Title: QoE-oriented Dependent Task Scheduling under Multi-dimensional QoS Constraints over Distributed Networks
Abstract: Task scheduling as an effective strategy can improve application performance on computing resource-limited devices over distributed networks. However, existing evaluation mechanisms fail to depict the complexity of diverse applications, which involve dependencies among tasks, computing resource requirements, and multi-dimensional quality of service (QoS) constraints. Furthermore, traditional QoS-oriented task scheduling strategies struggle to meet the performance requirements without considering differences in satisfaction and acceptance of application, leading application failures and resource wastage. To tackle these issues, a quality of experience (QoE) cost model is designed to evaluate application completion, depicting the relationship among application satisfaction, communications, and computing resources in the distributed networks. Specifically, considering the sensitivity and preference of QoS, we model the different dimensional QoS degradation cost functions for dependent tasks, which are then integrated into the QoE cost model. Based on the QoE model, the dependent task scheduling problem is formulated as the minimization of overall QoE cost, aiming to improve the application performance in the distributed networks, which is proven Np-hard. Moreover, a heuristic Hierarchical Multi-queue Task Scheduling Algorithm (HMTSA) is proposed to address the QoE-oriented task scheduling problem among multiple dependent tasks, which utilizes hierarchical multiple queues to determine the optimal task execution order and location according to different dimensional QoS priorities. Finally, extensive experiments demonstrate that the proposed algorithm can significantly improve the satisfaction of applications.


Title: Aggregation-diffusion phenomena: from microscopic models to free boundary problems
Abstract: This paper reviews (and expands) some recent results on the modeling of aggregation-diffusion phenomena at various scales, focusing on the emergence of collective dynamics as a result of the competition between attractive and repulsive phenomena - especially (but not exclusively) in the context of attractive chemotaxis phenomena. At microscopic scales, particles (or other agents) are represented by spheres of radius $\delta>0$ and we discuss both soft-sphere models (with a pressure term penalizing the overlap of the particles) and hard-sphere models (in which overlap is prohibited). The first case leads to so-called ``blob models" which have received some attention recently as a tool to approximate non-linear diffusion by particle systems. The hard-sphere model is similar to a classical model for congested crowd motion. We review well-posedness results for these models and discuss their relationship to classical continuum description of aggregation-diffusion phenomena in the limit $\delta\to0$: the classical nonlinear drift diffusion equation and its incompressible counterpart. In the second part of the paper, we discuss recent results on the emergence and evolution of sharp interfaces when a large population of particles is considered at appropriate space and time scales: At some intermediate time scale, phase separation occurs and a sharp interface appears which evolves according to a Stefan free boundary problem (and the density function eventually relaxes to a characteristic function - metastable steady state for the original problem). At a larger time scale the attractive forces lead to surface tension phenomena and the evolution of the sharp interface can be described by a Hele-Shaw free boundary problem with surface tension. At that same time scale, we will also discuss the emergence of contact angle conditions for problems set in bounded domains.


Title: An almost linear time algorithm testing whether the Markoff graph modulo $p$ is connected
Abstract: The Markoff graph modulo $p$ is known to be connected for all but finitely many primes $p$ (see Eddy, Fuchs, Litman, Martin, Tripeny, and Vanyo [arxiv:2308.07579]), and it is conjectured that these graphs are connected for all primes. In this paper, we provide an algorithmic realization of the process introduced by Bourgain, Gamburd, and Sarnak [arxiv:1607.01530] to test whether a Markoff graph modulo $p$ is connected for arbitrary primes. Our algorithm runs in $o(p^{1 + \epsilon})$ time for every $\epsilon > 0$. We demonstrate this algorithm by confirming that the Markoff graph modulo $p$ is connected for all primes less than one million.


Title: Contravariant Pseudo-Hessian manifolds and their associated Poisson structures
Abstract: A contravariant pseudo-Hessian manifold is a manifold $M$ endowed with a pair $(\nabla,h)$ where $\nabla$ is a flat connection and $h$ is a symmetric bivector field satisfying a contravariant Codazzi equation. When $h$ is invertible we recover the known notion of pseudo-Hessian manifold. Contravariant pseudo-Hessian manifolds have properties similar to Poisson manifolds and, in fact, to any contravariant pseudo-Hessian manifold $(M,\nabla,h)$ we associate naturally a Poisson tensor on $TM$. We investigate these properties and we study in details many classes of such structures in order to highlight the richness of the geometry of these manifolds.


Title: Covariant Dirac Operators on Quantum Groups
Abstract: We give a construction of a Dirac operator on a quantum group based on any simple Lie algebra of classical type. The Dirac operator is an element in the vector space $U_q(\g) \otimes \mathrm{cl}_q(\g)$ where the second tensor factor is a $q$-deformation of the classical Clifford algebra. The tensor space $ U_q(\g) \otimes \mathrm{cl}_q(\g)$ is given a structure of the adjoint module of the quantum group and the Dirac operator is invariant under this action. The purpose of this approach is to construct equivariant Fredholm modules and $K$-homology cycles. This work generalizes the operator introduced by Bibikov and Kulish in \cite{BK}.


Title: Properties of Mean Value Sets: Angle Conditions, Blowup Solutions, and Nonconvexity
Abstract: We study the mean values sets of the second order divergence form elliptic operator with principal coefficients defined as $$a^{ij}_k(x):= \begin{cases} \alpha_k \delta^{ij}(x) &x_n>0 \beta_k \delta^{ij}(x) &x_n<0. \end{cases}$$ In particular, we will show that the mean value sets associated to such an operator need not be convex as $\alpha_k$ and $\beta_k$ converge to 1. This example then leads to an example of nonconvex mean value sets for smooth $a^{ij}(x)$.


Title: Estimation of the incubation time distribution in the singly and doubly interval censored model
Abstract: We analyze nonparametric estimators for the distribution function of the incubation time in the singly and doubly interval censoring model. The classical approach is to use parametric families like Weibull, log-normal or gamma distributions in the estimation procedure. We propose nonparametric estimates which stay closer to the data than the classical parametric methods. We also give explicit limit distributions for discrete versions of the models and apply this to compute confidence intervals. The methods complement the analysis of the continuous model. R scripts for computation of the estimates are provided on https://github.com/pietg/incubationtime.


Title: Improved estimators in Bell regression model with application
Abstract: In this paper, we propose the application of shrinkage strategies to estimate coefficients in the Bell regression models when prior information about the coefficients is available. The Bell regression models are well-suited for modeling count data with multiple covariates. Furthermore, we provide a detailed explanation of the asymptotic properties of the proposed estimators, including asymptotic biases and mean squared errors. To assess the performance of the estimators, we conduct numerical studies using Monte Carlo simulations and evaluate their simulated relative efficiency. The results demonstrate that the suggested estimators outperform the unrestricted estimator when prior information is taken into account. Additionally, we present an empirical application to demonstrate the practical utility of the suggested estimators.


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


Title: Fundamental Theorem of Projective Geometry over Semirings
Abstract: We state the fundamental theorem of projective geometry for semimodules over semirings, which is facilitated by recent work in the study of bases in semimodules defined over semirings. In the process we explore in detail the linear algebra setup over semirings. We also provide more explicit results to understand the implications of our main theorem on maps between tropical lines in the tropical plane. Along with this we also look at geometrical connections to the rich theory of tropical geometry


Title: On the joint distributions of succession and Eulerian statistics
Abstract: The motivation of this paper is to investigate the joint distribution of succession and Eulerian statistics. We first investigate the enumerators for the joint distribution of descents, big ascents and successions over all permutations in the symmetric group. As an generalization a result of Diaconis-Evans-Graham (Adv. in Appl. Math., 61 (2014), 102--124), we show that two triple set-valued statistics of permutations are equidistributed on symmetric groups. We then introduce the definition of proper left-to-right minimum. We discover that the joint distribution of the succession and proper left-to-right minimum statistics over permutations is a symmetric distribution. In the final part, we discuss the relationship between the fix and cyc (p,q)-Eulerian polynomials and the joint distribution of succession and several Eulerian-type statistics.


Title: On the Structure of Boolean Functions with Small Spectral Norm
Abstract: In this paper we prove results regarding Boolean functions with small spectral norm (the spectral norm of f is $\|\hat{f}\|_1=\sum_{\alpha}|\hat{f}(\alpha)|$). Specifically, we prove the following results for functions $f:\{0,1\}^n \to \{0,1\}$ with $\|\hat{f}\|_1=A$. 1. There is a subspace $V$ of co-dimension at most $A^2$ such that $f|_V$ is constant. 2. f can be computed by a parity decision tree of size $2^{A^2}n^{2A}$. (a parity decision tree is a decision tree whose nodes are labeled with arbitrary linear functions.) 3. If in addition f has at most s nonzero Fourier coefficients, then f can be computed by a parity decision tree of depth $A^2 \log s$. 4. For every $0<\epsilon$ there is a parity decision tree of depth $O(A^2 + \log(1/\epsilon))$ and size $2^{O(A^2)} \cdot \min\{1/\epsilon^2,O(\log(1/\epsilon))^{2A}\}$ that \epsilon-approximates f. Furthermore, this tree can be learned, with probability $1-\delta$, using $\poly(n,\exp(A^2),1/\epsilon,\log(1/\delta))$ membership queries. All the results above also hold (with a slight change in parameters) to functions $f:Z_p^n\to \{0,1\}$.


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


Title: First order sensitivity analysis of symplectic eigenvalues
Abstract: For every $2n \times 2n$ positive definite matrix $A$ there are $n$ positive numbers $d_1(A) \leq \ldots \leq d_n(A)$ associated with $A$ called the symplectic eigenvalues of $A.$ It is known that $d_m$ are continuous functions of $A$ but are not differentiable in general. In this paper, we show that the directional derivative of $d_m$ exists and derive its expression. We also discuss various subdifferential properties of $d_m$ such as Clarke and Michel-Penot subdifferentials.


Title: Recursive Monte Carlo and Variational Inference with Auxiliary Variables
Abstract: A key design constraint when implementing Monte Carlo and variational inference algorithms is that it must be possible to cheaply and exactly evaluate the marginal densities of proposal distributions and variational families. This takes many interesting proposals off the table, such as those based on involved simulations or stochastic optimization. This paper broadens the design space, by presenting a framework for applying Monte Carlo and variational inference algorithms when proposal densities cannot be exactly evaluated. Our framework, recursive auxiliary-variable inference (RAVI), instead approximates the necessary densities using meta-inference: an additional layer of Monte Carlo or variational inference, that targets the proposal, rather than the model. RAVI generalizes and unifies several existing methods for inference with expressive approximating families, which we show correspond to specific choices of meta-inference algorithm, and provides new theory for analyzing their bias and variance. We illustrate RAVI's design framework and theorems by using them to analyze and improve upon Salimans et al.'s Markov Chain Variational Inference, and to design a novel sampler for Dirichlet process mixtures, achieving state-of-the-art results on a standard benchmark dataset from astronomy and on a challenging datacleaning task with Medicare hospital data.


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


Title: Schwartz $κ$-densities for the moduli stack of rank $2$ bundles on a curve over a local field
Abstract: Let $\rm{Bun}$ be the moduli stack of rank $2$ bundles with fixed determinant on a smooth proper curve $C$ over a local field $F$. We show how to associate with a Schwartz $\kappa$-density, for $\rm{Re}(\kappa)\ge 1/2$, a smooth function on the corresponding coarse moduli space of very stable bundles. In the non-archimedean case we also prove that the stack $\rm{Bun}$ is $\kappa$-bounded in the sense of Definition 2.10 of [arXiv:2112.08139] for any $\kappa\in\mathbb{C}$.


Title: $q$-deformation of Aomoto complex
Abstract: A degree one element of the Orlik-Solomon algebra of a hyperplane arrangement defines a cochain complex known as the Aomoto complex. The Aomoto complex can be considerd as the ``linear approximation'' of the twisted cochain complex with coefficients in a complex rank one local system. In this paper, we discuss $q$-deformations of the Aomoto complex. The $q$-deformation is defined by replacing the entries of representation matrices of the coboundary maps with their $q$-analogues. While the resulting maps do not generally define cochain complexes, for certain special basis derived from real structures, the $q$-deformation becomes again a cochain complex. Moreover, it exhibits universality in the sense that any specialization of $q$ to a complex number yields the cochain complex computing the corresponding local system cohomology group.


Title: Frequency-Adaptive Pan-Sharpening with Mixture of Experts
Abstract: Pan-sharpening involves reconstructing missing high-frequency information in multi-spectral images with low spatial resolution, using a higher-resolution panchromatic image as guidance. Although the inborn connection with frequency domain, existing pan-sharpening research has not almost investigated the potential solution upon frequency domain. To this end, we propose a novel Frequency Adaptive Mixture of Experts (FAME) learning framework for pan-sharpening, which consists of three key components: the Adaptive Frequency Separation Prediction Module, the Sub-Frequency Learning Expert Module, and the Expert Mixture Module. In detail, the first leverages the discrete cosine transform to perform frequency separation by predicting the frequency mask. On the basis of generated mask, the second with low-frequency MOE and high-frequency MOE takes account for enabling the effective low-frequency and high-frequency information reconstruction. Followed by, the final fusion module dynamically weights high-frequency and low-frequency MOE knowledge to adapt to remote sensing images with significant content variations. Quantitative and qualitative experiments over multiple datasets demonstrate that our method performs the best against other state-of-the-art ones and comprises a strong generalization ability for real-world scenes. Code will be made publicly at \url{https://github.com/alexhe101/FAME-Net}.


Title: Constant Step Size Least-Mean-Square: Bias-Variance Trade-offs and Optimal Sampling Distributions
Abstract: We consider the least-squares regression problem and provide a detailed asymptotic analysis of the performance of averaged constant-step-size stochastic gradient descent (a.k.a. least-mean-squares). In the strongly-convex case, we provide an asymptotic expansion up to explicit exponentially decaying terms. Our analysis leads to new insights into stochastic approximation algorithms: (a) it gives a tighter bound on the allowed step-size; (b) the generalization error may be divided into a variance term which is decaying as O(1/n), independently of the step-size $\gamma$, and a bias term that decays as O(1/$\gamma$ 2 n 2); (c) when allowing non-uniform sampling, the choice of a good sampling density depends on whether the variance or bias terms dominate. In particular, when the variance term dominates, optimal sampling densities do not lead to much gain, while when the bias term dominates, we can choose larger step-sizes that leads to significant improvements.


Title: Subgroups of bounded rank in hyperbolic 3-manifold groups
Abstract: We prove a finiteness theorem for subgroups of bounded rank in hyperbolic $3$-manifold groups. As a consequence, we show that every bounded rank covering tower of closed hyperbolic $3$-manifolds is a tower of finite covers associated to a fibration over a $1$-orbifold.


Title: Frechet differentiability of the metric projection operator in Banach spaces
Abstract: In this paper, we prove Frechet differentiability of the metric projection operator onto closed balls, closed and convex cylinders and positives cones in uniformly convex and uniformly smooth Banach spaces. With respect to these closed and convex subsets, we find the exact expressions for Frechet derivatives and Gateaux directional derivatives of the metric projection operator.


Title: Basmajian-type identities and Hausdorff dimension of limit sets
Abstract: In this paper, we study Basmajian-type series identities on holomorphic families of Cantor sets associated to one-dimensional complex dynamical systems. We show that the series is absolutely summable if and only if the Hausdorff dimension of the Cantor set is strictly less than one. Throughout the domain of convergence, these identities can be analytically continued and they exhibit nontrivial monodromy.


Title: Integrated Sensing and Communication with Massive MIMO: A Unified Tensor Approach for Channel and Target Parameter Estimation
Abstract: Benefitting from the vast spatial degrees of freedom, the amalgamation of integrated sensing and communication (ISAC) and massive multiple-input multiple-output (MIMO) is expected to simultaneously improve spectral and energy efficiencies as well as the sensing capability. However, a large number of antennas deployed in massive MIMO-ISAC raises critical challenges in acquiring both accurate channel state information and target parameter information. To overcome these two challenges with a unified framework, we first analyze their underlying system models and then propose a novel tensor-based approach that addresses both the channel estimation and target sensing problems. Specifically, by parameterizing the high-dimensional communication channel exploiting a small number of physical parameters, we associate the channel state information with the sensing parameters of targets in terms of angular, delay, and Doppler dimensions. Then, we propose a shared training pattern adopting the same time-frequency resources such that both the channel estimation and target parameter estimation can be formulated as a canonical polyadic decomposition problem with a similar mathematical expression. On this basis, we first investigate the uniqueness condition of the tensor factorization and the maximum number of resolvable targets by utilizing the specific Vandermonde


Title: On the boundary of the central quadratic hyperbolic component
Abstract: We give a concrete description for the boundary of the central quadratic hyperbolic component. The connectedness of the Julia sets of the boundary maps are also considered.


Title: Mechanizing the Metatheory of LF
Abstract: LF is a dependent type theory in which many other formal systems can be conveniently embedded. However, correct use of LF relies on nontrivial metatheoretic developments such as proofs of correctness of decision procedures for LF's judgments. Although detailed informal proofs of these properties have been published, they have not been formally verified in a theorem prover. We have formalized these properties within Isabelle/HOL using the Nominal Datatype Package, closely following a recent article by Harper and Pfenning. In the process, we identified and resolved a gap in one of the proofs and a small number of minor lacunae in others. We also formally derive a version of the type checking algorithm from which Isabelle/HOL can generate executable code. Besides its intrinsic interest, our formalization provides a foundation for studying the adequacy of LF encodings, the correctness of Twelf-style metatheoretic reasoning, and the metatheory of extensions to LF.


Title: Learning Traffic Speed Dynamics from Visualizations
Abstract: Space-time visualizations of macroscopic or microscopic traffic variables is a qualitative tool used by traffic engineers to understand and analyze different aspects of road traffic dynamics. We present a deep learning method to learn the macroscopic traffic speed dynamics from these space-time visualizations, and demonstrate its application in the framework of traffic state estimation. Compared to existing estimation approaches, our approach allows a finer estimation resolution, eliminates the dependence on the initial conditions, and is agnostic to external factors such as traffic demand, road inhomogeneities and driving behaviors. Our model respects causality in traffic dynamics, which improves the robustness of estimation. We present the high-resolution traffic speed fields estimated for several freeway sections using the data obtained from the Next Generation Simulation Program (NGSIM) and German Highway (HighD) datasets. We further demonstrate the quality and utility of the estimation by inferring vehicle trajectories from the estimated speed fields, and discuss the benefits of deep neural network models in approximating the traffic dynamics.


Title: Shayona@SMM4H23: COVID-19 Self diagnosis classification using BERT and LightGBM models
Abstract: This paper describes approaches and results for shared Task 1 and 4 of SMMH4-23 by Team Shayona. Shared Task-1 was binary classification of english tweets self-reporting a COVID-19 diagnosis, and Shared Task-4 was Binary classification of English Reddit posts self-reporting a social anxiety disorder diagnosis. Our team has achieved the highest f1-score 0.94 in Task-1 among all participants. We have leveraged the Transformer model (BERT) in combination with the LightGBM model for both tasks.


Title: Continual Learning: Forget-free Winning Subnetworks for Video Representations
Abstract: Inspired by the Lottery Ticket Hypothesis (LTH), which highlights the existence of efficient subnetworks within larger, dense networks, a high-performing Winning Subnetwork (WSN) in terms of task performance under appropriate sparsity conditions is considered for various continual learning tasks. It leverages pre-existing weights from dense networks to achieve efficient learning in Task Incremental Learning (TIL) scenarios. In Few-Shot Class Incremental Learning (FSCIL), a variation of WSN referred to as the Soft subnetwork (SoftNet) is designed to prevent overfitting when the data samples are scarce. Furthermore, the sparse reuse of WSN weights is considered for Video Incremental Learning (VIL). The use of Fourier Subneural Operator (FSO) within WSN is considered. It enables compact encoding of videos and identifies reusable subnetworks across varying bandwidths. We have integrated FSO into different architectural frameworks for continual learning, including VIL, TIL, and FSCIL. Our comprehensive experiments demonstrate FSO's effectiveness, significantly improving task performance at various convolutional representational levels. Specifically, FSO enhances higher-layer performance in TIL and FSCIL and lower-layer performance in VIL


Title: Quasi-invariant theorem on the Gaussian path space
Abstract: In this article, we will first introduce a class of Gaussian processes, and prove the quasi-invariant theorem with respect to the Gaussian Wiener measure, which is the law of the associated Gaussian process. In particular, it includes the case of the fractional Brownian motion. As applications, we will establish the integration by parts formula and Bismut-Elworthy-Li formula on the Gaussian path space, and by which some logarithmic Sobolev inequalities will be presented. Moreover, we will also provides some applications in the field of financial mathematics.


Title: Borel structurability on the 2-shift of a countable group
Abstract: We show that for any infinite countable group $G$ and for any free Borel action $G \curvearrowright X$ there exists an equivariant class-bijective Borel map from $X$ to the free part $\mathrm{Free}(2^G)$ of the $2$-shift $G \curvearrowright 2^G$. This implies that any Borel structurability which holds for the equivalence relation generated by $G \curvearrowright \mathrm{Free}(2^G)$ must hold a fortiori for all equivalence relations coming from free Borel actions of $G$. A related consequence is that the Borel chromatic number of $\mathrm{Free}(2^G)$ is the maximum among Borel chromatic numbers of free actions of $G$. This answers a question of Marks. Our construction is flexible and, using an appropriate notion of genericity, we are able to show that in fact the generic $G$-equivariant map to $2^G$ lands in the free part. As a corollary we obtain that for every $\epsilon > 0$, every free pmp action of $G$ has a free factor which admits a $2$-piece generating partition with Shannon entropy less than $\epsilon$. This generalizes a result of Danilenko and Park.


Title: Stochastic Approach for Price Optimization Problems with Decision-dependent Uncertainty
Abstract: Price determination is a central research topic of revenue management in marketing. The important aspect in pricing is controlling the stochastic behavior of demand, and the previous studies have tackled price optimization problems with uncertainties. However, many of those studies assumed that uncertainties are independent of decision variables (i.e., prices) and did not consider situations where demand uncertainty depends on price. Although some price optimization studies have dealt with decision-dependent uncertainty, they make application-specific assumptions in order to obtain an optimal solution or an approximation solution. To handle a wider range of applications with decision-dependent uncertainty, we propose a general non-convex stochastic optimization formulation. This approach aims to maximize the expectation of a revenue function with respect to a random variable representing demand under a decision-dependent distribution. We derived an unbiased stochastic gradient estimator by using a well-tuned variance reduction parameter and used it for a projected stochastic gradient descent method to find a stationary point of our problem. We conducted synthetic experiments and simulation experiments with real data on a retail service application. The results show that the proposed method outputs solutions with higher total revenues than baselines.


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


Title: Multi-stages attention Breast cancer classification based on nonlinear spiking neural P neurons with autapses
Abstract: Breast cancer(BC) is a prevalent type of malignant tumor in women. Early diagnosis and treatment are vital for enhancing the patients' survival rate. Downsampling in deep networks may lead to loss of information, so for compensating the detail and edge information and allowing convolutional neural networks to pay more attention to seek the lesion region, we propose a multi-stages attention architecture based on NSNP neurons with autapses. First, unlike the single-scale attention acquisition methods of existing methods, we set up spatial attention acquisition at each feature map scale of the convolutional network to obtain an fusion global information on attention guidance. Then we introduce a new type of NSNP variants called NSNP neurons with autapses. Specifically, NSNP systems are modularized as feature encoders, recoding the features extracted from convolutional neural network as well as the fusion of attention information and preserve the key characteristic elements in feature maps. This ensures the retention of valuable data while gradually transforming high-dimensional complicated info into low-dimensional ones. The proposed method is evaluated on the public dataset BreakHis at various magnifications and classification tasks. It achieves a classification accuracy of 96.32% at all magnification cases, outperforming state-of-the-art methods. Ablation studies are also performed, verifying the proposed model's efficacy. The source code is available at XhuBobYoung/Breast-cancer-Classification.


Title: Variational Autoencoders Without the Variation
Abstract: Variational autoencdoers (VAE) are a popular approach to generative modelling. However, exploiting the capabilities of VAEs in practice can be difficult. Recent work on regularised and entropic autoencoders have begun to explore the potential, for generative modelling, of removing the variational approach and returning to the classic deterministic autoencoder (DAE) with additional novel regularisation methods. In this paper we empirically explore the capability of DAEs for image generation without additional novel methods and the effect of the implicit regularisation and smoothness of large networks. We find that DAEs can be used successfully for image generation without additional loss terms, and that many of the useful properties of VAEs can arise implicitly from sufficiently large convolutional encoders and decoders when trained on CIFAR-10 and CelebA.


Title: Extremal results for odd cycles in sparse pseudorandom graphs
Abstract: We consider extremal problems for subgraphs of pseudorandom graphs. For graphs $F$ and $\Gamma$ the generalized Tur\'an density $\pi_F(\Gamma)$ denotes the density of a maximum subgraph of $\Gamma$, which contains no copy of~$F$. Extending classical Tur\'an type results for odd cycles, we show that $\pi_{F}(\Gamma)=1/2$ provided $F$ is an odd cycle and $\Gamma$ is a sufficiently pseudorandom graph. In particular, for $(n,d,\lambda)$-graphs $\Gamma$, i.e., $n$-vertex, $d$-regular graphs with all non-trivial eigenvalues in the interval $[-\lambda,\lambda]$, our result holds for odd cycles of length $\ell$, provided \[ \lambda^{\ell-2}\ll \frac{d^{\ell-1}}n\log(n)^{-(\ell-2)(\ell-3)}\,. \] Up to the polylog-factor this verifies a conjecture of Krivelevich, Lee, and Sudakov. For triangles the condition is best possible and was proven previously by Sudakov, Szab\'o, and Vu, who addressed the case when $F$ is a complete graph. A construction of Alon and Kahale (based on an earlier construction of Alon for triangle-free $(n,d,\lambda)$-graphs) shows that our assumption on $\Gamma$ is best possible up to the polylog-factor for every odd $\ell\geq 5$.


Title: LLM-SAP: Large Language Model Situational Awareness Based Planning
Abstract: This work pioneers evaluating emergent planning capabilities based on situational awareness in large language models. We contribute (i) novel benchmarks and metrics for standardized assessment; (ii) a unique dataset to spur progress; and (iii) demonstrations that prompting and multi-agent schemes significantly enhance planning performance in context-sensitive planning tasks. Positioning this within a situated agent and automated planning research, we highlight inherent reliability challenges--efficiently mapping world states to actions without environmental guidance remains open despite simulated domain advances. Although out-of-scope, limitations around validation methodology and data availability indicate exciting directions, including fine-tuning on expanded planning corpora and optimizations for triggering fast latent planning. By conclusively demonstrating current methods' promise and limitations via rigorous comparison, we catalyze investigating reliable goal-directed reasoning for situated agents.


Title: A finite difference scheme for two-dimensional singularly perturbed convection-diffusion problem with discontinuous source term
Abstract: We propose a finite difference scheme for the numerical solution of a two-dimensional singularly perturbed convection-diffusion partial differential equation whose solution features interacting boundary and interior layers, the latter due to discontinuities in source term. The problem is posed on the unit square. The second derivative is multiplied by a singular perturbation parameter, $\epsilon$, while the nature of the first derivative term is such that flow is aligned with a boundary. These two facts mean that solutions tend to exhibit layers of both exponential and characteristic type. We solve the problem using a finite difference method, specially adapted to the discontinuities, and applied on a piecewise-uniform (Shishkin). We prove that that the computed solution converges to the true one at a rate that is independent of the perturbation parameter, and is nearly first-order. We present numerical results that verify that these results are sharp.


Title: Simple loops on 2-bridge spheres in Heckoid orbifolds for the trivial knot
Abstract: In this paper, we give a necessary and sufficient condition for an essential simple loop on a $2$-bridge sphere in an even Heckoid orbifold for the trivial knot to be null-homotopic, peripheral or torsion in the orbifold. We also give a necessary and sufficient condition for two essential simple loops on a $2$-bridge sphere in an even Heckoid orbifold for the trivial knot to be homotopic in the orbifold.


Title: Stability over a predicate and prime closure
Abstract: We prove that in a theory $T$ stable over a predicate $P$, for any $\lambda > |T|$, there is a $\lambda$-prime model over any complete set A with a $\lambda$-saturated $P$-part.


Title: Holonomic D-modules on abelian varieties
Abstract: We study the Fourier-Mukai transform for holonomic D-modules on complex abelian varieties. Among other things, we show that the cohomology support loci of a holonomic D-module are finite unions of linear subvarieties, which go through points of finite order for objects of geometric origin; that the standard t-structure on the derived category of holonomic complexes corresponds, under the Fourier-Mukai transform, to a certain perverse coherent t-structure in the sense of Kashiwara and Arinkin-Bezrukavnikov; and that Fourier-Mukai transforms of simple holonomic D-modules are intersection complexes in this t-structure. This supports the conjecture that Fourier-Mukai transforms of holonomic D-modules are "hyperk\"ahler perverse sheaves".


Title: HCIZ integral formula as unitarity of a canonical map between reproducing kernel spaces
Abstract: In this article we prove that the Harish-Chandra-Itzykson-Zuber (HCIZ) integral formula is equivalent to the unitarity of a canonical map between invariant subspaces of Segal-Bargmann spaces. As a consequence, we provide alternative proofs of the HCIZ integral and other results.


Title: Foundations and Scoping of Data Science
Abstract: There has been an increasing recognition of the value of data and of data-based decision making. As a consequence, the development of data science as a field of study has intensified in recent years. However, there is no systematic and comprehensive treatment and understanding of data science. This article describes a systematic and end-to-end framing of the field based on an inclusive definition. It identifies the core components making up the data science ecosystem, presents its lifecycle modeling the development process, and argues its interdisciplinarity.


Title: Some combinatorial problems arising in the dimer model
Abstract: We discuss some diverse open problems in the dimer model, motivated by a geometric viewpoint. This is part of a conference proceedings for the OPAC 2022 conference.


Title: Learning Concept Embeddings with Combined Human-Machine Expertise
Abstract: This paper presents our work on "SNaCK," a low-dimensional concept embedding algorithm that combines human expertise with automatic machine similarity kernels. Both parts are complimentary: human insight can capture relationships that are not apparent from the object's visual similarity and the machine can help relieve the human from having to exhaustively specify many constraints. We show that our SNaCK embeddings are useful in several tasks: distinguishing prime and nonprime numbers on MNIST, discovering labeling mistakes in the Caltech UCSD Birds (CUB) dataset with the help of deep-learned features, creating training datasets for bird classifiers, capturing subjective human taste on a new dataset of 10,000 foods, and qualitatively exploring an unstructured set of pictographic characters. Comparisons with the state-of-the-art in these tasks show that SNaCK produces better concept embeddings that require less human supervision than the leading methods.


Title: An obstruction relating locally finite polygons to translation quadrangles
Abstract: One of the most fundamental open problems in Incidence Geometry, posed by Tits in the 1960s, asks for the existence of so-called "locally finite generalized polygons" | that is, generalized polygons with "mixed parameters" (one being finite and the other not). In a more specialized context, another long-standing problem (from the 1990s) is as to whether the endomorphism ring of any translation generalized quadrangle is a skew field (the answer of which is known in the finite case). (The analogous problem for projective planes, and its positive solution, the "Bruck-Bose construction," lies at the very base of the whole theory of translation planes.) In this short note, we introduce a category, representing certain very specific embeddings of generalized polygons, which surprisingly controls the solution of both (apparently entirely unrelated) problems.


Title: Finiteness conjecture for 3-manifolds obtained from handlebodies by attaching 2-handles
Abstract: We study a generalized Witten's finiteness conjecture for the skein modules of oriented compact 3-manifolds with boundary. We formulate an equivalent version of the generalized finiteness conjecture using handlebodies and 2-handles, and prove the conjecture for some classes with the handlebodies of genus 2 and 3 using the equivalent version.


Title: Acyclicity of Preferences, Nash Equilibria, and Subgame Perfect Equilibria: a Formal and Constructive Equivalence
Abstract: In 1953, Kuhn showed that every sequential game has a Nash equilibrium by showing that a procedure, named ``backward induction'' in game theory, yields a Nash equilibrium. It actually yields Nash equilibria that define a proper subclass of Nash equilibria. In 1965, Selten named this proper subclass subgame perfect equilibria. In game theory, payoffs are rewards usually granted at the end of a game. Although traditional game theory mainly focuses on real-valued payoffs that are implicitly ordered by the usual total order over the reals, works of Simon or Blackwell already involved partially ordered payoffs. This paper generalises the notion of sequential game by replacing real-valued payoff functions with abstract atomic objects, called outcomes, and by replacing the usual total order over the reals with arbitrary binary relations over outcomes, called preferences. This introduces a general abstract formalism where Nash equilibrium, subgame perfect equilibrium, and ``backward induction'' can still be defined. This paper proves that the following three propositions are equivalent: 1) Preferences over the outcomes are acyclic. 2) Every sequential game has a Nash equilibrium. 3) Every sequential game has a subgame perfect equilibrium. The result is fully computer-certified using Coq. Beside the additional guarantee of correctness, the activity of formalisation using Coq also helps clearly identify the useful definitions and the main articulations of the proof.


Title: Efficient UAVs Deployment and Resource Allocation in UAV-Relay Assisted Public Safety Networks for Video Transmission
Abstract: Wireless communication highly depends on the cellular ground base station (GBS). A failure of the cellular GBS, fully or partially, during natural or man-made disasters creates a communication gap in the disaster-affected areas. In such situations, public safety communication (PSC) can significantly save the national infrastructure, property, and lives. Throughout emergencies, the PSC can provide mission-critical communication and video transmission services in the affected area. Unmanned aerial vehicles (UAVs) as flying base stations (UAV-BSs) are particularly suitable for PSC services as they are flexible, mobile, and easily deployable. This manuscript considers a multi-UAV-assisted PSC network with an observational UAV receiving videos from the affected area's ground users (AGUs) and transmitting them to the nearby GBS via a relay UAV. The objective of the proposed study is to maximize the average utility of the video streams generated by the AGUs upon reaching the GBS. This is achieved by optimizing the positions of the observational and relay UAVs, as well as the distribution of communication resources, such as bandwidth, and transmit power, while satisfying the system-designed constraints, such as transmission rate, rate outage probability, transmit power budget, and available bandwidth. To this end, a joint UAVs placement and resource allocation problem is mathematically formulated. The proposed problem poses a significant challenge for a solution. Considering the block coordinate descent and successive convex approximation techniques, an efficient iterative algorithm is proposed. Finally, simulation results are provided which show that our proposed approach outperforms the existing methods.


Title: Leveraging SAM for Single-Source Domain Generalization in Medical Image Segmentation
Abstract: Domain Generalization (DG) aims to reduce domain shifts between domains to achieve promising performance on the unseen target domain, which has been widely practiced in medical image segmentation. Single-source domain generalization (SDG) is the most challenging setting that trains on only one source domain. Although existing methods have made considerable progress on SDG of medical image segmentation, the performances are still far from the applicable standards when faced with a relatively large domain shift. In this paper, we leverage the Segment Anything Model (SAM) to SDG to greatly improve the ability of generalization. Specifically, we introduce a parallel framework, the source images are sent into the SAM module and normal segmentation module respectively. To reduce the calculation resources, we apply a merging strategy before sending images to the SAM module. We extract the bounding boxes from the segmentation module and send the refined version as prompts to the SAM module. We evaluate our model on a classic DG dataset and achieve competitive results compared to other state-of-the-art DG methods. Furthermore, We conducted a series of ablation experiments to prove the effectiveness of the proposed method. The code is publicly available at https://github.com/SARIHUST/SAMMed.


Title: Emerging Language Spaces Learned From Massively Multilingual Corpora
Abstract: Translations capture important information about languages that can be used as implicit supervision in learning linguistic properties and semantic representations. In an information-centric view, translated texts may be considered as semantic mirrors of the original text and the significant variations that we can observe across various languages can be used to disambiguate a given expression using the linguistic signal that is grounded in translation. Parallel corpora consisting of massive amounts of human translations with a large linguistic variation can be applied to increase abstractions and we propose the use of highly multilingual machine translation models to find language-independent meaning representations. Our initial experiments show that neural machine translation models can indeed learn in such a setup and we can show that the learning algorithm picks up information about the relation between languages in order to optimize transfer leaning with shared parameters. The model creates a continuous language space that represents relationships in terms of geometric distances, which we can visualize to illustrate how languages cluster according to language families and groups. Does this open the door for new ideas of data-driven language typology with promising models and techniques in empirical cross-linguistic research?


Title: Learning Pixel Trajectories with Multiscale Contrastive Random Walks
Abstract: A range of video modeling tasks, from optical flow to multiple object tracking, share the same fundamental challenge: establishing space-time correspondence. Yet, approaches that dominate each space differ. We take a step towards bridging this gap by extending the recent contrastive random walk formulation to much denser, pixel-level space-time graphs. The main contribution is introducing hierarchy into the search problem by computing the transition matrix between two frames in a coarse-to-fine manner, forming a multiscale contrastive random walk when extended in time. This establishes a unified technique for self-supervised learning of optical flow, keypoint tracking, and video object segmentation. Experiments demonstrate that, for each of these tasks, the unified model achieves performance competitive with strong self-supervised approaches specific to that task. Project webpage: https://jasonbian97.github.io/flowwalk


Title: Dynamically Masked Discriminator for Generative Adversarial Networks
Abstract: Training Generative Adversarial Networks (GANs) remains a challenging problem. The discriminator trains the generator by learning the distribution of real/generated data. However, the distribution of generated data changes throughout the training process, which is difficult for the discriminator to learn. In this paper, we propose a novel method for GANs from the viewpoint of online continual learning. We observe that the discriminator model, trained on historically generated data, often slows down its adaptation to the changes in the new arrival generated data, which accordingly decreases the quality of generated results. By treating the generated data in training as a stream, we propose to detect whether the discriminator slows down the learning of new knowledge in generated data. Therefore, we can explicitly enforce the discriminator to learn new knowledge fast. Particularly, we propose a new discriminator, which automatically detects its retardation and then dynamically masks its features, such that the discriminator can adaptively learn the temporally-vary distribution of generated data. Experimental results show our method outperforms the state-of-the-art approaches.


Title: The Art of Deception: Robust Backdoor Attack using Dynamic Stacking of Triggers
Abstract: The area of Machine Learning as a Service (MLaaS) is experiencing increased implementation due to recent advancements in the AI (Artificial Intelligence) industry. However, this spike has prompted concerns regarding AI defense mechanisms, specifically regarding potential covert attacks from third-party providers that cannot be entirely trusted. Recent research has uncovered that auditory backdoors may use certain modifications as their initiating mechanism. DynamicTrigger is introduced as a methodology for carrying out dynamic backdoor attacks that use cleverly designed tweaks to ensure that corrupted samples are indistinguishable from clean. By utilizing fluctuating signal sampling rates and masking speaker identities through dynamic sound triggers (such as the clapping of hands), it is possible to deceive speech recognition systems (ASR). Our empirical testing demonstrates that DynamicTrigger is both potent and stealthy, achieving impressive success rates during covert attacks while maintaining exceptional accuracy with non-poisoned datasets.


Title: The distance signatures of the incidence graphs of affine resolvable designs
Abstract: In this note, we determined the distance signatures of the incidence matrices of affine resolvable designs. This proves a conjecture by Kohei Yamada.


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


Title: Improving Sequential Query Recommendation with Immediate User Feedback
Abstract: We propose an algorithm for next query recommendation in interactive data exploration settings, like knowledge discovery for information gathering. The state-of-the-art query recommendation algorithms are based on sequence-to-sequence learning approaches that exploit historical interaction data. Due to the supervision involved in the learning process, such approaches fail to adapt to immediate user feedback. We propose to augment the transformer-based causal language models for query recommendations to adapt to the immediate user feedback using multi-armed bandit (MAB) framework. We conduct a large-scale experimental study using log files from a popular online literature discovery service and demonstrate that our algorithm improves the per-round regret substantially, with respect to the state-of-the-art transformer-based query recommendation models, which do not make use of immediate user feedback. Our data model and source code are available at https://github.com/shampp/exp3_ss


Title: Distribution of primes represented by polynomials and Multiple Dedekind zeta functions
Abstract: n this paper, we state several conjectures regarding distribution of primes and of pairs of primes represented by irreducible homogeneous polynomial in two variables $f(a,b)$. We formulate conjectures with respect to the slope $t=b/a$ for any irreducible polynomial $f$. Here, we formulate a conjecture for all irreducible polynomials. We also consider conjectures for distribution of pairs of primes. It show unexpected relation to multiple Dedekind zeta function - at $s=2$ for one prime and at $(s_1,s_2)=(2,2)$ for pairs of primes. We tested the conjecture for pairs of primes for several quadratic fields. The conjecture for pairs of primes and multiple Dedekind zeta function over the Gaussian integers provide error less than a tenth of a percent. We also tested conjectures that compare sets of primes in a pair of different quadratic fields. Numerically, such quotients can be expressed in terms of regulators and class numbers. Some of the data, together with the code, is available on GitHub, (see \cite{Zouberou}).


Title: A Cybersecurity Risk Analysis Framework for Systems with Artificial Intelligence Components
Abstract: The introduction of the European Union Artificial Intelligence Act, the NIST Artificial Intelligence Risk Management Framework, and related norms demands a better understanding and implementation of novel risk analysis approaches to evaluate systems with Artificial Intelligence components. This paper provides a cybersecurity risk analysis framework that can help assessing such systems. We use an illustrative example concerning automated driving systems.


Title: Radon-type transforms for holomorphic and Hermitian monogenic functions
Abstract: The standard Radon transform of holomorphic functions is not always well defined, as the integration of such functions over planes may not converge. In this paper, we introduce new Radon-type transforms of co-(real)dimension $2$ for harmonic and holomorphic functions on the unit ball. These transforms are abstractly defined as orthogonal projections onto spaces of complex harmonic and holomorphic plane waves, respectively. The inversion formulas are derived based on the dual transform, while the latter is defined as an integration on a complex Stiefel manifold. Our transforms are extended to the Fock space and give rise to a new transform defined on the entire $L^{2}(\mathbb{R}^{n})$ through the Segal-Bargmann transform. Furthermore, we develop these transforms for Hermitian monogenic functions on the unit ball, thereby refining the Szeg\"o-Radon transform for monogenic functions introduced by Colombo, Sabadini and Sommen.


Title: Continuity of composition operators in Sobolev spaces
Abstract: We prove that all the composition operators $T_f(g):= f\circ g$, which take the Adams-Frazier space $W^{m}_{p}\cap \dot{W}^{1}_{mp}(\mathbb{R}^n)$ to itself, are continuous mappings from $W^{m}_{p}\cap \dot{W}^{1}_{mp}(\mathbb{R}^n)$ to itself, for every integer $m\geq 2$ and every real number $1\leq p<+\infty$. The same automatic continuity property holds for Sobolev spaces $W^m_p(\mathbb{R}^n)$ for $m\geq 2$ and $1\leq p<+\infty$.


Title: The triviality of a certain invariant of link maps in the four-sphere
Abstract: It is an open problem whether Kirk's $\sigma$ invariant is the complete obstruction to a link map $S^2\cup S^2\to S^4$ being link homotopically trivial. With the objective of constructing counterexamples, Li proposed a link homotopy invariant $\omega$ that is defined on the kernel of $\sigma$ and also obstructs link nullhomotopy. We show that $\omega$ is determined by $\sigma$, and is a strictly weaker invariant.


Title: Perfect numbers and Fibonacci primes
Abstract: In this paper, we introduce the concept of $F$-perfect number, which is a positive integer $n$ such that $\sum_{d|n,d<n}d^2=3n$. We prove that all the $F$-perfect numbers are of the form $n=F_{2k-1}F_{2k+1}$, where both $F_{2k-1}$ and $F_{2k+1}$ are Fibonacci primes. Moreover, we obtain other interesting results and raise a new conjecture on perfect numbers.


Title: Few-shot Adaptation of Multi-modal Foundation Models: A Survey
Abstract: Multi-modal (vision-language) models, such as CLIP, are replacing traditional supervised pre-training models (e.g., ImageNet-based pre-training) as the new generation of visual foundation models. These models with robust and aligned semantic representations learned from billions of internet image-text pairs and can be applied to various downstream tasks in a zero-shot manner. However, in some fine-grained domains like medical imaging and remote sensing, the performance of multi-modal foundation models often leaves much to be desired. Consequently, many researchers have begun to explore few-shot adaptation methods for these models, gradually deriving three main technical approaches: 1) prompt-based methods, 2) adapter-based methods, and 3) external knowledge-based methods. Nevertheless, this rapidly developing field has produced numerous results without a comprehensive survey to systematically organize the research progress. Therefore, in this survey, we introduce and analyze the research advancements in few-shot adaptation methods for multi-modal models, summarizing commonly used datasets and experimental setups, and comparing the results of different methods. In addition, due to the lack of reliable theoretical support for existing methods, we derive the few-shot adaptation generalization error bound for multi-modal models. The theorem reveals that the generalization error of multi-modal foundation models is constrained by three factors: domain gap, model capacity, and sample size. Based on this, we propose three possible solutions from the following aspects: 1) adaptive domain generalization, 2) adaptive model selection, and 3) adaptive knowledge utilization.


Title: On hypergraphs without loose cycles
Abstract: Recently, Mubayi and Wang showed that for $r\ge 4$ and $\ell \ge 3$, the number of $n$-vertex $r$-graphs that do not contain any loose cycle of length $\ell$ is at most $2^{O( n^{r-1} (\log n)^{(r-3)/(r-2)})}$. We improve this bound to $2^{O( n^{r-1} \log \log n) }$.


Title: On the Rainbow Ramsey theorem and the Canonical Ramsey Theorem for pairs without AC
Abstract: In set theory without the Axiom of Choice, we study the set-theoretic strength of a generalized version of the Rainbow Ramsey theorem and the Canonical Ramsey Theorem for pairs introduced by Erd\H{o}s and Rado, concerning their interrelation with several weak choice forms.


Title: Towards Open Set Deep Networks
Abstract: Deep networks have produced significant gains for various visual recognition problems, leading to high impact academic and commercial applications. Recent work in deep networks highlighted that it is easy to generate images that humans would never classify as a particular object class, yet networks classify such images high confidence as that given class - deep network are easily fooled with images humans do not consider meaningful. The closed set nature of deep networks forces them to choose from one of the known classes leading to such artifacts. Recognition in the real world is open set, i.e. the recognition system should reject unknown/unseen classes at test time. We present a methodology to adapt deep networks for open set recognition, by introducing a new model layer, OpenMax, which estimates the probability of an input being from an unknown class. A key element of estimating the unknown probability is adapting Meta-Recognition concepts to the activation patterns in the penultimate layer of the network. OpenMax allows rejection of "fooling" and unrelated open set images presented to the system; OpenMax greatly reduces the number of obvious errors made by a deep network. We prove that the OpenMax concept provides bounded open space risk, thereby formally providing an open set recognition solution. We evaluate the resulting open set deep networks using pre-trained networks from the Caffe Model-zoo on ImageNet 2012 validation data, and thousands of fooling and open set images. The proposed OpenMax model significantly outperforms open set recognition accuracy of basic deep networks as well as deep networks with thresholding of SoftMax probabilities.


Title: A spectral result for Hardy inequalities
Abstract: Let P be a linear, second order, elliptic operator satisfying a Hardy inequality with potential W (i.e. $P-W\geq0$) and best constant $\alpha$. We give conditions so that the spectrum of $W^{-1}P$ is $[\alpha,\infty)$. We apply this to several well-known Hardy inequalities: (improved) Hardy inequalities on a bounded convex domain with potential involving the distance to the boundary, and Hardy inequalities for minimal submanifolds of the Euclidean space.


Title: The Chern class for $K_3$ and the cyclic quantum dilogarithm
Abstract: In this note we confirm the conjecture of Calegari, Garoufalidis and Zagier in their recent paper in Ann. Sci. \'{E}cole Normale Sup. that $R_\zeta=c_\zeta^2$, where $R_\zeta$ is their map on $K_3$ defined using the cyclic quantum dilogarithm and $c_\zeta$ is the Chern class map on $K_3$.


Title: Large Language Model Capabilities in Perioperative Risk Prediction and Prognostication
Abstract: We investigate whether general-domain large language models such as GPT-4 Turbo can perform risk stratification and predict post-operative outcome measures using a description of the procedure and a patient's clinical notes derived from the electronic health record. We examine predictive performance on 8 different tasks: prediction of ASA Physical Status Classification, hospital admission, ICU admission, unplanned admission, hospital mortality, PACU Phase 1 duration, hospital duration, and ICU duration. Few-shot and chain-of-thought prompting improves predictive performance for several of the tasks. We achieve F1 scores of 0.50 for ASA Physical Status Classification, 0.81 for ICU admission, and 0.86 for hospital mortality. Performance on duration prediction tasks were universally poor across all prompt strategies. Current generation large language models can assist clinicians in perioperative risk stratification on classification tasks and produce high-quality natural language summaries and explanations.


Title: On-the-fly Adaptation of Patrolling Strategies in Changing Environments
Abstract: We consider the problem of efficient patrolling strategy adaptation in a changing environment where the topology of Defender's moves and the importance of guarded targets change unpredictably. The Defender must instantly switch to a new strategy optimized for the new environment, not disrupting the ongoing patrolling task, and the new strategy must be computed promptly under all circumstances. Since strategy switching may cause unintended security risks compromising the achieved protection, our solution includes mechanisms for detecting and mitigating this problem. The efficiency of our framework is evaluated experimentally.


Title: A dilation theoretic approach to approximation by inner functions
Abstract: Using results from theory of operators on a Hilbert space, we prove approximation results for matrix-valued holomorphic functions on the unit disc and the unit bidisc. The essential tools are the theory of unitary dilation of a contraction and the realization formula for functions in the unit ball of $H^\infty$. We first prove a generalization of a result of Carath\'eodory. This generalization has many applications. A uniform approximation result for matrix-valued holomorphic functions which extend continuously to the unit circle is proved using the Potapov factorization. This generalizes a theorem due to Fisher. Approximation results are proved for matrix-valued functions for whom a naturally associated kernel has finitely many negative squares. This uses the Krein-Langer factorization. Approximation results for $J$-contractive meromorphic functions where $J$ induces an indefinite metric on $\mathbb C^N$ are proved using the Potapov-Ginzburg Theorem. Moreover, approximation results for holomorphic functions on the unit disc with values in certain other domains of interest are also proved.


Title: Coded Beam Training
Abstract: In extremely large-scale multiple input multiple output (XL-MIMO) systems for future sixth-generation (6G) communications, codebook-based beam training stands out as a promising technology to acquire channel state information (CSI). Despite their effectiveness, when the pilot overhead is limited, existing beam training methods suffer from significant achievable rate degradation for remote users with low signal-to-noise ratio (SNR). To tackle this challenge, leverging the error-correcting capability of channel codes, we introduce channel coding theory into hierarchical beam training to extend the coverage area. Specifically, we establish the duality between hierarchical beam training and channel coding, and the proposed coded beam training scheme serves as a general framework. Then, we present two specific implementations exemplified by coded beam training methods based on Hamming codes and convolutional codes, during which the beam encoding and decoding processes are refined respectively to better accommodate to the beam training problem. Simulation results have demonstrated that, the proposed coded beam training method can enable reliable beam training performance for remote users with low SNR, while keeping training overhead low.


Title: The Cauchy problem on large time for the Water Waves equations with large topography variations
Abstract: We prove the local existence for the Water Waves equations with large bathymetric variations on a time interval of size 1/\epsilon, where $\epsilon$ measures the amplitude of the wave. We just need the presence of surface tension.


Title: The cardinality of orthogonal exponentials of planar self-affine measures with three-element digit sets
Abstract: In this paper, we consider the planar self-affine measures $\mu_{M,D}$ generated by an expanding matrix $M\in M_2(\mathbb{Z})$ and an integer digit set $ D=\left\{ {\left( {\begin{array}{*{20}{c}} 0\\ 0 \end{array}} \right),\left( {\begin{array}{*{20}{c}} \alpha_1\\ \alpha_2 \end{array}} \right),\left( {\begin{array}{*{20}{c}} \beta_1\\ \beta_2 \end{array}} \right)} \right\} $ with $\alpha_1\beta_2-\alpha_2\beta_1\neq0$. We show that if $\det(M)\notin 3\mathbb{Z}$, then the mutually orthogonal exponential functions in $L^2(\mu_{M,D})$ is finite, and the exact maximal cardinality is given.


Title: Heisenberg uncertainty principle and its analogues in higher dimension: via Wigdersons' method
Abstract: The following question was proposed by Avi Wigderson and Yuval Wigderson: Is it possible to use the method in their paper(The uncertainty principle: variations on a theme) to prove Heisenberg uncertainty principle in higher dimension R^d, and get the correct dependence of the constant on d? We answer this question affirmatively, and also prove some generalizations of Heisenberg uncertainty principle in R^d via Wigdersons' method.


Title: High-Resolution Image Inpainting with Iterative Confidence Feedback and Guided Upsampling
Abstract: Existing image inpainting methods often produce artifacts when dealing with large holes in real applications. To address this challenge, we propose an iterative inpainting method with a feedback mechanism. Specifically, we introduce a deep generative model which not only outputs an inpainting result but also a corresponding confidence map. Using this map as feedback, it progressively fills the hole by trusting only high-confidence pixels inside the hole at each iteration and focuses on the remaining pixels in the next iteration. As it reuses partial predictions from the previous iterations as known pixels, this process gradually improves the result. In addition, we propose a guided upsampling network to enable generation of high-resolution inpainting results. We achieve this by extending the Contextual Attention module to borrow high-resolution feature patches in the input image. Furthermore, to mimic real object removal scenarios, we collect a large object mask dataset and synthesize more realistic training data that better simulates user inputs. Experiments show that our method significantly outperforms existing methods in both quantitative and qualitative evaluations. More results and Web APP are available at https://zengxianyu.github.io/iic.


Title: Multiclass Common Spatial Pattern for EEG based Brain Computer Interface with Adaptive Learning Classifier
Abstract: In Brain Computer Interface (BCI), data generated from Electroencephalogram (EEG) is non-stationary with low signal to noise ratio and contaminated with artifacts. Common Spatial Pattern (CSP) algorithm has been proved to be effective in BCI for extracting features in motor imagery tasks, but it is prone to overfitting. Many algorithms have been devised to regularize CSP for two class problem, however they have not been effective when applied to multiclass CSP. Outliers present in data affect extracted CSP features and reduces performance of the system. In addition to this non-stationarity present in the features extracted from the CSP present a challenge in classification. We propose a method to identify and remove artifact present in the data during pre-processing stage, this helps in calculating eigenvectors which in turn generates better CSP features. To handle the non-stationarity, Self-Regulated Interval Type-2 Neuro-Fuzzy Inference System (SRIT2NFIS) was proposed in the literature for two class EEG classification problem. This paper extends the SRIT2NFIS to multiclass using Joint Approximate Diagonalization (JAD). The results on standard data set from BCI competition IV shows significant increase in the accuracies from the current state of the art methods for multiclass classification.


Title: A new combinatorial approach for edge universality of Wigner matrices
Abstract: In this paper we introduce a new combinatorial approach to analyze the trace of large powers of Wigner matrices. Our approach is motivated from the paper by \citet{sosh}. However the counting approach is different. We start with classical word sentence approach similar to \citet{AZ05} and take the motivation from \citet{sinaisosh}, \citet{sosh} and \citet{peche2009universality} to encode the words to objects similar to Dyck paths. To be precise the map takes a word to a Dyck path with some edges removed from it. Using this new counting we prove edge universality for large Wigner matrices with sub-Gaussian entries. One novelty of this approach is unlike \citet{sinaisosh}, \citet{sosh} and \citet{peche2009universality} we do not need to assume the entries of the matrices are symmetrically distributed around $0$. The main technical contribution of this paper is two folded. Firstly we produce an encoding of the ``contributing words" (for definition one might look at Section \ref{sec:word}) of the Wigner matrix which retrieves the edge universality. Hence this is the best one can do. We hope this method will be applicable to many other scenarios in random matrices. Secondly in course of the paper we give a combinatorial description of the GOE Tracy Widom law. The explanation for GUE is very similar. This explanation might be important for the models where exact calculations are not available but some combinatorial structures are present.


Title: Edge detection with trigonometric polynomial shearlets
Abstract: In this paper we show that certain trigonometric polynomial shearlets which are special cases of directional de la Vall\'{e}e Poussin type wavelets are able to detect singularities along boundary curves of periodic characteristic functions. Motivated by recent results for discrete shearlets in two dimensions, we provide lower and upper estimates for the magnitude of corresponding inner products. In the proof we use localization properties of trigonometric polynomial shearlets in the time and frequency domain and, among other things, bounds for certain Fresnel integrals. Moreover, we give numerical examples which underline the theoretical results.


Title: Attackers reveal their arsenal: An investigation of adversarial techniques in CTI reports
Abstract: Context: Cybersecurity vendors often publish cyber threat intelligence (CTI) reports, referring to the written artifacts on technical and forensic analysis of the techniques used by the malware in APT attacks. Objective: The goal of this research is to inform cybersecurity practitioners about how adversaries form cyberattacks through an analysis of adversarial techniques documented in cyberthreat intelligence reports. Dataset: We use 594 adversarial techniques cataloged in MITRE ATT\&CK. We systematically construct a set of 667 CTI reports that MITRE ATT\&CK used as citations in the descriptions of the cataloged adversarial techniques. Methodology: We analyze the frequency and trend of adversarial techniques, followed by a qualitative analysis of the implementation of techniques. Next, we perform association rule mining to identify pairs of techniques recurring in APT attacks. We then perform qualitative analysis to identify the underlying relations among the techniques in the recurring pairs. Findings: The set of 667 CTI reports documents 10,370 techniques in total, and we identify 19 prevalent techniques accounting for 37.3\% of documented techniques. We also identify 425 statistically significant recurring pairs and seven types of relations among the techniques in these pairs. The top three among the seven relationships suggest that techniques used by the malware inter-relate with one another in terms of (a) abusing or affecting the same system assets, (b) executing in sequences, and (c) overlapping in their implementations. Overall, the study quantifies how adversaries leverage techniques through malware in APT attacks based on publicly reported documents. We advocate organizations prioritize their defense against the identified prevalent techniques and actively hunt for potential malicious intrusion based on the identified pairs of techniques.


Title: Lie Algebroids and generalized projective structures on Riemann surfaces
Abstract: The space of generalized projective structures on a Riemann surface $\Sigma$ of genus g with n marked points is the affine space over the cotangent bundle to the space of SL(N)-opers. It is a phase space of $W_N$-gravity on $\Sigma\times\mathbb{R}$. This space is a generalization of the space of projective structures on the Riemann surface. We define the moduli space of $W_N$-gravity as a symplectic quotient with respect to the canonical action of a special class of Lie algebroids. This moduli space describes in particular the moduli space of deformations of complex structures on the Riemann surface by differential operators of finite order, or equivalently, by a quotient space of Volterra operators. We call these algebroids the Adler-Gelfand-Dikii (AGD) algebroids, because they are constructed by means of AGD bivector on the space of opers restricted on a circle. The AGD-algebroids are particular case of Lie algebroids related to a Poisson sigma-model. The moduli space of the generalized projective structure can be described by cohomology of a BRST-complex.


Title: Entropy-minimizing dynamical transport on Riemannian manifolds
Abstract: Given a smooth Riemannian manifold $(M,g)$, compact and without boundary, we analyze the dynamical optimal mass transport problem where the cost is given by the sum of the kinetic energy and the relative entropy with respect to a reference volume measure $e^{-V}dx$. Under the only assumption that the prescribed marginals lie in $L^1(M)$, and a lower bound on the Ricci curvature, we characterize the minimal curves as unique weak solutions of the optimality system coupling the continuity equation with a backward Hamilton-Jacobi equation (with source given by $\log (m)$). We give evidence that the entropic cost enhances diffusive effects in the evolution of the optimal densities, proving $L^1\to L^\infty$ regularization in time for any initial-terminal data, and smoothness of the solutions whenever the marginals are positive and smooth. We use displacement convexity arguments (in the Eulerian approach) and gradient bounds from quasilinear elliptic equations. We also prove the convergence of optimal curves towards the classical Wasserstein geodesics, as the entropic term is multiplied by a vanishing parameter, showing that this kind of functionals can be used to build a smoothing approximation of the standard optimal transport problem.


Title: Improving the Design of Linear Controllers for Homogeneous Platooning under Disturbances
Abstract: This paper addresses the problem of longitudinal platooning control of homogeneous vehicles subject to external disturbances, such as wind gusts, road slopes, and parametric uncertainties. Our control objective is to maintain the relative distance of the cars regarding their nearby teammates in a decentralized manner. Therefore, we proposed a novel control law to compute the acceleration commands of each vehicle that includes the integral of the spacing error, which endows the controller with the capability to mitigate external disturbances in steady-state conditions. We adopt a constant distance spacing policy and employ generalized look-ahead and bidirectional network topologies. We provide formal conditions for the controller synthesis that ensure the internal stability of the platoon under the proposed control law in the presence of constant and bounded disturbances affecting multiple vehicles. Experiments considering nonlinear vehicle models in the high-fidelity CARLA simulator environment under different disturbances, parametric uncertainties, and several network topologies demonstrate the effectiveness of our approach.


Title: Estimating continuous data of wrist joint angles using ultrasound images
Abstract: Ultrasound imaging has recently been introduced as a sensing interface for joint motion estimation. The use of ultrasound images as an estimation method is expected to improve the control performance of assistive devices and human--machine interfaces. This study aimed to estimate continuous wrist joint angles using ultrasound images. Specifically, in an experiment, joint angle information was obtained during extension--flexion movements, and ultrasound images of the associated muscles were acquired. Using the features obtained from ultrasound images, a multivariate linear regression model was used to estimate the joint angles. The coordinates of the feature points obtained using optical flow from the ultrasound images were used as explanatory variables of the multivariate linear regression model. The model was trained and tested for each trial by each participant to verify the estimation accuracy. The results show that the mean and standard deviation of the estimation accuracy for all trials were root mean square error (RMSE)=1.82 $\pm$ 0.54 deg and coefficient of determination (R2)=0.985 $\pm$ 0.009. Our method achieves a highly accurate estimation of joint angles compared with previous studies using other signals, such as surface electromyography, while the multivariate linear regression model is simple and both computational and model training costs are low.


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


Title: The Hochschild Cohomology of Uniform Roe Algebras
Abstract: In Rufus Willett's and the authors paper "Bounded Derivations on Uniform Roe Algebras" we showed that all bounded derivations on a uniform Roe algebra $C^*_u(X)$ associated to a bounded geometry metric space $X$ are inner. This naturally leads to the question of whether or not the higher dimensional Hochschild cohomology groups of the uniform Roe algebra vanish also. While we cannot answer this question completely, we are able to give necessary and sufficient conditions for the vanishing of $H^n_c(C_u^*(X),C_u^*(X))$. Lastly, we show that if the norm continuous Hochschild cohomology of a uniform Roe algebra vanishes in all dimensions then the ultraweak-weak* continuous Hochschild cohomology of that uniform Roe algebra vanishes also.


Title: Complex structures on stratified Lie algebras
Abstract: This paper investigates some properties of complex structures on Lie algebras. In particular, we focus on $\textit{nilpotent}$ $\textit{complex structures}$ that are characterized by a suitable $J$-invariant ascending or descending central series $\mathfrak{d}^j$ and $\mathfrak{d}_j$ respectively. In this article, we introduce a new descending series $\mathfrak{p}_j$ and use it to give proof of a new characterization of nilpotent complex structures. We examine also whether nilpotent complex structures on stratified Lie algebras preserve the strata. We find that there exists a $J$-invariant stratification on a step $2$ nilpotent Lie algebra with a complex structure.


Title: Construction of Jacobi forms using adjoint of Jacobi-Serre derivative
Abstract: In the article, we study the Oberdieck derivative defined on the space of weak Jacobi forms. We prove that the Oberdieck derivative maps a Jacobi form to a Jacobi form. Moreover, we study the adjoint of Oberdieck derivative of a Jacobi cusp form with respect to Petersson scalar product defined on the space of Jacobi forms. As a consequence, we also obtain the adjoint of Jacobi-Serre derivative (defined in an unpublished work of Oberdieck). As an application, we obtain certain relations among the Fourier coefficients of Jacobi forms.


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


Title: Machine Learning in Robotic Ultrasound Imaging: Challenges and Perspectives
Abstract: This article reviews the recent advances in intelligent robotic ultrasound (US) imaging systems. We commence by presenting the commonly employed robotic mechanisms and control techniques in robotic US imaging, along with their clinical applications. Subsequently, we focus on the deployment of machine learning techniques in the development of robotic sonographers, emphasizing crucial developments aimed at enhancing the intelligence of these systems. The methods for achieving autonomous action reasoning are categorized into two sets of approaches: those relying on implicit environmental data interpretation and those using explicit interpretation. Throughout this exploration, we also discuss practical challenges, including those related to the scarcity of medical data, the need for a deeper understanding of the physical aspects involved, and effective data representation approaches. Moreover, we conclude by highlighting the open problems in the field and analyzing different possible perspectives on how the community could move forward in this research area.


Title: SCALA: Sparsification-based Contrastive Learning for Anomaly Detection on Attributed Networks
Abstract: Anomaly detection on attributed networks aims to find the nodes whose behaviors are significantly different from other majority nodes. Generally, network data contains information about relationships between entities, and the anomaly is usually embodied in these relationships. Therefore, how to comprehensively model complex interaction patterns in networks is still a major focus. It can be observed that anomalies in networks violate the homophily assumption. However, most existing studies only considered this phenomenon obliquely rather than explicitly. Besides, the node representation of normal entities can be perturbed easily by the noise relationships introduced by anomalous nodes. To address the above issues, we present a novel contrastive learning framework for anomaly detection on attributed networks, \textbf{SCALA}, aiming to improve the embedding quality of the network and provide a new measurement of qualifying the anomaly score for each node by introducing sparsification into the conventional method. Extensive experiments are conducted on five benchmark real-world datasets and the results show that SCALA consistently outperforms all baseline methods significantly.


Title: Sharp phase transition for random loop models on trees
Abstract: We investigate the random loop model on the $d$-ary tree. For $d \geq 3$, we establish a (locally) sharp phase transition for the existence of infinite loops. Moreover, we derive rigorous bounds that in principle allow to determine the value of the critical parameter with arbitrary precision. Additionally, we prove the existence of an asymptotic expansion for the critical parameter in terms of $d^{-1}$. The corresponding coefficients can be determined in a schematic way and we calculated them up to order $6$.


Title: Nonlocal problems with critical Hardy nonlinearity
Abstract: By means of variational methods we establish existence and multiplicity of solutions for a class of nonlinear nonlocal problems involving the fractional p-Laplacian and a combined Sobolev and Hardy nonlinearity at subcritical and critical growth.


Title: Ricci flows which terminate in cones
Abstract: We prove that a complete solution to the Ricci flow on $M\times [-T, 0)$ which has quadratic curvature decay on some end of $M$ and converges locally smoothly to the end of a cone on that neighborhood as $t\nearrow 0$ must be a gradient shrinking soliton.


Title: Representing General Stochastic Processes as Martingale Laws
Abstract: Random variables $X^i$, $i=1,2$ are 'probabilistically equivalent' if they have the same law. Moreover, in any class of equivalent random variables it is easy to select canonical representatives. The corresponding questions are more involved for processes $X^i$ on filtered stochastic bases $(\Omega^i, \mathcal F^i, \mathbb P^i, (\mathcal F^i_t)_{t\in [0,1]})$. Here equivalence in law does not capture relevant properties of processes such as the solutions to stochastic control or multistage decision problems. This motivates Aldous to introduce the stronger notion of synonymity based on prediction processes. Stronger still, Hoover--Keisler formalize what it means that $X^i$, $i=1,2$ have the same probabilistic properties. We establish that canonical representatives of the Hoover--Keisler equivalence classes are given precisely by the set of all Markov-martingale laws on a specific nested path space $\mathsf M_\infty$. As a consequence we obtain that, modulo Hoover--Keisler equivalence, the class of stochastic processes forms a Polish space. On this space, processes are topologically close iff they model similar probabilistic phenomena. In particular this means that their laws as well as the information encoded in the respective filtrations are similar. Importantly, compact sets of processes admit a Prohorov-type characterization. We also obtain that for every stochastic process, defined on some abstract basis, there exists a process with identical probabilistic properties which is defined on a standard Borel space.


Title: Fast Discrete Linear Canonical Transform Based on CM-CC-CM Decomposition and FFT
Abstract: In this paper, a discrete LCT (DLCT) irrelevant to the sampling periods and without oversampling operation is developed. This DLCT is based on the well-known CM-CC-CM decomposition, that is, implemented by two discrete chirp multiplications (CMs) and one discrete chirp convolution (CC). This decomposition doesn't use any scaling operation which will change the sampling period or cause the interpolation error. Compared with previous works, DLCT calculated by direct summation and DLCT based on center discrete dilated Hermite functions (CDDHFs), the proposed method implemented by FFTs has much lower computational complexity. The relation between the proposed DLCT and the continuous LCT is also derived to approximate the samples of the continuous LCT. Simulation results show that the proposed method somewhat outperforms the CDDHFs-based method in the approximation accuracy. Besides, the proposed method has approximate additivity property with error as small as the CDDHFs-based method. Most importantly, the proposed method has perfect reversibility, which doesn't hold in many existing DLCTs. With this property, it is unnecessary to develop the inverse DLCT additionally because it can be replaced by the forward DLCT.


Title: CLAPP: Contrastive Language-Audio Pre-training in Passive Underwater Vessel Classification
Abstract: Existing research on audio classification faces challenges in recognizing attributes of passive underwater vessel scenarios and lacks well-annotated datasets due to data privacy concerns. In this study, we introduce CLAPP (Contrastive Language-Audio Pre-training in Passive Underwater Vessel Classification), a novel model. Our aim is to train a neural network using a wide range of vessel audio and vessel state text pairs obtained from an oceanship dataset. CLAPP is capable of directly learning from raw vessel audio data and, when available, from carefully curated labels, enabling improved recognition of vessel attributes in passive underwater vessel scenarios. Model's zero-shot capability allows predicting the most relevant vessel state description for a given vessel audio, without directly optimizing for the task. Our approach aims to solve 2 challenges: vessel audio-text classification and passive underwater vessel audio attribute recognition. The proposed method achieves new state-of-the-art results on both Deepship and Shipsear public datasets, with a notable margin of about 7%-13% for accuracy compared to prior methods on zero-shot task.


Title: Representation Learning of Multivariate Time Series using Attention and Adversarial Training
Abstract: A critical factor in trustworthy machine learning is to develop robust representations of the training data. Only under this guarantee methods are legitimate to artificially generate data, for example, to counteract imbalanced datasets or provide counterfactual explanations for blackbox decision-making systems. In recent years, Generative Adversarial Networks (GANs) have shown considerable results in forming stable representations and generating realistic data. While many applications focus on generating image data, less effort has been made in generating time series data, especially multivariate signals. In this work, a Transformer-based autoencoder is proposed that is regularized using an adversarial training scheme to generate artificial multivariate time series signals. The representation is evaluated using t-SNE visualizations, Dynamic Time Warping (DTW) and Entropy scores. Our results indicate that the generated signals exhibit higher similarity to an exemplary dataset than using a convolutional network approach.


Title: Child Face Age-Progression via Deep Feature Aging
Abstract: Given a gallery of face images of missing children, state-of-the-art face recognition systems fall short in identifying a child (probe) recovered at a later age. We propose a feature aging module that can age-progress deep face features output by a face matcher. In addition, the feature aging module guides age-progression in the image space such that synthesized aged faces can be utilized to enhance longitudinal face recognition performance of any face matcher without requiring any explicit training. For time lapses larger than 10 years (the missing child is found after 10 or more years), the proposed age-progression module improves the closed-set identification accuracy of FaceNet from 16.53% to 21.44% and CosFace from 60.72% to 66.12% on a child celebrity dataset, namely ITWCC. The proposed method also outperforms state-of-the-art approaches with a rank-1 identification rate of 95.91%, compared to 94.91%, on a public aging dataset, FG-NET, and 99.58%, compared to 99.50%, on CACD-VS. These results suggest that aging face features enhances the ability to identify young children who are possible victims of child trafficking or abduction.


Title: Long time behavior for collisional strongly magnetized plasma in three space dimensions
Abstract: We consider the long time evolution of a population of charged particles, under strong magnetic fields and collision mechanisms. We derive a fluid model and justify the asymptotic behavior toward smooth solutions of this regime. In three space dimensions, a constraint ocurs along the parallel direction. For eliminating the corresponding Lagrange multiplier, we average along the magnetic lines.