Title: Open Transactions on Shared Memory
Abstract: Transactional memory has arisen as a good way for solving many of the issues of lock-based programming. However, most implementations admit isolated transactions only, which are not adequate when we have to coordinate communicating processes. To this end, in this paper we present OCTM, an Haskell-like language with open transactions over shared transactional memory: processes can join transactions at runtime just by accessing to shared variables. Thus a transaction can co-operate with the environment through shared variables, but if it is rolled-back, also all its effects on the environment are retracted. For proving the expressive power of TCCS we give an implementation of TCCS, a CCS-like calculus with open transactions.


Title: Fast & Fair: Efficient Second-Order Robust Optimization for Fairness in Machine Learning
Abstract: This project explores adversarial training techniques to develop fairer Deep Neural Networks (DNNs) to mitigate the inherent bias they are known to exhibit. DNNs are susceptible to inheriting bias with respect to sensitive attributes such as race and gender, which can lead to life-altering outcomes (e.g., demographic bias in facial recognition software used to arrest a suspect). We propose a robust optimization problem, which we demonstrate can improve fairness in several datasets, both synthetic and real-world, using an affine linear model. Leveraging second order information, we are able to find a solution to our optimization problem more efficiently than a purely first order method.


Title: $F$-pure and $F$-injective singularities in equal characteristic zero
Abstract: Inspired by Schoutens' results, we introduce a variant of sharp $F$-purity and sharp $F$-injectivity in equal characteristic zero via ultraproducts. As an application, we show that if $R\to S$ is pure and $S$ is of dense $F$-pure type, then $R$ is of dense $F$-pure type.


Title: Shift Graphs, Chromatic Number and Acyclic One-Path Orientations
Abstract: Shift graphs, which were introduced by Erd\H{o}s and Hajnal, have been used to answer various questions in extremal graph theory. In this paper, we prove two new results using shift graphs and their induced subgraphs. 1. Recently Girao [Combinatorica2023], showed that for every graph $F$ with at least one edge, there is a constant $c_F$ such that there are graphs of arbitrarily large chromatic number and the same clique number as $F$, in which every $F$-free induced subgraph has chromatic number at most $c_F$. We significantly improve the value of the constant $c_F$ for the special case where $F$ is the complete bipartite graph $K_{a,b}$. We show that any $K_{a,b}$-free induced subgraph of the triangle-free shift graph $G_{n,2}$ has chromatic number at most $a+b$. 2. An undirected simple graph $G$ is said to have the AOP Property if it can be acyclically oriented such that there is at most one directed path between any two vertices. We prove that the shift graph $G_{n,2}$ does not have the AOP property for all $n\geq 9$. We then construct induced subgraphs of shift graph $G_{n,2}$ with an arbitrarily high chromatic number and odd-girth which have the AOP property. To the best of our knowledge, this gives the first constructive proof of the existence of graphs with arbitrarily high chromatic number and odd-girth that have the AOP property. Furthermore, we construct graphs with arbitrarily high odd-girth that do not have the AOP Property and also prove the existence of graphs with girth equal to $5$ that do not have the AOP property.


Title: The Log-Volume of Optimal Codes for Memoryless Channels, Asymptotically Within A Few Nats
Abstract: Shannon's analysis of the fundamental capacity limits for memoryless communication channels has been refined over time. In this paper, the maximum volume $M_\avg^*(n,\epsilon)$ of length-$n$ codes subject to an average decoding error probability $\epsilon$ is shown to satisfy the following tight asymptotic lower and upper bounds as $n \to \infty$: \[ \underline{A}_\epsilon + o(1) \le \log M_\avg^*(n,\epsilon) - [nC - \sqrt{nV_\epsilon} \,Q^{-1}(\epsilon) + \frac{1}{2} \log n] \le \overline{A}_\epsilon + o(1) \] where $C$ is the Shannon capacity, $V_\epsilon$ the $\epsilon$-channel dispersion, or second-order coding rate, $Q$ the tail probability of the normal distribution, and the constants $\underline{A}_\epsilon$ and $\overline{A}_\epsilon$ are explicitly identified. This expression holds under mild regularity assumptions on the channel, including nonsingularity. The gap $\overline{A}_\epsilon - \underline{A}_\epsilon$ is one nat for weakly symmetric channels in the Cover-Thomas sense, and typically a few nats for other symmetric channels, for the binary symmetric channel, and for the $Z$ channel. The derivation is based on strong large-deviations analysis and refined central limit asymptotics. A random coding scheme that achieves the lower bound is presented. The codewords are drawn from a capacity-achieving input distribution modified by an $O(1/\sqrt{n})$ correction term.


Title: Discrete Uniqueness Sets for Functions with Spectral Gaps
Abstract: It is well-known that entire functions whose spectrum belongs to a fixed bounded set $S$ admit real uniformly discrete uniqueness sets $\Lambda$. We show that the same is true for much wider spaces of continuous functions. In particular, Sobolev spaces have this property whenever $S$ is a set of infinite measure having "periodic gaps". The periodicity condition is crucial. For sets $S$ with randomly distributed gaps, we show that the uniformly discrete sets $\Lambda$ satisfy a strong non-uniqueness property: Every discrete function $c(\lambda)\in l^2(\Lambda)$ can be interpolated by an analytic $L^2$-function with spectrum in $S$.


Title: Quasi-Lie bialgebroids, Dirac structures and deformations of Poisson quasi-Nijenhuis manifolds
Abstract: We show how to deform a Poisson quasi-Nijenhuis manifold by means of a closed 2-form. Then we interpret this procedure in the context of quasi-Lie bialgebroids, as a particular case of the so called twisting of a quasi-Lie bialgebroid. Finally, we frame our result in the setting of Courant algebroids and Dirac structures.


Title: Parabolic Anderson model in bounded domains of recurrent metric measure spaces
Abstract: A metric measure space equipped with a Dirichlet form is called recurrent if its Hausdorff dimension is less than its walk dimension. In bounded domains of such spaces we study the parabolic Anderson models \[ \partial_{t} u(t,x) = \Delta u(t,x) + \beta u(t,x) \, \dot{W}_\alpha(t,x) \] where the noise $W_\alpha$ is white in time and colored in space when $\alpha >0$ while for $\alpha=0$ it is also white in space. Both Dirichlet and Neumann boundary conditions are considered. Besides proving existence and uniqueness in the It\^o sense we also get precise $L^p$ estimates for the moments and intermittency properties of the solution as a consequence. Our study reveals new exponents which are intrinsically associated to the geometry of the underlying space and the results for instance apply in metric graphs or fractals like the Sierpi\'nski gasket for which we prove scaling invariance properties of the models.


Title: Buildings, spiders, and geometric Satake
Abstract: Let G be a simple algebraic group. Labelled trivalent graphs called webs can be used to product invariants in tensor products of minuscule representations. For each web, we construct a configuration space of points in the affine Grassmannian. Via the geometric Satake correspondence, we relate these configuration spaces to the invariant vectors coming from webs. In the case G = SL(3), non-elliptic webs yield a basis for the invariant spaces. The non-elliptic condition, which is equivalent to the condition that the dual diskoid of the web is CAT(0), is explained by the fact that affine buildings are CAT(0).


Title: Competitive Searching over Terrains
Abstract: We study a variant of the searching problem where the environment consists of a known terrain and the goal is to obtain visibility of an unknown target point on the surface of the terrain. The searcher starts on the surface of the terrain and is allowed to fly above the terrain. The goal is to devise a searching strategy that minimizes the competitive ratio, that is, the worst-case ratio between the distance traveled by the searching strategy and the minimum travel distance needed to detect the target. For $1.5$D terrains we show that any searching strategy has a competitive ratio of at least $\sqrt{82}$ and we present a nearly-optimal searching strategy that achieves a competitive ratio of $3\sqrt{19/2} \approx \sqrt{82} + 0.19$. This strategy extends directly to the case where the searcher has no knowledge of the terrain beforehand. For $2.5$D terrains we show that the optimal competitive ratio depends on the maximum slope $\lambda$ of the terrain, and is hence unbounded in general. Specifically, we provide a lower bound on the competitive ratio of $\Omega(\sqrt{\lambda})$. Finally, we complement the lower bound with a searching strategy based on the maximum slope of the known terrain, which achieves a competitive ratio of $O(\sqrt{\lambda})$.


Title: Short note on the behavior of recurrent neural network for noisy dynamical system
Abstract: The behavior of recurrent neural network for the data-driven simulation of noisy dynamical systems is studied by training a set of Long Short-Term Memory Networks (LSTM) on the Mackey-Glass time series with a wide range of noise level. It is found that, as the training noise becomes larger, LSTM learns to depend more on its autonomous dynamics than the noisy input data. As a result, LSTM trained on noisy data becomes less susceptible to the perturbation in the data, but has a longer relaxation timescale. On the other hand, when trained on noiseless data, LSTM becomes extremely sensitive to a small perturbation, but is able to adjusts to the changes in the input data.


Title: The Optimal Paper Moebius Band
Abstract: In this paper we prove that a smooth embedded paper Moebius band must have aspect ratio greater than $\sqrt 3$. We also prove that any sequence of smooth embedded paper Moebius bands whose aspect ratio converges to $\sqrt 3$ must converge, up to isometry, to the famous triangular Moebius band. These results answer the minimum aspect ratio question discussed by W. Wunderlich in 1962 and prove the more specific conjecture of B Halpern and C. Weaver from 1977.


Title: Nonlinear analysis with resurgent functions
Abstract: We provide estimates for the convolution product of an arbitrary number of "resurgent functions", that is holomorphic germs at the origin of $C$ that admit analytic continuation outside a closed discrete subset of $C$ which is stable under addition. Such estimates are then used to perform nonlinear operations like substitution in a convergent series, composition or functional inversion with resurgent functions, and to justify the rules of "alien calculus"; they also yield implicitly defined resurgent functions. The same nonlinear operations can be performed in the framework of Borel-Laplace summability.


Title: Codes and Designs in Johnson Graphs From Symplectic Actions on Quadratic Forms
Abstract: The Johnson graph $J(v, k)$ has as vertices the $k$-subsets of $\mathcal{V}=\{1,\ldots, v\}$, and two vertices are joined by an edge if their intersection has size $k-1$. An \emph{$X$-strongly incidence-transitive code} in $J (v, k)$ is a proper vertex subset $\Gamma$ such that the subgroup $X$ of graph automorphisms leaving $\Gamma$ invariant is transitive on the set $\Gamma$ of `codewords', and for each codeword $\Delta$, the setwise stabiliser $X_\Delta$ is transitive on $\Delta \times (\mathcal{V}\setminus \Delta)$. We classify the \emph{$X$-strongly incidence-transitive codes} in $J(v,k)$ for which $X$ is the symplectic group $\mathrm{Sp}_{2n}(2)$ acting as a $2$-transitive permutation group of degree $2^{2n-1}\pm 2^{n-1}$, where the stabiliser $X_\Delta$ of a codeword $\Delta$ is contained in a \emph{geometric} maximal subgroup of $X$. In particular, we construct two new infinite families of strongly incidence-transitive codes associated with the reducible maximal subgroups of $\mathrm{Sp}_{2n}(2)$.


Title: A Connected Component Labeling Algorithm for Implicitly-Defined Domains
Abstract: A connected component labeling algorithm is developed for implicitly-defined domains specified by multivariate polynomials. The algorithm operates by recursively subdividing the constraint domain into hyperrectangular subcells until the topology thereon is sufficiently simple; in particular, we devise a topology test using properties of Bernstein polynomials. In many cases the algorithm produces a certificate guaranteeing its correctness, i.e., two points yield the same label if and only if they are path-connected. To robustly handle various kinds of edge cases, the algorithm may assign identical labels to distinct components, but only when they are exactly or nearly touching, relative to a user-controlled length scale. A variety of numerical experiments assess the effectiveness of the overall approach, including statistical analyses on randomly generated multi-component geometry in 2D and 3D, as well as specific examples involving cusps, self-intersections, junctions, and other kinds of singularities.


Title: Percolation threshold for metric graph loop soup
Abstract: In this short note, we show that the critical threshold for the percolation of metric graph loop soup on a large class of transient metric graphs (including quasi-transitive graphs such as $\mathbb{Z}^d$, $d\geq 3$) is $1/2$.


Title: Evasive Hardware Trojan through Adversarial Power Trace
Abstract: The globalization of the Integrated Circuit (IC) supply chain, driven by time-to-market and cost considerations, has made ICs vulnerable to hardware Trojans (HTs). Against this threat, a promising approach is to use Machine Learning (ML)-based side-channel analysis, which has the advantage of being a non-intrusive method, along with efficiently detecting HTs under golden chip-free settings. In this paper, we question the trustworthiness of ML-based HT detection via side-channel analysis. We introduce a HT obfuscation (HTO) approach to allow HTs to bypass this detection method. Rather than theoretically misleading the model by simulated adversarial traces, a key aspect of our approach is the design and implementation of adversarial noise as part of the circuitry, alongside the HT. We detail HTO methodologies for ASICs and FPGAs, and evaluate our approach using TrustHub benchmark. Interestingly, we found that HTO can be implemented with only a single transistor for ASIC designs to generate adversarial power traces that can fool the defense with 100% efficiency. We also efficiently implemented our approach on a Spartan 6 Xilinx FPGA using 2 different variants: (i) DSP slices-based, and (ii) ring-oscillator-based design. Additionally, we assess the efficiency of countermeasures like spectral domain analysis, and we show that an adaptive attacker can still design evasive HTOs by constraining the design with a spectral noise budget. In addition, while adversarial training (AT) offers higher protection against evasive HTs, AT models suffer from a considerable utility loss, potentially rendering them unsuitable for such security application. We believe this research represents a significant step in understanding and exploiting ML vulnerabilities in a hardware security context, and we make all resources and designs openly available online: https://dev.d18uu4lqwhbmka.amplifyapp.com


Title: On PFH and HF spectral invariants
Abstract: In this note, we define the link spectral invariants by using the cylindrical formulation of the quantitative Heegaard Floer homology. We call them HF spectral invariants. We deduce a relation between the HF spectral invariants and the PFH spectral invariants by using closed-open morphisms and open-closed morphisms. For the sphere, we prove that the homogenized HF spectral invariants at the unit are equal to the homogenized PFH spectral invariants. Moreover, we show that the homogenized PFH spectral invariants are quasimorphisms.


Title: Network Structure, Efficiency, and Performance in WikiProjects
Abstract: The internet has enabled collaborations at a scale never before possible, but the best practices for organizing such large collaborations are still not clear. Wikipedia is a visible and successful example of such a collaboration which might offer insight into what makes large-scale, decentralized collaborations successful. We analyze the relationship between the structural properties of WikiProject coeditor networks and the performance and efficiency of those projects. We confirm the existence of an overall performance-efficiency trade-off, while observing that some projects are higher than others in both performance and efficiency, suggesting the existence factors correlating positively with both. Namely, we find an association between low-degree coeditor networks and both high performance and high efficiency. We also confirm results seen in previous numerical and small-scale lab studies: higher performance with less skewed node distributions, and higher performance with shorter path lengths. We use agent-based models to explore possible mechanisms for degree-dependent performance and efficiency. We present a novel local-majority learning strategy designed to satisfy properties of real-world collaborations. The local-majority strategy as well as a localized conformity-based strategy both show degree-dependent performance and efficiency, but in opposite directions, suggesting that these factors depend on both network structure and learning strategy. Our results suggest possible benefits to decentralized collaborations made of smaller, more tightly-knit teams, and that these benefits may be modulated by the particular learning strategies in use.


Title: Urban Surface Reconstruction in SAR Tomography by Graph-Cuts
Abstract: SAR (Synthetic Aperture Radar) tomography reconstructs 3-D volumes from stacks of SAR images. High-resolution satellites such as TerraSAR-X provide images that can be combined to produce 3-D models. In urban areas, sparsity priors are generally enforced during the tomographic inversion process in order to retrieve the location of scatterers seen within a given radar resolution cell. However, such priors often miss parts of the urban surfaces. Those missing parts are typically regions of flat areas such as ground or rooftops. This paper introduces a surface segmentation algorithm based on the computation of the optimal cut in a flow network. This segmentation process can be included within the 3-D reconstruction framework in order to improve the recovery of urban surfaces. Illustrations on a TerraSAR-X tomographic dataset demonstrate the potential of the approach to produce a 3-D model of urban surfaces such as ground, fa\c{c}ades and rooftops.


Title: 2-Representations of Lie 2-groups and 2-Vector Bundles
Abstract: Murray, Roberts and Wockel showed that there is no strict model of the string 2-group using the free loop group. Instead, they construct the next best thing, a coherent model for the string 2-group using the free loop group, with explicit formulas for all structure. Based on their expectations, we build a category of 2-representations for coherent Lie 2-groups and some concrete examples. We also discuss the relation between this category of 2-representations and the category of representations. In addition, we construct a model of equivariant 2-vector bundles. At the end, we discuss the adjoint action on the string 2-representations.


Title: Remarks on the point character of Banach spaces and non-linear embeddings into~$c_0(\Ga)$
Abstract: We give a brief survey of the results on coarse or uniform embeddings of Banach spaces into $c_0(\Ga)$ and the point character of Banach spaces. In the process we prove several new results in this direction (for example we determine the point character of the spaces $L_p(\mu)$, $1\le p\le2$) solving open problems posed by C.~Avart, P.~Komjath, and V.~Roedl and by G.~Godefroy, G.~Lancien, and V.~Zizler. In particular, we show that $X=L_p(\mu)$, $1\le p<\infty$, bi-Lipschitz embeds into $c_0(\Ga)$ if and only if $\dens X<\om_\om$.


Title: Robust Collective Classification against Structural Attacks
Abstract: Collective learning methods exploit relations among data points to enhance classification performance. However, such relations, represented as edges in the underlying graphical model, expose an extra attack surface to the adversaries. We study adversarial robustness of an important class of such graphical models, Associative Markov Networks (AMN), to structural attacks, where an attacker can modify the graph structure at test time. We formulate the task of learning a robust AMN classifier as a bi-level program, where the inner problem is a challenging non-linear integer program that computes optimal structural changes to the AMN. To address this technical challenge, we first relax the attacker problem, and then use duality to obtain a convex quadratic upper bound for the robust AMN problem. We then prove a bound on the quality of the resulting approximately optimal solutions, and experimentally demonstrate the efficacy of our approach. Finally, we apply our approach in a transductive learning setting, and show that robust AMN is much more robust than state-of-the-art deep learning methods, while sacrificing little in accuracy on non-adversarial data.


Title: Sampling probabilities, diffusions, ancestral graphs, and duality under strong selection
Abstract: Wright-Fisher diffusions and their dual ancestral graphs occupy a central role in the study of allele frequency change and genealogical structure, and they provide expressions, explicit in some special cases but generally implicit, for the sampling probability, a crucial quantity in inference. Under a finite-allele mutation model, with possibly parent-dependent mutation, we consider the asymptotic regime where the selective advantage of one allele grows to infinity, while the other parameters remain fixed. In this regime, we show that the Wright-Fisher diffusion can be approximated either by a Gaussian process or by a process whose components are independent continuous-state branching processes with immigration, aligning with analogous results for Wright-Fisher models but employing different methods. While the first process becomes degenerate at stationarity, the latter does not and provides a simple, analytic approximation for the leading term of the sampling probability. Furthermore, using another approach based on a recursion formula, we characterise all remaining terms to provide a full asymptotic expansion for the sampling probability. Finally, we study the asymptotic behaviour of the rates of the block-counting process of the conditional ancestral selection graph and establish an asymptotic duality relationship between this and the diffusion.


Title: An infinite family of counterexamples to a conjecture on distance magic labeling
Abstract: This work is about a partition problem which is an instance of the distance magic graph labeling problem. Given positive integers $n,k$ and $p_1\le p_2\le \cdots\le p_k$ such that $p_1+\cdots+p_k=n$ and $k$ divides $\sum_{i=1}^ni$, we study the problem of characterizing the cases where it is possible to find a partition of the set $\{1,2,\ldots,n\}$ into $k$ subsets of respective sizes $p_1,\dots,p_k$, such that the element sum in each subset is equal. Using a computerized search we found examples showing that the necessary condition, $\sum_{i=1}^{p_1+\cdots+p_j} (n-i+1)\ge j{\binom{n+1}{2}}/k$ for all $j=1,\ldots,k$, is not generally sufficient, refuting a past conjecture. Moreover, we show that there are infinitely many such counter-examples. The question whether there is a simple characterization is left open and for all we know the corresponding decision problem might be NP-complete.


Title: On geometry of the unit ball of Paley-Wiener space over two symmetric intervals
Abstract: Let $PW_S^1$ be the space of integrable functions on $\mathbb{R}$ whose Fourier transform vanishes outside $S$, where $S = [-\sigma,-\rho]\cup[\rho,\sigma]$, $0<\rho<\sigma$. In the case $\rho>\sigma/2$, we present a complete description of the set of extreme and the set of exposed points of the unit ball of $PW^1_S$. The structure of these sets becomes more complicated when $\rho<\sigma/2$.


Title: Synchrony in Gene Regulatory Networks
Abstract: We consider two mathematical dynamical models of gene regulatory networks (GRNs) and obtain results on robust synchronization on these dynamical models based on the existing theoretical results in the coupled cell network formalism. We also explore the concepts of quotient networks and network lifting in the context of GRNs which are related to the process of gene duplication and the phenomenon of genetic redundancy.


Title: Bayesian Neural Network Versus Ex-Post Calibration For Prediction Uncertainty
Abstract: Probabilistic predictions from neural networks which account for predictive uncertainty during classification is crucial in many real-world and high-impact decision making settings. However, in practice most datasets are trained on non-probabilistic neural networks which by default do not capture this inherent uncertainty. This well-known problem has led to the development of post-hoc calibration procedures, such as Platt scaling (logistic), isotonic and beta calibration, which transforms the scores into well calibrated empirical probabilities. A plausible alternative to the calibration approach is to use Bayesian neural networks, which directly models a predictive distribution. Although they have been applied to images and text datasets, they have seen limited adoption in the tabular and small data regime. In this paper, we demonstrate that Bayesian neural networks yields competitive performance when compared to calibrated neural networks and conduct experiments across a wide array of datasets.


Title: Fusion Categories over Non-Algebriacally Closed Fields
Abstract: Several complications arise when attempting to work with fusion categories over arbitrary fields. Here we describe some of the new phenomena that occur when the field is not algebraically closed, and we adapt tools such as the Frobenius-Perron dimension in order to accommodate these new effects.


Title: Exact upper and lower bounds on the misclassification probability
Abstract: Exact lower and upper bounds on the best possible misclassification probability for a finite number of classes are obtained in terms of the total variation norms of the differences between the sub-distributions over the classes. These bounds are compared with the exact bounds in terms of the conditional entropy obtained by Feder and Merhav.


Title: The Mahler measure of exact polynomials in three variables
Abstract: We prove that under certain explicit conditions, the Mahler measure of a three-variable exact polynomial can be expressed in terms of elliptic curve $L$-functions and values of the Bloch-Wigner dilogarithm, conditionally on Beilinson's conjecture. In some cases, these dilogarithmic values simplify to Dirichlet $L$-values. This generalizes a result of Lal\'in for the polynomial $z + (x+1)(y+1)$. We apply our method to several other Mahler measure identities conjectured by Boyd and Brunault.


Title: Unleashing the Emergent Cognitive Synergy in Large Language Models: A Task-Solving Agent through Multi-Persona Self-Collaboration
Abstract: Human intelligence thrives on cognitive synergy, where collaboration among different minds yield superior outcomes compared to isolated individuals. In this work, we propose Solo Performance Prompting (SPP), which transforms a single LLM into a cognitive synergist by engaging in multi-turn self-collaboration with multiple personas. A cognitive synergist is an intelligent agent that collaboratively combines multiple minds' strengths and knowledge to enhance problem-solving in complex tasks. By dynamically identifying and simulating different personas based on task inputs, SPP unleashes the potential of cognitive synergy in LLMs. Our in-depth analysis shows that assigning multiple fine-grained personas in LLMs improves problem-solving abilities compared to using a single or fixed number of personas. We evaluate SPP on three challenging tasks: Trivia Creative Writing, Codenames Collaborative, and Logic Grid Puzzle, encompassing both knowledge-intensive and reasoning-intensive types. Unlike previous works, such as Chain-of-Thought, that solely enhance the reasoning abilities in LLMs, experimental results demonstrate that SPP effectively reduces factual hallucination, and maintains strong reasoning capabilities. Additionally, comparative experiments show that cognitive synergy only emerges in GPT-4 and does not appear in less capable models, such as GPT-3.5-turbo and Llama2-13b-chat, which draws an interesting analogy to human development. Code, data, and prompts can be found at: https://github.com/MikeWangWZHL/Solo-Performance-Prompting.git.


Title: Applications of Gorenstein projective $τ$-rigid modules
Abstract: We first introduce the notion of $CM$-$\tau$-tilting free algebras as the generalization of $CM$-free algebras and show the homological properties of $CM$-$\tau$-tilting free algebras. Then we give a bijection between Gorenstein projective $\tau$-rigid modules and certain modules by using an equivalence established by Kong and Zhang. Finally, we give a partial answer to Tachikawa's first conjecture by using Gorenstein projective $\tau$-rigid modules.


Title: Challenges and Opportunities in High-dimensional Variational Inference
Abstract: Current black-box variational inference (BBVI) methods require the user to make numerous design choices -- such as the selection of variational objective and approximating family -- yet there is little principled guidance on how to do so. We develop a conceptual framework and set of experimental tools to understand the effects of these choices, which we leverage to propose best practices for maximizing posterior approximation accuracy. Our approach is based on studying the pre-asymptotic tail behavior of the density ratios between the joint distribution and the variational approximation, then exploiting insights and tools from the importance sampling literature. Our framework and supporting experiments help to distinguish between the behavior of BBVI methods for approximating low-dimensional versus moderate-to-high-dimensional posteriors. In the latter case, we show that mass-covering variational objectives are difficult to optimize and do not improve accuracy, but flexible variational families can improve accuracy and the effectiveness of importance sampling -- at the cost of additional optimization challenges. Therefore, for moderate-to-high-dimensional posteriors we recommend using the (mode-seeking) exclusive KL divergence since it is the easiest to optimize, and improving the variational family or using model parameter transformations to make the posterior and optimal variational approximation more similar. On the other hand, in low-dimensional settings, we show that heavy-tailed variational families and mass-covering divergences are effective and can increase the chances that the approximation can be improved by importance sampling.


Title: Hopfield Neuronal Network of Fractional Order: A note on its numerical integration
Abstract: In this paper, the commensurate fractional-order variant of an Hopfield neuronal network is analyzed. The system is integrated with the ABM method for fractional-order equations. Beside the standard stability analysis of equilibria, the divergence of fractional order is proposed to determine the instability of the equilibria. The bifurcation diagrams versus the fractional order, and versus one parameter, reveal a strange phenomenon suggesting that the bifurcation branches generated by initial conditions outside neighborhoods of unstable equilibria are spurious sets although they look similar with those generated by initial conditions close to the equilibria. These spurious sets look ``delayed'' in the considered bifurcation scenario. Once the integration step-size is reduced, the spurious branches maintain their shapes but tend to the branches obtained from initial condition within neighborhoods of equilibria. While the spurious branches move once the integration step size reduces, the branches generated by the initial conditions near the equilibria maintain their positions in the considered bifurcation space. This phenomenon does not depend on the integration-time interval, and repeats in the parameter bifurcation space.


Title: A Finite Axiomatization of G-Dependence
Abstract: We show that a form of dependence known as G-dependence (originally introduced by Grelling) admits a very natural finite axiomatization, as well as Armstrong relations. We also give an explicit translation between functional dependence and G-dependence.


Title: The built-in selection bias of hazard ratios formalized
Abstract: It is known that the hazard ratio lacks a useful causal interpretation. Even for data from a randomized controlled trial, the hazard ratio suffers from built-in selection bias as, over time, the individuals at risk in the exposed and unexposed are no longer exchangeable. In this work, we formalize how the observed hazard ratio evolves and deviates from the causal hazard ratio of interest in the presence of heterogeneity of the hazard of unexposed individuals (frailty) and heterogeneity in effect (individual modification). For the case of effect heterogeneity, we define the causal hazard ratio. We show that the observed hazard ratio equals the ratio of expectations of the latent variables (frailty and modifier) conditionally on survival in the world with and without exposure, respectively. Examples with gamma, inverse Gaussian and compound Poisson distributed frailty, and categorical (harming, beneficial or neutral) effect modifiers are presented for illustration. This set of examples shows that an observed hazard ratio with a particular value can arise for all values of the causal hazard ratio. Therefore, the hazard ratio can not be used as a measure of the causal effect without making untestable assumptions, stressing the importance of using more appropriate estimands such as contrasts of the survival probabilities.


Title: Complete Geodesic Metrics in Big Classes
Abstract: Let $(X,\omega)$ be a compact K\"ahler manifold and $\theta$ be a smooth closed real $(1,1)$-form that represents a big cohomology class. In this paper, we show that for $p\geq 1$, the high energy space $\mathcal{E}^{p}(X,\theta)$ can be endowed with a metric $d_{p}$ that makes $(\mathcal{E}^{p}(X,\theta),d_{p})$ a complete geodesic metric space. The weak geodesics in $\mathcal{E}^{p}(X,\theta)$ are the metric geodesic for $(\mathcal{E}^{p}(X,\theta), d_{p})$. Moreover, for $p > 1$, the geodesic metric space $(\mathcal{E}^{p}(X,\theta), d_{p})$ is uniformly convex.


Title: Trajectory Optimization for Completion Time Minimization in UAV-Enabled Multicasting
Abstract: This paper studies an unmanned aerial vehicle (UAV)-enabled multicasting system, where a UAV is dispatched to disseminate a common file to a number of geographically distributed ground terminals (GTs). Our objective is to design the UAV trajectory to minimize its mission completion time, while ensuring that each GT is able to successfully recover the file with a high probability required. We consider the use of practical random linear network coding (RLNC) for UAV multicasting, so that each GT is able to recover the file as long as it receives a sufficiently large number of coded packets. However, the formulated UAV trajectory optimization problem is non-convex and difficult to be directly solved. To tackle this issue, we first derive an analytical lower bound for the success probability of each GT's file recovery. Based on this result, we then reformulate the problem into a more tractable form, where the UAV trajectory only needs to be designed to meet a set of constraints each on the minimum connection time with a GT, during which their distance is below a designed threshold. We show that the optimal UAV trajectory only needs to constitute connected line segments, thus it can be obtained by determining first the optimal set of waypoints and then UAV speed along the lines connecting the waypoints. We propose practical schemes for the waypoints design based on a novel concept of virtual base station (VBS) placement and by applying convex optimization techniques. Furthermore, for given set of waypoints, we obtain the optimal UAV speed over the resulting path efficiently by solving a linear programming (LP) problem. Numerical results show that the proposed UAV-enabled multicasting with optimized trajectory design achieves significant performance gains as compared to benchmark schemes.


Title: The near-parabolic geometry of external rays
Abstract: Using Lavaurs maps and near-parabolic renormalization, we describe the degenerating geometry of external rays for quadratic polynomials when a periodic cycle becomes parabolic. We similarly describe the geometry of parameter rays for the Mandelbrot set near parabolic points. Using this geometric control we establish new bounds on the size of limbs of the Mandelbrot set, for example providing a quadratic Pommerenke-Levin-Yoccoz inequality in the near-parabolic setting.


Title: Analytic Regularity for Linear Elliptic Systems in Polygons and Polyhedra
Abstract: We prove weighted anisotropic analytic estimates for solutions of second order elliptic boundary value problems in polyhedra. The weighted analytic classes which we use are the same as those introduced by Guo in 1993 in view of establishing exponential convergence for hp finite element methods in polyhedra. We first give a simple proof of the known weighted analytic regularity in a polygon, relying on a new formulation of elliptic a priori estimates in smooth domains with analytic control of derivatives. The technique is based on dyadic partitions near the corners. This technique can successfully be extended to polyhedra, providing isotropic analytic regularity. This is not optimal, because it does not take advantage of the full regularity along the edges. We combine it with a nested open set technique to obtain the desired three-dimensional anisotropic analytic regularity result. Our proofs are global and do not require the analysis of singular functions.


Title: A homological reformulation of the link condition
Abstract: We prove an equivalent condition for the existence of a link between prime ideals in terms of the structure of a certain cohomology module. We use this formulation to answer an open question regarding the nature of module extensions over one sided noetherian rings. We apply the techniques developed in this paper to the local link structure of prime ideals of small homological height and examine when certain noetherian rings satisfy the density condition.


Title: Drinfeld rational fractions for affine Kac-Moody quantum symmetric pairs
Abstract: We formulate a precise connection between the new Drinfeld presentation of a quantum affine algebra $U_q\widehat{\mathfrak{g}}$ and the new Drinfeld presentation of affine coideal subalgebras of split type recently discovered by Lu and Wang. In particular, we establish a ``factorization formula'', expressing the commuting ``affine Cartan''-type operators $\Theta_{i,k}$ in a coideal subalgebra in terms of the corresponding Drinfeld generators of $U_q\widehat{\mathfrak{g}}$, modulo the ``Drinfeld positive half" of $U_q\widehat{\mathfrak{g}}$. We study the spectra of these operators on finite dimensional representations, and describe them in terms of rational functions with an extra symmetry. These results can be seen as the starting point of a $q$-character theory for affine Kac--Moody quantum symmetric pairs. Additionally, we prove a compatibility result linking Lusztig's and the Lu-Ruan-Wang-Zhang braid group actions.


Title: Can We Distinguish Machine Learning from Human Learning?
Abstract: What makes a task relatively more or less difficult for a machine compared to a human? Much AI/ML research has focused on expanding the range of tasks that machines can do, with a focus on whether machines can beat humans. Allowing for differences in scale, we can seek interesting (anomalous) pairs of tasks T, T'. We define interesting in this way: The "harder to learn" relation is reversed when comparing human intelligence (HI) to AI. While humans seems to be able to understand problems by formulating rules, ML using neural networks does not rely on constructing rules. We discuss a novel approach where the challenge is to "perform well under rules that have been created by human beings." We suggest that this provides a rigorous and precise pathway for understanding the difference between the two kinds of learning. Specifically, we suggest a large and extensible class of learning tasks, formulated as learning under rules. With these tasks, both the AI and HI will be studied with rigor and precision. The immediate goal is to find interesting groundtruth rule pairs. In the long term, the goal will be to understand, in a generalizable way, what distinguishes interesting pairs from ordinary pairs, and to define saliency behind interesting pairs. This may open new ways of thinking about AI, and provide unexpected insights into human learning.


Title: Limit theorems for a supercritical remaining-lifetime age-structured branching process
Abstract: In a previous paper [9] we studied an age-structured branching model without immigration. Here we consider a special case of the model, where the system is founded by a single particle with a random lifetime and the reproduction regime is supercritical. We show that there is a necessary and sufficient condition for the convergence of the Malthus normalized random measures $e^{-\tilde{\alpha}t} X_t$, where $\tilde{\alpha}$ is a strictly positive Malthusian parameter. The convergence of $e^{-\tilde{\alpha}t} \langle X_t,f\rangle$ can be strengthened to hold with probability one under conditions weaker than those given in Jagers [24]. A central limit theorem of $\langle X_t,f\rangle$ is further proved.


Title: Bounded Homotopy Path Approach to Find the Solution of Linear Complementarity Problems
Abstract: In this article, we introduce a new homotopy function to trace the trajectory by applying modified homotopy continuation method for finding the solution of the linear complementarity problem. Earlier several authors attempted to propose homotopy functions based on original problems. We propose the homotopy function based on the Karush-Kuhn-Tucker condition of the corresponding quadratic programming problem. The proposed approach extends the processability of the larger class of linear complementarity problem and overcomes the limitations of other existing homotopy approaches. We show that the homotopy path approaching the solution is smooth and bounded with positive tangent direction of the homotopy path. Various classes of numerical examples are illustrated to show the effectiveness of the proposed algorithm and the superiority of the algorithm among other existing iterative methods.


Title: A Borsuk--Ulam theorem for well separated maps
Abstract: Suppose that $f_1,\ldots ,f_m : S(V)\to R$ are $m$ ($\geq 1$) continuous functions defined on the unit sphere in a Euclidean vector space $V$ of dimension $m+1$ satisfying $f_i(-v)=-f_i(v)$ for all $v\in S(V)$. The classical Borsuk-Ulam theorem asserts that the image of the map $(f_1,\ldots ,f_m) :S(V)\to R^m$ contains $0=(0,\ldots ,0)$. Pursuing ideas in papers of B\'ar\'any, Hubard and J\'eronimo (2008) and Frick and Wellner (2023), we show that a certain separation property will guarantee that the image contains an $m$-cube.


Title: On the Barcode Entropy of Reeb Flows
Abstract: In this paper we continue investigating connections between Floer theory and dynamics of Hamiltonian systems, focusing on the barcode entropy of Reeb flows. Barcode entropy is the exponential growth rate of the number of not-too-short bars in the Floer or symplectic homology persistence module. The key novel result is that the barcode entropy is bounded from below by the topological entropy of any hyperbolic invariant set. This, combined with the fact that the topological entropy bounds the barcode entropy from above, established by Fender, Lee and Sohn, implies that in dimension three the two types of entropy agree. The main new ingredient of the proof is a variant of the Crossing Energy Theorem for Reeb flows.


Title: Gesture-to-Gesture Translation in the Wild via Category-Independent Conditional Maps
Abstract: Recent works have shown Generative Adversarial Networks (GANs) to be particularly effective in image-to-image translations. However, in tasks such as body pose and hand gesture translation, existing methods usually require precise annotations, e.g. key-points or skeletons, which are time-consuming to draw. In this work, we propose a novel GAN architecture that decouples the required annotations into a category label - that specifies the gesture type - and a simple-to-draw category-independent conditional map - that expresses the location, rotation and size of the hand gesture. Our architecture synthesizes the target gesture while preserving the background context, thus effectively dealing with gesture translation in the wild. To this aim, we use an attention module and a rolling guidance approach, which loops the generated images back into the network and produces higher quality images compared to competing works. Thus, our GAN learns to generate new images from simple annotations without requiring key-points or skeleton labels. Results on two public datasets show that our method outperforms state of the art approaches both quantitatively and qualitatively. To the best of our knowledge, no work so far has addressed the gesture-to-gesture translation in the wild by requiring user-friendly annotations.


Title: Proof of Halin's normal spanning tree conjecture
Abstract: Halin conjectured 20 years ago that a graph has a normal spanning tree if and only if every minor of it has countable colouring number. We prove Halin's conjecture. This implies a forbidden minor characterisation for the property of having a normal spanning tree.


Title: An Algorithm for Training Polynomial Networks
Abstract: We consider deep neural networks, in which the output of each node is a quadratic function of its inputs. Similar to other deep architectures, these networks can compactly represent any function on a finite training set. The main goal of this paper is the derivation of an efficient layer-by-layer algorithm for training such networks, which we denote as the \emph{Basis Learner}. The algorithm is a universal learner in the sense that the training error is guaranteed to decrease at every iteration, and can eventually reach zero under mild conditions. We present practical implementations of this algorithm, as well as preliminary experimental results. We also compare our deep architecture to other shallow architectures for learning polynomials, in particular kernel learning.


Title: Physics-Inspired Discrete-Phase Optimization for 3D Beamforming with PIN-Diode Extra-Large Antenna Arrays
Abstract: Large antenna arrays can steer narrow beams towards a target area, and thus improve the communications capacity of wireless channels and the fidelity of radio sensing. Hardware that is capable of continuously-variable phase shifts is expensive, presenting scaling challenges. PIN diodes that apply only discrete phase shifts are promising and cost-effective; however, unlike continuous phase shifters, finding the best phase configuration across elements is an NP-hard optimization problem. Thus, the complexity of optimization becomes a new bottleneck for large-antenna arrays. To address this challenge, this paper suggests a procedure for converting the optimization objective function from a ratio of quadratic functions to a sequence of more easily solvable quadratic unconstrained binary optimization (QUBO) sub-problems. This conversion is an exact equivalence, and the resulting QUBO forms are standard input formats for various physics-inspired optimization methods. We demonstrate that a simulated annealing approach is very effective for solving these sub-problems, and we give performance metrics for several large array types optimized by this technique. Through numerical experiments, we report 3D beamforming performance for extra-large arrays with up to 10,000 elements.


Title: A Learning-Based Fast Uplink Grant for Massive IoT via Support Vector Machines and Long Short-Term Memory
Abstract: The current random access (RA) allocation techniques suffer from congestion and high signaling overhead while serving massive machine type communication (mMTC) applications. To this end, 3GPP introduced the need to use fast uplink grant (FUG) allocation in order to reduce latency and increase reliability for smart internet-of-things (IoT) applications with strict QoS constraints. We propose a novel FUG allocation based on support vector machine (SVM), First, MTC devices are prioritized using SVM classifier. Second, LSTM architecture is used for traffic prediction and correction techniques to overcome prediction errors. Both results are used to achieve an efficient resource scheduler in terms of the average latency and total throughput. A Coupled Markov Modulated Poisson Process (CMMPP) traffic model with mixed alarm and regular traffic is applied to compare the proposed FUG allocation to other existing allocation techniques. In addition, an extended traffic model based CMMPP is used to evaluate the proposed algorithm in a more dense network. We test the proposed scheme using real-time measurement data collected from the Numenta Anomaly Benchmark (NAB) database. Our simulation results show the proposed model outperforms the existing RA allocation schemes by achieving the highest throughput and the lowest access delay of the order of 1 ms by achieving prediction accuracy of 98 $\%$ when serving the target massive and critical MTC applications with a limited number of resources.


Title: On Einstein Lorentzian nilpotent Lie groups
Abstract: In this paper, we study Lorentzian left invariant Einstein metrics on nilpotent Lie groups. We show that if the center of such Lie groups is degenerate then they are Ricci-flat and their Lie algebras can be obtained by the double extension process from an abelian Euclidean Lie algebra. We show that all nilpotent Lie groups up to dimension $5$ endowed with a Lorentzian Einstein left invariant metric have degenerate center and we use this fact to give a complete classification of these metrics. We show that if $\mathfrak{g}$ is the Lie algebra of a nilpotent Lie group endowed with a Lorentzian left invariant Einstein metric with non zero scalar curvature then the center $Z(\mathfrak{g})$ of $\mathfrak{g}$ is nondegenerate Euclidean, the derived ideal $[\mathfrak{g},\mathfrak{g}]$ is nondegenerate Lorentzian and $Z(\mathfrak{g})\subset[\mathfrak{g},\mathfrak{g}]$. We give the first examples of Ricci-flat Lorentzian nilpotent Lie algebra with nondegenerate center.


Title: Hyperlinear approximations to amenable groups come from sofic approximations
Abstract: We provide a quantitative formulation of the equivalence between hyperlinearity and soficity for amenable groups, showing that every hyperlinear approximation to such a group is essentially produced from a sofic approximation. The proof is probabilistic, using the concentration of measure in high dimensional spheres to control the deviation of an operator's matrix coefficients from its trace. As a corollary, we obtain a result connecting stability of sofic approximations with stability of hyperlinear approximations.


Title: Microsoft COCO: Common Objects in Context
Abstract: We present a new dataset with the goal of advancing the state-of-the-art in object recognition by placing the question of object recognition in the context of the broader question of scene understanding. This is achieved by gathering images of complex everyday scenes containing common objects in their natural context. Objects are labeled using per-instance segmentations to aid in precise object localization. Our dataset contains photos of 91 objects types that would be easily recognizable by a 4 year old. With a total of 2.5 million labeled instances in 328k images, the creation of our dataset drew upon extensive crowd worker involvement via novel user interfaces for category detection, instance spotting and instance segmentation. We present a detailed statistical analysis of the dataset in comparison to PASCAL, ImageNet, and SUN. Finally, we provide baseline performance analysis for bounding box and segmentation detection results using a Deformable Parts Model.


Title: Orthogonal webs and semisimplification
Abstract: We define a diagrammatic category that is equivalent to tilting representations for the orthogonal group. Our construction works in characteristic not equal to two. We also describe the semisimplification of this category.


Title: VBFT: Veloce Byzantine Fault Tolerant Consensus for Blockchains
Abstract: Low latency is one of the most desirable features of partially synchronous Byzantine consensus protocols. Existing low-latency protocols have achieved consensus with just two communication steps by reducing the maximum number of faults the protocol can tolerate (from $f = \frac{n-1}{3}$ to $f = \frac{n+1}{5}$), \textcolor{black}{by relaxing protocol safety guarantees}, or by using trusted hardware like Trusted Execution Environment. Furthermore, these two-step protocols don't support rotating primary and low-cost view change (leader replacement), which are important features of many blockchain use cases. In this paper, we propose a protocol called VBFT which achieves consensus in just two communication steps without scarifying desirable features. In particular, VBFT tolerates $f = \frac{n-1}{3}$ faults (which is the best possible), guarantees strong safety for honest primaries, and requires no trusted hardware. Moreover, VBFT supports primary rotation and low-cost view change, thereby improving prior art on multiple axes.


Title: Rings Whose Clean and Nil-Clean Elements Have Some Clean-Like Properties
Abstract: We define two types of rings, namely the so-called CSNC and NCUC that are those rings whose clean elements are strongly nil-clean, respectively, whose nil-clean elements are uniquely clean. Our results obtained in this paper somewhat expand these obtained by Calugareanu-Zhou in Mediterr. J. Math. (2023) and by Cui-Danchev-Jin in Publ. Math. Debrecen (2024), respectively.


Title: Runs in Sequences of Random Ordered Variables
Abstract: We determine the distributions of lengths of runs in sequences of random elements from a total or partial order. In particular, we derive formulas for the expected value, variance, and probability generating function (PGF) of such lengths in the case of total orders (focusing on distributions with atoms). To do this, we define novel generating functions associated with a measure on an order. These generating functions behave nicely when splitting and combining measures on orders allowing us to solve the case of total orders.


Title: Inherently robust suboptimal MPC for autonomous racing with anytime feasible SQP
Abstract: In recent years, the increasing need for high-performance controllers in applications like autonomous driving has motivated the development of optimization routines tailored to specific control problems. In this paper, we propose an efficient inexact model predictive control (MPC) strategy for autonomous miniature racing with inherent robustness properties. We rely on a feasible sequential quadratic programming (SQP) algorithm capable of generating feasible intermediate iterates such that the solver can be stopped after any number of iterations, without jeopardizing recursive feasibility. In this way, we provide a strategy that computes suboptimal and yet feasible solutions with a computational footprint that is much lower than state-of-the-art methods based on the computation of locally optimal solutions. Under suitable assumptions on the terminal set and on the controllability properties of the system, we can state that, for any sufficiently small disturbance affecting the system's dynamics, recursive feasibility can be guaranteed. We validate the effectiveness of the proposed strategy in simulation and by deploying it onto a physical experiment with autonomous miniature race cars. Both the simulation and experimental results demonstrate that, using the feasible SQP method, a feasible solution can be obtained with moderate additional computational effort compared to strategies that resort to early termination without providing a feasible solution. At the same time, the proposed method is significantly faster than the state-of-the-art solver Ipopt.


Title: Miscellaneous problems about packing and covering
Abstract: In this paper we discuss various special problems on packing and covering. Among others we survey the problems and results concerning finite arrangements, Minkowskian, saturated, compact, and totally separable packings. We discuss shortest path problems and questions about stability of packings.


Title: Numerical solution of the Burgers' equation with high order splitting methods
Abstract: In this work, high order splitting methods have been used for calculating the numerical solutions of the Burgers' equation in one space dimension with periodic and Dirichlet boundary conditions. However, splitting methods with real coefficients of order higher than two necessarily have negative coefficients and can not be used for time-irreversible systems, such as Burgers equations, due to the time-irreversibility of the Laplacian operator. Therefore, the splitting methods with complex coefficients and extrapolation methods with real and positive coefficients have been employed. If we consider the system as the perturbation of an exactly solvable problem(or can be easily approximated numerically), it is possible to employ highly efficient methods to approximate Burgers' equation. The numerical results show that the methods with complex time steps having one set of coefficients real and positive, say $a_i\in\mathbb{R}^+$ and $b_i\in\mathbb{C}^+$, and high order extrapolation methods derived from a lower order splitting method produce very accurate solutions of the Burgers' equation.


Title: Nonexistence of Exceptional 5-class Association Schemes with Two $Q$-polynomial Structures
Abstract: In [H. Suzuki, Association schemes with multiple $Q$-polynomial structures, J. Algebraic Combin. 7 (1998) 181-196], Suzuki gave a classification of association schemes with multiple $Q$-polynomial structures, allowing for one exceptional case which has five classes. In this paper, we rule out the existence of this case. Hence Suzuki's theorem mirrors exactly the well-known counterpart for association schemes with multiple $P$-polynomial structures, a result due to Eiichi Bannai and Etsuko Bannai in 1980.


Title: On the classification of multiplicity-free Hamiltonian actions by regular proper symplectic groupoids
Abstract: In this paper we study a natural generalization of symplectic toric manifolds in the context of regular Poisson manifolds of compact types. To be more precise, we consider a class of multiplicity-free Hamiltonian actions by regular proper symplectic groupoids that we call faithful. Given such a groupoid, we classify its faithful multiplicity-free Hamiltonian actions in terms of what we call Delzant subspaces of its orbit space -- certain `suborbifolds with corners' satisfying the Delzant condition relative to the integral affine orbifold structure of the orbit space. This encompasses both the classification of symplectic toric manifolds (due to Delzant) in terms of Delzant polytopes and the classification of proper Lagrangian fibrations over an integral affine base manifold (due to Duistermaat) in terms of a sheaf cohomology group. Each Delzant subspace comes with an orbifold version of this cohomology, the degree one part of which classifies faithful multiplicity-free Hamiltonian actions with momentum map image equal to the Delzant subspace, provided there exists such an action. The obstruction to existence is encoded by a degree two class in this cohomology: the Lagrangian Dixmier-Douady class. In addition to the above, we introduce another invariant, which leads to a variation of our classification result involving only classical sheaf cohomology and the group cohomology of certain modules for the isotropy groups of the groupoid.


Title: Modification method for single-stage object detectors that allows to exploit the temporal behaviour of a scene to improve detection accuracy
Abstract: A simple modification method for single-stage generic object detection neural networks, such as YOLO and SSD, is proposed, which allows for improving the detection accuracy on video data by exploiting the temporal behavior of the scene in the detection pipeline. It is shown that, using this method, the detection accuracy of the base network can be considerably improved, especially for occluded and hidden objects. It is shown that a modified network is more prone to detect hidden objects with more confidence than an unmodified one. A weakly supervised training method is proposed, which allows for training a modified network without requiring any additional annotated data.


Title: Variational Bandwidth Auto-encoder for Hybrid Recommender Systems
Abstract: Hybrid recommendations have recently attracted a lot of attention where user features are utilized as auxiliary information to address the sparsity problem caused by insufficient user-item interactions. However, extracted user features generally contain rich multimodal information, and most of them are irrelevant to the recommendation purpose. Therefore, excessive reliance on these features will make the model overfit on noise and difficult to generalize. In this article, we propose a variational bandwidth auto-encoder (VBAE) for recommendations, aiming to address the sparsity and noise problems simultaneously. VBAE first encodes user collaborative and feature information into Gaussian latent variables via deep neural networks to capture non-linear user similarities. Moreover, by considering the fusion of collaborative and feature variables as a virtual communication channel from an information-theoretic perspective, we introduce a user-dependent channel to dynamically control the information allowed to be accessed from the feature embeddings. A quantum-inspired uncertainty measurement of the hidden rating embeddings is proposed accordingly to infer the channel bandwidth by disentangling the uncertainty information in the ratings from the semantic information. Through this mechanism, VBAE incorporates adequate auxiliary information from user features if collaborative information is insufficient, while avoiding excessive reliance on noisy user features to improve its generalization ability to new users. Extensive experiments conducted on three real-world datasets demonstrate the effectiveness of the proposed method. Codes and datasets are released at https://github.com/yaochenzhu/vbae.


Title: Classifying Words with 3-sort Automata
Abstract: Grammatical inference consists in learning a language or a grammar from data. In this paper, we consider a number of models for inferring a non-deterministic finite automaton (NFA) with 3 sorts of states, that must accept some words, and reject some other words from a given sample. We then propose a transformation from this 3-sort NFA into weighted-frequency and probabilistic NFA, and we apply the latter to a classification task. The experimental evaluation of our approach shows that the probabilistic NFAs can be successfully applied for classification tasks on both real-life and superficial benchmark data sets.


Title: Approximate Equilibria in Generalized Colonel Blotto and Generalized Lottery Blotto Games
Abstract: In the Colonel Blotto game, two players with a fixed budget simultaneously allocate their resources across n battlefields to maximize the aggregate value gained from the battlefields where they have the higher allocation. Despite its long-standing history and important applications, the Colonel Blotto game still lacks a complete Nash equilibrium characterization in its most general form where players are asymmetric and battlefields' values are heterogeneous across battlefields and different between the two players---this is called the Generalized Colonel Blotto game. In this work, we propose a simply-constructed class of strategies---the independently uniform strategies---and we prove that they are approximate equilibria of the Generalized Colonel Blotto game; moreover, we characterize the approximation error according to the game's parameters. We also consider an extension called the Generalized Lottery Blotto game, with stochastic winner-determination rules allowing more flexibility in modeling practical contests. We prove that the proposed strategies are also approximate equilibria of the Generalized Lottery Blotto game.


Title: New results in vertex sedentariness
Abstract: A vertex in a graph is said to be sedentary if a quantum state assigned on that vertex tends to stay on that vertex. Under mild conditions, we show that the direct product and join operations preserve vertex sedentariness. We also completely characterize sedentariness in blow-up graphs. These results allow us to construct new infinite families of graphs with sedentary vertices. We prove that a vertex with a twin is either sedentary or admits pretty good state transfer. Moreover, we give a complete characterization of twin vertices that are sedentary, and provide sharp bounds on their sedentariness. As an application, we determine the conditions in which perfect state transfer, pretty good state transfer and sedentariness occur in complete bipartite graphs and threshold graphs of any order.


Title: A Palm hierarchy for determinantal point processes with the confluent hypergeometric kernel, the decomposing measures in the problem of harmonic analysis on the infinite-dimensional unitary group
Abstract: The main result of this note is that the shift of the parameter by 1 in the parameter space of decomposing measures in the problem of harmonic analysis on the infinite-dimensional unitary group corresponds to the taking of the reduced Palm measure at infinity for our decomposing measures. The proof proceeds by finite-dimensional approximation of our measures by orthogonal polynomial ensembles. The key remark is that the taking the reduced Palm measure commutes with the scaling limit transition from finite to infinite particle systems.


Title: A Look at the Time Delays in CVSS Vulnerability Scoring
Abstract: This empirical paper examines the time delays that occur between the publication of Common Vulnerabilities and Exposures (CVEs) in the National Vulnerability Database (NVD) and the Common Vulnerability Scoring System (CVSS) information attached to published CVEs. According to the empirical results based on regularized regression analysis of over eighty thousand archived vulnerabilities, (i) the CVSS content does not statistically influence the time delays, which, however, (ii) are strongly affected by a decreasing annual trend. In addition to these results, the paper contributes to the empirical research tradition of software vulnerabilities by a couple of insights on misuses of statistical methodology.


Title: A Note on Nesting in Dyadic Deontic Logic
Abstract: The paper reports on some results concerning Aqvist's dyadic logic known as system G, which is one of the most influential logics for reasoning with dyadic obligations ("it ought to be the case that ... if it is the case that ..."). Although this logic has been known in the literature for a while, many of its properties still await in-depth consideration. In this short paper we show: that any formula in system G including nested modal operators is equivalent to some formula with no nesting; that the universal modality introduced by Aqvist in the first presentation of the system is definable in terms of the deontic modality.


Title: ShapeAug: Occlusion Augmentation for Event Camera Data
Abstract: Recently, Dynamic Vision Sensors (DVSs) sparked a lot of interest due to their inherent advantages over conventional RGB cameras. These advantages include a low latency, a high dynamic range and a low energy consumption. Nevertheless, the processing of DVS data using Deep Learning (DL) methods remains a challenge, particularly since the availability of event training data is still limited. This leads to a need for event data augmentation techniques in order to improve accuracy as well as to avoid over-fitting on the training data. Another challenge especially in real world automotive applications is occlusion, meaning one object is hindering the view onto the object behind it. In this paper, we present a novel event data augmentation approach, which addresses this problem by introducing synthetic events for randomly moving objects in a scene. We test our method on multiple DVS classification datasets, resulting in an relative improvement of up to 6.5 % in top1-accuracy. Moreover, we apply our augmentation technique on the real world Gen1 Automotive Event Dataset for object detection, where we especially improve the detection of pedestrians by up to 5 %.


Title: Analyzing Misinformation Claims During the 2022 Brazilian General Election on WhatsApp, Twitter, and Kwai
Abstract: This study analyzes misinformation from WhatsApp, Twitter, and Kwai during the 2022 Brazilian general election. Given the democratic importance of accurate information during elections, multiple fact-checking organizations collaborated to identify and respond to misinformation via WhatsApp tiplines and power a fact-checking feature within a chatbot operated by Brazil's election authority, the TSE. WhatsApp is installed on over 99% of smartphones in Brazil, and the TSE chatbot was used by millions of citizens in the run-up to the elections. During the same period, we collected social media data from Twitter (now X) and Kwai (a popular video-sharing app similar to TikTok). Using the WhatsApp, Kwai, and Twitter data along with fact-checks from three Brazilian fact-checking organizations, we find unique claims on each platform. Even when the same claims are present on different platforms, they often differ in format, detail, length, or other characteristics. Our research highlights the limitations of current claim matching algorithms to match claims across platforms with such differences and identifies areas for further algorithmic development. Finally, we perform a descriptive analysis examining the formats (image, video, audio, text) and content themes of popular misinformation claims.


Title: Symmetry Breaking in Symmetric Tensor Decomposition
Abstract: In this note, we consider the highly nonconvex optimization problem associated with computing the rank decomposition of symmetric tensors. We formulate the invariance properties of the loss function and show that critical points detected by standard gradient based methods are \emph{symmetry breaking} with respect to the target tensor. The phenomena, seen for different choices of target tensors and norms, make possible the use of recently developed analytic and algebraic tools for studying nonconvex optimization landscapes exhibiting symmetry breaking phenomena of similar nature.


Title: Towards a Solution to Bongard Problems: A Causal Approach
Abstract: Even though AI has advanced rapidly in recent years displaying success in solving highly complex problems, the class of Bongard Problems (BPs) yet remain largely unsolved by modern ML techniques. In this paper, we propose a new approach in an attempt to not only solve BPs but also extract meaning out of learned representations. This includes the reformulation of the classical BP into a reinforcement learning (RL) setting which will allow the model to gain access to counterfactuals to guide its decisions but also explain its decisions. Since learning meaningful representations in BPs is an essential sub-problem, we further make use of contrastive learning for the extraction of low level features from pixel data. Several experiments have been conducted for analyzing the general BP-RL setup, feature extraction methods and using the best combination for the feature space analysis and its interpretation.


Title: Nilpotent dessins: Decomposition theorem and classification of the abelian dessins
Abstract: A map is a 2-cell decomposition of an orientable closed surface. A dessin is a bipartite map with a fixed colouring of vertices. A dessin is regular if its group of colour- and orientation-preserving automorphisms acts transitively on the edges, and a regular dessin is symmetric if it admits an additional external symmetry transposing the vertex colours. Regular dessins with nilpotent automorphism groups are investigated. We show that each such dessin is a parallel product of regular dessins whose automorphism groups are the Sylow subgroups. Regular and symmetric dessins with abelian automorphism groups are classified and enumerated.


Title: Strauss- and Lions-type results for a class of Orlicz-Sobolev spaces and applications
Abstract: The main goal this work is to prove two results like Strauss and Lions for Orlicz-Sobolev spaces. After, we use these results for study the existence of solutions for a class of quasilinear problems in $\mathbb{R}^{N}$.


Title: Planar Para Algebras, Reflection Positivity
Abstract: We define a planar para algebra, which arises naturally from combining planar algebras with the idea of $\mathbb{Z}_{N}$ para symmetry in physics. A subfactor planar para algebra is a Hilbert space representation of planar tangles with parafermionic defects, that are invariant under para isotopy. For each $\mathbb{Z}_{N}$, we construct a family of subfactor planar para algebras which play the role of Temperley-Lieb-Jones planar algebras. The first example in this family is the parafermion planar para algebra (PAPPA). Based on this example, we introduce parafermion Pauli matrices, quaternion relations, and braided relations for parafermion algebras which one can use in the study of quantum information. An important ingredient in planar para algebra theory is the string Fourier transform (SFT), that we use on the matrix algebra generated by the Pauli matrices. Two different reflections play an important role in the theory of planar para algebras. One is the adjoint operator; the other is the modular conjugation in Tomita-Takesaki theory. We use the latter one to define the double algebra and to introduce reflection positivity. We give a new and geometric proof of reflection positivity, by relating the two reflections through the string Fourier transform.


Title: Explore Human Parsing Modality for Action Recognition
Abstract: Multimodal-based action recognition methods have achieved high success using pose and RGB modality. However, skeletons sequences lack appearance depiction and RGB images suffer irrelevant noise due to modality limitations. To address this, we introduce human parsing feature map as a novel modality, since it can selectively retain effective semantic features of the body parts, while filtering out most irrelevant noise. We propose a new dual-branch framework called Ensemble Human Parsing and Pose Network (EPP-Net), which is the first to leverage both skeletons and human parsing modalities for action recognition. The first human pose branch feeds robust skeletons in graph convolutional network to model pose features, while the second human parsing branch also leverages depictive parsing feature maps to model parsing festures via convolutional backbones. The two high-level features will be effectively combined through a late fusion strategy for better action recognition. Extensive experiments on NTU RGB+D and NTU RGB+D 120 benchmarks consistently verify the effectiveness of our proposed EPP-Net, which outperforms the existing action recognition methods. Our code is available at: https://github.com/liujf69/EPP-Net-Action.


Title: Propagation of Chaos for Mean Field Interacting Particle System with Multiplicative Noise
Abstract: In this paper, the quantitative propagation of chaos for mean field interacting particle system with multiplicative noise in $L^2$-Wasserstein distance is derived. When the diffusion is distribution free, the quantitative propagation of chaos in relative entropy as well as total variation distance is also obtained, where the initial distribution of mean field interacting particles is allowed to be singular with that of the limit equation. Furthermore, a general result on the long time quantitative propagation of chaos in relative entropy as well as in $L^2$-Wasserstein distance is provided and is applied in (path dependent) mean field interacting particle system as well as stochastic Hamiltonian system under dissipative condition.


Title: General Berndt-Type Integrals and Series Associated with Jacobi Elliptic Functions
Abstract: n this paper, we prove two structural theorems on the general Berndt-type integrals with the denominator having arbitrary positive degrees by contour integrations involving hyperbolic and trigonometric functions, and hyperbolic sums associated with Jacobi elliptic functions. We first establish explicit relations between these integrals and four classes of hyperbolic sums. Then, using our previous results on hyperbolic series and applying the matrix method from linear algebra, we compute explicitly several general hyperbolic sums and their higher derivatives. These enable us to express two families of general Berndt-type integrals as polynomials in $\Gamma^4(1/4)$ and $\pi^{-1}$ with rational coefficients, where $\Gamma$ is the Euler gamma function. At the end of the paper, we provide some conjectures of general Berndt-type integrals.


Title: Cofinal elements and fractional Dehn twist coefficients
Abstract: We show that for a surface $S$ with positive genus and one boundary component, the mapping class of a Dehn twist along a curve parallel to the boundary is cofinal in every left ordering of the mapping class group $\operatorname{Mod}(S)$. We apply this result to show that one of the usual definitions of the fractional Dehn twist coefficient -- via translation numbers of a particular action of $\operatorname{Mod}(S)$ on $\mathbb{R}$ -- is in fact independent of the underlying action when $S$ has genus larger than one. As an algebraic counterpart to this, we provide a formula that recovers the fractional Dehn twist coefficient of a homeomorphism of $S$ from an arbitrary left ordering of $\operatorname{Mod}(S)$.


Title: Radial Laplacian on rotation groups
Abstract: The Laplacian on the rotation group is invariant by conjugation. Hence, it maps class functions to class functions. A maximal torus consists of block diagonal matrices whose blocks are planar rotations. Class functions are determined by their values of this maximal torus. Hence, the Laplacian induces a second order operator on the maximal torus called the radial Laplacian. In this paper, we derive the expression of the radial Laplacian. Then, we use it to find the eigenvalues of the Laplacian, using that characters are class functions whose expressions are given by the Weyl character formula. Although this material is familiar to Lie-group experts, we gather it here in a synthetic and accessible way which may be useful to non experts who need to work with these concepts.


Title: Directed polymers in a random environment: a review of the phase transitions
Abstract: The model of directed polymer in a random environment is a fundamental model of interaction between a simple random walk and ambient disorder. This interaction gives rise to complex phenomena and transitions from a central limit theory to novel statistical behaviours. Despite its intense study, there are still many aspects and phases which have not yet been identified. In this review we focus on the current status of our understanding of the transition between weak and strong disorder phases, give an account of some of the methods that the study of the model has motivated and highlight some open questions.


Title: A Feynman-Kac type formula for a fixed delay CIR model
Abstract: Stochastic delay differential equations (SDDE's) have been used for financial modeling. In this article, we study a SDDE obtained by the equation of a CIR process, with an additional fixed delay term in drift; in particular, we prove that there exists a unique strong solution (positive and integrable) which we call fixed delay CIR process. Moreover, for the fixed delay CIR process, we derive a Feynman-Kac type formula, leading to a generalized exponential-affine formula, which is used to determine a bond pricing formula when the interest rate follows the delay's equation. It turns out that, for each maturity time T, the instantaneous forward rate is an affine function (with time dependent coefficients) of the rate process and of an auxiliary process (also depending on T). The coefficients satisfy a system of deterministic delay differential equations.


Title: A note on Jones polynomial and cosmetic surgery
Abstract: We show that two Dehn surgeries on a knot $K$ never yield manifolds that are homeomorphic as oriented manifolds if $V_K''(1)\neq 0$ or $V_K'''(1)\neq 0$. As an application, we verify the cosmetic surgery conjecture for all knots with no more than $11$ crossings except for three $10$-crossing knots and five $11$-crossing knots. We also compute the finite type invariant of order $3$ for two-bridge knots and Whitehead doubles, from which we prove several nonexistence results of purely cosmetic surgery.


Title: Probabilistic Galois Theory in Function Fields
Abstract: We study the irreducibility and Galois group of random polynomials over function fields. We prove that a random polynomial $f=y^n+\sum_{i=0}^{n-1}a_i(x)y^i\in\mathbb F_q[x][y]$ with i.i.d coefficients $a_i$ taking values in the set $\{a(x)\in\mathbb{F}_q[x]: \mathrm{deg}\, a\leq d\}$ with uniform probability, is irreducible with probability tending to $1-\frac{1}{q^d}$ as $n\to\infty$, where $d$ and $q$ are fixed. We also prove that with the same probability, the Galois group of this random polynomial contains the alternating group $A_n$. Moreover, we prove that if we assume a version of the polynomial Chowla conjecture over $\mathbb{F}_q[x]$, then the Galois group of this polynomial is actually equal to the symmetric group $S_n$ with probability tending to $1-\frac{1}{q^d}$. We also study the other possible Galois groups occurring with positive limit probability. Finally, we study the same problems with $n$ fixed and $d\to\infty$.


Title: CPG graphs: Some structural and hardness results
Abstract: In this paper we continue the systematic study of Contact graphs of Paths on a Grid (CPG graphs) initiated in [Deniz et al., 2018]. A CPG graph is a graph for which there exists a collection of pairwise interiorly disjoint paths on a grid in one-to-one correspondence with its vertex set such that two vertices are adjacent if and only if the corresponding paths touch at a grid-point. If every such path has at most $k$ bends for some $k \geq 0$, the graph is said to be $B_k$-CPG. We first show that, for any $k \geq 0$, the class of $B_k$-CPG graphs is strictly contained in the class of $B_{k+1}$-CPG graphs even within the class of planar graphs, thus implying that there exists no $k \geq 0$ such that every planar CPG graph is $B_k$-CPG. The main result of the paper is that recognizing CPG graphs and $B_k$-CPG graphs with $k \geq 1$ is $\mathsf{NP}$-complete. Moreover, we show that the same remains true even within the class of planar graphs in the case $k \geq 3$. We then consider several graph problems restricted to CPG graphs and show, in particular, that Independent Set and Clique Cover remain $\mathsf{NP}$-hard for $B_0$-CPG graphs. Finally, we consider the related classes $B_k$-EPG of edge-intersection graphs of paths with at most $k$ bends on a grid. Although it is possible to optimally color a $B_0$-EPG graph in polynomial time, as this class coincides with that of interval graphs, we show that, in contrast, 3-Colorability is $\mathsf{NP}$-complete for $B_1$-EPG graphs.


Title: Early Record of Divisibility and Primality
Abstract: We provide textual evidence on divisibility and primality in the ancient Vedic texts of India. Concern with divisibility becomes clear from the listing of all the fifteen pairs of divisors of the number 720. The total number of pairs of divisors of 10,800 is also given. The motivation behind finding the divisors was the theory that the number of divisors of a certain periodic process is related to the count associated with some other periodic process. For example, 720 (days and nights of the year) has 15 pairs of divisors, and this was related to the 15 days of the waxing and waning of the moon. Numbers that have no divisors appeared to have been used to symbolize the "transcendent" that is beyond periodicity and change.


Title: Essential dimension via prismatic cohomology
Abstract: For $X$ a smooth, proper complex variety such that $h^{0,i}_X \neq 0,$ we show that for almost all primes $p,$ the restriction of the mod $p$ cohomology $H^i(X,\mathbb{F}_p)$ to any Zariski open is nonzero. The proof uses the prismatic cohomology of Bhatt-Scholze. We use this result to obtain lower bounds on the $p$-essential dimension of covers of complex varieties. For example, we prove the $p$-incompressibility of the mod $p$ homology cover of an abelian variety, confirming a conjecture of Brosnan for sufficiently large $p.$ By combining these techniques with the theory of toroidal compactifications of Shimura varieties, we show that for any Hermitian symmetric domain $X,$ there exist $p$-congruence covers that are $p$-incompressible.


Title: Involutions under Bruhat order and labeled Motzkin Paths
Abstract: In this note, we introduce a statistic on Motzkin paths that describes the rank generating function of Bruhat order for involutions. Our proof relies on a bijection introduced by Philippe Biane from permutations to certain labeled Motzkin paths and a recently introduced interpretation of this rank generating function in terms of visible inversions. By restricting our identity to fixed-point-free (FPF) involutions, we recover an identity due to Louis Billera, Lionel Levine and Karola M\'esz\'aros with a previous bijective proof by Matthew Watson. Our work sheds new light on the Ethiopian dinner game.


Title: Virtual critical regularity of mapping class group actions on the circle
Abstract: We show that if $G_1$ and $G_2$ are non-solvable groups, then no $C^{1,\tau}$ action of $(G_1\times G_2)*\mathbb{Z}$ on $S^1$ is faithful for $\tau>0$. As a corollary, if $S$ is an orientable surface of complexity at least three then the critical regularity of an arbitrary finite index subgroup of the mapping class group $\mathrm{Mod}(S)$ with respect to the circle is at most one, thus strengthening a result of the first two authors with Baik.


Title: Error Approximation and Bias Correction in Dynamic Problems using a Recurrent Neural Network/Finite Element Hybrid Model
Abstract: This work proposes a hybrid modeling framework based on recurrent neural networks (RNNs) and the finite element (FE) method to approximate model discrepancies in time dependent, multi-fidelity problems, and use the trained hybrid models to perform bias correction of the low-fidelity models. The hybrid model uses FE basis functions as a spatial basis and RNNs for the approximation of the time dependencies of the FE basis' degrees of freedom. The training data sets consist of sparse, non-uniformly sampled snapshots of the discrepancy function, pre-computed from trajectory data of low- and high-fidelity dynamic FE models. To account for data sparsity and prevent overfitting, data upsampling and local weighting factors are employed, to instigate a trade-off between physically conforming model behavior and neural network regression. The proposed hybrid modeling methodology is showcased in three highly non-trivial engineering test-cases, all featuring transient FE models, namely, heat diffusion out of a heat sink, eddy-currents in a quadrupole magnet, and sound wave propagation in a cavity. The results show that the proposed hybrid model is capable of approximating model discrepancies to a high degree of accuracy and accordingly correct low-fidelity models.


Title: Human-in-the-Loop Policy Optimization for Preference-Based Multi-Objective Reinforcement Learning
Abstract: Multi-objective reinforcement learning (MORL) aims to find a set of high-performing and diverse policies that address trade-offs between multiple conflicting objectives. However, in practice, decision makers (DMs) often deploy only one or a limited number of trade-off policies. Providing too many diversified trade-off policies to the DM not only significantly increases their workload but also introduces noise in multi-criterion decision-making. With this in mind, we propose a human-in-the-loop policy optimization framework for preference-based MORL that interactively identifies policies of interest. Our method proactively learns the DM's implicit preference information without requiring any a priori knowledge, which is often unavailable in real-world black-box decision scenarios. The learned preference information is used to progressively guide policy optimization towards policies of interest. We evaluate our approach against three conventional MORL algorithms that do not consider preference information and four state-of-the-art preference-based MORL algorithms on two MORL environments for robot control and smart grid management. Experimental results fully demonstrate the effectiveness of our proposed method in comparison to the other peer algorithms.


Title: The compressible Euler equations in a physical vacuum: a comprehensive Eulerian approach
Abstract: This article is concerned with the local well-posedness problem for the compressible Euler equations in gas dynamics. For this system we consider the free boundary problem which corresponds to a physical vacuum. Despite the clear physical interest in this system, the prior work on this problemis limited to Lagrangian coordinates, in high regularity spaces. Instead, the objective of the present work is to provide a new, fully Eulerian approach to this problem, which provides a complete, Hadamard style well-posedness theory for this problem in low regularity Sobolev spaces. In particular we give new proofs for both existence, uniqueness, and continuous dependence on the data with sharp, scale invariant energy estimates, and continuation criterion.


Title: Fractional hypergraph isomorphism and fractional invariants
Abstract: Fractional graph isomorphism is the linear relaxation of an integer programming formulation of graph isomorphism. It preserves some invariants of graphs, like degree sequences and equitable partitions, but it does not preserve others like connectivity, clique and independence numbers, chromatic number, vertex and edge cover numbers, matching number, domination and total domination numbers. In this work, we extend the concept of fractional graph isomorphism to hypergraphs, and give an alternative characterization, analogous to one of those that are known for graphs. With this new concept we prove that the fractional packing, covering, matching and transversal numbers on hypergraphs are invariant under fractional hypergraph isomorphism. As a consequence, fractional matching, vertex and edge cover, independence, domination and total domination numbers are invariant under fractional graph isomorphism. This is not the case of fractional chromatic, clique, and clique cover numbers. In this way, most of the classical fractional parameters are classified with respect to their invariance under fractional graph isomorphism.


Title: On the heteroclinic connection problem for multi-well gradient systems
Abstract: We revisit the existence problem of heteroclinic connections in $\mathbb{R}^N$ associated with Hamiltonian systems involving potentials $W:\mathbb{R}^N\to \mathbb{R}$ having several global minima. Under very mild assumptions on $W$ we present a simple variational approach to first find geodesics minimizing length of curves joining any two of the potential wells, where length is computed with respect to a degenerate metric having conformal factor $\sqrt{W}.$ Then we show that when such a minimizing geodesic avoids passing through other wells of the potential at intermediate times, it gives rise to a heteroclinic connection between the two wells. This work improves upon the approach of P.Sternberg in $\texttt{Vector-valued local minimizers of nonconvex}$ $\texttt{variational problems}$, and represents a more geometric alternative to the approaches for finding such connections described, for example, by N.D. Alikakos and G.Fusco in $\texttt{On the connection problem for potentials with}$ $\texttt{several global minima}$, by S.V. Bolotin in $\texttt{Libration motions of natural dynamical systems}$, by J. Byeon, P. Montecchiari, and P. Rabinowitz in $\texttt{A double well potential}$ $\texttt{system}$, and by P. Rabinowitz in $\texttt{Homoclinic and heteroclinic orbits for a class of Hamiltonian}$ $\texttt{systems}$.


Title: Nested homotopy models of finite metric spaces and their spectral homology
Abstract: For a real $r\geq 0,$ we consider the notion of $r$-homotopy equivalence in the category quasimetric spaces, which includes metric spaces and directed graphs. We show that for a finite quasimetric space $X$ there is a unique (up to isometry) $r$-homotopy equivalent quasimetric space of the minimal possible cardinality. It is called $r$-minimal model of $X$. We use this to construct a decomposition of the magnitude-path spectral sequence of a digraph into a direct sum of spectral sequences with certain properties. We also construct an $r$-homotopy invariant ${\rm SH}^r_{n,I}(X)$ of a quasimetric space $X,$ called spectral homology, that generalises many other invariants: the pages of the magnitude-path spectral sequence, including path homology, magnitude homology, blurred magnitude homology and reachability homology.


Title: Group theoretic approach to cyclic cubic fields
Abstract: Let (k1,k2,k3,k4) be a quartet of cyclic cubic number fields sharing a common conductor c=pqr divisible by exactly three prime(power)s p,q,r. For those components k of the quartet whose 3-class group Cl(3,k) = Z/3Z x Z/3Z is elementary bicyclic, the automorphism group M = Gal(F(3,2,k)/k) of the maximal metabelian unramified 3-extension of k is determined by conditions for cubic residue symbols between p,q,r and for ambiguous principal ideals in subfields of the common absolute 3-genus field k* of k1,k2,k3,k4. With the aid of the relation rank d2(M), it is decided whether M coincides with the Galois group G = Gal(F(3,infinity,k)/k) of the maximal unramified pro-3-extension of k.


Title: Reciprocity between partitions and compositions
Abstract: In this paper, we extend the work of Andrews, Beck and Hopkins by considering partitions and compositions with bounded gaps between each pair of consecutive parts. We show that both their generating functions and two matrices determined by them satisfy certain reciprocal relations.


Title: The dimension of ergodic random sequences
Abstract: Let \mu be a computable ergodic shift-invariant measure over the Cantor space. Providing a constructive proof of Shannon-McMillan-Breiman theorem, V'yugin proved that if a sequence x is Martin-L\"of random w.r.t. \mu then the strong effective dimension Dim(x) of x equals the entropy of \mu. Whether its effective dimension dim(x) also equals the entropy was left as an problem question. In this paper we settle this problem, providing a positive answer. A key step in the proof consists in extending recent results on Birkhoff's ergodic theorem for Martin-L\"of random sequences.


Title: Implications of some mass-capacity inequalities
Abstract: Applying a family of mass-capacity related inequalities proved in \cite{M22}, we obtain sufficient conditions that imply the nonnegativity as well as positive lower bounds of the mass, on a class of manifolds with nonnegative scalar curvature with or without a singularity.


Title: Asymptotic Stability for Relativistic Vlasov-Maxwell-Landau System in Bounded Domain
Abstract: The control of plasma-wall interaction is one of the keys in a fusion device from both physical and mathematical standpoints. A classical perfect conducting boundary causes the Lorentz force to penetrate inside the domain, which may lead to grazing set singularity in the phase space, preventing the construction of global dynamics for PDEs in any kinetic plasma models. We establish the first global asymptotic stability for the relativistic Vlasov-Maxwell-Landau system for describing a collisional plasma specularly reflected at a perfect conducting boundary.


Title: Edge ideals of some edge-weighted graphs
Abstract: This paper presents exact formulas for the regularity and depth of powers of edge ideals of an edge-weighted star graph. Additionally, we provide exact formulas for the regularity of powers of the edge ideal of an edge-weighted integrally closed path, as well as lower bounds on the depth of powers of such an edge ideal.


Title: Integer-Forcing Message Recovering in Interference Channels
Abstract: In this paper, we propose a scheme referred to as integer-forcing message recovering (IFMR) to enable receivers to recover their desirable messages in interference channels. Compared to the state-of-the- art integer-forcing linear receiver (IFLR), our proposed IFMR approach needs to decode considerably less number of messages. In our method, each receiver recovers independent linear integer combinations of the desirable messages each from two independent equations. We propose an efficient algorithm to sequentially find the equations and integer combinations with maximum rates. We evaluate the performance of our scheme and compare the results with the minimum mean-square error (MMSE) and zero-forcing (ZF), as well as the IFLR schemes. The results indicate that our IFMR scheme outperforms the MMSE and ZF schemes, in terms of achievable rate, considerably. Also, compared to IFLR, the IFMR scheme achieves slightly less rates in moderate signal-to-noise ratios, with significantly less implementation complexity.