Title: The combinatorics of Farey words and their traces
Abstract: The set of Kleinian groups which are free on two parabolic generators is parameterised by the closed Riley slice of Schottky space. A Farey word is a word in such a group which represents a non-boundary-parallel geodesic that can be pinched down to a puncture; in the interior of the Riley slice such a word is loxodromic, and the pinching process corresponds to deforming the word to be parabolic. Keen and Series showed that the geometry of the Riley slice is detected by the real loci of the trace polynomials of these words. We study these trace polynomials from a combinatorial viewpoint, and give a recursion formula for them which enables efficient calculation of the polynomials without performing matrix multiplication; we also present some intriguing examples to show that there is much still to be learned about them.


Title: An entropy bound due to symmetries
Abstract: Let $H$ be a local net of real Hilbert subspaces of a complex Hilbert space on the family of double cones of the spacetime $\mathbb{R}^{d+1}$, covariant with respect to a positive energy, unitary representation $U$ of the Poincar\'e group, with the Bisognano-Wichmann property for the wedge modular group. We set an upper bound on the local entropy $S_H(\phi|\! | C)$ of a vector in a region $C$ that depends only on $U$ and the PCT anti-unitary canonically associated with $H$. A similar result holds for local, M\"obius covariant nets of standard subspaces on the circle. We compute the entropy increase and illustrate this bound for the nets associated with the $U(1)$-current derivatives.


Title: Inferring relevant features: from QFT to PCA
Abstract: In many-body physics, renormalization techniques are used to extract aspects of a statistical or quantum state that are relevant at large scale, or for low energy experiments. Recent works have proposed that these features can be formally identified as those perturbations of the states whose distinguishability most resist coarse-graining. Here, we examine whether this same strategy can be used to identify important features of an unlabeled dataset. This approach indeed results in a technique very similar to kernel PCA (principal component analysis), but with a kernel function that is automatically adapted to the data, or "learned". We test this approach on handwritten digits, and find that the most relevant features are significantly better for classification than those obtained from a simple gaussian kernel.


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: Center of Mass Technique and Affine Geometry
Abstract: The notion of center of mass, which is very useful in kinematics, proves to be very handy in geometry (see [1]-[2]). Countless applications of center of mass to geometry go back to Archimedes. Unfortunately, the center of mass cannot be defined for sets whose total mass equals zero. In the paper we improve this disadvantage and assign to an n-dimensional affine space L over any field k the (n+1)-dimensional vector space over the field k of weighty points and mass dipoles in L. In this space, the sum of weighted points with nonzero total mass is equal to the center of mass of these points equipped with their total mass. We present several interpretations of the space of weighty points and mass dipoles in L, and a couple of its applications to geometry. The paper is self-contained and is accessible for undergraduate students.


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: Investigating EEG-Based Functional Connectivity Patterns for Multimodal Emotion Recognition
Abstract: Compared with the rich studies on the motor brain-computer interface (BCI), the recently emerging affective BCI presents distinct challenges since the brain functional connectivity networks involving emotion are not well investigated. Previous studies on emotion recognition based on electroencephalography (EEG) signals mainly rely on single-channel-based feature extraction methods. In this paper, we propose a novel emotion-relevant critical subnetwork selection algorithm and investigate three EEG functional connectivity network features: strength, clustering coefficient, and eigenvector centrality. The discrimination ability of the EEG connectivity features in emotion recognition is evaluated on three public emotion EEG datasets: SEED, SEED-V, and DEAP. The strength feature achieves the best classification performance and outperforms the state-of-the-art differential entropy feature based on single-channel analysis. The experimental results reveal that distinct functional connectivity patterns are exhibited for the five emotions of disgust, fear, sadness, happiness, and neutrality. Furthermore, we construct a multimodal emotion recognition model by combining the functional connectivity features from EEG and the features from eye movements or physiological signals using deep canonical correlation analysis. The classification accuracies of multimodal emotion recognition are 95.08/6.42% on the SEED dataset, 84.51/5.11% on the SEED-V dataset, and 85.34/2.90% and 86.61/3.76% for arousal and valence on the DEAP dataset, respectively. The results demonstrate the complementary representation properties of the EEG connectivity features with eye movement data. In addition, we find that the brain networks constructed with 18 channels achieve comparable performance with that of the 62-channel network in multimodal emotion recognition and enable easier setups for BCI systems in real scenarios.


Title: Microlocal Morse theory of wrapped Fukaya categories
Abstract: The Nadler--Zaslow correspondence famously identifies the finite-dimensional Floer homology groups between Lagrangians in cotangent bundles with the finite-dimensional Hom spaces between corresponding constructible sheaves. We generalize this correspondence to incorporate the infinite-dimensional spaces of morphisms 'at infinity', given on the Floer side by Reeb trajectories (also known as "wrapping") and on the sheaf side by allowing unbounded infinite rank sheaves which are categorically compact. When combined with existing sheaf theoretic computations, our results confirm many new instances of homological mirror symmetry. More precisely, given a real analytic manifold $M$ and a subanalytic isotropic subset $\Lambda$ of its co-sphere bundle $S^*M$, we show that the partially wrapped Fukaya category of $T^*M$ stopped at $\Lambda$ is equivalent to the category of compact objects in the unbounded derived category of sheaves on $M$ with microsupport inside $\Lambda$. By an embedding trick, we also deduce a sheaf theoretic description of the wrapped Fukaya category of any Weinstein sector admitting a stable polarization.


Title: Unsupervised learning from videos using temporal coherency deep networks
Abstract: In this work we address the challenging problem of unsupervised learning from videos. Existing methods utilize the spatio-temporal continuity in contiguous video frames as regularization for the learning process. Typically, this temporal coherence of close frames is used as a free form of annotation, encouraging the learned representations to exhibit small differences between these frames. But this type of approach fails to capture the dissimilarity between videos with different content, hence learning less discriminative features. We here propose two Siamese architectures for Convolutional Neural Networks, and their corresponding novel loss functions, to learn from unlabeled videos, which jointly exploit the local temporal coherence between contiguous frames, and a global discriminative margin used to separate representations of different videos. An extensive experimental evaluation is presented, where we validate the proposed models on various tasks. First, we show how the learned features can be used to discover actions and scenes in video collections. Second, we show the benefits of such an unsupervised learning from just unlabeled videos, which can be directly used as a prior for the supervised recognition tasks of actions and objects in images, where our results further show that our features can even surpass a traditional and heavily supervised pre-training plus fine-tunning strategy.


Title: Hilbert modular forms and Galois representations
Abstract: In this expository article, we present a brief introduction to the theory of Hilbert modular forms and Galois representations, and describe what it means to attach a compatible system of Galois representations to a Hilbert modular form.


Title: Boundary regularity of stochastic PDEs
Abstract: The boundary behaviour of solutions of stochastic PDEs with Dirichlet boundary conditions can be surprisingly - and in a sense, arbitrarily - bad: as shown by Krylov, for any $\alpha>0$ one can find a simple $1$-dimensional constant coefficient linear equation whose solution at the boundary is not $\alpha$-H\"older continuous. We obtain a positive counterpart of this: under some mild regularity assumptions on the coefficients, solutions of semilinear SPDEs on $C^1$ domains are proved to be $\alpha$-H\"older continuous up to the boundary with some $\alpha>0$.


Title: Beyond Self-Promotion: How Software Engineering Research Is Discussed on LinkedIn
Abstract: LinkedIn is the largest professional network in the world. As such, it can serve to build bridges between practitioners, whose daily work is software engineering (SE), and researchers, who work to advance the field of software engineering. We know that such a metaphorical bridge exists: SE research findings are sometimes shared on LinkedIn and commented on by software practitioners. Yet, we do not know what state the bridge is in. Therefore, we quantitatively and qualitatively investigate how SE practitioners and researchers approach each other via public LinkedIn discussions and what both sides can contribute to effective science communication. We found that a considerable proportion of LinkedIn posts on SE research are written by people who are not the paper authors (39%). Further, 71% of all comments in our dataset are from people in the industry, but only every second post receives at least one comment at all. Based on our findings, we formulate concrete advice for researchers and practitioners to make sharing new research findings on LinkedIn more fruitful.


Title: Singular metrics and a conjecture by Campana and Peternell
Abstract: A conjecture by Campana and Peternell says that if a positive multiple of $K_X$ is linearly equivalent to an effective divisor $D$ plus a pseudo-effective divisor, then the Kodaira dimension of $X$ should be at least as big as the Iitaka dimension of $D$. This is a very useful generalization of the non-vanishing conjecture (which is the case $D = 0$). We use recent work about singular metrics on pluri-adjoint bundles to show that the Campana-Peternell conjecture is almost equivalent to the non-vanishing conjecture.


Title: Perceptual Musical Features for Interpretable Audio Tagging
Abstract: In the age of music streaming platforms, the task of automatically tagging music audio has garnered significant attention, driving researchers to devise methods aimed at enhancing performance metrics on standard datasets. Most recent approaches rely on deep neural networks, which, despite their impressive performance, possess opacity, making it challenging to elucidate their output for a given input. While the issue of interpretability has been emphasized in other fields like medicine, it has not received attention in music-related tasks. In this study, we explored the relevance of interpretability in the context of automatic music tagging. We constructed a workflow that incorporates three different information extraction techniques: a) leveraging symbolic knowledge, b) utilizing auxiliary deep neural networks, and c) employing signal processing to extract perceptual features from audio files. These features were subsequently used to train an interpretable machine-learning model for tag prediction. We conducted experiments on two datasets, namely the MTG-Jamendo dataset and the GTZAN dataset. Our method surpassed the performance of baseline models in both tasks and, in certain instances, demonstrated competitiveness with the current state-of-the-art. We conclude that there are use cases where the deterioration in performance is outweighed by the value of interpretability.


Title: Answers to Two Questions on the DP Color Function
Abstract: DP-coloring is a generalization of list coloring that was introduced in 2015 by Dvo\v{r}\'{a}k and Postle. The chromatic polynomial of a graph is a notion that has been extensively studied since the early 20th century. The chromatic polynomial of graph $G$ is denoted $P(G,m)$, and it is equal to the number of proper $m$-colorings of $G$. In 2019, Kaul and Mudrock introduced an analogue of the chromatic polynomial for DP-coloring; specifically, the DP color function of graph $G$ is denoted $P_{DP}(G,m)$. Two fundamental questions posed by Kaul and Mudrock are: (1) For any graph $G$ with $n$ vertices, is it the case that $P(G,m)-P_{DP}(G,m) = O(m^{n-3})$ as $m \rightarrow \infty$? and (2) For every graph $G$, does there exist $p,N \in \mathbb{N}$ such that $P_{DP}(K_p \vee G, m) = P(K_p \vee G, m)$ whenever $m \geq N$? We show that the answer to both these questions is yes. In fact, we show the answer to (2) is yes even if we require $p=1$.


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: Generalized Modularity Embedding: a General Framework for Network Embedding
Abstract: The network embedding problem aims to map nodes that are similar to each other to vectors in a Euclidean space that are close to each other. Like centrality analysis (ranking) and community detection, network embedding is in general considered as an ill-posed problem, and its solution may depend on a person's view on this problem. In this book chapter, we adopt the framework of sampled graphs that treat a person's view as a sampling method for a network. The modularity for a sampled graph, called the generalized modularity in the book chapter, is a similarity matrix that has a specific probabilistic interpretation. One of the main contributions of this book chapter is to propose using the generalized modularity matrix for network embedding and show that the network embedding problem can be treated as a trace maximization problem like the community detection problem. Our generalized modularity embedding approach is very general and flexible. In particular, we show that the Laplacian eigenmaps is a special case of our generalized modularity embedding approach. Also, we show that dimensionality reduction can be done by using a particular sampled graph. Various experiments are conducted on real datasets to illustrate the effectiveness of our approach.


Title: The singular limit of the Water-Waves equations in the rigid lid regime
Abstract: The re-scaled Water-Waves equations depend strongly on the ratio epsilon between the amplitude of the wave and the depth of the water. We investigate in this paper the convergence as epsilon goes to zero of the free surface Euler equations to the so called rigid lid model. We first prove that the only solutions of this model are zero. Due to the conservation of the Hamiltonian, the solutions of the free surface Euler equations converge weakly to zero, but not strongly in the general case, as epsilon goes to zero. We then study this default of convergence. More precisely, we show a strong convergence result of the solutions of the water waves equations in the Zakharov-Craig-Sulem formulation to the solutions of the linear water-waves equations. It is then easy to observe that these latter converge weakly to zero. The simple structure of this system also allows us to explain the mechanisms of the weak convergence to zero. Finally, we show that this convergence to the rigid lid model also holds for the solutions of the Euler equations. To this end we give a new proof of the equivalence of the free surface Euler equations and of the Zakharov-Craig-Sulem equation by building an extension of the velocity and pressure fields.


Title: Mid-point embedding of Hamiltonian systems and variational integrators
Abstract: Following the discrete embedding formalism, we give a new derivation of the mid-point variational integrators as developed by J.M. Wendlandt and J.E. Marsden by defining an adapted order two discrete differential and integral calculus. This allows us to obtain a clearer correspondence between the discrete and continuous case. We also discuss the corresponding definition of a discrete Hamiltonian system. A complete comparaison with the results of J.M. Wendlandt and J.E. Marsden is provided.


Title: Federated Calibration and Evaluation of Binary Classifiers
Abstract: We address two major obstacles to practical use of supervised classifiers on distributed private data. Whether a classifier was trained by a federation of cooperating clients or trained centrally out of distribution, (1) the output scores must be calibrated, and (2) performance metrics must be evaluated -- all without assembling labels in one place. In particular, we show how to perform calibration and compute precision, recall, accuracy and ROC-AUC in the federated setting under three privacy models (i) secure aggregation, (ii) distributed differential privacy, (iii) local differential privacy. Our theorems and experiments clarify tradeoffs between privacy, accuracy, and data efficiency. They also help decide whether a given application has sufficient data to support federated calibration and evaluation.


Title: Cyclic codes from low differentially uniform functions
Abstract: Cyclic codes have many applications in consumer electronics, communication and data storage systems due to their efficient encoding and decoding algorithms. An efficient approach to constructing cyclic codes is the sequence approach. In their articles [Discrete Math. 321, 2014] and [SIAM J. Discrete Math. 27(4), 2013], Ding and Zhou constructed several classes of cyclic codes from almost perfect nonlinear (APN) functions and planar functions over finite fields and presented some open problems on cyclic codes from highly nonlinear functions. This article focuses on these exciting works by investigating new insights in this research direction. Specifically, its objective is twofold. The first is to provide a complement with some former results and present correct proofs and statements on some known ones on the cyclic codes from the APN functions. The second is studying the cyclic codes from some known functions processing low differential uniformity. Along with this article, we shall provide answers to some open problems presented in the literature. The first one concerns Open Problem 1, proposed by Ding and Zhou in Discrete Math. 321, 2014. The two others are Open Problems 5.16 and 5.25, raised by Ding in [SIAM J. Discrete Math. 27(4), 2013].


Title: The relation between Granger causality and directed information theory: a review
Abstract: This report reviews the conceptual and theoretical links between Granger causality and directed information theory. We begin with a short historical tour of Granger causality, concentrating on its closeness to information theory. The definitions of Granger causality based on prediction are recalled, and the importance of the observation set is discussed. We present the definitions based on conditional independence. The notion of instantaneous coupling is included in the definitions. The concept of Granger causality graphs is discussed. We present directed information theory from the perspective of studies of causal influences between stochastic processes. Causal conditioning appears to be the cornerstone for the relation between information theory and Granger causality. In the bivariate case, the fundamental measure is the directed information, which decomposes as the sum of the transfer entropies and a term quantifying instantaneous coupling. We show the decomposition of the mutual information into the sums of the transfer entropies and the instantaneous coupling measure, a relation known for the linear Gaussian case. We study the multivariate case, showing that the useful decomposition is blurred by instantaneous coupling. The links are further developed by studying how measures based on directed information theory naturally emerge from Granger causality inference frameworks as hypothesis testing.


Title: A Distributed SDN Control Plane for Consistent Policy Updates
Abstract: Software-defined networking (SDN) is a novel paradigm that out-sources the control of packet-forwarding switches to a set of software controllers. The most fundamental task of these controllers is the correct implementation of the \emph{network policy}, i.e., the intended network behavior. In essence, such a policy specifies the rules by which packets must be forwarded across the network. This paper studies a distributed SDN control plane that enables \emph{concurrent} and \emph{robust} policy implementation. We introduce a formal model describing the interaction between the data plane and a distributed control plane (consisting of a collection of fault-prone controllers). Then we formulate the problem of \emph{consistent} composition of concurrent network policy updates (short: the \emph{CPC Problem}). To anticipate scenarios in which some conflicting policy updates must be rejected, we enable the composition via a natural \emph{transactional} interface with all-or-nothing semantics. We show that the ability of an $f$-resilient distributed control plane to process concurrent policy updates depends on the tag complexity, i. e., the number of policy labels (a.k.a. \emph{tags}) available to the controllers, and describe a CPC protocol with optimal tag complexity $f+2$.


Title: Design and Implementation Considerations for a Virtual File System Using an Inode Data Structure
Abstract: Virtual file systems are a tool to centralize and mobilize a file system that could otherwise be complex and consist of multiple hierarchies, hard disks, and more. In this paper, we discuss the design of Unix-based file systems and how this type of file system layout using inode data structures and a disk emulator can be implemented as a single-file virtual file system in Linux. We explore the ways that virtual file systems are vulnerable to security attacks and introduce straightforward solutions that can be implemented to help prevent or mitigate the consequences of such attacks.


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: Implementation Notes for the Soft Cosine Measure
Abstract: The standard bag-of-words vector space model (VSM) is efficient, and ubiquitous in information retrieval, but it underestimates the similarity of documents with the same meaning, but different terminology. To overcome this limitation, Sidorov et al. proposed the Soft Cosine Measure (SCM) that incorporates term similarity relations. Charlet and Damnati showed that the SCM is highly effective in question answering (QA) systems. However, the orthonormalization algorithm proposed by Sidorov et al. has an impractical time complexity of $\mathcal O(n^4)$, where n is the size of the vocabulary. In this paper, we prove a tighter lower worst-case time complexity bound of $\mathcal O(n^3)$. We also present an algorithm for computing the similarity between documents and we show that its worst-case time complexity is $\mathcal O(1)$ given realistic conditions. Lastly, we describe implementation in general-purpose vector databases such as Annoy, and Faiss and in the inverted indices of text search engines such as Apache Lucene, and ElasticSearch. Our results enable the deployment of the SCM in real-world information retrieval systems.


Title: Applications of machine learning and IoT for Outdoor Air Pollution Monitoring and Prediction: A Systematic Literature Review
Abstract: According to the World Health Organization (WHO), air pollution kills seven million people every year. Outdoor air pollution is a major environmental health problem affecting low, middle, and high-income countries. In the past few years, the research community has explored IoT-enabled machine learning applications for outdoor air pollution prediction. The general objective of this paper is to systematically review applications of machine learning and Internet of Things (IoT) for outdoor air pollution prediction and the combination of monitoring sensors and input features used. Two research questions were formulated for this review. 1086 publications were collected in the initial PRISMA stage. After the screening and eligibility phases, 37 papers were selected for inclusion. A cost-based analysis was conducted on the findings to highlight high-cost monitoring, low-cost IoT and hybrid enabled prediction. Three methods of prediction were identified: time series, feature-based and spatio-temporal. This review's findings identify major limitations in applications found in the literature, namely lack of coverage, lack of diversity of data and lack of inclusion of context-specific features. This review proposes directions for future research and underlines practical implications in healthcare, urban planning, global synergy and smart cities.


Title: Returns to the origin of the Pólya walk with stochastic resetting
Abstract: We consider the simple random walk (or P\'olya walk) on the one-dimensional lattice subject to stochastic resetting to the origin with probability $r$ at each time step. The focus is on the joint statistics of the numbers ${\mathcal{N}}_t^{\times}$ of spontaneous returns of the walker to the origin and ${\mathcal{N}}_t^{\bullet}$ of resetting events up to some observation time $t$. These numbers are extensive in time in a strong sense: all their joint cumulants grow linearly in $t$, with explicitly computable amplitudes, and their fluctuations are described by a smooth bivariate large deviation function. A non-trivial crossover phenomenon takes place in the regime of weak resetting and late times. Remarkably, the time intervals between spontaneous returns to the origin of the reset random walk form a renewal process described in terms of a single `dressed' probability distribution. These time intervals are probabilistic copies of the first one, the `dressed' first-passage time. The present work follows a broader study, covered in a companion paper, on general nested renewal processes.


Title: Universality in block dependent linear models with applications to nonparametric regression
Abstract: Over the past decade, characterizing the exact asymptotic risk of regularized estimators in high-dimensional regression has emerged as a popular line of work. This literature considers the proportional asymptotics framework, where the number of features and samples both diverge, at a rate proportional to each other. Substantial work in this area relies on Gaussianity assumptions on the observed covariates. Further, these studies often assume the design entries to be independent and identically distributed. Parallel research investigates the universality of these findings, revealing that results based on the i.i.d.~Gaussian assumption extend to a broad class of designs, such as i.i.d.~sub-Gaussians. However, universality results examining dependent covariates so far focused on correlation-based dependence or a highly structured form of dependence, as permitted by right rotationally invariant designs. In this paper, we break this barrier and study a dependence structure that in general falls outside the purview of these established classes. We seek to pin down the extent to which results based on i.i.d.~Gaussian assumptions persist. We identify a class of designs characterized by a block dependence structure that ensures the universality of i.i.d.~Gaussian-based results. We establish that the optimal values of the regularized empirical risk and the risk associated with convex regularized estimators, such as the Lasso and ridge, converge to the same limit under block dependent designs as they do for i.i.d.~Gaussian entry designs. Our dependence structure differs significantly from correlation-based dependence, and enables, for the first time, asymptotically exact risk characterization in prevalent nonparametric regression problems in high dimensions. Finally, we illustrate through experiments that this universality becomes evident quite early, even for relatively moderate sample sizes.


Title: On the Composability of Statistically Secure Random Oblivious Transfer
Abstract: We show that stand-alone statistically secure random oblivious transfer protocols based on two-party stateless primitives are statistically universally composable. I.e. they are simulatable secure with an unlimited adversary, an unlimited simulator and an unlimited environment machine. Our result implies that several previous oblivious transfer protocols in the literature which were proven secure under weaker, non-composable definitions of security can actually be used in arbitrary statistically secure applications without lowering the security.


Title: Performance Analysis of Clustered LoRa Networks
Abstract: In this paper, we investigate the uplink transmission performance of low-power wide-area (LPWA) networks with regards to coexisting radio modules. We adopt long range (LoRa) radio technique as an example of the network of focus even though our analysis can be easily extended to other situations. We exploit a new topology to model the network, where the node locations of LoRa follow a Poisson cluster process (PCP) while other coexisting radio modules follow a Poisson point process (PPP). Unlike most of the performance analysis based on stochastic geometry, we take noise into consideration. More specifically, two models, with a fixed and a random number of active LoRa nodes in each cluster, respectively, are considered. To obtain insights, both the exact and simple approximated expressions for coverage probability are derived. Based on them, area spectral efficiency and energy efficiency are obtained. From our analysis, we show how the performance of LPWA networks can be enhanced through adjusting the density of LoRa nodes around each LoRa receiver. Moreover, the simulation results unveil that the optimal number of active LoRa nodes in each cluster exists to maximize the area spectral efficiency.


Title: An Equivariant Tensor Product on Mackey Functors
Abstract: For all subgroups $H$ of a cyclic $p$-group $G$ we define norm functors that build a $G$-Mackey functor from an $H$-Mackey functor. We give an explicit construction of these functors in terms of generators and relations based solely on the intrinsic, algebraic properties of Mackey functors and Tambara functors. We use these norm functors to define a monoidal structure on the category of Mackey functors where Tambara functors are the commutative ring objects.


Title: Membrane-Dependent Neuromorphic Learning Rule for Unsupervised Spike Pattern Detection
Abstract: Several learning rules for synaptic plasticity, that depend on either spike timing or internal state variables, have been proposed in the past imparting varying computational capabilities to Spiking Neural Networks. Due to design complications these learning rules are typically not implemented on neuromorphic devices leaving the devices to be only capable of inference. In this work we propose a unidirectional post-synaptic potential dependent learning rule that is only triggered by pre-synaptic spikes, and easy to implement on hardware. We demonstrate that such a learning rule is functionally capable of replicating computational capabilities of pairwise STDP. Further more, we demonstrate that this learning rule can be used to learn and classify spatio-temporal spike patterns in an unsupervised manner using individual neurons. We argue that this learning rule is computationally powerful and also ideal for hardware implementations due to its unidirectional memory access.


Title: High order Lagrange-Galerkin methods for the conservative formulation of the advection-diffusion equation
Abstract: We introduce in this paper the numerical analysis of high order both in time and space Lagrange-Galerkin methods for the conservative formulation of the advection-diffusion equation. As time discretization scheme we consider the Backward Differentiation Formulas up to order $q=5$. The development and analysis of the methods are performed in the framework of time evolving finite elements presented in C. M. Elliot and T. Ranner, IMA Journal of Numerical Analysis \textbf{41}, 1696-1845 (2021). The error estimates show through their dependence on the parameters of the equation the existence of different regimes in the behavior of the numerical solution; namely, in the diffusive regime, that is, when the diffusion parameter $\mu$ is large, the error is $O(h^{k+1}+\Delta t^{q})$, whereas in the advective regime, $\mu \ll 1$, the convergence is $O(\min (h^{k},\frac{h^{k+1} }{\Delta t})+\Delta t^{q})$. It is worth remarking that the error constant does not have exponential $\mu ^{-1}$ dependence.


Title: Penalty Parameter Selection in Deconvolution by Estimating the Risk for a Smaller Sample Size
Abstract: We address the choice of penalty parameter in the Smoothness-Penalized Deconvolution (SPeD) method of estimating a probability density under additive measurement error. Cross-validation gives an unbiased estimate of the risk (for the present sample size n) with a given penalty parameter, and this function can be minimized as a function of the penalty parameter. Least-squares cross-validation, which has been proposed for the similar Deconvoluting Kernel Density Estimator (DKDE), performs quite poorly for SPeD. We instead estimate the risk function for a smaller sample size n_1 < n with a given penalty parameter, using this to choose the penalty parameter for sample size n_1, and then use the asymptotics of the optimal penalty parameter to choose for sample size n. In a simulation study, we find that this has dramatically better performance than cross-validation, is an improvement over a SURE-type method previously proposed for this estimator, and compares favorably to the classic DKDE with its recommended plug-in method. We prove that the maximum error in estimating the risk function is of smaller order than its optimal rate of convergence.


Title: On the homology of locally finite graphs
Abstract: We show that the topological cycle space of a locally finite graph is a canonical quotient of the first singular homology group of its Freudenthal compactification, and we characterize the graphs for which the two coincide. We construct a new singular-type homology for non-compact spaces with ends, which in dimension~1 captures precisely the topological cycle space of graphs but works in any dimension.


Title: A new characterization of $E_8 (p)$ via its vanishing elements
Abstract: Let $G$ be a finite group, and $g \in G$. Then $g$ is said to be a vanishing element of $G$, if there exists an irreducible character $\chi$ of $G$ such that $\chi (g)=0$. Denote by ${\rm Vo} (G)$ the set of the orders of vanishing elements of $G$. We say a non-abelian group $G$ is V-recognizable, if any group $N$ with ${\rm Vo} (N) = {\rm Vo} (G)$ is isomorphic to $G$. In this paper, we investigate the V-recognizability of $E_8 (p)$, where $p$ is a prime number. As an application, among the 610 primes $p$ with $p<10000$ and $p \equiv 0,1,4\,(\!\!\!\mod 5)$, we obtain that the method is always valid for confirming the V-recognizability of $E_8 (p)$ for all such $p$ but $ 919,1289,1931,3911,4691,5381$ and $7589 $.


Title: Extension of the Topological Abel-Jacobi Map for Cubic Threefolds
Abstract: The difference $[L_1]-[L_2]$ of a pair of skew lines on a cubic threefold defines a vanishing cycle on the cubic surface as the hyperplane section spanned by the two lines. By deforming the hyperplane, the flat translation of such vanishing cycle forms a 72-to-1 covering space $T_v$ of a Zariski open subspace of $(\mathbb P^4)^*$. Based on a lemma of Stein on the compactification of finite analytic covers, we found a compactification of $T_v$ to which the topological Abel-Jacobi map extends. Moreover, the boundary points of the compactification can be interpreted in terms of local monodromy and the singularities on cubic surfaces. We prove the associated map on fundamental groups of topological Abel-Jacobi map is surjective.


Title: Design and Actuator Optimization of Lightweight and Compliant Knee Exoskeleton for Mobility Assistance of Children with Crouch Gait
Abstract: Pediatric exoskeletons offer great promise to increase mobility for children with crouch gait caused by cerebral palsy. A lightweight, compliant and user-specific actuator is critical for maximizing the benefits of an exoskeleton to users. To date, pediatric exoskeletons generally use the same actuators as adult exoskeletons, which are heavy and resistive to natural movement. There is yet no easy way for robotic exoskeletons to accommodate the changes in design requirements that occur as a child ages. We developed a lightweight (1.65 kg unilateral mass) and compliant pediatric knee exoskeleton with a bandwidth of 22.6 Hz that can provide torque assistance to children with crouch gait using high torque density motor. Experimental results demonstrated that the robot exhibited low mechanical impedance (1.79 Nm average backdrive torque) under the unpowered condition and 0.32 Nm with zero-torque tracking control. Root mean square (RMS) error of torque tracking result is less than 0.73 Nm (5.7% with respect to 12 Nm torque). To achieve optimal age-specific performance, we proposed the first optimization framework that considered both motor and transmission of the actuator system that can produce optimal settings for children between 3 and 18 years old. The optimization generated an optimal motor air gap radius that monotonically increases with age from 0.011 to 0.033 meters, and optimal gear ratio varies from 2.6 to 11.6 (3-13 years old) and 11.6 to 10.2 (13-18 years old), leading to actuators of minimal mass.


Title: Deplatforming Norm-Violating Influencers on Social Media Reduces Overall Online Attention Toward Them
Abstract: From politicians to podcast hosts, online platforms have systematically banned (``deplatformed'') influential users for breaking platform guidelines. Previous inquiries on the effectiveness of this intervention are inconclusive because 1) they consider only few deplatforming events; 2) they consider only overt engagement traces (e.g., likes and posts) but not passive engagement (e.g., views); 3) they do not consider all the potential places users impacted by the deplatforming event might migrate to. We address these limitations in a longitudinal, quasi-experimental study of 165 deplatforming events targeted at 101 influencers. We collect deplatforming events from Reddit posts and then manually curate the data, ensuring the correctness of a large dataset of deplatforming events. Then, we link these events to Google Trends and Wikipedia page views, platform-agnostic measures of online attention that capture the general public's interest in specific influencers. Through a difference-in-differences approach, we find that deplatforming reduces online attention toward influencers. After 12 months, we estimate that online attention toward deplatformed influencers is reduced by -63% (95% CI [-75%,-46%]) on Google and by -43% (95% CI [-57%,-24%]) on Wikipedia. Further, as we study over a hundred deplatforming events, we can analyze in which cases deplatforming is more or less impactful, revealing nuances about the intervention. Notably, we find that both permanent and temporary deplatforming reduce online attention toward influencers; Overall, this work contributes to the ongoing effort to map the effectiveness of content moderation interventions, driving platform governance away from speculation.


Title: Ballistic random walks in random environment as rough paths: convergence and area anomaly
Abstract: Annealed functional CLT in the rough path topology is proved for the standard class of ballistic random walks in random environment. Moreover, the `area anomaly', i.e. a deterministic linear correction for the second level iterated integral of the rescaled path, is identified in terms of a stochastic area on a regeneration interval. The main theorem is formulated in more general settings, namely for any discrete process with uniformly bounded increments which admits a regeneration structure where the regeneration times have finite moments. Here the largest finite moment translates into the degree of regularity of the rough path topology. In particular, the convergence holds in the $\alpha$-H\"older rough path topology for all $\alpha<1/2$ whenever all moments are finite, which is the case for the class of ballistic random walks in random environment. The latter may be compared to a special class of random walks in Dirichlet environments for which the regularity $\alpha<1/2$ is bounded away from $1/2$, explicitly in terms of the corresponding trap parameter.


Title: Non-contractible closed geodesics on compact Finsler space forms without self-intersections
Abstract: Let $M=S^n/ \Gamma$ and $h \in \pi_1(M)$ be a non-trivial element of finite order $p$, where the integers $n, p\geq2$ and $\Gamma$ is a finite abelian group which acts on the sphere freely and isometrically. Therefore $M$ is diffeomorphic to a compact space form which is a typical non-simply connected manifold. For $\Gamma =\mathbb{Z}_2$, we obtain there are at least two non-contractible closed geodesics on $\mathbb{R}P^2$ whose lengths are bounded by geometry of the manifold from above. Moreover, suppose $g_0$ is standard Riemannian metric. We prove that there exists at least $n$ prime non-contractible closed geodesics on $(M,F)$ of prescribed class $[h]$ without self-intersections, provided $F^2 <(\frac{\lambda+1}{\lambda})^2 g_0$ and \[(\frac{\lambda}{\lambda+1})^2 < K \leq 1 \text{ for $n$ is odd or }\; 0<K \leq 1 \text{ for $n$ is even}, \] where $\lambda$ is the reversibility and $K$ is the flag curvature. Some results on stability are obtained.


Title: Weak Solutions of SPDEs in the space of Tempered distributions
Abstract: In this article, we construct weak solutions for a class of Stochastic PDEs in the space of tempered distributions via Girsanov's theorem. It is to be noted that our drift and diffusion coefficients $(L,A)$ of the considered Stochastic PDE satisfy a Monotonicity type inequality, rather than Lipschitz conditions. As such, we can not follow the usual infinite dimensional analysis as described in \cite[sections 10.2 and 10.3]{MR3236753}. Instead, we exploit related SDEs to obtain our desired result, and we point out an important observation that the same Novikov condition is used in changing the Brownian motion in both the SDEs and the Stochastic PDEs.


Title: A small time approximation for the solution to the Zakai Equation
Abstract: We propose a novel small time approximation for the solution to the Zakai equation from nonlinear filtering theory. We prove that the unnormalized filtering density is well described over short time intervals by the solution of a deterministic partial differential equation of Kolmogorov type; the observation process appears in a pathwise manner through the degenerate component of the Kolmogorov's type operator. The rate of convergence of the approximation is of order one in the lenght of the interval. Our approach combines ideas from Wong-Zakai-type results and Wiener chaos approximations for the solution to the Zakai equation. The proof of our main theorem relies on the well-known Feynman-Kac representation for the unnormalized filtering density and careful estimates which lead to completely explicit bounds.


Title: Deutsch paths and their enumeration
Abstract: A variation of Dyck paths allows for down-steps of arbitrary length, not just one. Credits for this invention are given to Emeric Deutsch. Surprisingly, the enumeration of them is somewhat akin to the analysis of Motzkin-paths; the last section contains a bijection.


Title: Test ideals in mixed characteristic: a unified theory up to perturbation
Abstract: Let $X$ be an integral scheme of finite type over a complete DVR of mixed characteristic. We provide a definition of a test ideal which agrees with the multiplier ideal after inverting $p$, can be computed from a sufficiently large alteration, agrees with previous mixed characteristic BCM test ideals after localizing and completing at any point of residue characteristic $p$ (up to small perturbation), and which satisfies the full suite of expected properties of a multiplier or test ideal. This object is obtained via the $p$-adic Riemann-Hilbert functor.


Title: Whittaker modules and hyperbolic Toda lattices
Abstract: Let $\sg$ be a complex finite-dimensional simple Lie algebra and let $\sg_l$ be the corresponding generalized Takiff algebra. This paper studies the affine variety $\ssf+\sb_l$ where $\ssf$ is similar to a principal nilpotent element of $\sg$ and $\sb_l$ is a subalgebra corresponding to the Borel subalgebra $\sb$ of $\sg$. Inspired by Kostant's work then we deal with two questions. One of them is to construct the Whittaker model for the $G_l$-invariants of symmetric algebra $S(\sg_l)$ where $G_l$ is the adjoint group of $\sg_l$ and $G_l$ acts on $S(\sg_l)$ by coadjoint action, and then to classify all nonsingular Whittaker modules over $\sg_l$. Another one is to describe the symplectic structure of the manifold $Z\subseteq\ssf+\sb_l$ of normalized Jacobi elements. Then the Hamiltonian corresponding to a fundamental invariant provides a class of hyperbolic Toda lattices. In particular, a simplest example describes the state of a dynamical system consisting of a positive mass particle and a negative mass particle.


Title: Functional Dimensionality of Koopman Eigenfunction Space
Abstract: This work presents the general form solution of Koopman Partial Differential Equation and shows that its functional dimensionality is finite. The dimensionality is as the dimensionality of the dynamics. Thus, the representation of nonlinear dynamics as a linear one with a finite set of Koopman eigenfunctions without error is possible. This formulation justifies the flowbox statement and provides a simple numerical method to find such representation.


Title: Constrained quantization for a uniform distribution
Abstract: Constrained quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with a finite number of supporting points lying on a specific set. The specific set is known as the constraint of the constrained quantization. A quantization without a constraint is known as an unconstrained quantization, which traditionally in the literature is known as quantization. Constrained quantization has recently been introduced by Pandey and Roychowdhury. In this paper, for a uniform distribution with support lying on a side of an equilateral triangle, and the constraint as the union of the other two sides, we obtain the optimal sets of $n$-points and the $n$th constrained quantization errors for all positive integers $n$. We also calculate the constrained quantization dimension and the constrained quantization coefficient.


Title: Superimposed Pilots are Superior for Mitigating Pilot Contamination in Massive MIMO
Abstract: In this paper, superimposed pilots are introduced as an alternative to time-multiplexed pilot and data symbols for mitigating pilot contamination in massive multiple-input multiple-output (MIMO) systems. We propose a non-iterative scheme for uplink channel estimation based on superimposed pilots and derive an expression for the uplink signal-to-interference-plus-noise ratio (SINR) at the output of a matched filter employing this channel estimate. Based on this expression, we observe that power control is essential when superimposed pilots are employed. Moreover, the quality of the channel estimate can be improved by reducing the interference that results from transmitting data alongside the pilots, and an intuitive iterative data-aided scheme that reduces this component of interference is also proposed. Approximate expressions for the uplink SINR are provided for the iterative data-aided method as well. In addition, we show that a hybrid system with users utilizing both time-multiplexed and superimposed pilots is superior to an optimally designed system that employs only time-multiplexed pilots, even when the non-iterative channel estimate is used to build the detector and precoder. We also describe a simple approach to implement this hybrid system by minimizing the overall inter and intra-cell interference. Numerical simulations demonstrating the performance of the proposed channel estimation schemes and the superiority of the hybrid system are also provided.


Title: GUESS:GradUally Enriching SyntheSis for Text-Driven Human Motion Generation
Abstract: In this paper, we propose a novel cascaded diffusion-based generative framework for text-driven human motion synthesis, which exploits a strategy named GradUally Enriching SyntheSis (GUESS as its abbreviation). The strategy sets up generation objectives by grouping body joints of detailed skeletons in close semantic proximity together and then replacing each of such joint group with a single body-part node. Such an operation recursively abstracts a human pose to coarser and coarser skeletons at multiple granularity levels. With gradually increasing the abstraction level, human motion becomes more and more concise and stable, significantly benefiting the cross-modal motion synthesis task. The whole text-driven human motion synthesis problem is then divided into multiple abstraction levels and solved with a multi-stage generation framework with a cascaded latent diffusion model: an initial generator first generates the coarsest human motion guess from a given text description; then, a series of successive generators gradually enrich the motion details based on the textual description and the previous synthesized results. Notably, we further integrate GUESS with the proposed dynamic multi-condition fusion mechanism to dynamically balance the cooperative effects of the given textual condition and synthesized coarse motion prompt in different generation stages. Extensive experiments on large-scale datasets verify that GUESS outperforms existing state-of-the-art methods by large margins in terms of accuracy, realisticness, and diversity. Code is available at https://github.com/Xuehao-Gao/GUESS.


Title: Verifiable Computation with Massively Parallel Interactive Proofs
Abstract: As the cloud computing paradigm has gained prominence, the need for verifiable computation has grown increasingly urgent. The concept of verifiable computation enables a weak client to outsource difficult computations to a powerful, but untrusted, server. Protocols for verifiable computation aim to provide the client with a guarantee that the server performed the requested computations correctly, without requiring the client to perform the computations herself. By design, these protocols impose a minimal computational burden on the client. However, existing protocols require the server to perform a large amount of extra bookkeeping in order to enable a client to easily verify the results. Verifiable computation has thus remained a theoretical curiosity, and protocols for it have not been implemented in real cloud computing systems. Our goal is to leverage GPUs to reduce the server-side slowdown for verifiable computation. To this end, we identify abundant data parallelism in a state-of-the-art general-purpose protocol for verifiable computation, originally due to Goldwasser, Kalai, and Rothblum, and recently extended by Cormode, Mitzenmacher, and Thaler. We implement this protocol on the GPU, obtaining 40-120x server-side speedups relative to a state-of-the-art sequential implementation. For benchmark problems, our implementation reduces the slowdown of the server to factors of 100-500x relative to the original computations requested by the client. Furthermore, we reduce the already small runtime of the client by 100x. Similarly, we obtain 20-50x server-side and client-side speedups for related protocols targeted at specific streaming problems. We believe our results demonstrate the immediate practicality of using GPUs for verifiable computation, and more generally that protocols for verifiable computation have become sufficiently mature to deploy in real cloud computing systems.


Title: Boltzmann equation with mixed boundary condition
Abstract: We study the Boltzmann equation in a smooth bounded domain featuring a mixed boundary condition. Specifically, gas particles experience specular reflection in two parallel plates, while diffusive reflection occurs in the remaining portion between these two specular regions. The boundary is assumed to be motionless and isothermal. Our main focus is on constructing global-in-time small-amplitude solutions around global Maxwellians for the corresponding initial-boundary value problem. The proof relies on the $L^2$ hypocoercivity at the linear level, utilizing the weak formulation and various functional inequalities on the test functions, such as Poincar\'e and Korn inequalities. It also extends to the linear problem involving Maxwell boundary conditions, where the accommodation coefficient can be a piecewise constant function on the boundary, allowing for more general bounded domains. Moreover, we develop a delicate application of the $L^2-L^\infty$ bootstrap argument, which relies on the specific geometry of our domains, to effectively handle this mixed-type boundary condition.


Title: Introduction to twisted commutative algebras
Abstract: This article is an expository account of the theory of twisted commutative algebras, which simply put, can be thought of as a theory for handling commutative algebras with large groups of linear symmetries. Examples include the coordinate rings of determinantal varieties, Segre-Veronese embeddings, and Grassmannians. The article is meant to serve as a gentle introduction to the papers of the two authors on the subject, and also to point out some literature in which these algebras appear. The first part reviews the representation theory of the symmetric groups and general linear groups. The second part introduces a related category and develops its basic properties. The third part develops some basic properties of twisted commutative algebras from the perspective of classical commutative algebra and summarizes some of the results of the authors. We have tried to keep the prerequisites to this article at a minimum. The article is aimed at graduate students interested in commutative algebra, algebraic combinatorics, or representation theory, and the interactions between these subjects.


Title: Flip colouring of graphs II
Abstract: We give results concerning two problems on the recently introduced flip colourings of graphs, a new class of local v. global phenomena. We prove that for $(b, r)$-flip sequences with $4 \leq b < r < b + 2 \left\lfloor\frac{b+2}{6}\right\rfloor^2$, small constructions of $(b,r)$-flip graphs on $O(b+r)$ vertices are possible. Furthermore, we prove that there exists $k$-flip sequences $(a_1, \dots, a_k)$ where $k > 4$, such that $a_k$ can be arbitrarily large whilst $a_i$ is constant for $1 \leq i < \frac{k}{4}$.


Title: A Generative AI Assistant to Accelerate Cloud Migration
Abstract: We present a tool that leverages generative AI to accelerate the migration of on-premises applications to the cloud. The Cloud Migration LLM accepts input from the user specifying the parameters of their migration, and outputs a migration strategy with an architecture diagram. A user study suggests that the migration LLM can assist inexperienced users in finding the right cloud migration profile, while avoiding complexities of a manual approach.


Title: Bounds on the minimum distance of locally recoverable codes
Abstract: We consider locally recoverable codes (LRCs) and aim to determine the smallest possible length $n=n_q(k,d,r)$ of a linear $[n,k,d]_q$-code with locality $r$. For $k\le 7$ we exactly determine all values of $n_2(k,d,2)$ and for $k\le 6$ we exactly determine all values of $n_2(k,d,1)$. For the ternary field we also state a few numerical results. As a general result we prove that $n_q(k,d,r)$ equals the Griesmer bound if the minimum Hamming distance $d$ is sufficiently large and all other parameters are fixed.


Title: The convolution algebra of an absolutely locally compact topos
Abstract: We introduce a class of toposes called "absolutely locally compact" toposes and of "admissible" sheaf of rings over such toposes. To any such ringed topos $(\mathcal{T},A)$ we attach an involutive convolution algebra $\mathcal{C}_c(\mathcal{T},A)$ which is well defined up to Morita equivalence and characterized by the fact that the category of non-degenerate modules over $\mathcal{C}_c(\mathcal{T},A)$ is equivalent to the category of sheaf of $A$-module over $\mathcal{T}$. In the case where $A$ is the sheaf of real or complex Dedekind numbers, we construct several norms on this involutive algebra that allows to complete it in various Banach and $C^*$-algebras: $L^1(\mathcal{T},A)$, $C^*_{red}(\mathcal{T},A)$ and $C^*_{max}(\mathcal{T},A)$. We also give some examples where this construction corresponds to well known constructions of involutive algebras, like groupoids convolution algebra and Leavitt path algebras.


Title: Shifted Composition II: Shift Harnack Inequalities and Curvature Upper Bounds
Abstract: We apply the shifted composition rule -- an information-theoretic principle introduced in our earlier work [AC23] -- to establish shift Harnack inequalities for the Langevin diffusion. We obtain sharp constants for these inequalities for the first time, allowing us to investigate their relationship with other properties of the diffusion. Namely, we show that they are equivalent to a sharp "local gradient-entropy" bound, and that they imply curvature upper bounds in a compelling reflection of the Bakry-Emery theory of curvature lower bounds. Finally, we show that the local gradient-entropy inequality implies optimal concentration of the score, a.k.a. the logarithmic gradient of the density.


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: Local semicircle law with imprimitive variance matrix
Abstract: We extend the proof of the local semicircle law for generalized Wigner matrices given in [4] to the case when the matrix of variances has an eigenvalue $ -1 $. In particular, this result provides a short proof of the optimal local Marchenko-Pastur law at the hard edge (i.e. around zero) for sample covariance matrices $ \boldsymbol{\mathrm{X}}^\ast \boldsymbol{\mathrm{X}} $, where the variances of the entries of $ \boldsymbol{\mathrm{X}} $ may vary.


Title: A Non-Holonomic Systems Approach to Special Function Identities
Abstract: We extend Zeilberger's approach to special function identities to cases that are not holonomic. The method of creative telescoping is thus applied to definite sums or integrals involving Stirling or Bernoulli numbers, incomplete Gamma function or polylogarithms, which are not covered by the holonomic framework. The basic idea is to take into account the dimension of appropriate ideals in Ore algebras. This unifies several earlier extensions and provides algorithms for summation and integration in classes that had not been accessible to computer algebra before.


Title: On mild solutions to some dissipative SPDEs on $L^p$ spaces with additive noise
Abstract: We establish well-posedness in the mild sense for a class of stochastic semilinear evolution equations on $L^p$ spaces on bounded domains of $\mathbb{R}^n$ with a nonlinear drift term given by the superposition operator generated by a monotone function on the real line with power-like growth. The noise is of additive type with respect to a cylindrical Wiener process, with diffusion coefficient not necessarily of $\gamma$-Radonifying type.


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: Multi-Source Domain Adaptation with Transformer-based Feature Generation for Subject-Independent EEG-based Emotion Recognition
Abstract: Although deep learning-based algorithms have demonstrated excellent performance in automated emotion recognition via electroencephalogram (EEG) signals, variations across brain signal patterns of individuals can diminish the model's effectiveness when applied across different subjects. While transfer learning techniques have exhibited promising outcomes, they still encounter challenges related to inadequate feature representations and may overlook the fact that source subjects themselves can possess distinct characteristics. In this work, we propose a multi-source domain adaptation approach with a transformer-based feature generator (MSDA-TF) designed to leverage information from multiple sources. The proposed feature generator retains convolutional layers to capture shallow spatial, temporal, and spectral EEG data representations, while self-attention mechanisms extract global dependencies within these features. During the adaptation process, we group the source subjects based on correlation values and aim to align the moments of the target subject with each source as well as within the sources. MSDA-TF is validated on the SEED dataset and is shown to yield promising results.


Title: Characters and chromatic symmetric functions
Abstract: Let $P$ be a poset, $inc(P)$ its incomparability graph, and $X_{inc(P)}$ the corresponding chromatic symmetric function, as defined by Stanley in {\em Adv. Math.}, {\bf 111} (1995) pp.~166--194. Certain conditions on $P$ imply that the expansions of $X_{inc(P)}$ in standard symmetric function bases yield coefficients which have simple combinatorial interpretations. By expressing these coefficients as character evaluations, we extend several of these interpretations to {\em all} posets $P$. Consequences include new combinatorial interpretations of the permanent and other immanants of totally nonnegative matrices, and of the sum of elementary coefficients in the Shareshian-Wachs chromatic quasisymmetric function $X_{inc(P),q}$ when $P$ is a unit interval order.


Title: Global Invariant Branches of Non-degenerate Foliations on Projective Toric Surfaces
Abstract: We show that the isolated invariant branches globalize to algebraic curves, when we consider weak toric type complex hyperbolic foliations on projective toric ambient surfaces. To do it, we pass through a characterization of weak toric type foliations in terms of "non-degeneracy" conditions, associated to Newton polygons. We also give a description of the relationship between invariant algebraic curves and isolated invariant branches, valid for the case of toric type, by means of the following dichotomy. Either there is a rational first integral and there are no isolated invariant branches or we have only finitely many global invariant curves, all of them extending isolated invariant branches.


Title: Sorting Can Exponentially Speed Up Pure Dynamic Programming
Abstract: Many discrete minimization problems, including various versions of the shortest path problem, can be efficiently solved by dynamic programming (DP) algorithms that are "pure" in that they only perform basic operations, as min, max, +, but no conditional branchings via if-then-else in their recursion equations. It is known that any pure (min,+) DP algorithm solving the minimum weight spanning tree problem on undirected n-vertex graphs must perform at least $2^{\Omega(\sqrt{n})}$ operations. We show that this problem can be solved by a pure (min,max,+) DP algorithm performing only $O(n^3)$ operations. The algorithm is essentially a (min,max) algorithm: addition operations are only used to output the final values. The presence of both min and max operations means that now DP algorithms can sort: this explains the title of the paper.


Title: Multidimensional Sticky Brownian Motions: Tail Behaviour of the Joint Stationary Distribution
Abstract: Sticky Brownian motions, as time-changed semimartingale reflecting Brownian motions, have various applications in many fields, including queuing theory and mathematical finance. In this paper, we are concerned about the stationary distributions of a multidimensional sticky Brownian motion, provided it is stable. We will study the large deviations principle for stationary distribution and the tail behaviour of the joint stationary distribution.


Title: Spin systems with hyperbolic symmetry: a survey
Abstract: Spin systems with hyperbolic symmetry originated as simplified models for the Anderson metal--insulator transition, and were subsequently found to exactly describe probabilistic models of linearly reinforced walks and random forests. In this survey we introduce these models, discuss their origins and main features, some existing tools available for their study, recent probabilistic results, and relations to other well-studied probabilistic models. Along the way we discuss some of the (many) open questions that remain.


Title: EcoFed: Efficient Communication for DNN Partitioning-based Federated Learning
Abstract: Efficiently running federated learning (FL) on resource-constrained devices is challenging since they are required to train computationally intensive deep neural networks (DNN) independently. DNN partitioning-based FL (DPFL) has been proposed as one mechanism to accelerate training where the layers of a DNN (or computation) are offloaded from the device to the server. However, this creates significant communication overheads since the intermediate activation and gradient need to be transferred between the device and the server during training. While current research reduces the communication introduced by DNN partitioning using local loss-based methods, we demonstrate that these methods are ineffective in improving the overall efficiency (communication overhead and training speed) of a DPFL system. This is because they suffer from accuracy degradation and ignore the communication costs incurred when transferring the activation from the device to the server. This article proposes EcoFed - a communication efficient framework for DPFL systems. EcoFed eliminates the transmission of the gradient by developing pre-trained initialization of the DNN model on the device for the first time. This reduces the accuracy degradation seen in local loss-based methods. In addition, EcoFed proposes a novel replay buffer mechanism and implements a quantization-based compression technique to reduce the transmission of the activation. It is experimentally demonstrated that EcoFed can reduce the communication cost by up to 133x and accelerate training by up to 21x when compared to classic FL. Compared to vanilla DPFL, EcoFed achieves a 16x communication reduction and 2.86x training time speed-up. EcoFed is available from https://github.com/blessonvar/EcoFed.


Title: Contractibility of the orbit space of a saturated fusion system after Steinberg
Abstract: Recently, Steinberg used discrete Morse theory to give a new proof of a theorem of Symonds that the orbit space of the poset of nontrivial $p$-subgroups of a finite group is contractible. We extend Steinberg's argument in two ways, covering more general versions of the theorem that were already known. In particular, following a strategy of Libman, we give a discrete Morse theoretic argument for the contractibility of the orbit space of a saturated fusion system.


Title: The Rank of the Odd Normal Out
Abstract: Say we have a collection of independent random variables $X_0, ... , X_n$, where $X_0 \sim \mathcal{N}(\mu_0, \sigma_0^2)$, but $X_i \sim \mathcal{N}(\mu, \sigma^2)$, for $1 \leq i \leq n$. We characterize the distribution of $R_0 := 1 + \sum_{i=1}^{n} \mathbf{1}\{X_i \leq X_0\}$, the rank of the random variable whose distribution potentially differs from that of the others -- the odd normal out. We show that $R_0 - 1$ is approximately beta-binomial, an approximation that becomes equality as $\sigma/\sigma_0$ or $(\mu-\mu_0)/\sigma_0$ become large or small. The intra-class correlation of the approximating beta-binomial depends on $\Pr(X_1 \leq X_0)$ and $\Pr(X_1 \leq X_0, X_2 \leq X_0)$. Our approach relies on the conjugacy of the beta distribution for the binomial: $\Phi((X_0-\mu)/\sigma)$ is approximately $\mathrm{Beta}(\alpha(\sigma/\sigma_0, (\mu-\mu_0)/\sigma_0), \beta(\sigma/\sigma_0, (\mu-\mu_0)/\sigma_0))$ for functions $\alpha, \beta > 0$. We study the distributions of the in-normal ranks. Throughout, simulations corroborate the formulae we derive.


Title: Towards a Formal Modelling, Analysis, and Verification of a Clone Node Attack Detection Scheme in the Internet of Things
Abstract: In a clone node attack, an attacker attempted to physically capture the devices to gather sensitive information to conduct various insider attacks. Several solutions for detecting clone node attacks on IoT networks have been presented in the viewpoints above. These solutions are focused on specific system designs, processes, and feature sets and act as a high-level abstraction of underlying system architectures based on a few performance requirements. However, critical features like formal analysis, modelling, and verification are frequently overlooked in existing proposed solutions aimed at verifying the correctness and robustness of systems in order to ensure that no problematic scenarios or anomalies exist. This paper presents a formal analysis, modelling, and verification of our existing proposed clone node attack detection scheme in IoT. Firstly, we modelled the architectural components of the proposed scheme using High-Level Petri Nets (HLPNs) and then mapped them using their specified functionalities. Secondly, we defined and analysed the behavioural properties of the proposed scheme using Z specification language. Furthermore, we used the Satisfiability Modulo Theories Library (SMT-Lib) and the Z3 Solver to validate and demonstrate the overall functionality of the proposed scheme. Finally, in addition to modelling and analysis, this work employs Coloured Petri Nets (CPNs), which combine Petri Nets with a high-level programming language, making them more suitable for large-scale system modelling. To perform the simulations in CPN, we used both timed and untimed models, where timed models are used to evaluate performance, and untimed models are used to validate logical validity.


Title: Divides with cusps and symmetric links
Abstract: A Divide with cusps is the image of a proper generic immersion from finite intervals and circles into a $2$-disk which allows to have cusps. A divide with cusps is the generalization of the notion of the divide which is introduced by A'Campo. From a divide with cusps, we can define the associated link in $S^3$. In this paper, we give the characterization of the link in $S^3$ which can be described as the associated link of a divide with cusps. In particular, we prove that every strongly invertible link and $2$-periodic link can be described as the link of a divide with cusps.


Title: On the Uniqueness of Bayesian Coarse Correlated Equilibria in Standard First-Price and All-Pay Auctions
Abstract: In first-price and all-pay auctions under the standard symmetric independent private-values model, we show that the unique Bayesian Coarse Correlated Equilibrium with symmetric, differentiable and strictly increasing bidding strategies is the unique strict Bayesian Nash Equilibrium. Interestingly, this result does not require assumptions on the prior distribution. The proof is based on a dual bound of the infinite-dimensional linear program. Numerical experiments without restrictions on bidding strategies show that for first-price auctions and discretisations up to 21 of the type and bid space, increasing discretisation sizes actually increase the concentration of Bayesian Coarse Correlated Equilibrium over the Bayesian Nash Equilibrium, so long as the prior c.d.f. is concave. Such a concentration is also observed for all-pay auctions, independent of the prior distribution. Overall, our results imply that the equilibria of these important class of auctions are indeed learnable.


Title: HawkRover: An Autonomous mmWave Vehicular Communication Testbed with Multi-sensor Fusion and Deep Learning
Abstract: Connected and automated vehicles (CAVs) have become a transformative technology that can change our daily life. Currently, millimeter-wave (mmWave) bands are identified as the promising CAV connectivity solution. While it can provide high data rate, their realization faces many challenges such as high attenuation during mmWave signal propagation and mobility management. Existing solution has to initiate pilot signal to measure channel information, then apply signal processing to calculate the best narrow beam towards the receiver end to guarantee sufficient signal power. This process takes significant overhead and time, hence not suitable for vehicles. In this study, we propose an autonomous and low-cost testbed to collect extensive co-located mmWave signal and other sensors data such as LiDAR (Light Detection and Ranging), cameras, ultrasonic, etc, traditionally for ``automated'', to facilitate mmWave vehicular communications. Intuitively, these sensors can build a 3D map around the vehicle and signal propagation path can be estimated, eliminating iterative the process via pilot signals. This multimodal data fusion, together with AI, is expected to bring significant advances in ``connected'' research.


Title: Effects of forward scattering on the onset of phototactic bioconvection in an algal suspension under diffuse flux without collimated flux
Abstract: Phototaxis refers to the directed swimming response influenced by the sensed light intensity in microorganisms. Positive phototaxis involves motion toward the light source, while negative phototaxis entails motion away from it. This study explores the phototactic bioconvection in a suspension of anisotropic scattering phototactic algae, illuminated by diffuse flux without direct collimated flux. The basic state is characterized by zero fluid flow, with the balance between upward and downward swimming due to positive and negative phototaxis, respectively, counteracted by microorganism diffusion. The paper conducts a thorough numerical analysis of linear stability, placing particular emphasis on the impact of forward scattering. The onset of bioconvection manifests either through a stationary mode or an oscillatory mode. The transition between these modes is observed with varying anisotropic coefficients for specific parameter values.


Title: TSGAN: An Optical-to-SAR Dual Conditional GAN for Optical based SAR Temporal Shifting
Abstract: In contrast to the well-investigated field of SAR-to-Optical translation, this study explores the lesser-investigated domain of Optical-to-SAR translation, a challenging field due to the ill-posed nature of this translation. The complexity arises as a single optical data can have multiple SAR representations based on the SAR viewing geometry. We propose a novel approach, termed SAR Temporal Shifting, which inputs an optical data from the desired timestamp along with a SAR data from a different temporal point but with a consistent viewing geometry as the expected SAR data, both complemented with a change map of optical data during the intervening period. This model modifies the SAR data based on the changes observed in optical data to generate the SAR data for the desired timestamp. Our model, a dual conditional Generative Adversarial Network (GAN), named Temporal Shifting GAN (TSGAN), incorporates a siamese encoder in both the Generator and the Discriminator. To prevent the model from overfitting on the input SAR data, we employed a change weighted loss function. Our approach surpasses traditional translation methods by eliminating the GAN's fiction phenomenon, particularly in unchanged regions, resulting in higher SSIM and PSNR in these areas. Additionally, modifications to the Pix2Pix architecture and the inclusion of attention mechanisms have enhanced the model's performance on all regions of the data. This research paves the way for leveraging legacy optical datasets, the most abundant and longstanding source of Earth imagery data, extending their use to SAR domains and temporal analyses. To foster further research, we provide the code, datasets used in our study, and a framework for generating paired SAR-Optical datasets for new regions of interest. These resources are available on github.com/moienr/TemporalGAN


Title: On the expected L2-discrepancy of stratified samples from parallel lines
Abstract: We study the expected $\mathcal{L}_2$-discrepancy of stratified samples generated from special equi-volume partitions of the unit square. The partitions are defined via parallel lines that are all orthogonal to the diagonal of the square. It is shown that the expected discrepancy of stratified samples derived from these partitions is a factor 2 smaller than the expected discrepancy of the same number of i.i.d uniformly distributed random points in the unit square. We conjecture that this is best possible among all partitions generated from parallel lines.


Title: A Simple Construction of Tournaments with Finite and Uncountable Dichromatic Number
Abstract: The dichromatic number $\chi(\vec{G})$ of a digraph $\vec{G}$ is the minimum number of colors needed to color the vertices $V(\vec{G})$ in such a way that no monochromatic directed cycle is obtained. In this note, for any $k\in \mathbb{N}$, we give a simple construction of tournaments with dichromatic number exactly equal to $k$. The proofs are based on a combinatorial lemma on partitioning a checkerboard which may be of independent interest. We also generalize our finite construction to give an elementary construction of a complete digraph of cardinality equal to the cardinality of $\mathbb{R}$ and having an uncountable dichromatic number. Furthermore, we also construct an oriented balanced complete $n$-partite graph $\vec{K}^{(m)}_n$, such that the minimum number of colors needed to color its vertices such that there is no monochromatic directed triangle is greater than or equal to $nm/(n+2m-2)$.


Title: Inverse questions for the large sieve
Abstract: Suppose that an infinite set $A$ occupies at most $\frac{1}{2}(p+1)$ residue classes modulo $p$, for every sufficiently large prime $p$. The squares, or more generally the integer values of any quadratic, are an example of such a set. By the large sieve inequality the number of elements of $A$ that are at most $X$ is $O(X^{1/2})$, and the quadratic examples show that this is sharp. The simplest form of the inverse large sieve problem asks whether they are the only examples. We prove a variety of results and formulate various conjectures in connection with this problem, including several improvements of the large sieve bound when the residue classes occupied by $A$ have some additive structure. Unfortunately we cannot solve the problem itself.


Title: Thread With Caution: Proactively Helping Users Assess and Deescalate Tension in Their Online Discussions
Abstract: Incivility remains a major challenge for online discussion platforms, to such an extent that even conversations between well-intentioned users can often derail into uncivil behavior. Traditionally, platforms have relied on moderators to -- with or without algorithmic assistance -- take corrective actions such as removing comments or banning users. In this work we propose a complementary paradigm that directly empowers users by proactively enhancing their awareness about existing tension in the conversation they are engaging in and actively guides them as they are drafting their replies to avoid further escalation. As a proof of concept for this paradigm, we design an algorithmic tool that provides such proactive information directly to users, and conduct a user study in a popular discussion platform. Through a mixed methods approach combining surveys with a randomized controlled experiment, we uncover qualitative and quantitative insights regarding how the participants utilize and react to this information. Most participants report finding this proactive paradigm valuable, noting that it helps them to identify tension that they may have otherwise missed and prompts them to further reflect on their own replies and to revise them. These effects are corroborated by a comparison of how the participants draft their reply when our tool warns them that their conversation is at risk of derailing into uncivil behavior versus in a control condition where the tool is disabled. These preliminary findings highlight the potential of this user-centered paradigm and point to concrete directions for future implementations.


Title: Nonassociative $\mathrm{L}^p$-spaces and embeddings in noncommutative $\mathrm{L}^p$-spaces
Abstract: We define a notion of nonassociative $\mathrm{L}^p$-space associated to a $\mathrm{JBW}^*$-algebra (Jordan von Neumann algebra) equipped with a normal faithful state $\varphi$. In the particular case of $\mathrm{JW}^*$-algebras underlying von Neumann algebras, we connect these spaces to a complex interpolation theorem of Ricard and Xu on noncommutative $\mathrm{L}^p$-spaces. We also make the link with the nonassociative $\mathrm{L}^p$-spaces of Iochum associated to $\mathrm{JBW}$-algebras and the investigation of contractively complemented subspaces of noncommutative $\mathrm{L}^p$-spaces. More precisely, we show that our nonassociative $\mathrm{L}^p$-spaces contain isometrically the $\mathrm{L}^p$-spaces of Iochum and that all tracial nonassociative $\mathrm{L}^p$-spaces from $\mathrm{JW}^*$-factors arise as positively contractively complemented subspaces of noncommutative $\mathrm{L}^p$-spaces.


Title: Duality for convex infinite optimization on linear spaces
Abstract: This note establishes a limiting formula for the conic Lagrangian dual of a convex infinite optimization problem, correcting the classical version of Karney [Math. Programming 27 (1983) 75-82] for convex semi-infinite programs. A reformulation of the convex infinite optimization problem with a single constraint leads to a limiting formula for the corresponding Lagrangian dual, called sup-dual, and also for the primal problem in the case when strong Slater condition holds, which also entails strong sup-duality.


Title: Policy-regularized Offline Multi-objective Reinforcement Learning
Abstract: In this paper, we aim to utilize only offline trajectory data to train a policy for multi-objective RL. We extend the offline policy-regularized method, a widely-adopted approach for single-objective offline RL problems, into the multi-objective setting in order to achieve the above goal. However, such methods face a new challenge in offline MORL settings, namely the preference-inconsistent demonstration problem. We propose two solutions to this problem: 1) filtering out preference-inconsistent demonstrations via approximating behavior preferences, and 2) adopting regularization techniques with high policy expressiveness. Moreover, we integrate the preference-conditioned scalarized update method into policy-regularized offline RL, in order to simultaneously learn a set of policies using a single policy network, thus reducing the computational cost induced by the training of a large number of individual policies for various preferences. Finally, we introduce Regularization Weight Adaptation to dynamically determine appropriate regularization weights for arbitrary target preferences during deployment. Empirical results on various multi-objective datasets demonstrate the capability of our approach in solving offline MORL problems.


Title: Learning to Prompt with Text Only Supervision for Vision-Language Models
Abstract: Foundational vision-language models such as CLIP are becoming a new paradigm in vision, due to their excellent generalization abilities. However, adapting these models for downstream tasks while maintaining their generalization remains a challenge. In literature, one branch of methods adapts CLIP by learning prompts using visual information. While effective, most of these works require labeled data which is not practical, and often struggle to generalize towards new datasets due to over-fitting on the source data. An alternative approach resorts to training-free methods by generating class descriptions from large language models (LLMs) and perform prompt ensembling. However, these methods often generate class specific prompts that cannot be transferred to other classes, which incur higher costs by generating LLM descriptions for each class separately. In this work, we propose to combine the strengths of these both streams of methods by learning prompts using only text data derived from LLMs. As supervised training of prompts is not trivial due to absence of images, we develop a training approach that allows prompts to extract rich contextual knowledge from LLM data. Moreover, with LLM contextual data mapped within the learned prompts, it enables zero-shot transfer of prompts to new classes and datasets potentially cutting the LLM prompt engineering cost. To the best of our knowledge, this is the first work that learns generalized prompts using text only data. We perform extensive evaluations on 4 benchmarks where our method improves over prior ensembling works while being competitive to those utilizing labeled images. Our code and pre-trained models are available at https://github.com/muzairkhattak/ProText.


Title: PEGASUS: Physically Enhanced Gaussian Splatting Simulation System for 6DOF Object Pose Dataset Generation
Abstract: We introduce Physically Enhanced Gaussian Splatting Simulation System (PEGASUS) for 6DOF object pose dataset generation, a versatile dataset generator based on 3D Gaussian Splatting. Environment and object representations can be easily obtained using commodity cameras to reconstruct with Gaussian Splatting. PEGASUS allows the composition of new scenes by merging the respective underlying Gaussian Splatting point cloud of an environment with one or multiple objects. Leveraging a physics engine enables the simulation of natural object placement within a scene through interaction between meshes extracted for the objects and the environment. Consequently, an extensive amount of new scenes - static or dynamic - can be created by combining different environments and objects. By rendering scenes from various perspectives, diverse data points such as RGB images, depth maps, semantic masks, and 6DoF object poses can be extracted. Our study demonstrates that training on data generated by PEGASUS enables pose estimation networks to successfully transfer from synthetic data to real-world data. Moreover, we introduce the Ramen dataset, comprising 30 Japanese cup noodle items. This dataset includes spherical scans that captures images from both object hemisphere and the Gaussian Splatting reconstruction, making them compatible with PEGASUS.


Title: On the construction of Cohn's universal localization
Abstract: For an associative ring we investigate a construction of Cohn's universal ring of fractions defined relative to a multiplicative set of matrices. The construction avoids the Ore condition, which is necessary to construct a ring of fractions relative to a multiplicative set of elements. But a similar condition, which we call the ``pseudo-Ore'' condition, plays an important role in the construction of Cohn's localization. We show that this condition in fact determines the equivalence relation used in the construction.


Title: Green functions for GJMS operators on spheres, Gegenbauer polynomials and rigidity theorems
Abstract: We derive explicit representation formulae of Green functions for GJMS operators on $n$-spheres, including the fractional ones. These formulae not only have natural geometric interpretations concerning the extrinsic geometry of the round sphere, but also reflect the spherical rigidity among closed embedded hypersurfaces in $\mathbb{R}^{n+1}$.


Title: Sharing Non-Anonymous Costs of Multiple Resources Optimally
Abstract: In cost sharing games, the existence and efficiency of pure Nash equilibria fundamentally depends on the method that is used to share the resources' costs. We consider a general class of resource allocation problems in which a set of resources is used by a heterogeneous set of selfish users. The cost of a resource is a (non-decreasing) function of the set of its users. Under the assumption that the costs of the resources are shared by uniform cost sharing protocols, i.e., protocols that use only local information of the resource's cost structure and its users to determine the cost shares, we exactly quantify the inefficiency of the resulting pure Nash equilibria. Specifically, we show tight bounds on prices of stability and anarchy for games with only submodular and only supermodular cost functions, respectively, and an asymptotically tight bound for games with arbitrary set-functions. While all our upper bounds are attained for the well-known Shapley cost sharing protocol, our lower bounds hold for arbitrary uniform cost sharing protocols and are even valid for games with anonymous costs, i.e., games in which the cost of each resource only depends on the cardinality of the set of its users.


Title: Frequency Domain Nuances Mining for Visible-Infrared Person Re-identification
Abstract: The key of visible-infrared person re-identification (VIReID) lies in how to minimize the modality discrepancy between visible and infrared images. Existing methods mainly exploit the spatial information while ignoring the discriminative frequency information. To address this issue, this paper aims to reduce the modality discrepancy from the frequency domain perspective. Specifically, we propose a novel Frequency Domain Nuances Mining (FDNM) method to explore the cross-modality frequency domain information, which mainly includes an amplitude guided phase (AGP) module and an amplitude nuances mining (ANM) module. These two modules are mutually beneficial to jointly explore frequency domain visible-infrared nuances, thereby effectively reducing the modality discrepancy in the frequency domain. Besides, we propose a center-guided nuances mining loss to encourage the ANM module to preserve discriminative identity information while discovering diverse cross-modality nuances. To the best of our knowledge, this is the first work that explores the potential frequency information for VIReID research. Extensive experiments show that the proposed FDNM has significant advantages in improving the performance of VIReID. Specifically, our method outperforms the second-best method by 5.2\% in Rank-1 accuracy and 5.8\% in mAP on the SYSU-MM01 dataset under the indoor search mode, respectively. Besides, we also validate the effectiveness and generalization of our method on the challenging visible-infrared face recognition task. \textcolor{magenta}{The code will be available.}


Title: Improving Deep Pancreas Segmentation in CT and MRI Images via Recurrent Neural Contextual Learning and Direct Loss Function
Abstract: Deep neural networks have demonstrated very promising performance on accurate segmentation of challenging organs (e.g., pancreas) in abdominal CT and MRI scans. The current deep learning approaches conduct pancreas segmentation by processing sequences of 2D image slices independently through deep, dense per-pixel masking for each image, without explicitly enforcing spatial consistency constraint on segmentation of successive slices. We propose a new convolutional/recurrent neural network architecture to address the contextual learning and segmentation consistency problem. A deep convolutional sub-network is first designed and pre-trained from scratch. The output layer of this network module is then connected to recurrent layers and can be fine-tuned for contextual learning, in an end-to-end manner. Our recurrent sub-network is a type of Long short-term memory (LSTM) network that performs segmentation on an image by integrating its neighboring slice segmentation predictions, in the form of a dependent sequence processing. Additionally, a novel segmentation-direct loss function (named Jaccard Loss) is proposed and deep networks are trained to optimize Jaccard Index (JI) directly. Extensive experiments are conducted to validate our proposed deep models, on quantitative pancreas segmentation using both CT and MRI scans. Our method outperforms the state-of-the-art work on CT [11] and MRI pancreas segmentation [1], respectively.


Title: Eulerian 2-Complexes
Abstract: It is shown that Euler's theorem for graphs can be generalized for 2-complexes. Two notions that generalize cycle and Eulerian tour are introduced (``circlet'' and ``Eulerian cover''), and we show that for a strongly-connected, pure 2-complex, the following are equivalent: (i) each edge meets a positive even number of 2-cells (faces), (ii) the complex can be decomposed as the face-disjoint union of circlets, and (iii) the complex has an Eulerian cover. A number of examples are provided.


Title: Betting strategies with bounded splits
Abstract: We show that a pair of Kolmogorov-Loveland betting strategies cannot win on every non-Martin-L\"of random sequence if either of the two following conditions is true: (I) There is an unbounded computable function $g$ such that both betting strategies, when betting on an infinite binary sequence, almost surely, for almost all $\ell$, bet on at most $\ell-g(\ell)$ positions among the first $\ell$ positions of the sequence. (II) There is a sublinear function $g$ such that both betting strategies, when betting on an infinite binary sequence, almost surely, for almost all $\ell$, bet on at least $\ell-g(\ell)$ positions among the first $\ell$ positions of the sequence.