0.10045973$\\ 3 & 0.00175476 & 0.97296386 & $1\times 0.3353396 +2\times 0.2309162 +1\times0.1757919$\\ 4 & 0.00016548 & 1.08649082 & $2\times 0.30870218+2\times0.15042053+1\times0.08412272+1\times0.08412269$\\ \hline \end{tabular}
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Moments and the optimized permutation norm.
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2201.09680v1_train__303d0ea0-85ed-4c84-98f7-2639fe1f74de
2201.09680v1
\begin{tabular}{c|l|c|c|c}\toprule& \textbf{Model} & \textbf{\# Params} & \textbf{Dev} & \textbf{Test} \\ \midrule% & TXL small$^a$ & 151M & - & 24.0 \\ %& TXL large$^a$ & 257M & - & \textbf{18.3}\\ \multirow{4}{*}[-0.0ex]{\rotatebox[origin=c]{90}{WikiText}} & Transformer-XL & 122M & 19.0 & 19.9\\ & \textsc{RelationLM} & 124M & 18.5 & 19.2\\ & \textsc{Spalm} & 122M & 18.1 & 19.0 \\ & $\;\hookrightarrow$ + \textsc{RelationLM} & 124M & \textbf{17.7} & \textbf{18.6} \\ \midrule\multirow{4}{*}[0.1ex]{\rotatebox[origin=c]{90}{WMT19}} & Transformer-XL & 114M & 21.7 & 21.5\\ & \textsc{RelationLM} & 116M & 21.0 & 20.7 \\ & \textsc{Spalm} & 114M & 20.4 & 20.3\\ & $\;\hookrightarrow$ + \textsc{RelationLM} & 116M & \textbf{19.8} & \textbf{19.6} \\ \midrule%& transformer-XL$^a$ & 88M & - & 1.03 \\ \multirow{4}{*}[-0.1ex]{\rotatebox[origin=c]{90}{enwik8}} & Transformer-XL & 93M & 1.05 & 1.03\\ & \textsc{RelationLM} & 95M & 1.04 & 1.02 \\ & \textsc{Spalm} & 93M & 1.04 & 1.02\\ & $\;\hookrightarrow$ + \textsc{RelationLM} & 95M & \textbf{1.03} & \textbf{1.01} \\ \bottomrule\end{tabular}
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We use perplexity ($\downarrow$) on WikiText-103 and WMT19 and bits per character ($\downarrow$) on enwik8 for evaluation. \label{tab:dataset_result
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2312.03055v1_train__aa21b793-c609-4725-8a2f-00b64862c1f6
2312.03055v1
\begin{tabular}{ll|cccc}\hline & & \multicolumn{4}{c}{epoch}\\ component & parameter & 2017 & 2020 & 2021 & 2022\\ \hline \texttt{TBabs}$_1$ &$N_\textup{H}\,(10^{22}\,{\rm atoms/cm}^2)$ & \multicolumn{4}{c}{$0.95_{-0.12}^{+0.14}$ (t)} \\ \hline \multirow{2}{*}{\texttt{vapec}$_1$} & $kT\,({\rm keV})$ & $0.057\pm0.004$ (t) & $0.062\pm0.004$ & $0.057\pm0.004$ (t) & $0.057\pm0.004$ (t)\\ & Norm & \multicolumn{4}{c}{$5.4_{-3.0}^{+10.7}$}\\ \hline \multirow{2}{*}{\texttt{vapec}$_2$} & $kT\,({\rm keV})$ & $0.30\pm0.01$ (t) & $0.65\pm0.06$ & $0.30\pm0.01$ (t) & $0.30\pm0.01$ (t)\\ & Norm & \multicolumn{4}{c}{$(2.7\pm0.5)\times10^{-4}$ (t)} \\ \hline & $F_\textup{0.5-2 keV}$ (erg/cm$^2$/s) & $(6.6\pm0.3)\times10^{-14}$ (t) & $(1.67\pm0.04)\times10^{-13}$ & $(6.6\pm0.3)\times10^{-14}$ (t) & $(6.5\pm0.4)\times10^{-14}$\\ \hline \multirow{2}{*}{\texttt{powerlaw}} & $\Gamma$ & \multicolumn{4}{c}{$-1.3\pm0.2$ (t)} \\ & Norm & \multicolumn{3}{c}{$(8.6\pm0.2)\times10^{-7}$ (t)} & $(4.1\pm0.1)\times10^{-7}$\\ \hline & $F_\textup{2-5 keV}$ (erg/cm$^2$/s) & $(1.55\pm0.03)\times10^{-13}$ & $(1.67\pm0.03)\times10^{-13}$ & $(1.43\pm0.04)\times10^{-13}$ & $(6.1\pm0.3)\times10^{-14}$\\ \hline \texttt{TBabs}$_2$ & $N_\textup{H}\,(10^{22}\,{\rm atoms/cm}^2)$ & \multicolumn{2}{c}{$110\pm5$ (t)} & $116\pm5$ & $134\pm12$\\ \hline \multirow{2}{*}{\texttt{vapec}$_3$} & $kT\,({\rm keV})$ & \multicolumn{4}{c}{$6.2\pm0.3$ (t)}\\ & Norm & \multicolumn{3}{c}{$(1.5\pm0.1)\times10^{-2}$ (t)} & $(0.91\pm0.01)\times10^{-2}$ \\ \hline & $F_\textup{5-8 keV}$ (erg/cm$^2$/s) & $(2.05\pm0.02)\times10^{-12}$ & $(2.05\pm0.02)\times10^{-12}$ & $(1.94\pm0.02)\times10^{-12}$ & $(1.01\pm0.03)\times10^{-12}$\\ \hline \multirow{3}{*}{\texttt{Gauss}} & $E\,({\rm keV})$ & \multicolumn{4}{c}{6.4 (f)}\\ & $\sigma\,({\rm keV})$ & \multicolumn{4}{c}{$0.10\pm0.01$ (t)} \\ & Norm & \multicolumn{3}{c}{$(1.4\pm0.1)\times10^{-4}$ (t)} & $(1.1\pm0.1)\times10^{-4}$ \\ \hline & $F_\textup{Gauss}$ (erg/cm$^2$/s) & $(3.7\pm0.2)\times10^{-13}$ & $(3.7\pm0.2)\times10^{-13}$ & $(3.5\pm0.2)\times10^{-12}$ & $(2.2\pm0.2)\times10^{-13}$ \\ \hline \end{tabular}
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Spectral parameters of the best-fitting model of the central region. Values are reported with $1\sigma$ uncertainties. Parameters indicated by (f) and (t) are, respectively, fixed and tied together during the fitting procedure.
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2312.03055v1_train__d0998d88-9c3e-4905-9c48-a232df73c6c2
2312.03055v1
\begin{tabular}{cccc}\hline \multirow{2}{*}{epoch} & $N_\textup{H}$ & $kT$ & $F_{0.5-2\,{\rm keV}}$\\ & ($10^{22}\,{\rm atoms/cm}^2$) & (keV) & ($10^{-14}\,{\rm erg/s/cm}^2$)\\ \hline 2017 & $0.28\pm0.07$ & $0.18\pm0.01$ & $3.9\pm0.1$\\ 2020 & $0.55\pm0.12$ & $0.20\pm0.02$ & $1.8\pm0.2$\\ 2021 & $0.44\pm0.16$ & $0.16\pm0.02$ & $1.4\pm0.3$\\ 2022 & $0.88\pm0.32$ & $0.17\pm0.02$ & $0.3\pm0.2$\\ \end{tabular}
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Best-fit spectral parameters of the blob. Values are reported with $1\sigma$ uncertainties. \label{tab:blob_spec
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2012.00745v5_train__bf853ec0-acef-410b-a7cd-98bf596e09de
2012.00745v5
\begin{tabular}{c|cccccc}\hline \hline & true & bias & sd & RMSE & meanSE & coverage \\ \hline $n$=2000 & \multicolumn{6}{c}{ } \\ DML MAR & 1.000 & -0.120 & 0.055 & 0.132 & 0.052 & 0.374 \\ DML IV & 1.000 & -0.020 & 0.071 & 0.074 & 0.065 & 0.907 \\ \hline $n$=8000 & \multicolumn{6}{c}{ } \\ DML MAR & 1.000 & -0.116 & 0.028 & 0.119 & 0.027 & 0.009 \\ DML IV & 1.000 & 0.006 & 0.040 & 0.040 & 0.036 & 0.915 \\ \hline \end{tabular}
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Simulation results under nonignorable selection
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2012.00745v5_train__2ce4857b-5e9d-43bf-8efe-102508572835
2012.00745v5
\begin{tabular}{c|cccccc}\hline \hline & true & bias & sd & RMSE & meanSE & coverage \\ \hline $n$=2000 & \multicolumn{6}{c}{} \\ DML MAR & 1.000 & 0.003 & 0.060 & 0.060 & 0.063 & 0.939 \\ DML IV & 1.000 & 0.003 & 0.060 & 0.060 & 0.063 & 0.939 \\ \hline $n$=8000 & \multicolumn{6}{c}{ } \\ DML MAR & 1.000 & 0.012 & 0.031 & 0.033 & 0.034 & 0.934 \\ DML IV & 1.000 & 0.012 & 0.031 & 0.033 & 0.034 & 0.939 \\ \hline \end{tabular}
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Simulation results under MAR
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2012.00745v5_train__3cd0e013-4299-426a-a495-6cf01e04935a
2012.00745v5
\begin{tabular}{cc}\hline \hline treatment & observations \\ \hline randomized out of JC & 1698 \\ controls (no training) & 200 \\ academic training & 830 \\ vocational training & 843 \\ \hline \end{tabular}
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Treatment distribution
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2207.03126v1_train__fa00dc0c-59d0-45b6-b16d-17824df8ff9b
2207.03126v1
\begin{tabular}{|c|c|c|c|c|c|c|c|}\hline \centering$T_{eff}^0$~~&$P_{eff}^0$~~& $x_{1}$~~&$x_{2}$~~&$\phi_{+1}$~~&$\phi_{+2}$~~&$R_1$~~&$R_2$ \\ \hline ~~$0.99T_{eff}^c$ ~~&0.0005663~~&0.6399~~&0.6707~~&0.3343~~&0.4235~~&0.759027~~&0.808721\\ \hline $0.992T_{eff}^c$~~&0.0005697~~&0.6416~~&0.6693~~&0.3386~~&0.4186~~&0.84761~&0.903014\\ \hline $0.994T_{eff}^c$~~&0.0005732~~& 0.6439~~& 0.6677~~& 0.3442~~& 0.4133~~& 0.994135~~& 1.01518\\ \hline $0.995T_{eff}^c$~~&0.0005749~~& 0.6448~~&0.6668~~& 0.3466~~& 0.4102~~& 1.05345~~& 1.09469\\ \hline $0.996T_{eff}^c$~~&0.000576653~~& 0.6462~~&0.6657~~&0.3502~~&0.4064~~& 1.16212~~& 1.20905\\ \hline $0.997T_{eff}^c$~~&0.000578405~~& 0.6467~~&0.6646~~& 0.3538~~& 0.4029~~& 1.29083~~& 1.3191\\ \hline $0.998T_{eff}^c$~~&0.0005801595~~& 0.6493~~& 0.6631~~& 0.3584~~& 0.3982~~& 1.46474~~& 1.49429\\ \hline $0.999T_{eff}^c$~~&0.0005819201~~& 0.6514~~& 0.6612~~& 0.3639~~& 0.3922~~& 1.80019~~& 1.82641\\ \hline $0.9993T_{eff}^c$~~&0.0005824486~~& 0.6522~~& 0.6604~~& 0.3662~~& 0.3899~~& 1.92668~~& 1.94651\\ \hline $0.9995T_{eff}^c$~~&0.000582804~~& 0.6529~~& 0.6598~~& 0.3681~~& 0.3881~~& 2.10521~~& 2.08337\\ \hline $T_{eff}^c$~~&$P_{eff}^c=0.000583686$~~&$x^c=0.65646$~~&$x^c=0.65646$~~&$\phi_+^c=0.378244$~~&$\phi_+^c=0.378244$~~&$R^c=3.12592$ ~~&$R^c=3.12592$ \\ \hline \end{tabular}
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the thermodynamic quantities of two coexistent phases for $T_{eff
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2309.03888v2_train__5ab311df-6da1-460f-8f69-516f3198333c
2309.03888v2
\begin{tabular}{c|cccc|cccc}\hline \hline & \multicolumn{4}{c|}{S CrA} & \multicolumn{4}{c}{$\lambda$ Aql} \\ \cline{1-9}Filter & Time & Seeing & Airmass & I.Q. & Time & Seeing & Airmass & I.Q. \\ & [UT] & [$^{\prime\prime}$] & & [$^{\prime\prime}$] & [UT] & [$^{\prime\prime}$] & & [$^{\prime\prime}$] \\ \cline{0-8}L3244 & 2021-09-18T02:51:58.8391 & 0.7 & 1.295 & 1.0 & 2021-09-18T03:51:09.7134 & 1.11 & 1.926 & 0.84\\ L3262 & 2021-09-18T03:00:15.5436 & 0.94 & 1.327 & 1.22 & 2021-09-18T03:56:48.2035 & 0.98 & 1.999 & 0.85\\ L3302 & 2021-09-18T03:07:22.7153 & 1.05 & 1.357 & 1.03 & 2021-09-18T04:21:26.7844 & 1.31 & 2.413 & 0.93\\ L3340, P.A. 1 & 2021-09-18T02:37:17.0365 & 0.68 & 1.245 & 0.91 & 2021-09-18T03:45:20.0723 & 1.22 & 1.857 & 1.02\\ L3340, P.A. 2 & 2021-09-18T02:44:34.2579 & 0.63 & 1.269 & 0.93 & 2021-09-18T03:45:20.0723 & 1.22 & 1.857 & 1.02\\ L3377 & 2021-09-18T03:15:12.8397 & 0.7 & 1.392 & 0.94 & 2021-09-18T04:27:17.7477 & 1.02 & 2.542 & 0.72\\ L3412 & 2021-09-18T03:22:25.3378 & 0.91 & 1.428 & 1.08 & 2021-09-18T04:32:54.9032 & 1.05 & 2.682 & 0.73\\ L3426 & 2021-09-18T03:29:31.5921 & 0.86 & 1.465 & 0.96 & 2021-09-18T04:38:11.7044 & 1.06 & 2.828 & 0.83\\ M4187 & 2021-09-18T23:44:52.1024 & 0.43 & 1.024 & 0.77 & 2021-09-19T01:08:23.3365 & 0.29 & 1.115 & 0.63\\ M4211 & 2021-09-18T23:52:33.3342 & 0.43 & 1.023 & 0.77 & 2021-09-19T01:16:29.1057 & 0.33 & 1.128 & 0.65\\ M4266 & 2021-09-19T00:00:24.7822 & 0.31 & 1.024 & 0.75 & 2021-09-19T01:26:28.1670 & 0.39 & 1.147 & 0.67\\ M4318 & 2021-09-19T00:08:30.8910 & 0.29 & 1.025 & 0.73 & 2021-09-19T01:34:27.2257 & 0.25 & 1.163 & 0.67\\ M4368, P.A. 1 & 2021-09-18T23:16:27.7131 & 0.51 & 1.033 & 0.73 & 2021-09-19T01:00:22.7853 & 0.33 & 1.104 & 0.68\\ M4368, P.A. 2 & 2021-09-18T23:36:45.9149 & 0.36 & 1.025 & 0.76 & 2021-09-19T01:00:22.7853 & 0.33 & 1.104 & 0.68\\ M4416 & 2021-09-19T00:18:05.5455 & 0.32 & 1.028 & 0.77 & 2021-09-19T01:43:49.4897 & 0.34 & 1.186 & 0.61\\ M4461 & 2021-09-19T00:26:07.9014 & 0.49 & 1.032 & 0.73 & 2021-09-19T01:51:10.0201 & 0.33 & 1.205 & 0.66\\ M4504 & 2021-09-19T00:34:53.1912 & 0.33 & 1.037 & 0.73 & 2021-09-19T01:58:46.7159 & 0.28 & 1.227 & 0.59\\ M4519 & 2021-09-19T00:42:57.2216 & 0.28 & 1.043 & 0.74 & 2021-09-19T02:06:01.9413 & 0.29 & 1.25 & 0.6\\ \hline \hline \end{tabular}
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Observing time, seeing, airmass, and airmass corrected seeing (I.Q.) for our observations.
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2204.08269v4_train__de269108-0fc1-4536-b614-4e615a903f55
2204.08269v4
\begin{tabular}{c|c |c}\textbf{} & \textbf{channels} & \textbf{kernel size} \\ \hline Conv & $195$ & $(7, 7)$ \\ Batch Norm, ReLU & $195$ & \\ Max Pool & & $(2, 2)$ \\ \hline Conv & $390$ & $(5, 5)$ \\ Batch Norm & $390$ & \\ SqueezeExcite, ReLU & $390$ & \\ \hline Conv & $780$ & $(3, 3)$ \\ Batch Norm & $780$ & \\ SqueezeExcite, ReLU & $780$ & \\ Global Average Pool & & \\ \hline Linear, ReLU, Dropout $0.5$ & $64$ & \\ Linear, Softmax & $8$ & \\ \end{tabular}
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Table outlining the 2-D convnet architecture that process the time--frequency scattering tensor. The channels column indicates the number of channels or hidden units output after a layer.
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2204.08269v4_train__b0d65d06-eb59-4ed3-8d51-307da9181cc5
2204.08269v4
\begin{tabular}{|c| c c c c c c c c |c|}\hline & \textbf{tenor sax.} & \textbf{trumpet} & \textbf{flute} & \textbf{clarinet} & \textbf{female singer} & \textbf{dist. guitar} & \textbf{violin} & \textbf{piano} & \textbf{avg} \\ \hline \multirow{2}{*}{\textbf{CQT}} & 5.7 & \textbf{80.9} & 40.2 & \textbf{85.3} & 84.4 & 87.8 & 64.2 & 98.5 & 68.4 \\ & $\pm$ 3.8 & $\pm$ 3.5 & $\pm$ 5.3 & $\pm$ 5.1 & $\pm$ 0.7 & $\pm$ 1.8 & $\pm$ 12.8 & $\pm$ 1.4 & $\pm$ 1.8 \\ \hline \multirow{1}{*}{\textbf{Scattering1D}} & 54.8 & 70.9 & 43.9 & 60.1 & 93.7 & 96.1 & 74.1 & 98.7 & 74.0 \\ & $\pm$ 9.8 & $\pm$ 9.7 & $\pm$ 8.9 & $\pm$ 7.9 & $\pm$ 2.4 & $\pm$ 1.1 & $\pm$ 4.3 & $\pm$ 0.2 & $\pm$ 2.4 \\ \hline \multirow{2}{*}{\textbf{JTFS}} & \textbf{71.5} & 77.8 & \textbf{57.0} & 59.5 & \textbf{96.3} & \textbf{96.4} & \textbf{93.0} & \textbf{99.8} & \textbf{81.4} \\ & $\pm$ 5.9 & $\pm$ 8.7 & $\pm$ 4.3 & $\pm$ 1.3 & $\pm$ 0.7 & $\pm$ 0.0 & $\pm$ 5.6 & $\pm$ 0.1 & $\pm$ 0.6 \\ \hline \end{tabular}
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Test set classwise and macro average accuracy for 2-D convnet architectures trained for musical instrument classification on Medley-solos-DB. Classes are in ascending order (left to right) of number of training set examples. We report the results of CQT, time scattering and time--frequency scattering frontends for a convnet classifier. See Section \ref{sec:convnet
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2106.08042v1_train__f83777ed-04b3-408e-acf9-73970103c962
2106.08042v1
\begin{tabular}{ |c|c|c|c|c|c|c|c|c|c| }\hline Approach & $m_{pos}$ & $m_{neg}$ & $m_{triplet}$ & $\alpha_{triplet}$ & $m_{own}$ & $m_{other}$ & $\alpha_{own}$ & $\alpha_{other}$ & $delay$ \\ \hline Batch-hard Triplet loss (baseline) & - & - & 0.289 & - & - & - & - & - & - \\ Contrastive loss & 0.330 & 0.691 & - & - & - & - & - & - & - \\ Contrastive-Triplet & 0.030 & 0.742 & 0 & 1 & - & - & - & - & - \\ \hline \end{tabular}
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Optimal hyperparameters of approaches for the CUB200 dataset (top) and the Hotels-50k dataset chain recognition task (bottom) found via Bayesian optimization. Dashes mark hyperparameters that are not used by an approach.
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2106.08042v1_train__9b04a8ec-86b8-4731-927b-0084924e02aa
2106.08042v1
\begin{tabular}{ |c|c|c|c|c| }\hline Approach & MAP@R & MAP@R confidence & P(1) & P(1) confidence \\ \hline Untrained backbone & 0.134 & - & 0.524 & - \\ Triplet loss (baseline) & 0.243 & [0.237, 0.249] & 0.647 & [0.639, 0.655] \\ Contrastive & \textbf{0.260} & [0.257, 0.264] & 0.668 & [0.664, 0.671] \\ Contrastive-Triplet & 0.258 & [0.254, 0.262] & 0.670 & [0.665, 0.675] \\ \hline \end{tabular}
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Benchmark results on CUB200.
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2206.05196v2_train__9e9dc089-e6de-4c0b-a507-8b00969dd85a
2206.05196v2
\begin{tabular}{l|c|c|c|cc}\hline \hline $Y_{c\bar c}$ State& $s_0$~\mbox{[GeV$^2$]}&$M^2$~\mbox{[GeV$^2$]}& \mbox{PC (average)} & \mbox{OPE}\\ \hline \hline $J^1_\mu$& $ 25.0-27.0$ & $ 5.0-7.0 $&$46 \%$& $<2\%$\\ $J^2_\mu$& $ 25.0-27.0$ & $ 5.0-7.0 $&$45 \%$&$<3\%$\\ $J^3_\mu$ & $ 22.0-24.0$ & $ 4.5-6.5 $&$43 \%$&$<2\%$\\ $J^4_\mu$ & $ 25.0-27.0$ & $ 5.0-7.0 $&$44 \%$&$<3\%$\\ $J^5_\mu$ & $ 24.0-26.0$ & $ 5.0-7.0 $&$43 \%$&$<2\%$\\ $J^6_\mu$ & $ 24.0-26.0$ & $ 5.0-7.0 $&$43 \%$&$<3\%$\\ $J^7_\mu$ & $ 24.0-26.0$ & $ 5.0-7.0 $&$45 \%$&$<2\%$\\ $J^8_\mu$ & $ 24.0-26.0$ & $ 5.0-7.0 $&$44 \%$&$<2\%$\\ \hline \hline \end{tabular}
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Working regions of the Borel mass parameters, continuum threshold, PC and OPE convergence for magnetic moments.
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2107.12733v1_train__6cf97303-969e-4fb0-b062-25bc4985c07b
2107.12733v1
\begin{tabular}{c|cc|cc|cc|cc}\multicolumn{1}{c}{$\lambda$}&\multicolumn{2}{c}{$u_{\bot}(0)\: [10^{-2}nm] $}&\multicolumn{2}{c}{$u_{\bot}(L)\:[10^{-2}nm]$}&\multicolumn{2}{c}{$\varphi(L)\: [10^{-3}]$}&\multicolumn{2}{c}{$u^{tot}_{max}(0) \:[10^{-2}nm] $} \\ $ $ & $ m = 0.3 $ & $ m = 0.6 $ & $ m = 0.3 $ & $ m = 0.6 $ & $ m = 0.3 $ & $ m = 0.6 $ & $ m = 0.3 $ & $ m = 0.6 $ \\ %$\lambda$ & $u_{\bot}(L) [10^{-2}nm] $ & $u_{t}(L) [10^{-2}nm]$ & $\varphi(L) [10^{-3}]$ & $u_{max}^{tot}(L) [10^{-2}nm] $ \\ %$ $ & $ $ & $ $ & $ $ & $ $ & $ $ & $ $ & $ $ & $ $\\ \hline \cline{1-9}0,1 & 3,665 & 3,809 & -3,527 & -3,652& -3,945& -4,073 & 3,665 & 3,809\\ \cline{1-9}0,2 & 3,321 & 3,613 & -3,196 & -3,463& -3,652 & -3,905& 3,321 & 3,613 \\ \cline{1-9}0,3 & 3,030 & 3,447 & -2,911 & -3,300& -3,383 & -3,751 & 3,030 & 3,447\\ \cline{1-9}0,4 & 2,798 & 3,314 & -2,683 & -3,170& -3,152 & -3,619& 2,798 & 3,314 \\ \cline{1-9}0,5 & 2,613 & 3,208 & -2,502 & -3,067 & -2,959 & -3,509& 2,613 & 3,208 \\ \cline{1-9}0,6 & 2,464 & 3,123 & -2,357 & -2,984 & -2,797 & -3,417 & 2,464 & 3,123\\ \cline{1-9}0,7 & 2,342 & 3,054 & -2,239 & -2,916 & -2,662 & -3,339& 2,342 & 3,054 \\ \cline{1-9}0,8 & 2,241 & 2,996 & -2,141 & -2,860 & -2,547 & -3,274& 2,241 & 2,996 \\ \cline{1-9}0,9 & 2,156 & 2,947 & -2,058 & -2,813 & -2,450 & -3,218& 2,156 & 2,947 \\ \end{tabular}
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Slider and roller supported beam: numerical outcomes.
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2107.12733v1_train__1fdbcf53-ea5f-42c4-acf9-8ff3fdd0fd27
2107.12733v1
\begin{tabular}{c|cc|cc|c|c}\multicolumn{1}{c}{$\lambda$}&\multicolumn{2}{c}{$u_{\bot}(L)\: [10^{-2}nm] $}&\multicolumn{2}{c}{$\varphi(L)\: [10^{-3}]$}&\multicolumn{1}{c}{$u^{tot}_{max}(s^*) \:[10^{-2}nm] $}&\multicolumn{1}{c}{$u^{tot}_{max}(s^*) \:[10^{-2}nm] $} \\ $ $ & $ m = 0.3 $ & $ m = 0.6 $ & $ m = 0.3 $ & $ m = 0.6 $ & $ m = 0.3 $ & $ m = 0.6 $ \\ %$\lambda$ & $u_{\bot}(L) [10^{-2}nm] $ & $u_{t}(L) [10^{-2}nm]$ & $\varphi(L) [10^{-3}]$ & $u_{max}^{tot}(L) [10^{-2}nm] $ \\ %$ $ & $ $ & $ $ & $ $ & $ $ & $ $ & $ $ & $ $ & $ $\\ \hline \cline{1-7}0,1 & -1,036 & -1,135 & -1,658 & -1,751 & 1,136 \:\: $s^*$ = 5,892 & 1,241 \:\: $s^*$ = 5,738 \\ \cline{1-7}0,2 & -0,815 & -1,010 & -1,474 & -1,648 & 0,921 \:\: $s^*$ = 6,041 & 1,117 \:\: $s^*$ = 5,788 \\ \cline{1-7}0,3 & -0,667 & -0,926 & -1,330 & -1,568 & 0,787 \:\: $s^*$ = 6,063 & 1,041 \:\: $s^*$ = 5,774 \\ \cline{1-7}0,4 & -0,574 & -0,874 & -1,221 & -1,506 & 0,703 \:\: $s^*$ = 6,042 & 0,993 \:\: $s^*$ = 5,750 \\ \cline{1-7}0,5 & -0,515 & -0,840 & -1,137 & -1,458 & 0,648 \:\: $s^*$ = 6,009 & 0,962 \:\: $s^*$ = 5,727 \\ \cline{1-7}0,6 & -0,477 & -0,818 & -1,072 & -1,421 & 0,609 \:\: $s^*$ = 5,974 & 0,940 \:\: $s^*$ = 5,707 \\ \cline{1-7}0,7 & -0,450 & -0,802 & -1,020 & -1,391 & 0,580 \:\: $s^*$ = 5,940 & 0,923 \:\: $s^*$ = 5,691 \\ \cline{1-7}0,8 & -0,431 & -0,791 & -0,977 & -1,366 & 0,559 \:\: $s^*$ = 5,910 & 0,911 \:\: $s^*$ = 5,678 \\ \cline{1-7}0,9 & -0,418 & -0,784 & -0,942 & -1,346 & 0,542 \:\: $s^*$ = 5,884 & 0,902 \:\: $s^*$ = 5,667 \\ \end{tabular}
Please generate the necessary LaTeX script to draw this table.
Clamped and roller supported beam: numerical outcomes.
May I have a caption for this LaTeX table?
2107.12733v1_train__802194d8-16a0-4dbb-a656-4398e1a0e06b
2107.12733v1
\begin{tabular}{c|cc|cc|cc|cc}\multicolumn{1}{c}{$\lambda$}&\multicolumn{2}{c}{$u_{\bot}(L)\: [10^{-2}nm] $}&\multicolumn{2}{c}{$u_{t}(L) \:[10^{-2}nm]$}&\multicolumn{2}{c}{$\varphi(L)\: [10^{-3}]$}&\multicolumn{2}{c}{$u^{tot}_{max}(L) \:[10^{-2}nm] $} \\ $ $ & $ m = 0.3 $ & $ m = 0.6 $ & $ m = 0.3 $ & $ m = 0.6 $ & $ m = 0.3 $ & $ m = 0.6 $ & $ m = 0.3 $ & $ m = 0.6 $ \\ %$\lambda$ & $u_{\bot}(L) [10^{-2}nm] $ & $u_{t}(L) [10^{-2}nm]$ & $\varphi(L) [10^{-3}]$ & $u_{max}^{tot}(L) [10^{-2}nm] $ \\ %$ $ & $ $ & $ $ & $ $ & $ $ & $ $ & $ $ & $ $ & $ $\\ \hline \cline{1-9}0,1 & 4,131 & 4,289 & -2,633 & -2,732 & 3,808 & 3,916 & 4,899 & 5,085 \\ \cline{1-9}0,2 & 3,744 & 4,068 & -2,406 & -2,602 & 3,528 & 3,756 & 4,450 & 4,829 \\ \cline{1-9}0,3 & 3,414 & 3,879 & -2,209 & -2,490 & 3,264 & 3,605 & 4,066 & 4,609 \\ \cline{1-9}0,4 & 3,149 & 3,728 & -2,048 & -2,398 & 3,037 & 3,475 & 3,756 & 4,432 \\ \cline{1-9}0,5 & 2,939 & 3,608 & -1,916 & -2,323 & 2,847 & 3,367 & 3,509 & 4,291 \\ \cline{1-9}0,6 & 2,770 & 3,511 & -1,809 & -2,261 & 2,690 & 3,277 & 3,308 & 4,176 \\ \cline{1-9}0,7 & 2,632 & 3,432 & -1,721 & -2,211 & 2,558 & 3,202 & 3,145 & 4,083 \\ \cline{1-9}0,8 & 2,518 & 3,367 & -1,647 & -2,169 & 2,447 & 3,138 & 3,008 & 4,005 \\ \cline{1-9}0,9 & 2,422 & 3,312 & -1,584 & -2,133 & 2,352 & 3,084 & 2,894 & 3,939 \\ \end{tabular}
I need the LaTeX code to create this table, please.
Cantilever beam: numerical outcomes.
Can you suggest a caption for this LaTeX table?
2107.12733v1_train__ee754b79-1a4e-4c5f-8795-63a04e095799
2107.12733v1
\begin{tabular}{c|cc|cc|cc|cc}\multicolumn{1}{c}{$\lambda$}&\multicolumn{2}{c}{$u_{\bot}(0)\: [10^{-2}nm] $}&\multicolumn{2}{c}{$u_{\bot}(L)\:[10^{-2}nm]$}&\multicolumn{2}{c}{$\varphi(L)\: [10^{-3}]$}&\multicolumn{2}{c}{$u^{tot}_{max}(0) \:[10^{-2}nm] $} \\ $ $ & $ m = 0.3 $ & $ m = 0.6 $ & $ m = 0.3 $ & $ m = 0.6 $ & $ m = 0.3 $ & $ m = 0.6 $ & $ m = 0.3 $ & $ m = 0.6 $ \\ %$\lambda$ & $u_{\bot}(L) [10^{-2}nm] $ & $u_{t}(L) [10^{-2}nm]$ & $\varphi(L) [10^{-3}]$ & $u_{max}^{tot}(L) [10^{-2}nm] $ \\ %$ $ & $ $ & $ $ & $ $ & $ $ & $ $ & $ $ & $ $ & $ $\\ \hline \cline{1-9}0,1 & 3,665 & 3,809 & -3,527 & -3,652& -3,945& -4,073 & 3,665 & 3,809\\ \cline{1-9}0,2 & 3,321 & 3,613 & -3,196 & -3,463& -3,652 & -3,905& 3,321 & 3,613 \\ \cline{1-9}0,3 & 3,030 & 3,447 & -2,911 & -3,300& -3,383 & -3,751 & 3,030 & 3,447\\ \cline{1-9}0,4 & 2,798 & 3,314 & -2,683 & -3,170& -3,152 & -3,619& 2,798 & 3,314 \\ \cline{1-9}0,5 & 2,613 & 3,208 & -2,502 & -3,067 & -2,959 & -3,509& 2,613 & 3,208 \\ \cline{1-9}0,6 & 2,464 & 3,123 & -2,357 & -2,984 & -2,797 & -3,417 & 2,464 & 3,123\\ \cline{1-9}0,7 & 2,342 & 3,054 & -2,239 & -2,916 & -2,662 & -3,339& 2,342 & 3,054 \\ \cline{1-9}0,8 & 2,241 & 2,996 & -2,141 & -2,860 & -2,547 & -3,274& 2,241 & 2,996 \\ \cline{1-9}0,9 & 2,156 & 2,947 & -2,058 & -2,813 & -2,450 & -3,218& 2,156 & 2,947 \\ \end{tabular}
Provide LaTeX code for this table.
Slider and roller supported beam: numerical outcomes.
Please write a caption that describes this LaTeX table.
2107.12733v1_train__9ff17ac9-de35-4557-a63a-7e6b5e6d5a96
2107.12733v1
\begin{tabular}{c|cc|cc|c|c}\multicolumn{1}{c}{$\lambda$}&\multicolumn{2}{c}{$u_{\bot}(L)\: [10^{-2}nm] $}&\multicolumn{2}{c}{$\varphi(L)\: [10^{-3}]$}&\multicolumn{1}{c}{$u^{tot}_{max}(s^*) \:[10^{-2}nm] $}&\multicolumn{1}{c}{$u^{tot}_{max}(s^*) \:[10^{-2}nm] $} \\ $ $ & $ m = 0.3 $ & $ m = 0.6 $ & $ m = 0.3 $ & $ m = 0.6 $ & $ m = 0.3 $ & $ m = 0.6 $ \\ %$\lambda$ & $u_{\bot}(L) [10^{-2}nm] $ & $u_{t}(L) [10^{-2}nm]$ & $\varphi(L) [10^{-3}]$ & $u_{max}^{tot}(L) [10^{-2}nm] $ \\ %$ $ & $ $ & $ $ & $ $ & $ $ & $ $ & $ $ & $ $ & $ $\\ \hline \cline{1-7}0,1 & -1,036 & -1,135 & -1,658 & -1,751 & 1,136 \:\: $s^*$ = 5,892 & 1,241 \:\: $s^*$ = 5,738 \\ \cline{1-7}0,2 & -0,815 & -1,010 & -1,474 & -1,648 & 0,921 \:\: $s^*$ = 6,041 & 1,117 \:\: $s^*$ = 5,788 \\ \cline{1-7}0,3 & -0,667 & -0,926 & -1,330 & -1,568 & 0,787 \:\: $s^*$ = 6,063 & 1,041 \:\: $s^*$ = 5,774 \\ \cline{1-7}0,4 & -0,574 & -0,874 & -1,221 & -1,506 & 0,703 \:\: $s^*$ = 6,042 & 0,993 \:\: $s^*$ = 5,750 \\ \cline{1-7}0,5 & -0,515 & -0,840 & -1,137 & -1,458 & 0,648 \:\: $s^*$ = 6,009 & 0,962 \:\: $s^*$ = 5,727 \\ \cline{1-7}0,6 & -0,477 & -0,818 & -1,072 & -1,421 & 0,609 \:\: $s^*$ = 5,974 & 0,940 \:\: $s^*$ = 5,707 \\ \cline{1-7}0,7 & -0,450 & -0,802 & -1,020 & -1,391 & 0,580 \:\: $s^*$ = 5,940 & 0,923 \:\: $s^*$ = 5,691 \\ \cline{1-7}0,8 & -0,431 & -0,791 & -0,977 & -1,366 & 0,559 \:\: $s^*$ = 5,910 & 0,911 \:\: $s^*$ = 5,678 \\ \cline{1-7}0,9 & -0,418 & -0,784 & -0,942 & -1,346 & 0,542 \:\: $s^*$ = 5,884 & 0,902 \:\: $s^*$ = 5,667 \\ \end{tabular}
Convert this table into LaTeX code.
Clamped and roller supported beam: numerical outcomes.
I need a caption for this LaTeX table, please.
2401.00692v1_train__c394a786-f3e0-4cec-a730-5d16d5053d1a
2401.00692v1
\begin{tabular}{lccc}\toprule& \text{Crop} & \text{Flip} & \text{Rotate} \\ \midrule\text{Probability} & 1.0 & 0.25 & 0.25 \\ \bottomrule\end{tabular}
Create LaTeX code to produce this table.
Probabilities for augmentations.
Can you give me a caption for this LaTeX table?
2401.00692v1_train__eed9238f-2e78-44bf-9c06-c506b0cacc2e
2401.00692v1
\begin{tabular}{l|cc|c}\textbf{Lesion Type} & \textbf{f1-score(sup)} & \textbf{f1-score (self-sup)} & \textbf{Support} \\ \hline Actinic keratosis & 0.44 & 0.45 & 498 \\ Basal cell carcinoma & 0.72 & 0.73 & 2549 \\ Benign keratosis & 0.48 & 0.49 & 1663 \\ Dermatofibroma & 0.33 & 0.37 & 173 \\ Melanoma & 0.56 & 0.57 & 3339 \\ Melanocytic nevus & 0.77 & 0.82 & 10601 \\ Squamous cell carcinoma & 0.35 & 0.39 & 414 \\ Vascular lesion & 0.31 & 0.51 & 186 \\ \hline Weighted avg. & 0.68 & 0.71 & 19423 \\ Accuracy & 0.66 & 0.70 & 19423 \\ \end{tabular}
Create a LaTeX script to illustrate this table.
Combined classification report for skin lesion classification model. Each value is a mean across 35 runs.
Please give a caption for the LaTeX table.
2401.00692v1_train__10f689a0-e642-41be-a1e4-1421b9b21ac3
2401.00692v1
\begin{tabular}{l|ccc|c}\textbf{Lesion Type} & \textbf{precision} & \textbf{recall} & \textbf{f1-score} & \textbf{support} \\ \hline Actinic keratosis & 0.37 & 0.57 & 0.45 & 498 \\ Basal cell carcinoma & 0.70 & 0.75 & 0.73 & 2549 \\ Benign keratosis & 0.49 & 0.50 & 0.49 & 1663 \\ Dermatofibroma & 0.43 & 0.32 & 0.37 & 173 \\ Melanoma & 0.52 & 0.63 & 0.57 & 3339 \\ Melanocytic nevus & 0.86 & 0.78 & 0.82 & 10601 \\ Squamous cell carcinoma & 0.48 & 0.34 & 0.39 & 414 \\ Vascular lesion & 0.53 & 0.51 & 0.51 & 186 \\ \hline Weighted avg. & 0.72 & 0.70 & 0.71 & 19423 \\ Accuracy & & & & 0.70\end{tabular}
Generate the LaTeX code to recreate this table.
Self-supervised weights. Mean classification report.
Could you generate a caption for this LaTeX table?
2401.00692v1_train__6f925000-72e4-4f0b-b733-0b81e46c1a46
2401.00692v1
\begin{tabular}{l|ccc|c}\textbf{Lesion Type} & \textbf{precision} & \textbf{recall} & \textbf{f1-score} & \textbf{support} \\ \hline Actinic keratosis & 0.36 & 0.57 & 0.44 & 498 \\ Basal cell carcinoma & 0.70 & 0.76 & 0.72 & 2549 \\ Benign keratosis & 0.47 & 0.49 & 0.48 & 1663 \\ Dermatofibroma & 0.37 & 0.30 & 0.33 & 173 \\ Melanoma & 0.50 & 0.63 & 0.56 & 3339 \\ Melanocytic nevus & 0.85 & 0.70 & 0.77 & 10601 \\ Squamous cell carcinoma & 0.36 & 0.34 & 0.35 & 414 \\ Vascular lesion & 0.25 & 0.67 & 0.35 & 186 \\ \hline Weighted avg. & 0.70 & 0.66 & 0.68 & 19423 \\ Accuracy & & & & 0.66\end{tabular}
Write the LaTeX code for this table.
Supervised weights. Mean classification report
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2105.08075v1_train__c298b8c7-56f9-41c0-9a66-af0cce5526e4
2105.08075v1
\begin{tabular}{l l l l l l}\hline Reference & $k_{r}$ \quad\quad & $k_{nr_{0}}$ \quad\quad & $k_{nr_{1}}$ \quad\quad & $k_{m_{0}}$ \quad\quad & $k_{m_{\pm 1}}$ \quad\\ \hline Robledo et al.\,\cite{robledoSpinDynamicsOptical2011} \quad\quad & 65 & 11 & 80 & 3.0 & 2.6 \\ Tetienne et al.\,\cite{Tetienne2012} \quad\quad & 65.9 & 7.9 & 53.3 & 0.98 & 0.73 \\ Gupta et al.\,\cite{guptaEfficientSignalProcessing2016} \quad\quad & 66.8 & 10.5 &90.7 &4.8 &2.2\\ \hline \end{tabular}
I need the LaTeX code to create this table, please.
Experimentally measured transition rates at zero field. All of the rates are in MHz.
Can you suggest a caption for this LaTeX table?
2105.08075v1_train__08f1e8eb-9b24-4a27-b42e-71dc9c9c84e8
2105.08075v1
\begin{tabular}{l l l l l l l l }\hline NV-Sample \qquad & $\delta_\perp$ (GHz) \qquad & $\phi_\delta$ ($^\circ$) & $g_l$ \qquad\qquad\qquad & $\theta_B$ ($^\circ$) & $\beta_{E_x}$ \qquad\quad\, & $\beta_{E_y}$ \qquad\quad\, & $I_{\rm bck}^{-}$ (cps) \\ \hline NV1-S1 & 4.444(3) & -11.6(1.3) & 0.1395(9) & 1.14(3) & 0.0221(3) & 0.0242(5) & 4378(92) \\ NV2-S2 & 38.6(7) & 1(59) & (fixed to 0.14) & 0.61(3) & 0.085(5) & 0.186(14) & 70910(244) \\ NV3-S2 & 55.9(6) & -32.2(6) & (fixed to 0.14) & 0.502(10) & 0.240(6) & 0.64(2) & 9091(231) \\ NV5-S2 & 32.0(5) & -29(3) & (fixed to 0.14) & 0.20(2) & 0.43(3) & 0.52(5) & 83198(883) \\ NV4-S3 & 42.3(5) & -26(2) & (fixed to 0.14) & 1.06(3) & 0.102(3) & 0.164(7) & 158011(234)\end{tabular}
Could you please provide me the LaTeX code to generate this table?
Summary of the fit results of the $I_{\rm PL
Could you generate a caption for this LaTeX table?
2401.14578v1_train__5596a52d-879a-40f9-a049-99d7a3687fcf
2401.14578v1
\begin{tabular}{ll|ccc|cccc}\toprule&& BA- & BA- & Tree- & BA- & \multirow{2}{*}{Mutagenicity} & \multirow{2}{*}{NCI1} \\ && Shapes & Community & Grid & 2Motifs & &\\ \midrule\multicolumn{2}{l|}{\# Graphs} & 1&1&1& 1,000 &4,337 &4,110 \\ \multicolumn{2}{l|}{\# Nodes (avg)} & 700 & 1,400 &1,231 &25 & 30.32 & 29.87\\ \multicolumn{2}{l|}{\# Edges (avg)} & 4,110 & 8,920 & 3,410& 25.48 & 30.77 & 32.30\\ \multicolumn{2}{l|}{\# Classes } & 4 & 8 & 2&2&2&2\\ \midrule\multirow{3}{*}{Test ACC} &GCN &0.97&0.91&0.97& 1.00 & 0.82&0.81\\ &GraphSAGE & -&-&- & 1.00 & 0.80&0.80\\ &GIN & -&-&- & 1.00 & 0.89&0.83\\ \bottomrule\end{tabular}
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Statistics of the datasets used and the classification accuracy of the trained GNNs.
Please write a caption that describes this LaTeX table.
2312.15396v1_train__197434de-2543-4dc3-aff6-030a6a75652f
2312.15396v1
\begin{tabular}{|l|cccccc|cccccc|}\hline Category & \multicolumn{12}{c|}{Dose Level}\\ \hline & 1 & 2 & 3 & 4 & 5 & 6 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline & \multicolumn{6}{c|}{Scenario 1} & \multicolumn{6}{c|}{Scenario 2} \\ Toxicity & 0.01 & 0.03 & 0.05 & 0.10 & 0.18 & \textbf{0.24} & 0.03 & 0.05 & 0.10 & 0.15 & \textbf{0.20} & 0.41 \\ Efficacy & 0.05 & 0.10 & 0.20 & 0.30 & 0.45 & \textbf{0.55} & 0.05 & 0.10 & 0.20 & 0.40 & \textbf{0.55} & 0.65 \\ PK & 1000 & 1500 & 2500 & 3600 & 4800 & \textbf{6500} & 1000 & 2000 & 3500 & 6000 & \textbf{7500} & 8500 \\ \hline & \multicolumn{6}{c|}{Scenario 3} & \multicolumn{6}{c|}{Scenario 4} \\ Toxicity & 0.20 & \textbf{0.30} & 0.40 & 0.50 & 0.60 & 0.70 & \textbf{0.30} & 0.40 & 0.50 & 0.60 & 0.70 & 0.80 \\ Efficacy & 0.40 & \textbf{0.55} & 0.60 & 0.65 & 0.70 & 0.75 & \textbf{0.50} & 0.55 & 0.60 & 0.65 & 0.70 & 0.75 \\ PK & 4500 & \textbf{6000} & 7000 & 8000 & 9000 & 9500 & \textbf{6500} & 7000 & 7500 & 8000 & 8500 & 9000 \\ \hline & \multicolumn{6}{c|}{Scenario 5} & \multicolumn{6}{c|}{Scenario 6} \\ Toxicity & 0.03 & 0.05 & 0.10 & \textbf{0.20} & 0.30 & 0.45 & 0.10 & 0.15 & 0.21 & \textbf{0.24} & 0.27 & 0.30 \\ Efficacy & 0.10 & 0.30 & 0.45 & \textbf{0.55} & 0.55 & 0.55 & 0.20 & 0.30 & 0.40 & \textbf{0.55} & 0.55 & 0.55 \\ PK & 1000 & 2000 & 4000 & \textbf{6000} & 7500 & 9000 & 2000 & 3000 & 4000 & \textbf{6000} & 6500 & 7000 \\ \hline & \multicolumn{6}{c|}{Scenario 7} & \multicolumn{6}{c|}{Scenario 8} \\ Toxicity & 0.10 & 0.15 & \textbf{0.21} & 0.24 & 0.27 & 0.30 & 0.10 & \textbf{0.21} & 0.24 & 0.27 & 0.30 & 0.33 \\ Efficacy & 0.30 & 0.40 & \textbf{0.55} & 0.55 & 0.55 & 0.55 & 0.40 & \textbf{0.55} & 0.55 & 0.55 & 0.55 & 0.55 \\ PK & 2000 & 4000 & \textbf{6000} & 6500 & 7000 & 7500 & 4000 & \textbf{6000} & 6500 & 7000 & 7500 & 8000 \\ \hline & \multicolumn{6}{c|}{Scenario 9} & \multicolumn{6}{c|}{Scenario 10} \\ Toxicity & 0.20 & \textbf{0.25} & 0.30 & 0.40 & 0.45 & 0.50 & 0.10 & 0.20 & \textbf{0.30} & 0.45 & 0.50 & 0.55 \\ Efficacy & 0.30 & \textbf{0.50} & 0.45 & 0.40 & 0.35 & 0.30 & 0.30 & 0.40 & \textbf{0.55} & 0.60 & 0.55 & 0.45 \\ PK & 5000 & \textbf{6500} & 7500 & 8000 & 8500 & 9000 & 4000 & 5000 & \textbf{6000} & 7000 & 7500 & 8000 \\ \hline & \multicolumn{6}{c|}{Scenario 11} & \multicolumn{6}{c|}{Scenario 12} \\ Toxicity & 0.03 & 0.05 & 0.10 & 0.15 & \textbf{0.20} & 0.25 & \textbf{0.05} & 0.10 & 0.20 & 0.45 & 0.55 & 0.65 \\ Efficacy & 0.10 & 0.30 & 0.40 & 0.50 & \textbf{0.65} & 0.55 & \textbf{0.50} & 0.50 & 0.50 & 0.50 & 0.50 & 0.50 \\ PK & 1500 & 3000 & 4500 & 6000 & \textbf{7500} & 9000 & \textbf{6000} & 7000 & 7500 & 8000 & 8500 & 9000 \\ \hline & \multicolumn{6}{c|}{Scenario 13} & \multicolumn{6}{c|}{Scenario 14} \\ Toxicity & 0.01 & 0.03 & 0.05 & 0.10 & 0.12 & 0.14 & 0.45 & 0.50 & 0.55 & 0.60 & 0.65 & 0.70 \\ Efficacy & 0.03 & 0.05 & 0.10 & 0.20 & 0.20 & 0.20 & 0.30 & 0.40 & 0.55 & 0.55 & 0.55 & 0.55 \\ PK & 500 & 900 & 1500 & 2600 & 3600 & 4600 & 6000 & 6500 & 7000 & 7500 & 8000 & 8500 \\ \hline \end{tabular}
Please create LaTeX code to produce this table.
True toxicity probabilities, efficacy probabilities, and PK values for each dose level
Please provide an appropriate caption for this LaTeX table.
2312.15396v1_train__1093e3dd-1163-48e3-8ab8-9916f664bf33
2312.15396v1
\begin{tabular}{|c|cc|cc|cc|cc|cc|}\hline Scenario & \multicolumn{2}{c|}{$g_P = 0$} & \multicolumn{2}{c|}{$g_P = 0.5$} & \multicolumn{2}{c|}{$g_P = 1$} & \multicolumn{2}{c|}{$g_P = 1.5$} & \multicolumn{2}{c|}{$g_P = 2$} \\ \hline & B & P & B & P & B & P & B & P & B & P \\ \hline 1 & 37.1 & 51.6 & 37.4 & 51.8 & 36.9 & 53.8 & 38.2 & 56.0 & 37.4 & 57.0 \\ 2 & 49.6 & 51.4 & 45.6 & 52.3 & 50.0 & 53.2 & 51.6 & 51.5 & 50.6 & 52.7 \\ 3 & 46.1 & 58.2 & 44.8 & 58.3 & 45.9 & 59.2 & 46.5 & 57.2 & 46.5 & 58.3 \\ 4 & 69.7 & 70.1 & 69.8 & 69.3 & 69.8 & 70.2 & 69.2 & 70.8 & 70.8 & 70.3 \\ 5 & 40.5 & 56.9 & 38.0 & 56.6 & 37.7 & 58.0 & 37.2 & 58.0 & 41.1 & 61.0 \\ 6 & 32.8 & 44.4 & 31.9 & 43.9 & 34.0 & 47.1 & 34.4 & 46.8 & 34.8 & 47.0 \\ 7 & 35.7 & 44.6 & 36.7 & 44.2 & 34.8 & 45.1 & 35.9 & 45.9 & 34.3 & 47.9 \\ 8 & 37.5 & 47.2 & 35.0 & 44.4 & 37.9 & 47.0 & 36.4 & 45.8 & 37.0 & 45.6 \\ 9 & 55.9 & 59.9 & 55.8 & 61.3 & 55.6 & 61.2 & 56.9 & 61.6 & 57.0 & 62.5 \\ 10 & 38.7 & 57.6 & 38.0 & 55.3 & 38.4 & 57.5 & 38.2 & 59.5 & 38.6 & 57.8 \\ 11 & 43.4 & 44.6 & 44.8 & 45.8 & 43.1 & 45.1 & 44.5 & 46.0 & 42.8 & 43.0 \\ 12 & 42.8 & 42.4 & 41.1 & 44.8 & 41.6 & 44.5 & 43.6 & 46.1 & 41.1 & 45.6 \\ 13 & 0.1 & 84.5 & 0.4 & 85.0 & 0.3 & 84.7 & 0.2 & 85.8 & 0.2 & 86.2 \\ 14 & 57.0 & 56.9 & 55.5 & 57.0 & 56.4 & 54.8 & 55.3 & 55.5 & 56.5 & 59.2 \\ \hline \end{tabular}
Generate the LaTeX code to recreate this table.
OBD selection probabilities for BOIN12 (B) and PKBOIN-12 (P) across all scenarios given different values of $g_P$
Can you suggest a caption for this LaTeX table?
2010.01791v1_train__0ca582cc-9629-46ed-9b8b-45583e280504
2010.01791v1
\begin{tabular}{l|l|l}\hline \textbf{Hyperparameter} & \textbf{Pre-training} & \textbf{Fine-tuning}\\ \hline Number of layers & 12 & 12\\ Hidden size & 768 & 768\\ FFN inner hidden size & 3072 & 3072 \\ Attention heads & 12 & 12\\ Attention head size & 64 & 64\\ Embedding size & 768 & 768\\ Mask percent & 15 & -\\ Learning rate decay & linear & linear\\ Layerwise LR decay & - & 0.8 \\ Warmup steps & 10000 & -\\ Warmup fraction & - & 0.1 \\ Learning Rate & 2e-4 & 1e-4\\ Adam $\epsilon$ & 1e-6 & 1e-6\\ Adam $\beta_1$ & 0.9 & 0.9\\ Adam & 0.999 & 0.999\\ Attention dropout & 0.1 & 0.1\\ Dropout & 0.1 & 0.1\\ Weight decay & 0.01 & 0.01\\ $\textit{l}_1$ regularization factor & - & 0.01 \\ Batch size & 2048 & 32\\ Train steps & 1M & -\\ Train epochs & - & 3.0/iter for MRPC, \\ & & 1.0 for others \\ \hline \end{tabular}
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Pre-training and Fine-tuning hyperparameters
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2111.01246v1_train__e7df06a8-490a-4ebd-bafe-ab7e7394465d
2111.01246v1
\begin{tabular}{|l|c|c|c|c|} \hline \textbf{Dataset} & \textbf{\# of Frames} &\textbf{Radar} & \textbf{LiDAR} & \textbf{Camera} \\ \hline nuScenes \cite{nuScenes} & $40,000$ & Sparse point clouds & $\surd$ & $\surd$ \\ Oxford Radar \cite{Oxford_radar_robotcar} & $240,000$ & High resolution radar image & $\surd$ & $\surd$ \\ Astyx \cite{Astyx} & $500$ & Sparse point clouds & $\surd$ & $\surd$ \\ RADIATE \cite{RADIATE} & $44,000$ & High resolution radar image & $\surd$ & $\surd$ \\ CRUW \cite{CRUW} & $396,241$ & Low resolution radar image & $ \times$ & $\surd$\\ Zendar \cite{Zendar} & $94,460$ & SAR with low resolution radar & $\surd$ & $\surd$ \\ CARRADA \cite{CARRADA} & $12,666$ & Sparse point clouds & $ \times$ & $\surd$\\ RadarScenes \cite{RadarScenes} & $975$ & Sparse point clouds & $ \times$ & $\surd$\\ \hline \end{tabular}
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Overview of publicly available radar data sets.
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2111.01246v1_train__dec36eea-c5b8-4c81-a17b-ed8cb90dd022
2111.01246v1
\begin{tabular}{|l|l |c|}\hline {\bf Sensors} & {\bf Model}\\ \hline Radar & TI Imaging Radar, Azimuth Resolution: $1.2^\circ$, Azimuth FOV: $70^\circ$ \\ \hline LiDAR & Velodyne Ultra Puck VLP-32C, Azimuth Resolution: $0.1^\circ$ - $0.4^\circ$\\ & Vertical FOV: $40^\circ$, Maximum Range: 200 m \\ \hline Camera & Teledyne FLIR Blackfly S, Stereo, Image Resolution: 2048 × 1536 \\ \hline \end{tabular}
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Multi-Modal Sensors
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2111.01246v1_train__5945fd86-bb62-497d-9dba-96f65137d4fc
2111.01246v1
\begin{tabular}{|l |l|c|}\hline {\bf Parameters} & {\bf Frame $n$} & {\bf Frame $n+1$}\\ % [0.5ex]\hline Max Range & 150 m & 150 m\\ \hline Max Velocity & 5.15 m/s & 3.97 m/s\\ \hline Range Resolution & 0.6 m & 0.6 m\\ \hline Angle Resolution & $1.2^\circ$ & $1.2^\circ$ \\ %[1ex]\hline \end{tabular}
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Radar Parameters
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2111.01246v1_train__637b6e22-71b8-4e5f-a537-ee7732cc95a1
2111.01246v1
\begin{tabular}{|l| c |c| c| c|}\hline {\bf Model} & {\bf AP} & {\bf [email protected]} & {\bf [email protected]} & {\bf AR}\\ % [0.5ex]\hline Faster R-CNN Resnet-50 & 75.6\% & 96.1\% & 89 \%& 79.7\%\\ \hline \end{tabular}
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Evaluation Metrics
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2112.10356v2_train__e223a576-4b7d-4c4f-8cdd-0d2b8c046add
2112.10356v2
\begin{tabular}{|c|p{2.4cm}|p{3.4cm}|p{2.4cm}|}\hline \multirow{2}{*}{\textbf{Priority}} & \multicolumn{3}{c|}{\textbf{Data Source}}\\ \cline{2-4}& \textbf{Bugzilla} & \textbf{Mozilla Advisory} & \textbf{NVD}\\ \hline 1st & V2, V7, V8 & V1, V2, V4, V6, V7, V8, V10 & V1, V2, V4, V8, V10 \\ \hline 2nd & V1, V3, V4 ,V5, V10 & V9 & V3, V5 \\ \hline 3rd & V6, V9 & V3, V5 & V6, V7, V9 \\ \hline \end{tabular}
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The prioritization scheme for SVs fixed in Firefox 77 that is inferred directly from the severity rankings in table \ref{tab:sev_example
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2112.10356v2_train__99a7c5ad-c0cd-4be1-94dc-768ce5b31d8f
2112.10356v2
\begin{tabular}{c|cccc}\hline \multirow{2}{*}{\textbf{Data Source}} & \multicolumn{4}{c}{\textbf{Severity Rankings}}\\ \cline{2-5}& \textbf{1st} & \textbf{2nd} & \textbf{3rd} & \textbf{4th}\\ \hline Bugzilla & blocker (S1) & critical/major (S2) & normal (S3) & minor (S4)\\ \hline Mozilla Adv. & critical & high & moderate & low\\ \hline NVD & critical & high & medium & low\\ \hline \hline \textit{Normalized} & \textit{critical} & \textit{high} & \textit{medium} & \textit{low}\\ \hline \end{tabular}
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Normalization of data source severity rankings.
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2112.10356v2_train__5ebde93d-e087-49ec-8da3-682286cabb62
2112.10356v2
\begin{tabular}{|p{1.5cm}|p{3.25cm}|p{6.5cm}|p{6cm}|}\hline \textbf{Category} & \textbf{Name} & \textbf{Definition} & \textbf{Rationale}\\ \hline \multirow{3}{1.5cm}{Fix Difficulty} & Number of Patches & The number of patches that were submitted to fix the SV. & \multirow{3}{6cm}{If an SV is difficult to remediate, developers may not be able to properly assess it due to a lack of comprehension.}\\ \cline{2-3}& Number of Files & The number of files edited across all patches. & \\ \cline{2-3}& Number of Changes & The number of lines added, modified or deleted across all patches. & \\ \hline \multirow{4}{1.5cm}{Review Process} & Fix Time & Time to fix a bug (resolved date - opened date). & Quickly resolved bugs may be ill-considered. \\ \cline{2-4}& Number of Comments & The number of comments on the bug report. & \multirow{2}{6cm}{Extensive discussion may imply uncertainty of the evaluation of the SV.}\\ \cline{2-3}& Number of Users & The number of users who comment on the bug report. & \\ \cline{2-4}& Number of CC & The number of users in the mailing list for the bug report. & Heavy interest may imply better SV assessment. \\ \hline \multirow{2}{1.5cm}{SV Nature} & Description Length & The number of words in the description. & More explanation may provide easier assessment.\\ \cline{2-4}& Is Crash & Whether the string `crash' in the description. & Crashes have been shown to be indicative of severity label noise \cite{tian2016unreliability}. \\ \hline \multirow{9}{2cm}{Reporter Expertise} & Reporter Bugs Filed & The number of bugs filed by the user. & \multirow{2}{6cm}{Users who are good at reporting bugs may also be good at assessing them.}\\ \cline{2-3}& Reporter Comments & The number of comments made by the user. & \\ \cline{2-4}& Reporter Patches Submitted & The number of patches submitted by the user. & \multirow{6}{6cm}{Users who are good at resolving bugs may also be good at assessing them.}\\ \cline{2-3}& Reporter Patches Reviewed & The number of patches reviewed by the user. & \\ \cline{2-3}& Reporter Bugs Resolved & The number of bugs resolved by the user. & \\ \cline{2-3}& Reporter Bugs Fixed & The number of bugs fixed by the user. & \\ \cline{2-3}& Reporter Bugs Verified & The number of bugs verified by the user. & \\ \cline{2-3}& Reporter Bugs Invalid & The number of bugs invalidated by the user. & \\ \cline{2-4}& Reporter Profile Age & The profile age of the user (current date - creation date). & Older users may be better at assessing SVs. \\ \hline \end{tabular}
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Attributes of a bug report that may influence SV severity misjudgment.
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2112.10356v2_train__25412f4f-de18-4a1e-894a-48e5a3735beb
2112.10356v2
\begin{tabular}{p{1cm}p{3cm}p{1cm}p{1cm}p{1cm}}\hline \textbf{CWE ID} & \textbf{Category} & \textbf{\# Cases} & \textbf{\# Consistent} & \textbf{\% Consistent}\\ \hline CWE 664 & Improper Control of a Resource Through its Lifetime & 1566 & 239 & 15.26\\ \hline CWE 707 & Improper Neutralization & 188 & 91 & 48.4\\ \hline CWE 264 & Permissions, Privileges \& Access Controls & 123 & 44 & 35.77\\ \hline CWE 693 & Protection Mechanism Failure & 34 & 14 & 41.18\\ \hline CWE 399 & Resource Management Errors & 32 & 5 & 15.63\\ \hline \end{tabular}
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Number and percentage of consistently assessed SVs for the five most dominant CWE categories (cases $>$ 30).
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2112.10356v2_train__52e4fdf9-5f16-4ce5-ad79-0663494dc4c9
2112.10356v2
\begin{tabular}{cccc}\hline \textbf{Description Source} & \textbf{Severity Source} & \textbf{MCC} & \textbf{\% Change}\\ \hline \hline Bugzilla & Bugzilla & 0.184 & -\\ \hline Bugzilla & Mozilla Advisory & 0.042 & -77.17\\ \hline Bugzilla & NVD & 0.124 & -32.61\\ \hline \hline Mozilla Advisory & Mozilla Advisory & 0.16 & -\\ \hline Mozilla Advisory & Bugzilla & 0.051 & -68.13\\ \hline Mozilla Advisory & NVD & 0.231 & +44.38\\ \hline \hline NVD & NVD & 0.217 & -\\ \hline NVD & Bugzilla & 0.062 & -71.43\\ \hline NVD & Mozilla Advisory & 0.086 & -60.37\\ \hline \end{tabular}
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Severity prediction model performance for different SV description and severity ranking data sources. \% Change indicates the percentage change in MCC from using a uniform description and severity data source.
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2306.00323v3_train__2fc2f2cd-ee53-4061-970c-a3a22b9e2ff0
2306.00323v3
\begin{tabular}{|c|c|}\hline \textbf{Hyperparameter} & \textbf{Value} \\ \hline Adam $\beta_1$ & 0.9 \\ \hline Adam $\beta_2$ & 0.99 \\ \hline Adam $\epsilon$ & $10^{-5}$ \\ \hline Entropy Coefficient & 0.01 \\ \hline Image Embedding Dimension & 128 \\ \hline Text Embedding Dimension & 256 \\ \hline Memory Dimension & 2048 \\ \hline \end{tabular}
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Hyperparameter Settings
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2401.13184v1_train__b7b70613-e945-4f6d-8900-de4c9d5dfabe
2401.13184v1
\begin{tabular}{cccc}& \multicolumn{3}{c}{Susceptibility}\\ \cline{2-4}\noalign{\vskip0.1cm}Real or Imaginary & Gaussian\textsuperscript{a} & Lorentzian & Rectangle \\ \midrule\noalign{\vskip0.5cm}$\chi'(\omega)$ & $-\frac{g^{2}N\sqrt{2}}{\sigma}F(\frac{\omega-\omega_{0}}{\sqrt{2}\sigma})$ & $-g^{2}N\frac{(\omega-\omega_{0})}{(\omega-\omega_{0})^{2}+(\sigma/2)^{2}}$ & $-\frac{g^{2}N}{\sigma}\ln|\frac{\omega-\omega_{0}+\sigma/2}{\omega-\omega_{0}-\sigma/2}|$ \\ \noalign{\vskip0.5cm}$\chi''(\omega)$ & $\frac{g^{2}N}{\sigma}\sqrt{\frac{\pi}{2}}\exp[-\frac{1}{2}(\frac{\omega-\omega_{0}}{\sigma})^{2}],$ & $g^{2}N\frac{\sigma/2}{(\omega-\omega_{0})^{2}+(\sigma/2)^{2}}$ & $\frac{g^{2}N\pi}{\sigma}\text{rec}[2(\omega-\omega_{0})/\sigma],$ \\ \noalign{\vskip0.5cm}\midrule\noalign{\vskip0.1cm}\multicolumn{4}{c}{\textsuperscript{a}Here $F(y)=\exp[-y^{2}]\int_{0}^{y}dte^{t^{2}}$ isthe Dawson function.}\\ \end{tabular}
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Real and imaginary parts of the molecular susceptibility\label{tab:Real-and-imaginary
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2401.13184v1_train__f7d47af8-da0a-42d1-8973-0145d52f1392
2401.13184v1
\begin{tabular}{ccccccccc}\multicolumn{1}{l}{} & \multicolumn{2}{c}{{\footnotesize{}Gaussian}} & & \multicolumn{2}{c}{{\footnotesize{}Lorentzian}\textsuperscript{}} & & \multicolumn{2}{c}{{\footnotesize{}Rectangle}}\\ \cline{2-9}\noalign{\vskip0.1cm}{\footnotesize{}Optical Signal} & {\footnotesize{}$\text{\ensuremath{\sigma<g\sqrt{N}}}$} & {\footnotesize{}$\sigma>g\sqrt{N}$} & & {\footnotesize{}$\text{\ensuremath{\sigma<g\sqrt{N}}}$} & {\footnotesize{}$\sigma>g\sqrt{N}$} & & {\footnotesize{}$\text{\ensuremath{\sigma<g\sqrt{N}}}$} & {\footnotesize{}$\sigma>g\sqrt{N}$}\\ \midrule{\footnotesize{}$A(\omega)$} & {\footnotesize{}increases} & {\footnotesize{}decreases} & & {\footnotesize{}decreases} & {\footnotesize{}decreases} & & {\footnotesize{}increases} & {\footnotesize{}decreases; narrow side bands}\\ {\footnotesize{}$T(\omega)$} & {\footnotesize{}increases} & {\footnotesize{}decreases} & & {\footnotesize{}increases} & {\footnotesize{}decreases} & & {\footnotesize{}increases} & {\footnotesize{}decreases; narrow side bands}\\ {\footnotesize{}$R(\omega)$} & {\footnotesize{}increases} & {\footnotesize{}decreases} & & {\footnotesize{}increases or decreases}\textsuperscript{{\footnotesize{}a}} & {\footnotesize{}decreases} & & {\footnotesize{}increases} & {\footnotesize{}decreases; narrow side bands}\\ \midrule\multicolumn{9}{l}{{\footnotesize{}}\textsubscript{}{\footnotesize{}}\textsuperscript{{\footnotesize{}a}}{\footnotesize{}Forthe Lorenzian, the VRS in the reflection spectrum increases if $\kappa_{L}^{2}/\kappa_{R}^{2}<1$and decreases if $\kappa_{L}^{2}/\kappa_{R}^{2}>1$ (See Table \ref{tab:Vacuum-Rabi-Splitting})}}\\ \end{tabular}
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Vacuum Rabi splitting trends with disorder \label{tab:Trends
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2401.13184v1_train__db3b881d-caa6-4c70-8a17-3fa3028dd90c
2401.13184v1
\begin{tabular}{cccc}& \multicolumn{3}{c}{Vacuum Rabi Splitting}\tabularnewline\cline{2-4}Optical Signal & Gaussian & Lorentzian\textsuperscript{a} & Rectangle\\ \midrule\noalign{\vskip0.5cm}$A(\omega)$ & 0 & $2g\sqrt{N}-\frac{\sigma^{2}}{8\sqrt{g^{2}N-\frac{\kappa^{2}}{8}}}$ & 0\\ \noalign{\vskip0.5cm}$T(\omega)$ & $2\sqrt{\frac{1}{2}g^{2}N+\frac{1}{2}\sqrt{g^{4}N^{2}+4g^{2}N\sigma^{2}}}$ & $2g\sqrt{N}+\frac{\kappa\sigma}{4g\sqrt{N}}$ & $2\sqrt{\frac{1}{2}g^{2}N+\frac{1}{2}\sqrt{g^{4}N^{2}+\frac{\sigma^{2}g^{2}N}{3}}}$\\ \noalign{\vskip0.5cm}$R(\omega)$ & $2\sqrt{\frac{1}{2}g^{2}N+\frac{1}{2}\sqrt{g^{4}N^{2}+4g^{2}N\sigma^{2}}}$ & $2g\sqrt{N}-\frac{(\frac{\kappa_{L}^{2}}{\kappa_{R}}-\kappa_{R})\sigma}{8g\sqrt{N}}$ & $2\sqrt{\frac{1}{2}g^{2}N+\frac{1}{2}\sqrt{g^{4}N^{2}+\frac{\sigma^{2}g^{2}N}{3}}}$\\ \noalign{\vskip0.5cm}\midrule\noalign{\vskip0.1cm}\multicolumn{4}{c}{\textsuperscript{a}For larger values of $\sigma$, Eqs. \ref{eq:Lorentzian_up_lp_abs}-\ref{eq:Lorentzian_up_lp_refl}should be used to extract the correct value for $g\sqrt{N}$.}\\ \end{tabular}
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Vacuum Rabi splitting expressions for when $\sigma\ll g\sqrt{N
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2402.13030v1_train__b83d2df7-2ef0-48dc-bfe1-168b3a2798a6
2402.13030v1
\begin{tabular}{cccc}\hline Threshold Quantile & Transition in $U$ & Memory Compr. & SSIM \\ \hline 0 & $0.003628 \pm 10^{-7}$ & - & - \\ 0.91 & $0.003628 \pm 10^{-7}$ & 0.82 & 1.0 \\ 0.93 & $0.003628 \pm 10^{-7}$ & 0.86 & 1.0 \\ 0.95 & $0.003628 \pm 10^{-7}$ & 0.90 & 1.0 \\ 0.97 & $0.003628 \pm 10^{-7}$ & 0.94 & 0.999 \\ 0.99 & $0.003628 \pm 10^{-7}$ & 0.98 & 0.901 \\ \hline \end{tabular}
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Value of the Hubbard $U$ where the lowest eigenvalue of the reconstructed generalized charge susceptibility $\chi^c$ at $\beta=1000$ vanishes, for a decomposition level of $l=6$ and a frequency size of $512\times512$ for various threshold quantiles. Additionally, the compression metric for the memory and the SSIM are reported. The divergence in the original, uncompressed vertex is also found to be at $U = 0.003628 \pm 10^{-7
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2402.13030v1_train__6b724279-e646-415e-9027-ebcfa5846b53
2402.13030v1
\begin{tabular}{ccccc}\hline Threshold Quantile & Value of $\lambda_{max}$ & $\lambda_{max} \times w_{max}$ & Memory Compr. & SSIM \\ \hline 0 & 987605.434 & 326.211 & - & - \\ 0.91 & $987577.921$ & 326.203 & 0.82 & 0.857 \\ 0.93 & $987569.835$ & 326.202 & 0.86 & 0.835 \\ 0.95 & $987553.718$ & 326.198 & 0.90 & 0.790 \\ 0.97 & $987503.102$ & 326.184 & 0.94 & 0.699 \\ 0.99 & $987246.247$ & 326.117 & 0.98 & 0.525 \\ \hline \end{tabular}
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Value of the maximal eigenvalue of the generalized charge susceptibility at $U=1$ and $\beta=1000$ vanishes, for a decomposition level of $l=6$ and a frequency size of $512\times512$ for various threshold quantiles. Additionally, the compression metric for the memory and the SSIM are reported. The magnitude of the maximal eigenvalue of the original, uncompressed susceptibility is $\lambda_{max
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1910.09136v2_train__1a28f230-9caa-4114-ba25-c519d8be37b0
1910.09136v2
\begin{tabular}{|c|c|}\hline \textbf{Parameter} & \textbf{Value} \\ \hline Modulation scheme & 4-QAM \\ \hline Transmit antennas, $M$ & 32 \\ \hline Reflecting elements, $N$ & 64 \\ \hline Channel fading & $\mathbf{H}^H_{s,u} , \mathbf{h}^H_{d,u} \sim \mathcal{CN}(0, 1)$ \\ \hline Pathloss & $\frac{10^{-2}}{d^{-3.75}}$ \\ \hline AWGN & $n \sim \mathcal{CN}(0, SNR)$ \\ \hline SNR during training & $0\text{dB}$ - $30\text{dB}$ \\ \hline Batch size & 64 \\ \hline No. of training data samples & $7 \times 10^4$ \\ \hline Validation split & 20\% \\ \hline Validation patience & 50 \\ \hline Total training steps & 1000 \\ \hline Optimizer & Adam, $\delta_{1} = 0.9$, $\delta_{2} = 0.999$ \\ \hline Regularization & $\lambda = 0.0001$ , $p = 0.5$ \\ \hline Learning rate, $\eta$ & 0.01 \\ \hline \end{tabular}
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Parameters used for simulations
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2211.12057v1_train__8eb11894-19f8-4d80-81c3-76310458f763
2211.12057v1
\begin{tabular}{|c|c|c|c|c|c|c|c|c|}\hline label & $a$ (fm) & $L^3\times T$ & $m_\pi$ (MeV) & $m_S$ (MeV) & $m_\pi L$ & \#configs & sep. & \#low modes \\ \hline 96 & 0.05684 & $96^3\times 192$ & 134.3 & 153 & 3.71 & 77 & 60 & 8000\\ 64 & 0.08787 & $64^3\times 96$ & 129.5 & 212 & 3.69 & 78 & 100 & 8000\\ 48I & 0.12121 & $48^3\times 64$ & 132.7 & 326 & 3.91 & 32 & 100 & 8000\\ 32 & 0.15148 & $32^3\times 48$ & 133.0 & 418 & 3.27 & 48 & 40 & 8000 \\ 48II & 0.15099 & $48^3\times 64$ & 134.3 & 418 & 4.93 & 40 & 100 & 8000\\ \hline \end{tabular}
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{\it Parameters defining the lattice ensembles. Columns contain a label to refer to the ensemble, the lattice spacing $a$, the spatial volume $L^3$ times the temporal direction $T$ (in lattice units), the Nambu--Goldstone pion mass $m_\pi$, the maximum pion mass $m_S$ in the pion taste multiplet, $m_\pi L$, the number of configurations in the ensemble, the separation between measurements ({\rm ``sep.''
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2210.01884v1_train__0facb638-1cfe-42a2-bad2-a5cc88391486
2210.01884v1
\begin{tabular}{l|c|c|c|c}\hline Name & Supervision & Sampling & Matching & mIoU \\ \hline BaR & labels & \textbf{Ba}lanced & \textbf{R}egion & \textbf{73.4} \\ BaX & labels & \textbf{Ba}lanced & e\textbf{X}act & 61.2 \\ RaR & labels & \textbf{Ra}ndom & \textbf{R}egion & 48.6 \\ RaX & labels & \textbf{Ra}ndom & e\textbf{X}act & 60.5 \\ \hline \end{tabular}
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Supervised Baselines
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2210.01884v1_train__1bb31865-f79b-43e9-8826-395424f53aa7
2210.01884v1
\begin{tabular}{l|c|c}\hline Weights & mIoU (AVD-easy) & mIoU (AVD-hard) \\ \hline \hline Random & 66.7 & 49.1 \\ \hline ADE20K & 69.3 & \textbf{69.1} \\ \hline RegConsist (Ours) & \textbf{69.5} & 64.8 \\ \hline \end{tabular}
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Results on AVD
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2210.01884v1_train__6913d983-d17f-4591-bca8-bc9f891d9c7e
2210.01884v1
\begin{tabular}{l|c|c|c|c}\hline Labeled Images & 5\% & 10\% & 20\% & 30\% \\ \hline ADE20K & 59.2 & 67.2 & 76.8 & 80.1 \\ \hline RegConsist (Ours) & \textbf{62.7} & \textbf{67.8} & \textbf{77.3} & \textbf{80.5} \\ \hline \end{tabular}
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Number of Labeled Examples
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2210.01884v1_train__158d53df-3357-4e97-9cd8-6f50d659aca9
2210.01884v1
\begin{tabular}{l|c|c|c}\hline Initialization & Dataset & Training & mIoU \\ \hline Random & -- & None & 57.0 \\ ImageNet-sup & ImageNet & Supervised & 56.7 \\ PixPro-400 \cite{PixPro} & ImageNet & Self-supervised & \textbf{57.4} \\ \hline \end{tabular}
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Starting Weights
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2312.05627v1_train__1b5acf13-0600-4984-a585-ad98fae98d72
2312.05627v1
\begin{tabular}{||c| c |c| c||}\hline LP & X & Y & C \\ [0.5ex]\hline L1 & -0.8443 & 0 & 2.8575 \\ L2 & -1.1256 & 0 & 2.8719 \\ L3 & 0.9696 & 0 & 3.5446 \\ [1ex]\hline \end{tabular}
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Location of the Collinear Lagrange Equilibrium points.
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2312.05627v1_train__691859aa-5233-42dd-a8e8-faab72b114ea
2312.05627v1
\begin{tabular}{||l|c|c|c||}\hline Exoplanet systems & $\beta$ & $\mu$ & $a$ \\ [0.5ex]\hline CoRoT-2b & 0.0155 & 0.0032 & 0.9997 \\ TOI-1278 b & 0.0023 & 0.0318 & 0.9999 \\ HAT-P-20 b & 0.0052 & 0.0093 & 0.9999 \\ Kepler-75 b & 0.0118 & 0.0105 & 0.8214 \\ WASP- 89 b & 0.0097 & 0.0060 & 0.9940 \\ TIC 172900988 b & 0.0381 & 0.0020 & 0.9966 \\ NGTS 9b & 0.0422 & 0.0021 & 0.9982 \\ LP 714 - 47 b & 0.0026 & 0.0002 & 0.9992 \\ WASP- 162 b & 0.0189 & 0.0052 & 0.9009 \\ XO- 3 b & 0.0498 & 0.0092 & 0.9656 \\ \hline \end{tabular}
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Numerical Data
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2312.05627v1_train__40206776-e401-4957-845d-3ca116d1a2cd
2312.05627v1
\begin{tabular}{||c| c |c| c||}\hline Exoplanet systems & $L_1$ & $\pm \lambda_{1,2}$ & $\pm \lambda_{3,4}$ \\ [0.5ex]\hline CoRoT-2b & $(-0.8957,0)$ & $0.9824$ & $2.0847\it{i}$ \\ TOI-1278 b & $(-0.7639,0)$ & $1.4432$ & $2.5594\it{i}$ \\ HAT-P-20 b & $(-0.8516,0)$ & $1.1161$ & $2.21248it{i}$ \\ Kepler-75 b & $(-0.8525,0)$ & $1.1111$ & $2.2078\it{i}$ \\ WASP- 89 b & $(-0.8724,0)$ & $1.0498$ & $2.1480\it{i}$ \\ TIC 172900988 b & $(-0.9086,0)$ & $0.9319$ & $2.0389\it{i}$ \\ NGTS 9b & $(-0.9069,0)$ & $0.9327$ & $2.0397\it{i}$\\ LP 714 - 47 b & $(-0.9626,0)$ & $0.8298$ & $1.9512\it{i}$ \\ WASP- 162 b & $(-0.8808,0)$ & $1.0207$ & $2.1204\it{i}$\\ XO- 3 b & $(-0.8475,0)$ & $1.0923$ & $2.1893\it{i}$ \\ \hline \end{tabular}
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Characterstic roots for $L_1$ point
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2312.05627v1_train__41c06480-e8d2-46b9-9fc8-28b3d7973586
2312.05627v1
\begin{tabular}{||c| c |c| c||}\hline Exoplanet systems & $L_2$ & $\pm \lambda_{1,2}$ & $\pm \lambda_{3,4}$ \\ [0.5ex]\hline CoRoT-2b & (-1.1013,0) & 0.5211 & 1.737832\it{i} \\ TOI-1278 b & (-1.2040,0) & 0.3478 & 1.650364\it{i} \\ HAT-P-20 b & (-1.1428,0) & 0.4545 & 1.698284\it{i} \\ Kepler-75 b & (-1.1373,0) & 0.4628 & 1.702496\it{i} \\ WASP- 89 b & (-1.1240,0) & 0.4887 & 1.716077\it{i} \\ TIC 172900988 b & (-1.0839,0) & 0.5451 & 1.747966\it{i} \\ NGTS 9b & (-1.0846,0) & 0.5405 & 1.745227\it{i} \\ LP 714 - 47 b & (-1.0374,0) & 0.6680 & 1.827509\it{i} \\ WASP- 162 b & (-1.1135,0) & 0.5016 & 1.723090\it{i} \\ XO- 3 b & (-1.1366,0) & 0.4292 & 1.685871\it{i} \\ \hline \end{tabular}
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Characterstic roots for $L_2$ point
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2312.05627v1_train__bc908c09-9f5e-4dd2-955e-da3bc4ff51a1
2312.05627v1
\begin{tabular}{||c| c |c| c||}\hline Exoplanet systems & $L_3$ & $\lambda_{1,2}$ & $ \lambda_{3,4}$ \\ %[0.5ex]\hline CoRoT-2b & (0.9962,0) & $\pm 4116$ & $\pm 5836$\\ TOI-1278 b & (1.0125,0) & $\pm 19.037$ \it{i} & $\pm 27.231$ \it{i} \\ HAT-P-20 b & (1.0021,0) & $\pm78.975$\it{i} & $\pm111.76$\it{i} \\ Kepler-75 b & (1.0003,0) & $\pm82.518$\it{i} & $\pm116.771$\it{i} \\ WASP- 89 b & 0.9992,0) & $\pm 196.43$\it{i} & $\pm 289.32$\it{i} \\ TIC 172900988 b & (0.9880,0) & $\pm 44.539$ & $\pm 62.852$\\ NGTS 9b & (0.9866,0) & $\pm 37.681$ & $\pm 53.128$ \\ LP 714 - 47 b & (0.9992,0) & $1110.13$ & $784.261 $ \\ WASP- 162 b & (0.9958,0) & $\pm 0.00111$ \it{i} & $\pm 3721.4 $ \it{i} \\ XO- 3 b & (0.9870,0) & $\pm 414.1784$ & $\pm 585.51$ \\ \hline \end{tabular}
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Characterstic roots for $L_3$ point
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2203.05412v2_train__d5b734c4-cf80-48d7-b8b1-90fcfb22c598
2203.05412v2
\begin{tabular}{@{}cccccccc@{}}\toprule[2pt]\multirow{2}{*}{Model} & \multirow{2}{*}{Element} & \multicolumn{3}{c}{NYT$^*$} & \multicolumn{3}{c}{WebNLG$^*$} \\ \cmidrule(l){3-5} \cmidrule(l){6-8}& & Prec. & Rec. & F1 & Prec. & Rec. & F1 \\ \midrule\multirow{3}{*}{CasRel} & $(h, t)$& 89.2 & 90.1 & 89.7 & 95.3 & 91.7 & 93.5 \\ & $r$ & 96.0 & 93.8 & 94.9 & 96.6 & 91.5 & 94.0 \\ & $(h, r, t)$ & 89.7 & 89.5 & 89.6 & 93.4 & 90.1 & 91.8 \\ \midrule\multirow{3}{*}{SPN} & $(h, t)$ & 93.2 & 92.7 & 92.9 & 95.0 & 95.4 & 95.2 \\ & $r$ & 96.3 & 95.7 & 96.0 & 95.2 & 95.7 & 95.4 \\ & $(h, r, t)$ & 93.3 & 91.7 & 92.5 & 93.1 & 93.6 & 93.4 \\ \midrule\multirow{3}{*}{PRGC} & $(h, t)$ & \textbf{94.0} & 92.3 & 93.1 & 96.0 & 93.4 & 94.7 \\ & $r$ & 95.3 & 96.3 & 95.8 & 92.8 & 96.2 & 94.5 \\ & $(h, r, t)$ & \textbf{93.3} & 91.9 & 92.6 & 94.0 & 92.1 & 93.0 \\ \midrule\multirow{3}{*}{OneRel} & $(h, t)$ & 93.3 & \textbf{93.4} & \textbf{93.3} & \textbf{96.2} & \textbf{96.5} & \textbf{96.3}\\ & $r$ & \textbf{96.7} & \textbf{96.9} & \textbf{96.8} & \textbf{96.7} & \textbf{97.0} & \textbf{96.8} \\ & $(h, r, t)$ & 92.8 & \textbf{92.9} & \textbf{92.8} & \textbf{94.1} & \textbf{94.4} & \textbf{94.3} \\ \bottomrule[2pt]\end{tabular}
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Results on triple elements. $(h, t)$ denotes the entity pair and $r$ means the relation.
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2203.05412v2_train__4d376895-4557-4e7b-8510-b4c65297b9d8
2203.05412v2
\begin{tabular}{@{}ccccc@{}}\toprule[2pt]Dataset & Model & Training Time & Inference Time & F1 \\ \midrule\multirow{2}{*}{NYT$^*$} & TPLinker & 1592 & 46.2 & 91.9 \\ & OneRel & \textbf{1195} & \textbf{41.5} & \textbf{92.9} \\ \midrule\multirow{2}{*}{WebNLG$^*$} & TPLinker & 599 & \textbf{40.1} & 91.9 \\ & OneRel & \textbf{88} & 45 & \textbf{94.3} \\ \bottomrule[2pt]\end{tabular}
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Comparison of the model efficiency. Training Time (s) means the time required to train one epoch, Inference Time (ms) is the time to predict triples of one sentence.
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2202.01820v2_train__5fbac734-b0b4-4188-8ff8-412c0bc1b437
2202.01820v2
\begin{tabular}{lccc}\hline $T$ (MeV) & $k_2$ & $R$ (km) & $\lambda$ (10$^{36}$gr cm$^2$ s$^2$) \\ \hline 0.01 & 0.1005 & 12.21 & 2.73 \\ 0.1 & 0.0984 & 12.26 & 2.73 \\ 1 & 0.0788 & 12.82 & 2.73 \\ 5 & 0.0315 & 15.48 & 2.79 \\ 10 & 0.0127 & 18.92 & 3.02 \\ \hline \end{tabular}
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Values of radius and tidal parameters related to the temperature, for a $1.4\;M_\odot$ neutron star and for the Lattimer and Swesty EoSs~\cite{Lattimer-91
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2202.01820v2_train__527610d4-6c5f-4bca-8644-20283e3f9c42
2202.01820v2
\begin{tabular}{ccccccc}\hline \multirow{2}{*}{S ($\mathrm{k_B}$)} & \multicolumn{3}{c}{Shen {\it et al.}~\cite{Shen-2011}} & \multicolumn{3}{c}{Lattimer and Swesty~\cite{Lattimer-91}} \\ \cline{2-7}& $k_2$ & $R$ (km) & $\lambda$ (10$^{36}$gr cm$^2$ s$^2$) & $k_2$ & $R$ (km) & $\lambda$ (10$^{36}$gr cm$^2$ s$^2$) \\ \hline 0.1 & 0.0830 & 12.06 & 2.114 & 0.0817 & 12.10 & 2.114 \\ 0.2 & 0.0835 & 12.05 & 2.119 & 0.0834 & 12.05 & 2.119 \\ 0.5 & 0.0806 & 12.18 & 2.162 & 0.0814 & 12.16 & 2.161 \\ \hline \end{tabular}
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Values of radius and tidal parameters related to the entropy, for a $1.4\;M_\odot$ neutron star and for both crust considerations (Shen \textit{et al.
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2310.04280v2_train__2d2f271d-5cd2-46af-a5f6-b8492e9d02c5
2310.04280v2
\begin{tabular}{@{}clllll@{}}\hline \\ & \textbf{OIL DRILLING} & : & ``oil-drilling'' ($82\%$) & ``gas-pipeline'' ($9\%$) & ``fracking'' ($7\%$)\\ [5pt]& \textbf{METAL}& : & ``metal'' ($46\%$) & ``ferrous'' ($37\%$) & ``nonferrous'' ($14\%$)\\ [5pt]& \textbf{WOOD}& : & ``wood'' ($64\%$) & ``timber'' ($27\%$) & ``lumber'' ($10\%$)\\ [5pt]& \textbf{MEAT}& : & ``meat'' ($49\%$) & ``red-meat'' ($18\%$) & ``poultry'' ($16\%$)\\ [5pt]& \textbf{MARIJUANA}& : & ``marijuana'' ($54\%$) & ``cannabis'' ($44\%$) & ``t.h.c.'' ($2\%$)\\ [5pt]\hline \end{tabular}
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Subset of MIS Commodities Industries
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2310.04280v2_train__85885ddf-6ddb-4ad4-8549-4cac28485c05
2310.04280v2
\begin{tabular}{@{}cllll@{}}\hline \\ & \textbf{ONCOLOGY :} & ``oncology'' ($85\%$) & ``carcinoma'' ($10\%$) & ``lymphoma'' ($9\%$)\\ [5pt]& \textbf{MICROBIOLOGY :} & ``microbiology'' ($58\%$) & ``virology'' ($18\%$) & ``bacteriology'' ($15\%$)\\ [5pt]& \textbf{GENOMICS :} & ``genomics'' ($66\%$) & ``gene-editing'' ($23\%$) & ``d.n.a.'' ($10\%$)\\ [5pt]& \textbf{SURGERY :} & ``surgery'' ($72\%$) & ``organ-transplant'' ($17\%$) & ``orthopedics'' ($12\%$)\\ [5pt]& \textbf{CARDIOLOGY :} & ``cardiology'' ($65\%$) & ``heart-attack'' ($22\%$) & ``heart'' ($11\%$)\\ [5pt]\hline \end{tabular}
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Subset of MIS Healthcare Industries
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2310.04280v2_train__a21bdf3f-7992-4587-9a79-07a7d9dd9642
2310.04280v2
\begin{tabular}{@{}cllll@{}}\hline \\ & \textbf{A.I. :} & ``artificial-intelligence'' ($60\%$) & ``computer-vision'' ($23\%$) & ``n.l.p.'' ($15\%$)\\ [5pt]& \textbf{STREAMING :} & ``media-streaming'' ($49\%$) & ``television'' ($21\%$) & ``music-streaming'' ($14\%$)\\ [5pt]& \textbf{BLOCKCHAIN :} & ``blockchain'' ($56\%$) & ``cryptocurrency'' ($44\%$) & -\\ [5pt]& \textbf{ROBOTICS :} & ``robotics'' ($59\%$) & ``factory-automation'' ($31\%$) & -\\ [5pt]& \textbf{CAD :} & ``c.a.d.'' ($52\%$) & ``3d-print'' ($48\%$) & -\\ [5pt]\hline \end{tabular}
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Subset of MIS Tech Industries
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2105.11622v2_train__a1ef0bc7-931b-470a-9281-ee280be0cacc
2105.11622v2
\begin{tabular}{cccccccccc}\hline &&\multicolumn{8}{c}{\textbf{Year}} \\ &\%& 1994& 1999 & 2001 & 2002 & 2004 & 2006 & 2008 & 2010 \\ \cline{2-10}&Mass (Mt) & 0 & 2.3 & 4.2 & 5.1 & 6.9 & 8.4 & 10.1 & 12.0 \\ \hline \label{tab:inject}\end{tabular}
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The total amount of CO$_2$ injected volume along with the time
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2202.08348v1_train__eb3a9d8c-18da-4a74-90fa-af91dd00d4ad
2202.08348v1
\begin{tabular}{ @{\extracolsep{3pt}} c c c c c c c c }\hline \hline \multicolumn{4}{c}{\textbf{Model}} &\multicolumn{2}{c}{\textbf{cycle6.10}} &\multicolumn{2}{c}{\textbf{ax54}} \\ \cline{1-4} \cline{5-6} \cline{7-8}${\bf \Sigma_{g,0}}$ &${\bf q}$ &${\bf a_p}$ &\textbf{\textbf{Flux}} &\textbf{\textbf{Loss}} &\textbf{\textbf{RMS}} &\textbf{\textbf{Loss}} &\textbf{\textbf{RMS}} \\ $[{\rm g/cm^2}]$ & $[M_{\oplus}/M_{\odot}]$ & [au] & [mJy] & & [$\mu{}$Jy/beam] & & [$\mu{}$Jy/beam]\\ % $[\rm{g}/\rm{cm^2}]$ & $[M_{\oplus}/M_{\odot}]$ &% [au] &% [mJy] &% [\%] &% [$\mu$Jy/beam] &% [\%] &% [$\mu$Jy/beam]% \\ \hline 300 & 1 & 2 & 69 &3.2\% & 11.2 &3.2\% & 8.4 \\ 300 & 10 & 2 & 67 &2.6\% & 9.7 &3.4\% & 8.4 \\ 300 & 1 & 3 & 97 &5.7\% & 9.9 &6.4\% & 8.3 \\ 300 & 10 & 3 & 94 &5.6\% & 9.6 &6.5\% & 8.3 \\ 300 & 1 & 5 & 142 &4.3\% & 9.5 &4.8\% & 8.4 \\ 300 & 10 & 5 & 137 &16\% & 10.8 &15\% & 8.7 \\ 100 & 1 & 2 & 42 &3.8\% & 9.7 &5.4\% & 8.4 \\ 100 & 10 & 5 & 80 &25.1\% & 10.5 &21.7\% & 8.4 \\ 2400 & 1 & 2 & 92 &2.2\% & 9.7 &2.4\% & 8.4 \\ 2400 & 10 & 5 & 186 &12.0\% & 10.8 &10.4\% & 8.5 \\ \hline \hline \end{tabular}
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\footnotesize{Total flux, flux loss with respect to the model flux and due to interferometric spatial filtering, and RMS noise for selected models, given an integration time of 8 hours and central wavelength of 0.88 mm.
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2105.10728v1_train__82f813e0-2adb-4c67-9482-aa88deaa6805
2105.10728v1
\begin{tabular}{ |c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}\hline & $m_h$[GeV]& $m_H[GeV]$ & $m_{H^{\pm}}$[GeV]& $m_A$[GeV] & $\tan\beta$ & $\cos \left(\beta-\alpha \right)$ & $m_{12}^2~GeV^2$ & $\lambda_1$ & $\lambda_2$ & $\lambda_3$ & $\lambda_4$ & $\lambda_5$ & $T_c$ & $\delta s/s[\%]$\\ \hline BM1 & $125$ & $500$ & $500$ & $500$ & $2$ & $0$ & $10^5$ & $0.258$ & $0.258$ & $0.258$ & $0$ & $0$ & $ 161.36$ & $57$ \\ \hline BM2 &" &" &" & " &" & $0.06$ & " &$1.14$ & $0.037$ & $0.63$ & $0$ & $0$ & $ 167.95$ & $59$ \\ \hline BM3 & " & " & " & " & $10$ & $0$ & $24752.5$ & $0.258$ & $0.258$ & $0.258$ &$0$ & $0$ & $161.02$ & $56$\\ \hline BM4 & "& " & " & " & $10$ & $0.1$ & $24752.5$ & $4.13$ & $0.22$ & $4.15$ & $0$ & $0$ & $255.71$ & $73$\\ \hline BM5 & " & " & " & $485$ & $2$ & $0.0$ & $10^5$ & $0.26$ & $0.26$ & $0.26$ & $-0.244$ & $0.244$ & $161.53 $ & $57$\\ \hline BM6 & " & " & " & $485$ & $2$ & $0.07$ & $10^5$ & $1.28$ & $0.002$ & $0.7$ & $-0.244$ & $0.244$ & $169.81 $ & $60$\\ \hline BM7 & " & " & " & $477$ & $2$ & $0.07$ & $10^5$ & $1.28$ & $0.002$ & $0.7$ & $-0.37$ & $0.37$ & $169.53 $ & $60$ \\ \hline BM8 & " & " & " & $485$ & $10$ & $0.0$ & $24752.5$ & $0.258$ & $0.258$ & $0.258$ & $-0.244$ & $0.244$ & $160.76 $ & $56$ \\ \hline BM9 & " & " & " & $350$ & $10$ & $0.1$ & $24752.5$ & $4.13$ & $0.22$ & $4.15$ & $-2.1$ & $2.1$ & $209.87 $ & $68$ \\ \hline BM10 & " & " & $485$ & $500$ & $2$ & $0.00$ & $10^5$ & $0.258$ & $.258$ & $-0.23$ & $0.49$ & $0$ & $153.27 $ & $53$ \\ \hline BM11 & " & " & $485$ & $500$ & $2$ & $0.07$ & $10^5$ & $1.28$ & $0.002$ & $0.21$ & $0.49$ & $0$ & $169.28 $ & $60$ \\ \hline BM12 & " & " & $485$ & $500$ & $10$ & $0.0$ & $24752.5$ & $0.258$ & $0.258$ & $-0.23$ & $0.49$ & $0$ & $160.51 $ & $56$ \\ \hline BM13 & " & " & $485$ & $500$ & $10$ & $0.1$ & $24752.5$ & $4.13$ & $0.22$ & $3.66$ & $0.49$ & $0$ & $241.75 $ & $70$ \\ \hline BM14 & " & " & $485$ & $485$ & $2$ & $0$ & $10^5$ & $0.258$ & $0.258$ & $-0.23$ & $0.24$ & $0.24$ & ${ 159.76 }$ & $59$ \\ \hline BM15 & " & " & $485$ & $485$ & $2$ & $0.07$& $10^5$ & $1.28$ & $0.002$ & $0.21$ & $0.244$ & $0.244$ & ${ 168.61}$ & $59$ \\ \hline BM16 & " & " & $485$ & $485$ & $10$ & $0$ & $24752.5$ & $0.258$ & $0.258$ & $-0.23$ & $0.244$ & $0.244$ &${ 160.19 }$ & $56$\\ \hline BM17 &" & $485$ & $485$ & $485$ & $2$ & $0.0$ &$94090$ & $0.258$ & $0.258$ & $0.258$ & $0$ & $0$ &${ 161.31 }$ & $57$ \\ \hline %BM1 & & & & & & & & & & & & &${ }$ \\ % \hline BM18 & " & $485$ & $485$ & $485$ & $2$ & $0.07$ & $94090$ & $1.22$ & $0.02$ & $0.67$ & $0$ & $0$ & ${ 169.7 }$ & $60$ \\ \hline BM19 & " & $485$ & $485$ & $485$ & $10$ & $0$ & $23289.6$ & $0.258$ & $0.258$ & $0.258$ & $0$ & $0$ & ${ 160.96}$ & $57$ \\ \hline BM20 & " & $485$ & $485$ & $485$ & $10$ & $0.1$& $23289.6$ & $3.9$ & $0.22$ & $3.9$ & $0$ & $0$ & ${ 230.18 }$ & $70$ \\ \hline BM21 & " & $485$ & $485$ & $500$ & $2$ & $0$ & $94090$ & $0.258$ & $0.258$ & $0.258$ & $0$ & $0$ & ${ 161.31}$ & $57$ \\ \hline BM22 & " & $90$ & $200$ & $300$ & $2$ & $0$ & $3240$ & $0.258$ & $0.258$ & $1.31$ & $0.3$ & $-1.35$ & ${ 150.76 }$ & $51$ \\ \hline BM23 & " & $90$ & $200$ & $300$ & $10$ & $0$ & $801.98$ & $0.258$ & $0.258$ & $1.31$ & $0.3$ & $-1.35$ & ${ 135.38 }$ & $37$ \\ \hline BM24 & " & $90$ & $200$ & $300$ & $10$ & $0.2$ & $801.98$ & $0.263$ & $0.258$ & $1.06$ & $0.3$ & $-1.35$ & ${ 141.06 }$ & $42$ \\ \hline %BM1 & " & $$ & $$ & $$ & $$ & $$ & $$ & $$ & $$ & $$ & $$ & $$ & ${ }$ \\ \end{tabular}
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2HDM Benchmark points for entropy production
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2205.11603v3_train__94cdf3bb-73a2-4e1e-bac7-e1938f519152
2205.11603v3
\begin{tabular}{ccccccccc}\toprule%\multicolumn{8}{c}{Average Rank}\\ %\midrule\# samples $\downarrow$ & STD++ & DA & WC & ReInit & R3F & \cnrt & \cprt \\ \midrule%\midrule%\multicolumn{8}{c}{250 Training datapoints}\\ %\midrule250 & 5.62 & 4.92 & 4.62 & 3.00 & 4.04 & {\bf 2.50} & 3.31 \\ % & Mean-unfiltered & 67.61 & 73.21 & 75.76 & {\bf 77.05} & 72.57 & 76.66 & 76.26 \\ %& Average Rank-unfiltered & 6.54 & 4.85 & 3.46 & 2.92 & 4.62 & {\bf 2.54} & 3.08 \\ %\midrule%\multicolumn{8}{c}{500 Training datapoints}\\ %\midrule500 & 6.08 & 4.38 & 3.69 & 3.31 & 4.85 & {\bf 2.77} & 2.92 \\ %& Mean-unfiltered & 67.61 & 73.21 & 75.76 & {\bf 77.05} & 72.57 & 76.66 & 76.26 \\ %&Average Rank-unfiltered & 6.54 & 4.85 & 3.46 & 2.92 & 4.62 & {\bf 2.54} & 3.08 \\ %\midrule%\midrule%\multicolumn{8}{c}{1000 Training Datapoints}\\ %\midrule1000 & 5.69 & 4.00 & 3.62 & 3.54 & 4.62 & {\bf 2.69} & 3.85 \\ %& Mean-unfiltered & 69.8 & 75.02 & 78.52 & 79.0 & 74.38 & {\bf 79.61} & 78.54 \\ %& Average Rank-unfiltered & 6.0 & 4.54 & 3.23 & 3.54 & 4.77 & {\bf 2.15} & 3.77 \\ \bottomrule\end{tabular}
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Average rank of different methods for few-shot learning. \cnrt: \concort, \cprt: \capcort.
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2108.02400v1_train__8cf804e7-d4ac-422a-ade5-548b59c8858a
2108.02400v1
\begin{tabular}{cccccc} \hline B{3}\textbf{\textit{Key size}} & \textbf{\textit{Error}}& \multicolumn{2}{c}{\textbf{\textit{OU-ISIR}}} & \multicolumn{2}{c}{\textbf{\textit{whuGAIT}}} \\ (bits)&\textit{\textbf{Tolerability}}& $FAR (\%)$ & $FRR (\%)$& $FAR (\%)$ & $FRR (\%)$\\ \hline B{2}% $99$ & $23$ & $0.004$ & $2.083$ \\ %\hline % $107$ & $22$ & $0.003$ & $2.083$ \\ %\hline $115$ & $21$ & $0.001$ & $2.083$ &$0.022$ & $2.177$ \\ %\hline $123$ & $19$ & $0$ & $4.167$ &$0.005$ & $2.66$ \\ %\hline $131$ & $18$ & $0$ & $4.167$ &$0$ & $3.265$\\ %\hline $139$ & $15$ & $0$ & $4.167$ &$0$ & $5.441$\\ %\hline $147$ & $14$ & $0$ & $6.25$ &$0$ & $6.771$\\ \hline B{3}\end{tabular}
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Performances at different key sizes when using BCH code of length $255$ and symbol size $\phi=2$.
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2108.02400v1_train__7d64def5-c21f-43c4-81d8-88943a647137
2108.02400v1
\begin{tabular}{ccccccc} \hline B{3}\multirow{2}{*}{\textbf{\textit{Study}}} & \textbf{\textit{Data}}&\multirow{2}{*}{\textbf{\textit{Key size}}} & \multirow{2}{*}{\textbf{\textit{Performance}}} & \multirow{2}{*}{\textbf{\textit{R}}} &\multirow{2}{*}{\textbf{\textit{I}}}& \multirow{2}{*}{\textbf{\textit{U}}} \\ &\textbf{\textit{Length}}& &&&& \\ \hline B{2}%Hoang \textit{et al.} & \multirow{2}{*}{$16$ cycles} & \multirow{2}{*}{$139$ bits}&FAR: $0\%$ &\multirow{2}{*}{$-$}&\multirow{2}{*}{$-$}&\multirow{2}{*}{$-$}\\ %\hline 2015 \cite{hoang2015gait} &&&FRR: $16.18\%$&&&\\ \hline %%Tran \textit{et al.} & \multirow{2}{*}{$26$ cycles}& \multirow{2}{*}{$148$ bits}&FAR: $6\times 10^{-5}\%$ &\multirow{2}{*}{$-$}&\multirow{2}{*}{$-$}&\multirow{2}{*}{$-$}\\ %\hline 2017 \cite{tran2017improving} &&&FRR: $9.2\%$&&&\\ \hline % 12 templates, each one has 4 cycles, overlapped 50%%%\multirow{4}{*}{This study} & \multirow{4}{*}{$5$ cycles}&\multirow{2}{*}{$139$ bits} & FAR: $0\%$ &\multirow{4}{*}{Yes}&\multirow{4}{*}{Yes}&\multirow{4}{*}{Yes}\\ &&&FRR: $5.56\%$&&&\\ && \multirow{2}{*}{$147$ bits} & FAR: $0\%$ &&&\\ &&&FRR: $7.64\%$&&&\\ \hline B{3}\end{tabular}
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A comparison on different factors between our model and existing gait cryptosystems, where R, I, and U mean Revocability, Irreversibility, and Unlinkability, respectively.
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2202.10992v2_train__1b24c634-0e1b-4119-86d3-338314f99532
2202.10992v2
\begin{tabular}{rlll}\toprule&Empirical&\multicolumn{2}{c}{95\% CI}\\ \cline{3-4}$q$ & coverage & Lower & Upper \\ \midrule0.01 & 0.953 & 0.949 & 0.957 \\ 0.10 & 0.949 & 0.944 & 0.953 \\ 0.25 & 0.950 & 0.946 & 0.955 \\ 0.50 & 0.949 & 0.945 & 0.954 \\ \hline \end{tabular}
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Empirical coverage rate for the confidence intervals produced by Algorithm \ref{poi-bootstrap-two-sample-fast
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2202.10992v2_train__6e69052c-a541-49d4-81e7-d605623439cc
2202.10992v2
\begin{tabular}{r|llll}&Min time&Median time &Max time & Memory usage \\ \hline Algorithm \ref{poi-bootstrap-two-sample}& 1726 ms&1821ms &1902ms&2.39 GiB\\ Algorithm \ref{poi-bootstrap-two-sample-fast} & 2.055ms & 2.214ms&3.502ms & 407.08 KiB \\ \hline \end{tabular}
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Time and mempry consumption comparison between a standard Poisson bootstrap algorithm (Algorithm \ref{poi-bootstrap-two-sample
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2112.05818v1_train__fcc0e61b-8e91-4c27-b7fa-af7b3973969f
2112.05818v1
\begin{tabular}{|l|l|l|l|l|l|l|l|}\hline \multirow{2}{*}{Benchmark} & \multirow{2}{*}{Method} & \multicolumn{3}{l|}{Simulation IIA} & \multicolumn{3}{l|}{Simulation IIB} \\ \cline{3-8}& & $\sigma_\mu$=0 & $\sigma_\mu$=0.4 & $\sigma_\mu$=0.6 & $\sigma_\mu$=0 & $\sigma_\mu$=0.4 & $\sigma_\mu$=0.6 \\ \hline \multirow{8}{*}{Power and type I error} & MANOVA & 0.35 & 0.53 & 0.85 & 0.78 & 0.78 & 0.94 \\ \cline{2-8}& aSPU.ind & 0.05 & 0.42 & 0.67 & 0.05 & 0.45 & 0.69 \\ \cline{2-8}& aSPU.ex & 0.05 & 0.41 & 0.67 & 0.05 & 0.44 & 0.7 \\ \cline{2-8}& TATES & 0.05 & 0.12 & 0.32 & 0.05 & 0.12 & 0.32 \\ \cline{2-8}& minP & 0.05 & 0.33 & 0.84 & 0.05 & 0.77 & 0.97 \\ \cline{2-8}& Fisher & 0.05 & 0.43 & 0.86 & 0.05 & 0.71 & 0.88 \\ \cline{2-8}& AFz & 0.05 & 0.39 & 0.89 & 0.05 & 0.77 & 0.97 \\ \cline{2-8}& AFp & 0.05 & 0.42 & 0.9 & 0.05 & 0.77 & 0.96 \\ \hline \multirow{2}{*}{Sensitivity} & AFz & - & 0.39 & 0.57 & - & 0.18 & 0.2 \\ \cline{2-8}& AFp & - & 0.45 & 0.72 & - & 0.48 & 0.76 \\ \hline \multirow{2}{*}{Specificity} & AFz & - & 0.92 & 0.97 & - & 0.97 & 0.99 \\ \cline{2-8}& AFp & - & 0.86 & 0.9 & - & 0.9 & 0.91 \\ \hline \end{tabular}
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The result of Simulation IIA and IIB. For $\sigma_\mu=0$, type I error is shown and since there is no association between genes and phenotypes (i.e., true weights are all 0), sensitivity and specificity of weight estimation is omitted. For $\sigma_\mu=0.6$ and 0.8, power, sensitivity and specificity are shown.
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2206.03857v1_train__4721e3ce-8fe7-40cd-b413-96d973245699
2206.03857v1
\begin{tabular}{|l||ccc|c|c||ccc|c|c|}\hline & & bids & & VCG & VCG-nearest & & bids$'$ & & VCG$'$ & VCG-nearest$'$\\ & $\{1\}$ & $\{2\}$ & $\{1,2\}$ & & & $\{1\}$ & $\{2\}$ & $\{1,2\}$ & &\\ \hline \hline Bidder \#1 & $4^*$ & & & 2 & 3 & $4^*$ &&& 3 & 3.5\\ Bidder \#2 & &$4^*$& 5 & 2 & 3 & &$4^*$& \textbf{7} & 2 & 2.5\\ Bidder \#3 & 2 & 2 & 6 & 0 & 0 & 2 & 2 & 6 & 0 & 0\\ \hline \end{tabular}
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Auction where 3 bidders are bidding on 2 goods. Winning bids are marked with an $^*$. Bidder 2 increases his bid on a non-winning bundle (marked in bold), which decreases his payment on his winning bundle, while the allocation remains constant.
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2206.03857v1_train__aadc36ad-4f20-4eb6-9bbe-d58cc0a24952
2206.03857v1
\begin{tabular}{|l||c|c|c|c||c|c|c|}\hline & bundle of interest & bid & VCG & VCG-nearest & bid$'$ & VCG$'$ &VCG-nearest$'$\\ \hline \hline Bidder \#1 & $\{1\}$ & 5 & 2 & $37 / 12$ & 5 & 1 & $36 / 12$ \\ Bidder \#2 & $\{2\}$ & 5 & 0 & $16 / 12$ & 5 & 0 & $18 / 12$ \\ Bidder \#3 & $\{3\}$ & 4 & 1 & $37 / 12$ & \textbf{5} & 1 & $36 / 12$ \\ Bidder \#4 & $\{4\}$ & 1 & 0 & $\phantom{0} 7 / 12$ & 1 & 0 & $\phantom{0} 6 / 12$ \\ Bidder \#5 & $\{5\}$ & 1 & 0 & $\phantom{0} 7 / 12$ & 1 & 0 & $\phantom{0} 6 / 12$ \\ Bidder \#6 & $\{6\}$ & 1 & 0 & $10 / 12$ & 1 & 0 & $12 / 12$ \\ Bidder \#7 & $\{1,2,4\}$ & 5 & & $ $ & 5 & & $ $ \\ Bidder \#8 & $\{2,3,5\}$ & 5 & & $ $ & 5 & & $ $ \\ Bidder \#9 & $\{1,3,6\}$ & 7 & & $ $ & 7 & & $ $ \\ Bidder \#10 & $\{4,5,6\}$ & 2 & & $ $ & 2 & & $ $ \\ Bidder \#11 & $\{2,3,4\}$ & 5 & & $ $ & 5 & & $ $ \\ \hline \end{tabular}
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Auction where 11 single-minded bidders are bidding on 6 goods. We show VCG and VCG-nearest payments for each bidder. If bidder 3 increases his bid (marked in bold), this decreases bidder 1's VCG payment, which in turn decreases bidder 3's VCG-nearest payment.
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2307.07487v1_train__57736a2a-410a-414d-bf4b-43eb5e9fe475
2307.07487v1
\begin{tabular}{lcccc}\hline & LSUN & FFHQ & ImagetNet & BDD100K \\ \hline resolution & 256x256 & 256x256 & 256x256 & 128x256 \\ diffusion steps & 1000 & 1000 & 1000 & 1000 \\ noise Schedule & linear & linear & linear & linear \\ channels & 256 & 256 & 256 & 128 \\ depth & 2 & 2 & 2 & 2 \\ channels multiple & 1,1,2,2,4,4 & 1,1,2,2,4,4 & 1,1,2,2,4,4 & 1,1,2,2,3,4 \\ heads Channels & 64 & 64 & 64 & 32 \\ attention resolution & 32,16,8 & 32,16,8 & 32,16,8 & 16,8 \\ dropout & 0.1 & 0.1 & 0.0 & 0.0 \\ batch size & 256 & 256 & 256 & 256 \\ learning rate & 1e-4 & 1e-4 & 1e-4 & 1e-4 \\ \hline \end{tabular}
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%\textbf{Hyperparameters for diffusion models used in the paper.
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2307.07487v1_train__6d58dbfe-b92b-4040-9121-5e5163cc1d01
2307.07487v1
\begin{tabular}{lcccc}\hline & LSUN & FFHQ & ImagetNet & BDD100K \\ \hline resolution & 256x256 & 256x256 & 256x256 & 128x256/512x1024 \\ noise steps & 50 & 50 & 150 & 50 \\ optimizer & AdamW & AdamW & LAMB & AdamW \\ base learning rate & 4e-3 & 4e-3 & 4e-3 & 4e-3 \\ weight decay & 0.05 & 0.05 & 0.05 & 0.05 \\ optimizer momentum & $\beta_1,\beta_2=0.9,0.95$ & $\beta_1,\beta_2=0.9,0.95$ & $\beta_1,\beta_2=0.9,0.95$ & $\beta_1,\beta_2=0.9,0.95$ \\ batch size & 256 & 256 & 2048 & 256 \\ training epochs & 100 & 100 & 200 & 600 \\ learning rate schedule & cosine decay & cosine decay & cosine decay & cosine decay \\ warmup epochs & 20 & 20 & 30 & 30 \\ augmentation & horizontal flip & horizontal flip & horizontal flip & horizontal flip \\ \hline \end{tabular}
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%\textbf{Hyperparameters for pre-training the image backbones.
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2307.07487v1_train__a4d5469d-b4ac-4c56-a9ca-a3aa67abec57
2307.07487v1
\begin{tabular}{l|c|c|c|c|c|c|c|c}method & backbone & params & pre-data & Bedroom-28 & FFHQ-34 & Cat-15 & Horse-21 & Car-20\\ \hline classific. sup. & RN101 & 43M & IN1k-1M & 34.4 & 53.6 & 38.8 & 51.1 & 55.9\\ classific. sup. & ConvNX-B & 89M & IN21k-14M & 41.0 & 59.2 & 47.3 & 56.0 & 59.3\\ classific. sup. & Swin-L & 197M & IN21k-14M & 42.3 & 57.3 & 47.6 & 57.7 & 59.4\\ \hline DatasetGAN\cite{zhang2021datasetgan} & RN101 & 43M & task domains & 31.3 & 57.0 & 36.5 & 45.4 & 68.4 \\ DatasetDDPM\cite{baranchuk2021labelefficient} & RN101 & 43M & task domains & 47.9 & 56.0 & 47.6 & 60.8 & -\\ DDPM-seg\cite{baranchuk2021labelefficient} & UNet & 554M & task domains & 49.4 & 59.1 & 53.7 & 65.0 & -\\ \hline DT-mix.distil. (ours)& RN101 & 43M & task domains& 49.9 & 59.4 & 56.7 & 65.9 & -\\ DT-mix.distil. (ours)& ConvNX-B & 89M & task domains& \textbf{54.8} & \textbf{61.2} & \textbf{58.6} & \textbf{67.6} & ?\\ \hline DDPM-seg(our interp.) & UNet & 554M & task domains & 49.8 & 60.1 & 57.6 & 64.0 & 75.4\\ DDPM-seg(our interp.) & UNet & 554M & IN1k-1M & 36.1 & 59.2 & 49.8 & 56.6 & 69.9\\ \end{tabular}
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\textbf{Label-efficient semantic segmentation benchmark.
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2012.07246v1_train__41a4784a-7be3-4b2c-b3f3-269719c009d6
2012.07246v1
\begin{tabular}{c c c c c c c}\hline \multicolumn{1}{|p{2cm}|}{\centering Simulation} & \multicolumn{1}{|p{2cm}|}{\centering Total \\ Smoke (Mg)} & \multicolumn{1}{|p{2cm}|}{\centering Smoke above \\ 9 km (Mg)} & \multicolumn{1}{|p{2cm}|}{\centering Smoke above \\ 9 km (\%)} & \multicolumn{1}{|p{2cm}|}{\centering Smoke above \\ 12 km (Mg)} & \multicolumn{1}{|p{2cm}|}{\centering Smoke above \\ 12 km (\%)} & \multicolumn{1}{|p{2cm}|}{\centering Total Error (\%)} \\ \hline Base\_2 & 3.2E3 & 296.1 & 9.25 & 6.6 & 0.21 & 2.45 \\ CalmWi\_2 & 3.4E3 & 504.1 & 15.03 & 43.3 & 1.29 & -2.26 \\ MidWi\_2 & 4.1E3 & 67.2 & 1.64 & 0.5 & 0.01 & -4.27 \\ HiWi\_2 & 4.8E3 & 0.6 & 0.01 & 0.0 & 0.00 & -1.13 \\ Shear\_2 & 3.2E3 & 279.6 & 8.71 & 6.9 & 0.22 & 2.39 \\ M50\_2 & 3.3E3 & 699.4 & 21.17 & 37.3 & 1.13 & 1.20 \\ MR25\_2 & 4.0E3 & 287.7 & 7.23 & 4.3 & 0.11 & -3.12 \\ MR50\_2 & 3.5E3 & 518.3 & 14.77 & 33.6 & 0.96 & 2.14 \\ MR75\_2 & 3.2E3 & 987.9 & 30.79 & 222.6 & 6.94 & 2.21 \\ Stable\_2 & 3.2E3 & 102.2 & 3.16 & 4.0 & 0.12 & 2.34 \\ \hline \end{tabular}
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Smoke generation, upper atmosphere and stratospheric smoke lofting, with the 2-km radius ignition area. Negative error values indicate an overestimation of total smoke in the atmosphere, compared with actual smoke generation at the surface, while positive values indicate an underestimation.
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2012.07246v1_train__748bdfd9-5343-47db-ba6e-de3d9627ef32
2012.07246v1
\begin{tabular}{c c c c c c c}\hline \multicolumn{1}{|p{2cm}|}{\centering Simulation} & \multicolumn{1}{|p{2cm}|}{\centering Total \\ Smoke (kg)} & \multicolumn{1}{|p{2cm}|}{\centering Smoke above \\ 9 km (kg)} & \multicolumn{1}{|p{2cm}|}{\centering Smoke above \\ 9 km (\%)} & \multicolumn{1}{|p{2cm}|}{\centering Smoke above \\ 12 km (kg)} & \multicolumn{1}{|p{2cm}|}{\centering Smoke above \\ 12 km (\%)} & \multicolumn{1}{|p{2cm}|}{\centering Total Error (\%)} \\ \hline Base\_4 & 1.3E4 & 394.0 & 3.02 & 103.5 & 0.79 & 0.56 \\ CalmWi\_4 & 1.3E4 & 779.2 & 6.13 & 129.6 & 1.02 & 2.80 \\ MidWi\_4 & 1.4E4 & 388.9 & 2.43 & 18.6 & 0.13 & -1.62 \\ HiWi\_4 & 1.5E4 & 576.6 & 3.92 & 56.7 & 0.39 & -1.58 \\ Shear\_4 & 1.3E4 & 682.7 & 5.09 & 124.2 & 0.93 & -1.71 \\ M50\_4 & 1.3E4 & 1921.6 & 14.37 & 134.16 & 1.00 & -1.84 \\ MR25\_4 & 1.3E4 & 780.2 & 5.93 & 77.0 & 0.59 & 2.14 \\ MR50\_4 & 1.3E4 & 1972.6 & 14.76 & 235.2 & 1.76 & 0.54 \\ MR75\_4 & 1.3E4 & 2642.5 & 19.79 & 349.3 & 2.62 & -1.75 \\ Stable\_4 & 1.3E4 & 251.7 & 1.95 & 99.1 & 0.77 & 1.49 \\ \hline \end{tabular}
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Smoke generation, upper atmosphere and stratospheric smoke lofting, with the 4-km radius ignition area. Negative error values indicate an overestimation of total smoke in the atmosphere, compared with actual smoke generation at the surface, while positive values indicate an underestimation.
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2304.08753v1_train__627fefee-a16c-45d4-96fc-9b27ccad76de
2304.08753v1
\begin{tabular}{l|c|c}\hline Lattice size &$\beta$ &$\sigma_a/\sigma_F$ \\ \hline $12^4$ & 5.6& 0.87(13)\\ \hline $16^4$ & 5.6& 1.05(9)\\ \hline $12^4$ &5.7& 0.91(8)\\ \hline $12^4$&5.8& 1.01(11)\\ \hline \end{tabular}
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The ratio of the Abelian and the non-Abelian string tensions $\sigma_a/\sigma_F$ determined by applying the multilevel method in the Wilson action. The data are cited from Ref.\cite{IHS:202207
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