Title: Existence and rigidity of quantum isometry groups for compact metric spaces
Abstract: We prove the existence of a quantum isometry groups for new classes of metric spaces: (i) geodesic metrics for compact connected Riemannian manifolds (possibly with boundary) and (ii) metric spaces admitting a uniformly distributed probability measure. In the former case it also follows from recent results of the second author that the quantum isometry group is classical, i.e. the commutative $C^*$-algebra of continuous functions on the Riemannian isometry group.


Title: DEM: A Method for Certifying Deep Neural Network Classifier Outputs in Aerospace
Abstract: Software development in the aerospace domain requires adhering to strict, high-quality standards. While there exist regulatory guidelines for commercial software in this domain (e.g., ARP-4754 and DO-178), these do not apply to software with deep neural network (DNN) components. Consequently, it is unclear how to allow aerospace systems to benefit from the deep learning revolution. Our work here seeks to address this challenge with a novel, output-centric approach for DNN certification. Our method employs statistical verification techniques, and has the key advantage of being able to flag specific inputs for which the DNN's output may be unreliable - so that they may be later inspected by a human expert. To achieve this, our method conducts a statistical analysis of the DNN's predictions for other, nearby inputs, in order to detect inconsistencies. This is in contrast to existing techniques, which typically attempt to certify the entire DNN, as opposed to individual outputs. Our method uses the DNN as a black-box, and makes no assumptions about its topology. We hope that this work constitutes another step towards integrating DNNs in safety-critical applications - especially in the aerospace domain, where high standards of quality and reliability are crucial.


Title: Crafting, Communality, and Computing: Building on Existing Strengths To Support a Vulnerable Population
Abstract: In Nepal, sex-trafficking survivors and the organizations that support them have limited resources to assist the survivors in their on-going journey towards reintegration. We take an asset-based approach wherein we identify and build on the strengths possessed by such groups. In this work, we present reflections from introducing a voice-annotated web application to a group of survivors. The web application tapped into and built upon two elements of pre-existing strengths possessed by the survivors -- the social bond between them and knowledge of crafting as taught to them by the organization. Our findings provide insight into the array of factors influencing how the survivors act in relation to one another as they created novel use practices and adapted the technology. Experience with the application seemed to open knowledge of computing as a potential source of strength. Finally, we articulate three design desiderata that could help promote communal spaces: make activity perceptible to the group, create appropriable steps, and build in fun choices.


Title: Not Only Rewards But Also Constraints: Applications on Legged Robot Locomotion
Abstract: Several earlier studies have shown impressive control performance in complex robotic systems by designing the controller using a neural network and training it with model-free reinforcement learning. However, these outstanding controllers with natural motion style and high task performance are developed through extensive reward engineering, which is a highly laborious and time-consuming process of designing numerous reward terms and determining suitable reward coefficients. In this work, we propose a novel reinforcement learning framework for training neural network controllers for complex robotic systems consisting of both rewards and constraints. To let the engineers appropriately reflect their intent to constraints and handle them with minimal computation overhead, two constraint types and an efficient policy optimization algorithm are suggested. The learning framework is applied to train locomotion controllers for several legged robots with different morphology and physical attributes to traverse challenging terrains. Extensive simulation and real-world experiments demonstrate that performant controllers can be trained with significantly less reward engineering, by tuning only a single reward coefficient. Furthermore, a more straightforward and intuitive engineering process can be utilized, thanks to the interpretability and generalizability of constraints. The summary video is available at https://youtu.be/KAlm3yskhvM.


Title: On gamma factors for representations of finite general linear groups
Abstract: We use the Langlands--Shahidi method in order to define the Shahidi gamma factor for a pair of irreducible generic representations of $\operatorname{GL}_n\left(\mathbb{F}_q\right)$ and $\operatorname{GL}_m\left(\mathbb{F}_q\right)$. We prove that the Shahidi gamma factor is multiplicative and show that it is related to the Jacquet--Piatetski-Shapiro--Shalika gamma factor. As an application, we prove a converse theorem based on the absolute value of the Shahidi gamma factor, and improve the converse theorem of Nien. As another application, we give explicit formulas for special values of the Bessel function of an irreducible generic representation of $\operatorname{GL}_n\left(\mathbb{F}_q\right)$.


Title: Nonconforming virtual element method for an incompressible miscible displacement problem in porous media
Abstract: This article presents a priori error estimates of the miscible displacement of one incompressible fluid by another through a porous medium characterized by a coupled system of nonlinear elliptic and parabolic equations. The study utilizes the $H(\rm{div})$ conforming virtual element method (VEM) for the approximation of the velocity, while a non-conforming virtual element approach is employed for the concentration. The pressure is discretised using the standard piecewise discontinuous polynomial functions. These spatial discretization techniques are combined with a backward Euler difference scheme for time discretization. The article also includes numerical results that validate the theoretical estimates presented.


Title: A note on Laguerre truncated polynomials and quadrature formula
Abstract: In this contribution we deal with Gaussian quadrature rules based on orthogonal polynomials associated with a weight function $w(x)= x^{\alpha} e^{-x}$ supported on an interval $(0,z)$, $z>0.$ The modified Chebyshev algorithm is used in order to test the accuracy in the computation of the coefficients of the three-term recurrence relation, the zeros and weights, as well as the dependence on the parameter $z.$


Title: Wasserstein Nonnegative Tensor Factorization with Manifold Regularization
Abstract: Nonnegative tensor factorization (NTF) has become an important tool for feature extraction and part-based representation with preserved intrinsic structure information from nonnegative high-order data. However, the original NTF methods utilize Euclidean or Kullback-Leibler divergence as the loss function which treats each feature equally leading to the neglect of the side-information of features. To utilize correlation information of features and manifold information of samples, we introduce Wasserstein manifold nonnegative tensor factorization (WMNTF), which minimizes the Wasserstein distance between the distribution of input tensorial data and the distribution of reconstruction. Although some researches about Wasserstein distance have been proposed in nonnegative matrix factorization (NMF), they ignore the spatial structure information of higher-order data. We use Wasserstein distance (a.k.a Earth Mover's distance or Optimal Transport distance) as a metric and add a graph regularizer to a latent factor. Experimental results demonstrate the effectiveness of the proposed method compared with other NMF and NTF methods.


Title: Cellular Automata to More Efficiently Compute the Collatz Map
Abstract: The Collatz, or 3x+1, Conjecture claims that for every positive integer n, there exists some k such that T^k(n)=1, where T is the Collatz map. We present three cellular automata (CA) that transform the global problem of mimicking the Collatz map in bases 2, 3, and 4 into a local one of transforming the digits of iterates. The CAs streamline computation first by bypassing calculation of certain parts of trajectories: the binary CA bypasses division by two altogether. In addition, they allow for multiple trajectories to be calculated simultaneously, representing both a significant improvement upon existing sequential methods of computing the Collatz map and a demonstration of the efficacy of using a massively parallel approach with cellular automata to tackle iterative problems like the Collatz Conjecture.


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


Title: Spectral conditions for factor-criticality of graphs
Abstract: A graph $G$ is $k$-factor-critical if $G-S$ has a perfect matching for any $k$-subset $S$ of the vertex set of $G$. In this paper, we investigate the factor-criticality of graphs with fixed minimum degree and provide sufficient conditions for such graphs to be $k$-factor-critical in terms of spectral radius and signless Laplacian spectral radius.


Title: A note on $t$-designs in isodual codes
Abstract: In the present paper, we construct 3-designs using extended binary quadratic residue codes and their dual codes.


Title: Age-Aware Dynamic Frame Slotted ALOHA for Machine-Type Communications
Abstract: Information aging has gained prominence in characterizing communication protocols for timely remote estimation and control applications. This work proposes an Age of Information (AoI)-aware threshold-based dynamic frame slotted ALOHA (T-DFSA) for contention resolution in random access machine-type communication networks. Unlike conventional DFSA that maximizes the throughput in each frame, the frame length and age-gain threshold in T-DFSA are determined to minimize the normalized average AoI reduction of the network in each frame. At the start of each frame in the proposed protocol, the common Access Point (AP) stores an estimate of the age-gain distribution of a typical node. Depending on the observed status of the slots, age-gains of successful nodes, and maximum available AoI, the AP adjusts its estimation in each frame. The maximum available AoI is exploited to derive the maximum possible age-gain at each frame and thus, to avoid overestimating the age-gain threshold, which may render T-DFSA unstable. Numerical results validate our theoretical analysis and demonstrate the effectiveness of the proposed T-DFSA compared to the existing optimal frame slotted ALOHA, threshold-ALOHA, and age-based thinning protocols in a considerable range of update generation rates.


Title: One-sided reflected Brownian motions and the KPZ fixed point
Abstract: We consider the system of one-sided reflected Brownian motions which is in variational duality with Brownian last passage percolation. We show that it has integrable transition probabilities, expressed in terms of Hermite polynomials and hitting times of exponential random walks, and that it converges in the 1:2:3 scaling limit to the KPZ fixed point, the scaling invariant Markov process defined in [MQR17] and believed to govern the long time large scale fluctuations for all models in the KPZ universality class. Brownian last passage percolation was shown recently in [DOV18] to converge to the Airy sheet (or directed landscape), defined there as a strong limit of a functional of the Airy line ensemble. This establishes the variational formula for the KPZ fixed point in terms of the Airy sheet.


Title: Termination of Rewriting on Reversible Boolean Circuits as a Free 3-Category Problem
Abstract: Reversible Boolean Circuits are an interesting computational model under many aspects and in different fields, ranging from Reversible Computing to Quantum Computing. Our contribution is to describe a specific class of Reversible Boolean Circuits - which is as expressive as classical circuits - as a bi-dimensional diagrammatic programming language. We uniformly represent the Reversible Boolean Circuits we focus on as a free 3-category Toff. This formalism allows us to incorporate the representation of circuits and of rewriting rules on them, and to prove termination of rewriting. Termination follows from defining a non-identities-preserving functor from our free 3-category Toff into a suitable 3-category Move that traces the "moves" applied to wires inside circuits.


Title: Image of Lie polynomial of degree $2$ evaluated on Nilpotent Lie algebra
Abstract: We delineate the image of multilinear Lie polynomial of degree $2$ evaluated on $L$ where $L$ is a finite-dimensional nilpotent Lie algebra over field $k$ with $\dim L' \leq 4$.


Title: An eigenvalue problem for self-similar patterns in Hele-Shaw flows
Abstract: Hele-Shaw problems are prototypes to study the interface dynamics. Linear theory suggests the existence of self-similar patterns in a Hele-Shaw flow. That is, with a specific injection flux the interface shape remains unchanged while its size increases. In this paper, we explore the existence of self-similar patterns in the nonlinear regime and develop a rigorous nonlinear theory characterizing their fundamental features. Using a boundary integral formulation, we pose the question of self-similarity as a generalized nonlinear eigenvalue problem, involving two nonlinear integral operators. The flux constant $C$ is the eigenvalue and the corresponding self-similar pattern $\mathbf{x}$ is the eigenvector. We develop a quasi-Newton method to solve the problem and show the existence of nonlinear shapes with $k$-fold dominated symmetries. The influence of initial guesses on the self-similar patterns is investigated. We are able to obtain a desired self-similar shape once the initial guess is properly chosen. Our results go beyond the predictions of linear theory and establish a bridge between the linear theory and simulations.


Title: Splitting of Uniform bundles on generalized Grassmannians and Kumar's conjecture
Abstract: Let $E$ be a uniform bundle on an arbitrary generalised Grassmannian $X$. We show that if the rank of $E$ is smaller than $e.d.(\mathrm{VMRT})$, then $E$ is necessarily splitting. For some generalised Grassmannians, we prove that the upper bound $e.d.(\mathrm{VMRT})$ is optimal. On the other hand, Kumar's conjecture predicts that if the minss rank of $G'/P'$ is bigger that the maxss rank of $G/P$, then any morphism $f:G'/P'\rightarrow G/P$ is constant. We prove some partially affirmative results about this conjecture.


Title: Detecting Unseen Falls from Wearable Devices using Channel-wise Ensemble of Autoencoders
Abstract: A fall is an abnormal activity that occurs rarely, so it is hard to collect real data for falls. It is, therefore, difficult to use supervised learning methods to automatically detect falls. Another challenge in using machine learning methods to automatically detect falls is the choice of engineered features. In this paper, we propose to use an ensemble of autoencoders to extract features from different channels of wearable sensor data trained only on normal activities. We show that the traditional approach of choosing a threshold as the maximum of the reconstruction error on the training normal data is not the right way to identify unseen falls. We propose two methods for automatic tightening of reconstruction error from only the normal activities for better identification of unseen falls. We present our results on two activity recognition datasets and show the efficacy of our proposed method against traditional autoencoder models and two standard one-class classification methods.


Title: Algorithms Transcending the SAT-Symmetry Interface
Abstract: Dedicated treatment of symmetries in satisfiability problems (SAT) is indispensable for solving various classes of instances arising in practice. However, the exploitation of symmetries usually takes a black box approach. Typically, off-the-shelf external, general-purpose symmetry detection tools are invoked to compute symmetry groups of a formula. The groups thus generated are a set of permutations passed to a separate tool to perform further analyzes to understand the structure of the groups. The result of this second computation is in turn used for tasks such as static symmetry breaking or dynamic pruning of the search space. Within this pipeline of tools, the detection and analysis of symmetries typically incurs the majority of the time overhead for symmetry exploitation. In this paper we advocate for a more holistic view of what we call the SAT-symmetry interface. We formulate a computational setting, centered around a new concept of joint graph/group pairs, to analyze and improve the detection and analysis of symmetries. Using our methods, no information is lost performing computational tasks lying on the SAT-symmetry interface. Having access to the entire input allows for simpler, yet efficient algorithms. Specifically, we devise algorithms and heuristics for computing finest direct disjoint decompositions, finding equivalent orbits, and finding natural symmetric group actions. Our algorithms run in what we call instance-quasi-linear time, i.e., almost linear time in terms of the input size of the original formula and the description length of the symmetry group returned by symmetry detection tools. Our algorithms improve over both heuristics used in state-of-the-art symmetry exploitation tools, as well as theoretical general-purpose algorithms.


Title: Relations Between $p$-Means of Convex Bodies and a New Suggestion for the Definition of the Geometric Mean
Abstract: In light of the log-Brunn-Minkowski conjecture, various attempts have been made to define the geometric mean of convex bodies. Many of these constructions are fairly complex and/or fail to satisfy some natural properties one would expect of such a mean. We remedy this by providing a new geometric mean that is both technically simple and inherits all the natural properties expected. To improve our understanding of potential geometric mean definitions, we first study general $p$-means of convex bodies, with the usual definition extended to two series ranging over all $p \in [-\infty,\infty]$. We characterize their equality cases and obtain (in almost all instances tight) inequalities that quantify how well these means approximate each other. As a corollary, we establish that every Minkowski centered body is equidistant from all its $p$-symmetrizations with respect to the Banach-Mazur distance. Finally, we show that our geometric mean satisfies all the properties considered in recent literature and extend this list with some properties regarding symmetrization and asymmetry.


Title: Aggregation over Metric Spaces: Proposing and Voting in Elections, Budgeting, and Legislation
Abstract: We present a unifying framework encompassing many social choice settings. Viewing each social choice setting as voting in a suitable metric space, we consider a general model of social choice over metric spaces, in which---similarly to the spatial model of elections---each voter specifies an ideal element of the metric space. The ideal element functions as a vote, where each voter prefers elements that are closer to her ideal element. But it also functions as a proposal, thus making all participants equal not only as voters but also as proposers. We consider Condorcet aggregation and a continuum of solution concepts, ranging from minimizing the sum of distances to minimizing the maximum distance. We study applications of the abstract model to various social choice settings, including single-winner elections, committee elections, participatory budgeting, and participatory legislation. For each setting, we compare each solution concept to known voting rules and study various properties of the resulting voting rules. Our framework provides expressive aggregation for a broad range of social choice settings while remaining simple for voters, and may enable a unified and integrated implementation for all these settings, as well as unified extensions such as sybil-resiliency, proxy voting, and deliberative decision making.


Title: Pseudorandom Hashing for Space-bounded Computation with Applications in Streaming
Abstract: We revisit Nisan's classical pseudorandom generator (PRG) for space-bounded computation (STOC 1990) and its applications in streaming algorithms. We describe a new generator, HashPRG, that can be thought of as a symmetric version of Nisan's generator over larger alphabets. Our generator allows a trade-off between seed length and the time needed to compute a given block of the generator's output. HashPRG can be used to obtain derandomizations with much better update time and \emph{without sacrificing space} for a large number of data stream algorithms, such as $F_p$ estimation in the parameter regimes $p > 2$ and $0 < p < 2$ and CountSketch with tight estimation guarantees as analyzed by Minton and Price (SODA 2014) which assumed access to a random oracle. We also show a recent analysis of Private CountSketch can be derandomized using our techniques. For a $d$-dimensional vector $x$ being updated in a turnstile stream, we show that $\|x\|_{\infty}$ can be estimated up to an additive error of $\varepsilon\|x\|_{2}$ using $O(\varepsilon^{-2}\log(1/\varepsilon)\log d)$ bits of space. Additionally, the update time of this algorithm is $O(\log 1/\varepsilon)$ in the Word RAM model. We show that the space complexity of this algorithm is optimal up to constant factors. However, for vectors $x$ with $\|x\|_{\infty} = \Theta(\|x\|_{2})$, we show that the lower bound can be broken by giving an algorithm that uses $O(\varepsilon^{-2}\log d)$ bits of space which approximates $\|x\|_{\infty}$ up to an additive error of $\varepsilon\|x\|_{2}$. We use our aforementioned derandomization of the CountSketch data structure to obtain this algorithm, and using the time-space trade off of HashPRG, we show that the update time of this algorithm is also $O(\log 1/\varepsilon)$ in the Word RAM model.


Title: Hessian estimates for special Lagrangian equation by doubling
Abstract: New, doubling proofs are given for the interior Hessian estimates of the special Lagrangian equation. These estimates were originally shown by Chen-Warren-Yuan in CPAM 2009 and Wang-Yuan in AJM 2014. This yields a higher codimension analogue of Korevaar's 1987 pointwise proof of the gradient estimate for minimal hypersurfaces, without using the Michael-Simon mean value inequality.


Title: Fast and Continual Learning for Hybrid Control Policies using Generalized Benders Decomposition
Abstract: Hybrid model predictive control with both continuous and discrete variables is widely applicable to robotic control tasks, especially those involving contact with the environment. Due to the combinatorial complexity, the solving speed of hybrid MPC can be insufficient for real-time applications. In this paper, we proposed a hybrid MPC solver based on Generalized Benders Decomposition (GBD). The algorithm enumerates and stores cutting planes online inside a finite buffer. After a short cold-start phase, the stored cuts provide warm-starts for the new problem instances to enhance the solving speed. Despite the disturbance and randomly changing environment, the solving speed maintains. Leveraging on the sparsity of feasibility cuts, we also propose a fast algorithm for Benders master problems. Our solver is validated through controlling a cart-pole system with randomly moving soft contact walls, and a free-flying robot navigating around obstacles. The results show that with significantly less data than previous works, the solver reaches competitive speeds to the off-the-shelf solver Gurobi despite the Python overhead.


Title: Optimal transport for types and convex analysis for definable predicates in tracial $\mathrm{W}^*$-algebras
Abstract: We investigate the connections between continuous model theory, free probability, and optimal transport/convex analysis in the context of tracial von Neumann algebras. In particular, we give an analog of Monge-Kantorovich duality for optimal couplings where the role of probability distributions on $\mathbb{C}^n$ is played by model-theoretic types, the role of real-valued continuous functions is played by definable predicates, and the role of continuous function $\mathbb{C}^n \to \mathbb{C}^n$ is played by definable functions. In the process, we also advance the understanding of definable predicates and definable functions by showing that all definable predicates can be approximated by "$C^1$ definable predicates" whose gradients are definable functions. As a consequence, we show that every element in the definable closure of $\mathrm{W}^*(x_1,\dots,x_n)$ can be expressed as a definable function of $(x_1,\dots,x_n)$. We give several classes of examples showing that the definable closure can be much larger than $\mathrm{W}^*(x_1,\dots,x_n)$ in general.


Title: Outage Analysis for Active Reconfigurable Intelligent Surface-Enhanced Wireless Powered Communication Networks
Abstract: Wireless powered communication (WPC) involves the integration of energy harvesting and data transmission. This allows devices to communicate without constant battery replacements or wired power sources. Reconfigurable intelligent surfaces (RISs) can dynamically manipulate radio signals. In this paper, we explore the use of active elements to mitigate double-fading challenges inherent in RIS-aided links. We enhance the reliability performance for an energy-constrained user by combining active RIS and WPC. The theoretical closed-form analysis, which includes transmission rate, harvested energy, and outage probability, provides valuable insights that inform parameter selection.


Title: Optimal Decomposition and Recombination of Isostatic Geometric Constraint Systems for Designing Layered Materials
Abstract: Optimal recursive decomposition (or DR-planning) is crucial for analyzing, designing, solving or finding realizations of geometric constraint sytems. While the optimal DR-planning problem is NP-hard even for general 2D bar-joint constraint systems, we describe an O(n^3) algorithm for a broad class of constraint systems that are isostatic or underconstrained. The algorithm achieves optimality by using the new notion of a canonical DR-plan that also meets various desirable, previously studied criteria. In addition, we leverage recent results on Cayley configuration spaces to show that the indecomposable systems---that are solved at the nodes of the optimal DR-plan by recombining solutions to child systems---can be minimally modified to become decomposable and have a small DR-plan, leading to efficient realization algorithms. We show formal connections to well-known problems such as completion of underconstrained systems. Well suited to these methods are classes of constraint systems that can be used to efficiently model, design and analyze quasi-uniform (aperiodic) and self-similar, layered material structures. We formally illustrate by modeling silica bilayers as body-hyperpin systems and cross-linking microfibrils as pinned line-incidence systems. A software implementation of our algorithms and videos demonstrating the software are publicly available online (visit http://cise.ufl.edu/~tbaker/drp/index.html.)


Title: LLaMA Pro: Progressive LLaMA with Block Expansion
Abstract: Humans generally acquire new skills without compromising the old; however, the opposite holds for Large Language Models (LLMs), e.g., from LLaMA to CodeLLaMA. To this end, we propose a new post-pretraining method for LLMs with an expansion of Transformer blocks. We tune the expanded blocks using only new corpus, efficiently and effectively improving the model's knowledge without catastrophic forgetting. In this paper, we experiment on the corpus of code and math, yielding LLaMA Pro-8.3B, a versatile foundation model initialized from LLaMA2-7B, excelling in general tasks, programming, and mathematics. LLaMA Pro and its instruction-following counterpart (LLaMA Pro-Instruct) achieve advanced performance among various benchmarks, demonstrating superiority over existing open models in the LLaMA family and the immense potential of reasoning and addressing diverse tasks as an intelligent agent. Our findings provide valuable insights into integrating natural and programming languages, laying a solid foundation for developing advanced language agents that operate effectively in various environments.


Title: On some anabelian properties of arithmetic curves
Abstract: In this paper we generalize an argument of Neukirch from birational anabelian geometry to the case of arithmetic curves. In contrast to the function field case, it seems to be more complicate to describe the position of decomposition groups of points at the boundary of the scheme $\Spec \caO_{K,S}$, where $K$ is a number field and $S$ a set of primes of $K$, intrinsically in terms of the fundamental group. We prove that it is equivalent to give the following pieces of information additionally with the fundamental group $\pi_1(\Spec \caO_{K,S})$: the location of decomposition groups of boundary points inside it, the $p$-part of the cyclotomic character, the number of points on the boundary of all finite etale covers, etc. Under certain finiteness hypothesis on Tate-Shafarevich groups with divisible coefficients, one can reconstruct all this quantities from the fundamental group alone.


Title: Higher depth quantum modular forms and plumbed $3$-manifolds
Abstract: In this paper we study new invariants $\widehat{Z}_{\boldsymbol{a}}(q)$ attached to plumbed $3$-manifolds that were introduced by Gukov, Pei, Putrov, and Vafa. These remarkable $q$-series at radial limits conjecturally compute WRT invariants of the corresponding plumbed $3$-manifold. Here we investigate the series $\widehat{Z}_{0}(q)$ for unimodular plumbing ${\tt H}$-graphs with six vertices. We prove that for every positive definite unimodular plumbing matrix, $\widehat{Z}_{0}(q)$ is a depth two quantum modular form on $\mathbb{Q}$.


Title: Dissipative SymODEN: Encoding Hamiltonian Dynamics with Dissipation and Control into Deep Learning
Abstract: In this work, we introduce Dissipative SymODEN, a deep learning architecture which can infer the dynamics of a physical system with dissipation from observed state trajectories. To improve prediction accuracy while reducing network size, Dissipative SymODEN encodes the port-Hamiltonian dynamics with energy dissipation and external input into the design of its computation graph and learns the dynamics in a structured way. The learned model, by revealing key aspects of the system, such as the inertia, dissipation, and potential energy, paves the way for energy-based controllers.


Title: A note about the invariance of the basic reproduction number for stochastically perturbed SIS models
Abstract: We try to justify rigorously, using a Wong-Zakai approximation argument, the susceptible-infected-susceptible (SIS) stochastic differential equation proposed in [2]. We discover that according to this approach the "right" stochastic model to be considered should be the Stratonovich version of the It\^o equation analyzed in [2]. Surprisingly, this alternative model presents the following feature: the threshold value characterizing the two different asymptotic regimes of the solution coincides with the one describing the classical SIS deterministic equation.


Title: Context-Free TextSpotter for Real-Time and Mobile End-to-End Text Detection and Recognition
Abstract: In the deployment of scene-text spotting systems on mobile platforms, lightweight models with low computation are preferable. In concept, end-to-end (E2E) text spotting is suitable for such purposes because it performs text detection and recognition in a single model. However, current state-of-the-art E2E methods rely on heavy feature extractors, recurrent sequence modellings, and complex shape aligners to pursue accuracy, which means their computations are still heavy. We explore the opposite direction: How far can we go without bells and whistles in E2E text spotting? To this end, we propose a text-spotting method that consists of simple convolutions and a few post-processes, named Context-Free TextSpotter. Experiments using standard benchmarks show that Context-Free TextSpotter achieves real-time text spotting on a GPU with only three million parameters, which is the smallest and fastest among existing deep text spotters, with an acceptable transcription quality degradation compared to heavier ones. Further, we demonstrate that our text spotter can run on a smartphone with affordable latency, which is valuable for building stand-alone OCR applications.


Title: Hereditary $n$-exangulated categories
Abstract: Herschend-Liu-Nakaoka introduced the concept of $n$-exangulated categories as higher-dimensional analogues of extriangulated categories defined by Nakaoka-Palu. The class of $n$-exangulated categories contains $n$-exact categories and $(n+2)$-angulated categories as specific examples. In this article, we introduce the notion of hereditary $n$-exangulated categories, which generalize hereditary extriangulated categories. We provide two classes of hereditary $n$-exangulated categories through closed subfunctors. Additionally, we define the concept of $0$-Auslander $n$-exangulated categories and discuss the circumstances under which these two classes of hereditary $n$-exangulated categories become $0$-Auslander.


Title: MULTI-CASE: A Transformer-based Ethics-aware Multimodal Investigative Intelligence Framework
Abstract: AI-driven models are increasingly deployed in operational analytics solutions, for instance, in investigative journalism or the intelligence community. Current approaches face two primary challenges: ethical and privacy concerns, as well as difficulties in efficiently combining heterogeneous data sources for multimodal analytics. To tackle the challenge of multimodal analytics, we present MULTI-CASE, a holistic visual analytics framework tailored towards ethics-aware and multimodal intelligence exploration, designed in collaboration with domain experts. It leverages an equal joint agency between human and AI to explore and assess heterogeneous information spaces, checking and balancing automation through Visual Analytics. MULTI-CASE operates on a fully-integrated data model and features type-specific analysis with multiple linked components, including a combined search, annotated text view, and graph-based analysis. Parts of the underlying entity detection are based on a RoBERTa-based language model, which we tailored towards user requirements through fine-tuning. An overarching knowledge exploration graph combines all information streams, provides in-situ explanations, transparent source attribution, and facilitates effective exploration. To assess our approach, we conducted a comprehensive set of evaluations: We benchmarked the underlying language model on relevant NER tasks, achieving state-of-the-art performance. The demonstrator was assessed according to intelligence capability assessments, while the methodology was evaluated according to ethics design guidelines. As a case study, we present our framework in an investigative journalism setting, supporting war crime investigations. Finally, we conduct a formative user evaluation with domain experts in law enforcement. Our evaluations confirm that our framework facilitates human agency and steering in security-sensitive applications.


Title: Tailor: Size Recommendations for High-End Fashion Marketplaces
Abstract: In the ever-changing and dynamic realm of high-end fashion marketplaces, providing accurate and personalized size recommendations has become a critical aspect. Meeting customer expectations in this regard is not only crucial for ensuring their satisfaction but also plays a pivotal role in driving customer retention, which is a key metric for the success of any fashion retailer. We propose a novel sequence classification approach to address this problem, integrating implicit (Add2Bag) and explicit (ReturnReason) user signals. Our approach comprises two distinct models: one employs LSTMs to encode the user signals, while the other leverages an Attention mechanism. Our best model outperforms SFNet, improving accuracy by 45.7%. By using Add2Bag interactions we increase the user coverage by 24.5% when compared with only using Orders. Moreover, we evaluate the models' usability in real-time recommendation scenarios by conducting experiments to measure their latency performance.


Title: JPEG XT Image Compression with Hue Compensation for Two-Layer HDR Coding
Abstract: We propose a novel JPEG XT image compression with hue compensation for two-layer HDR coding. LDR images produced from JPEG XT bitstreams have some distortion in hue due to tone mapping operations. In order to suppress the color distortion, we apply a novel hue compensation method based on the maximally saturated colors. Moreover, the bitstreams generated by using the proposed method are fully compatible with the JPEG XT standard. In an experiment, the proposed method is demonstrated not only to produce images with small hue degradation but also to maintain well-mapped luminance, in terms of three kinds of criterion: TMQI, hue value in CIEDE2000, and the maximally saturated color on the constant-hue plane.


Title: Using Locality-sensitive Hashing for Rendezvous Search
Abstract: The multichannel rendezvous problem is a fundamental problem for neighbor discovery in many IoT applications. The existing works in the literature focus mostly on improving the worst-case performance, and the average-case performance is often not as good as that of the random algorithm. As IoT devices (users) are close to each other, their available channel sets, though they might be different, are similar. Using the locality-sensitive hashing (LSH) technique in data mining, we propose channel hopping algorithms that exploit the similarity between the two available channel sets to increase the rendezvous probability. For the synchronous setting, our algorithms have the expected time-to-rendezvous (ETTR) inversely proportional to a well-known similarity measure called the Jaccard index. For the asynchronous setting, we use dimensionality reduction to speed up the rendezvous process. Our numerical results show that our algorithms can outperform the random algorithm in terms of ETTR.


Title: Stationary Distributions for Two-Dimensional Sticky Brownian Motions: Exact Tail Asymptotics and Extreme Value Distributions
Abstract: In this paper, we consider a two-dimensional sticky Brownian motion. Sticky Brownian motions can be viewed as time-changed semimartingale reflecting Brownian motions, which find applications in many areas including queueing theory and mathematical finance. For example, a sticky Brownian motion can be used to model a storage system.with exceptional services. In this paper, we focus on stationary distributions for sticky Brownian motions. The main results obtained here include tail asymptotic properties in boundary stationary distributions, marginal distributions, and joint distributions. The kernel method, copula concept and extreme value theory are main tools used in our analysis.


Title: Two point concentration of maximum degree in sparse random planar graphs
Abstract: Let $P(n,m)$ be a graph chosen uniformly at random from the class of all planar graphs on vertex set $\left\{1, \ldots, n\right\}$ with $m=m(n)$ edges. We show that in the sparse regime, when $\limsup_{n \to \infty} m/n<1$, with high probability the maximum degree of $P(n,m)$ takes at most two different values.


Title: Minimum Sobolev norm interpolation of derivative data
Abstract: We study the problem of reconstructing a function on a manifold satisfying some mild conditions, given data on the values and some derivatives of the function at arbitrary points on the manifold. While the problem of finding a polynomial of two variables with total degree $\le n$ given the values of the polynomial and some of its derivatives at exactly the same number of points as the dimension of the polynomial space is sometimes impossible, we show that such a problem always has a solution in a very general situation if the degree of the polynomials is sufficiently large. We give estimates on how large the degree should be, and give explicit constructions for such a polynomial even in a far more general case. As the number of sampling points at which the data is available increases, our polynomials converge to the target function on the set where the sampling points are dense. Numerical examples in single and double precision show that this method is stable and of high-order.


Title: Improving Approximate Optimal Transport Distances using Quantization
Abstract: Optimal transport (OT) is a popular tool in machine learning to compare probability measures geometrically, but it comes with substantial computational burden. Linear programming algorithms for computing OT distances scale cubically in the size of the input, making OT impractical in the large-sample regime. We introduce a practical algorithm, which relies on a quantization step, to estimate OT distances between measures given cheap sample access. We also provide a variant of our algorithm to improve the performance of approximate solvers, focusing on those for entropy-regularized transport. We give theoretical guarantees on the benefits of this quantization step and display experiments showing that it behaves well in practice, providing a practical approximation algorithm that can be used as a drop-in replacement for existing OT estimators.


Title: Parametric change point detection with random occurrence of the change point
Abstract: We are concerned with the problem of detecting a single change point in the model parameters of time series data generated from an exponential family. In contrast to the existing literature, we allow that the true location of the change point is itself random, possibly depending on the data. Under the alternative, we study the case when the size of the change point converges to zero while the sample size goes to infinity. Moreover, we concentrate on change points in the "middle of the data", i.e., we assume that the change point fraction (the location of the change point relative to the sample size) converges weakly to a random variable $\lambda^*$ which takes its values almost surely in a closed subset of $(0,1).$ We show that the known statistical results from the literature also transfer to this setting. We substantiate our theoretical results with a simulation study.


Title: Smoothing Methods for Automatic Differentiation Across Conditional Branches
Abstract: Programs involving discontinuities introduced by control flow constructs such as conditional branches pose challenges to mathematical optimization methods that assume a degree of smoothness in the objective function's response surface. Smooth interpretation (SI) is a form of abstract interpretation that approximates the convolution of a program's output with a Gaussian kernel, thus smoothing its output in a principled manner. Here, we combine SI with automatic differentiation (AD) to efficiently compute gradients of smoothed programs. In contrast to AD across a regular program execution, these gradients also capture the effects of alternative control flow paths. The combination of SI with AD enables the direct gradient-based parameter synthesis for branching programs, allowing for instance the calibration of simulation models or their combination with neural network models in machine learning pipelines. We detail the effects of the approximations made for tractability in SI and propose a novel Monte Carlo estimator that avoids the underlying assumptions by estimating the smoothed programs' gradients through a combination of AD and sampling. Using DiscoGrad, our tool for automatically translating simple C++ programs to a smooth differentiable form, we perform an extensive evaluation. We compare the combination of SI with AD and our Monte Carlo estimator to existing gradient-free and stochastic methods on four non-trivial and originally discontinuous problems ranging from classical simulation-based optimization to neural network-driven control. While the optimization progress with the SI-based estimator depends on the complexity of the program's control flow, our Monte Carlo estimator is competitive in all problems, exhibiting the fastest convergence by a substantial margin in our highest-dimensional problem.


Title: Coalition Formation Games for Collaborative Spectrum Sensing
Abstract: Collaborative Spectrum Sensing (CSS) between secondary users (SUs) in cognitive networks exhibits an inherent tradeoff between minimizing the probability of missing the detection of the primary user (PU) and maintaining a reasonable false alarm probability (e.g., for maintaining a good spectrum utilization). In this paper, we study the impact of this tradeoff on the network structure and the cooperative incentives of the SUs that seek to cooperate for improving their detection performance. We model the CSS problem as a non-transferable coalitional game, and we propose distributed algorithms for coalition formation. First, we construct a distributed coalition formation (CF) algorithm that allows the SUs to self-organize into disjoint coalitions while accounting for the CSS tradeoff. Then, the CF algorithm is complemented with a coalitional voting game for enabling distributed coalition formation with detection probability guarantees (CF-PD) when required by the PU. The CF-PD algorithm allows the SUs to form minimal winning coalitions (MWCs), i.e., coalitions that achieve the target detection probability with minimal costs. For both algorithms, we study and prove various properties pertaining to network structure, adaptation to mobility and stability. Simulation results show that CF reduces the average probability of miss per SU up to 88.45% relative to the non-cooperative case, while maintaining a desired false alarm. For CF-PD, the results show that up to 87.25% of the SUs achieve the required detection probability through MWC


Title: Solutions to complex $m$-Hessian type equation and its application
Abstract: In this paper, we introduce the class $\mathcal{E}_{m,F}(\Omega)$ and prove the existence of solutions of the complex $m-$Hessian type equation $-F(u(z),z)H_{m}(u)=\mu$ where $\mu$ vanishes on all of $m-$polar sets in the class $\mathcal{E}_{m,F}(\Omega).$ Next, we prove the existence of solutions of this equation in the class $\mathcal{E}_{m,F}(\Omega)$ if there exists subsolution in this class. Using the above results, we study subextension in the class $\mathcal{E}_{m,F}(\Omega).$


Title: Phase transition and diffusion among socially interacting self-propelled agents
Abstract: We consider a hydrodynamic model of swarming behavior derived from the kinetic description of a particle system combining a noisy Cucker-Smale consensus force and self-propulsion. In the large self-propulsion force limit, we provide evidence of a phase transition from disordered to ordered motion which manifests itself as a change of type of the limit model (from hyperbolic to diffusive) at the crossing of a critical noise intensity. In the hyperbolic regime, the resulting model, referred to as the `Self-Organized Hydrodynamics (SOH)', consists of a system of compressible Euler equations with a speed constraint. We show that the range of SOH models obtained by this limit is restricted. To waive this restriction, we compute the Navier-Stokes diffusive corrections to the hydrodynamic model. Adding these diffusive corrections, the limit of a large propulsion force yields unrestricted SOH models and offers an alternative to the derivation of the SOH using kinetic models with speed constraints.


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


Title: Two dimensional dimers beyond planarity
Abstract: We consider a generalisation of the double dimer model which includes several models of interest, such as the monomer double dimer model, the dimer model, the Spin O(N) model, and it is related to the loop O(N) model. We prove that on two-dimension like graphs (such as slabs), both the correlation function and the probability that a loop visits two vertices converge to zero as the distance between such vertices gets large. Our analysis is by introducing a new (complex) spin representation for all models belonging to this class, and by deriving a new proof of the Mermin-Wagner theorem which does not require the positivity of the Gibbs measure. Even for the well studied dimer and double dimer model our results are new since - not relying on solvability and Kasteleyn's theorem - they hold beyond the framework of planar graphs.


Title: Propagation of Input Tail Uncertainty in Rare-Event Estimation: A Light versus Heavy Tail Dichotomy
Abstract: We consider the estimation of small probabilities or other risk quantities associated with rare but catastrophic events. In the model-based literature, much of the focus has been devoted to efficient Monte Carlo computation or analytical approximation assuming the model is accurately specified. In this paper, we study a distinct direction on the propagation of model uncertainty and how it impacts the reliability of rare-event estimates. Specifically, we consider the basic setup of the exceedance of i.i.d. sum, and investigate how the lack of tail information of each input summand can affect the output probability. We argue that heavy-tailed problems are much more vulnerable to input uncertainty than light-tailed problems, reasoned through their large deviations behaviors and numerical evidence. We also investigate some approaches to quantify model errors in this problem using a combination of the bootstrap and extreme value theory, showing some positive outcomes but also uncovering some statistical challenges.


Title: Matchings and loose cycles in the semirandom hypergraph model
Abstract: We study the 2-offer semirandom 3-uniform hypergraph model on $n$ vertices. At each step, we are presented with 2 uniformly random vertices. We choose any other vertex, thus creating a hyperedge of size 3. We show a strategy that constructs a perfect matching, and another that constructs a loose Hamilton cycle, both succeeding asymptotically almost surely within $\Theta(n)$ steps. Both results extend to $s$-uniform hypergraphs. Much of the analysis is done on an auxiliary graph that is a uniform $k$-out subgraph of a random bipartite graph, and this tool may be useful in other contexts.


Title: List-Coloring Packing and Correspondence-Coloring Packing of Planar Graphs
Abstract: For a graph $G$ and a list assignment $L$ with $|L(v)|=k$ for all $v$, an $L$-packing consists of $L$-colorings $\varphi_1,\cdots,\varphi_k$ such that $\varphi_i(v)\ne\varphi_j(v)$ for all $v$ and all distinct $i,j\in\{1,\ldots,k\}$. Let $\chi^{\star}_{\ell}(G)$ denote the smallest $k$ such that $G$ has an $L$-packing for every $L$ with $|L(v)|=k$ for all $v$. Let $\mathcal{P}_k$ denote the set of all planar graphs with girth at least $k$. We show that (i) $\chi^{\star}_{\ell}(G)\le 8$ for all $G\in \mathcal{P}_3$ and (ii) $\chi^{\star}_{\ell}(G)\le 5$ for all $G\in \mathcal{P}_4$ and (iii) $\chi^{\star}_{\ell}(G)\le 4$ for all $G\in \mathcal{P}_5$. Part (i) makes progress on a problem of Cambie, Cames van Batenburg, Davies, and Kang. We also construct outerplanar graphs $G$ such that $\chi^{\star}_{\ell}(G)=4$, which matches the known upper bound $\chi^{\star}_{\ell}(G)\le 4$ for all outerplanar graphs. Finally, we consider the analogue of $\chi^{\star}_{\ell}$ for correspondence coloring, $\chi^{\star}_c$. In fact, all bounds stated above for $\chi^{\star}_{\ell}$ also hold for $\chi^{\star}_c$.


Title: Visual Relationship Forecasting in Videos
Abstract: Real-world scenarios often require the anticipation of object interactions in unknown future, which would assist the decision-making process of both humans and agents. To meet this challenge, we present a new task named Visual Relationship Forecasting (VRF) in videos to explore the prediction of visual relationships in a reasoning manner. Specifically, given a subject-object pair with H existing frames, VRF aims to predict their future interactions for the next T frames without visual evidence. To evaluate the VRF task, we introduce two video datasets named VRF-AG and VRF-VidOR, with a series of spatio-temporally localized visual relation annotations in a video. These two datasets densely annotate 13 and 35 visual relationships in 1923 and 13447 video clips, respectively. In addition, we present a novel Graph Convolutional Transformer (GCT) framework, which captures both object-level and frame-level dependencies by spatio-temporal Graph Convolution Network and Transformer. Experimental results on both VRF-AG and VRF-VidOR datasets demonstrate that GCT outperforms the state-of-the-art sequence modelling methods on visual relationship forecasting.


Title: Structural properties of weak cotype 2 spaces
Abstract: Several characterizations of weak cotype 2 and weak Hilbert spaces are given in terms of basis constants and other structural invariants of Banach spaces. For finite-dimensional spaces, characterizations depending on subspaces of fixed proportional dimension are proved.


Title: Asymptotic expansion and optimal symmetry of minimal gradient graph equations in dimension 2
Abstract: In this paper, we study asymptotic expansion at infinity and symmetry of zero mean curvature equations of gradient graph in dimension 2, which include the Monge--Amp\`ere equation, inverse harmonic Hessian equation and the special Lagrangian equation. This refines the research of asymptotic behavior, gives the precise gap between exterior minimal gradient graph and the entire case, and extends the classification results of Monge--Amp\`ere equations.


Title: Non-associative Frobenius algebras of type $E_7$
Abstract: Recently, Maurice Chayet and Skip Garibaldi introduced a class of commutative non-associative algebras. In previous work, we gave an explicit description of these algebras for groups of type $G_2,F_4$ and certain forms of $E_6$ in terms of octonion and Albert algebras. In this paper, we extend this further by dealing with $E_7$ in terms of generalised Freudenthal triple systems.


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


Title: A note on the growth of regularity with respect to Frobenius
Abstract: Let $R=k[x_1,\dots,x_n]/I$ be a standard graded $k$-algebra where $k$ is a field of prime characteristic and let $J$ be a homogeneous ideal in $R$. Denote $(x_1,\dots,x_n)$ by $\mathfrak{m}$. We prove that there is a constant $C$ (independent of $e$) such that the regularity of $H^s_{\mathfrak{m}}(R/J^{[p^e]})$ is bounded above by $Cp^e$ for all $e\geq 1$ and all integers $s$ such that $s+1$ is at least the dimension of the locus where $R/J$ doesn't have finite projective dimension.


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


Title: On the Effects of Battery Imperfections in an Energy Harvesting Device
Abstract: Energy Harvesting allows the devices in a Wireless Sensor Network to recharge their batteries through environmental energy sources. While in the literature the main focus is on devices with ideal batteries, in reality several inefficiencies have to be considered to correctly design the operating regimes of an Energy Harvesting Device (EHD). In this work we describe how the throughput optimization problem changes under \emph{real battery} constraints in an EHD. In particular, we consider imperfect knowledge of the state of charge of the battery and storage inefficiencies, \emph{i.e.}, part of the harvested energy is wasted in the battery recharging process. We formulate the problem as a Markov Decision Process, basing our model on some realistic observations about transmission, consumption and harvesting power. We find the performance upper bound with a real battery and numerically discuss the novelty introduced by the real battery effects. We show that using the \emph{old} policies obtained without considering the real battery effects is strongly sub-optimal and may even result in zero throughput.


Title: Higher convexity and iterated sum sets
Abstract: Let $f$ be a smooth real function with strictly monotone first $k$ derivatives. We show that for a finite set $A$, with $|A+A|\leq K|A|$, $|2^kf(A)-(2^k-1)f(A)|\gg_k |A|^{k+1-o(1)}/K^{O_k(1)}$. We deduce several new sum-product type implications, e.g. that $A+A$ being small implies unbounded growth for a many enough times iterated product set $A \cdots A$.


Title: Examining the Challenges in Archiving Instagram
Abstract: To prevent the spread of disinformation on Instagram, we need to study the accounts and content of disinformation actors. However, due to their malicious nature, Instagram often bans accounts that are responsible for spreading disinformation, making these accounts inaccessible from the live web. The only way we can study the content of banned accounts is through public web archives such as the Internet Archive. However, there are many issues present with archiving Instagram pages. Specifically, we focused on the issue that many Wayback Machine Instagram mementos redirect to the Instagram login page. In this study, we determined that mementos of Instagram account pages on the Wayback Machine began redirecting to the Instagram login page in August 2019. We also found that Instagram mementos on Archive.today, Arquivo.pt, and Perma.cc are also not well archived in terms of quantity and quality. Moreover, we were unsuccessful in all our attempts to archive Katy Perry's Instagram account page on Archive.today, Arquivo.pt, and Conifer. Although in the minority, replayable Instagram mementos exist in public archives and contain valuable data for studying disinformation on Instagram. With that in mind, we developed a Python script to web scrape Instagram mementos. As of August 2023, the Python script can scrape Wayback Machine archives of Instagram account pages between November 7, 2012 and June 8, 2018.


Title: Cross-modal Prototype Driven Network for Radiology Report Generation
Abstract: Radiology report generation (RRG) aims to describe automatically a radiology image with human-like language and could potentially support the work of radiologists, reducing the burden of manual reporting. Previous approaches often adopt an encoder-decoder architecture and focus on single-modal feature learning, while few studies explore cross-modal feature interaction. Here we propose a Cross-modal PROtotype driven NETwork (XPRONET) to promote cross-modal pattern learning and exploit it to improve the task of radiology report generation. This is achieved by three well-designed, fully differentiable and complementary modules: a shared cross-modal prototype matrix to record the cross-modal prototypes; a cross-modal prototype network to learn the cross-modal prototypes and embed the cross-modal information into the visual and textual features; and an improved multi-label contrastive loss to enable and enhance multi-label prototype learning. XPRONET obtains substantial improvements on the IU-Xray and MIMIC-CXR benchmarks, where its performance exceeds recent state-of-the-art approaches by a large margin on IU-Xray and comparable performance on MIMIC-CXR.


Title: Spiker+: a framework for the generation of efficient Spiking Neural Networks FPGA accelerators for inference at the edge
Abstract: Including Artificial Neural Networks in embedded systems at the edge allows applications to exploit Artificial Intelligence capabilities directly within devices operating at the network periphery. This paper introduces Spiker+, a comprehensive framework for generating efficient, low-power, and low-area customized Spiking Neural Networks (SNN) accelerators on FPGA for inference at the edge. Spiker+ presents a configurable multi-layer hardware SNN, a library of highly efficient neuron architectures, and a design framework, enabling the development of complex neural network accelerators with few lines of Python code. Spiker+ is tested on two benchmark datasets, the MNIST and the Spiking Heidelberg Digits (SHD). On the MNIST, it demonstrates competitive performance compared to state-of-the-art SNN accelerators. It outperforms them in terms of resource allocation, with a requirement of 7,612 logic cells and 18 Block RAMs (BRAMs), which makes it fit in very small FPGA, and power consumption, draining only 180mW for a complete inference on an input image. The latency is comparable to the ones observed in the state-of-the-art, with 780us/img. To the authors' knowledge, Spiker+ is the first SNN accelerator tested on the SHD. In this case, the accelerator requires 18,268 logic cells and 51 BRAM, with an overall power consumption of 430mW and a latency of 54 us for a complete inference on input data. This underscores the significance of Spiker+ in the hardware-accelerated SNN landscape, making it an excellent solution to deploy configurable and tunable SNN architectures in resource and power-constrained edge applications.


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


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


Title: Exact Computation of LTI Reach Set from Integrator Reach Set with Bounded Input
Abstract: We present a semi-analytical method for exact computation of the boundary of the reach set of a single-input controllable linear time invariant (LTI) system with given bounds on its input range. In doing so, we deduce a parametric formula for the boundary of the reach set of an integrator linear system with time-varying bounded input. This formula generalizes recent results on the geometry of an integrator reach set with time-invariant bounded input. We show that the same ideas allow for computing the volume of the LTI reach set.


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


Title: Noncompact $n$-dimensional Einstein spaces as attractors for the Einstein flow
Abstract: We prove that along with the Einstein flow, any small perturbations of an $n(n \geq 4)$-dimensional, non-compact negative Einstein space with some "non-positive Weyl tensor" lead to a unique and global solution, and the solution will be attracted to a noncompact Einstein space that is close to the background one. The $n=3$ case has been addressed in [30], while in dimension $n \geq 4$, as we know, negative Einstein metrics in general have non-trivial moduli spaces. This fact is reflected on the structure of Einstein equations, which further indicates no decay for the spatial Weyl tensor. Furthermore, it is suggested in the proof that the mechanic preventing the metric from flowing back to the original Einstein metric lies in the non-decaying character of spatial Weyl tensor. In contrary to the compact case considered in Andersson-Moncrief [4], our proof is independent of the theory of infinitesimal Einstein deformations. Instead, we take advantage of the inherent geometric structures of Einstein equations and develop an approach of energy estimates for a hyperbolic system of Maxwell type.


Title: Local well-posedness of a coupled Jordan-Moore-Gibson-Thompson-Pennes model of nonlinear ultrasonic heating
Abstract: In this work, we investigate a mathematical model of nonlinear ultrasonic heating based on the Jordan-Moore-Gibson-Thompson equation (JMGT) with temperature-dependent medium parameters coupled to the semilinear Pennes equation for the bioheat transfer. The equations are coupled via the temperature in the coefficients of the JMGT equation and via a nonlinear source term within the Pennes equation, which models the absorption of acoustic energy by the surrounding tissue. Using the energy method together with a fixed point argument, we prove that our model is locally well-posed, provided that the initial data are regular, small in a lower topology and the final time is short enough.


Title: Generalized domination structure in cubic graphs
Abstract: In this paper, we consider generalized domination structure in graphs, which stipulates the structure of a minimum dominating set. Two cycles of length 0 mod 3 intersecting with one path are the constituents of the domination structure and by taking every three vertices on the cycles we can obtain a minimum dominating set. For a cubic graph, we construct generalized domination structure by adding edges in a certain way. We prove that the minimum dominating set of a cubic graph is determined in polynomial time.


Title: Communication games, sequential equilibrium, and mediators
Abstract: We consider $k$-resilient sequential equilibria, strategy profiles where no player in a coalition of at most $k$ players believes that it can increase its utility by deviating, regardless of its local state. We prove that all $k$-resilient sequential equilibria that can be implemented with a trusted mediator can also be implemented without the mediator in a synchronous system of $n$ players if $n >3k$. In asynchronous systems, where there is no global notion of time and messages may take arbitrarily long to get to their recipient, we prove that a $k$-resilient sequential equilibrium with a mediator can be implemented without the mediator if $n > 4k$. These results match the lower bounds given by Abraham, Dolev, and Halpern (2008) and Geffner and Halpern (2023) for implementing a Nash equilibrium without a mediator (which are easily seen to apply to implementing a sequential equilibrium) and improve the results of Gerardi, who showed that, in the case that $k=1$, a sequential equilibrium can be implemented in synchronous systems if $n \ge 5$.


Title: Sensing Aided Covert Communications: Turning Interference into Allies
Abstract: In this paper, we investigate the realization of covert communication in a general radar-communication cooperation system, which includes integrated sensing and communications as a special example. We explore the possibility of utilizing the sensing ability of radar to track and jam the aerial adversary target attempting to detect the transmission. Based on the echoes from the target, the extended Kalman filtering technique is employed to predict its trajectory as well as the corresponding channels. Depending on the maneuvering altitude of adversary target, two channel state information (CSI) models are considered, with the aim of maximizing the covert transmission rate by jointly designing the radar waveform and communication transmit beamforming vector based on the constructed channels. For perfect CSI under the free-space propagation model, by decoupling the joint design, we propose an efficient algorithm to guarantee that the target cannot detect the transmission. For imperfect CSI due to the multi-path components, a robust joint transmission scheme is proposed based on the property of the Kullback-Leibler divergence. The convergence behaviour, tracking MSE, false alarm and missed detection probabilities, and covert transmission rate are evaluated. Simulation results show that the proposed algorithms achieve accurate tracking. For both channel models, the proposed sensing-assisted covert transmission design is able to guarantee the covertness, and significantly outperforms the conventional schemes.


Title: Two open problems in the fixed point theory of contractive type mappings on first-countable quasimetric spaces
Abstract: Two open problems in the fixed point theory of quasi metric spaces posed in [Berinde, V. and Choban, M. M., {\it Generalized distances and their associate metrics. Impact on fixed point theory}, Creat. Math. Inform. {\bf 22} (2013), no. 1, 23--32] are considered. We give a complete answer to the first problem, a partial answer to the second one, and also illustrate the complexity and relevance of these problems by means of four very interesting and comprehensive examples.


Title: Trajectory-Oriented Policy Optimization with Sparse Rewards
Abstract: Deep reinforcement learning (DRL) remains challenging in tasks with sparse rewards. These sparse rewards often only indicate whether the task is partially or fully completed, meaning that many exploration actions must be performed before the agent obtains useful feedback. Hence, most existing DRL algorithms fail to learn feasible policies within a reasonable time frame. To overcome this problem, we develop an approach that exploits offline demonstration trajectories for faster and more efficient online RL in sparse reward settings. Our key insight is that by regarding offline demonstration trajectories as guidance, instead of imitating them, our method learns a policy whose state-action visitation marginal distribution matches that of offline demonstrations. Specifically, we introduce a novel trajectory distance based on maximum mean discrepancy (MMD) and formulate policy optimization as a distance-constrained optimization problem. Then, we show that this distance-constrained optimization problem can be reduced into a policy-gradient algorithm with shaped rewards learned from offline demonstrations. The proposed algorithm is evaluated on extensive discrete and continuous control tasks with sparse and deceptive rewards. The experimental results indicate that our proposed algorithm is significantly better than the baseline methods regarding diverse exploration and learning the optimal policy.


Title: Phototactic bioconvection in an algal suspension with a free top wall due to diffuse flux in the absence of direct collimated flux
Abstract: In this article, the effect of diffuse flux in the absence of direct collimated flux on the onset of phototactic bioconvection is investigated. The main effect of diffuse flux in the absence of collimated flux is on the swimming behaviour of microorganisms in the suspension. At higher diffuse flux, the horizontal component of swimming orientation exhibits a higher magnitude, which slows the rate of pattern formation in the suspension. Also, the linear stability of the suspension predicts that the most unstable mode of disturbance transits from stationary (oscillatory) to oscillatory (stationary) at the variation in the magnitude of diffuse flux for some fixed parameters. The overstable nature of disturbance is mostly observed at the high value of swimming speed and extinction coefficient. Moreover, the suspension shows a more stable behaviour at the higher magnitude of diffuse flux.


Title: Formal manifolds: foundations, function spaces, and Poincaré's lemma
Abstract: This is the first paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In this paper, we lay the foundations for this study by introducing the notion of formal manifolds in the context of differential geometry, inspired by the notion of formal schemes in algebraic geometry. We develop the basic theory for formal manifolds, including a generalization of the theory of vector-valued distributions and generalized functions on smooth manifolds to the setting of formal manifolds. Additionally, we establish Poincar\'e's lemma for de Rham complexes with coefficients in formal functions, formal generalized functions, compactly supported formal densities, or compactly supported formal distributions.


Title: Post-hoc evaluation of nodes influence in information cascades: the case of coordinated accounts
Abstract: In the last years, social media has gained an unprecedented amount of attention, playing a pivotal role in shaping the contemporary landscape of communication and connection. However, Coordinated Inhautentic Behaviour (CIB), defined as orchestrated efforts by entities to deceive or mislead users about their identity and intentions, has emerged as a tactic to exploit the online discourse. In this study, we quantify the efficacy of CIB tactics by defining a general framework for evaluating the influence of a subset of nodes in a directed tree. We design two algorithms that provide optimal and greedy post-hoc placement strategies that lead to maximising the configuration influence. We then consider cascades from information spreading on Twitter to compare the observed behaviour with our algorithms. The results show that, according to our model, coordinated accounts are quite inefficient in terms of their network influence, thus suggesting that they may play a less pivotal role than expected. Moreover, the causes of these poor results may be found in two separate aspects: a bad placement strategy and a scarcity of resources.


Title: Global existence, boundedness and stabilization in a high-dimensional chemotaxis system with consumption
Abstract: This paper deals with the homogeneous Neumann boundary-value problem for the chemotaxis-consumption system \begin{eqnarray*} \begin{array}{llc} u_t=\Delta u-\chi\nabla\cdot (u\nabla v)+\kappa u-\mu u^2,\\ v_t=\Delta v-uv, \end{array} \end{eqnarray*} in $N$-dimensional bounded smooth domains for suitably regular positive initial data. We shall establish the existence of a global bounded classical solution for suitably large $\mu$ and prove that for any $\mu>0$ there exists a weak solution. Moreover, in the case of $\kappa>0$ convergence to the constant equilibrium $(\frac{\kappa}{\mu},0)$ is shown.


Title: Sequential choice functions and stability problems
Abstract: The concept of sequential choice functions is introduced and studied. This concept applies to the reduction of the problem of stable matchings with sequential workers to a situation where the workers are linear.


Title: Synthetic projective lines, geometric closure and AB-sets
Abstract: In this note, we introduce a new approach to abstract ``synthetic'' projective lines. We discuss various aspects of our approach, and compare these aspects with the classical one. A number of intriguing questions arise. Amongst these aspects, we discuss geometric closures, and introduce automorphism-blocking sets. We also construct a number of (counter) examples in infinite cases.


Title: A note on minor antichains of uncountable graphs
Abstract: A simplified construction is presented for Komj\'ath's result that for every uncountable cardinal $\kappa$, there are $2^\kappa$ graphs of size $\kappa$ none of them being a minor of another.


Title: C*-Algebras of one-sided subshifts over arbitrary alphabets
Abstract: We associate a C*-algebra $\widetilde{\mathcal{O}}_{\textsf{X}}$ with a subshift over an arbitrary, possibly infinite, alphabet. We show that $\widetilde{\mathcal{O}}_{\textsf{X}}$ is a full invariant for topological conjugacy of the subshifts of Ott, Tomforde, and Willis. When the alphabet is countable, we show that $\widetilde{\mathcal{O}}_{\textsf{X}}$ is an invariant for isometric conjugacy of subshifts with the product metric. For a suitable partial action associated with a subshift over a countable alphabet, we show that $\widetilde{\mathcal{O}}_{\textsf{X}}$ is also an invariant for continuous orbit equivalence. Additionally, we give a concrete way to compute the K-theory of $\widetilde{\mathcal{O}}_{\textsf{X}}$ and illustrate it with two examples.


Title: Counterexamples to the local-global principle associated with Swinnerton-Dyer's cubic form
Abstract: In this paper, we imitate a classical construction of a counterexample to the local-global principle of cubic forms of 4 variables which was discovered first by Swinnerton-Dyer (Mathematica (1962)). Our construction gives new explicit families of counterexamples in homogeneous forms of $4, 5, 6, ..., 2n+2$ variables of degree $2n+1$ for infinitely many integers $n$. It is contrastive to Swinnerton-Dyer's original construction that we do not need any concrete calculation in the proof of local solubility.


Title: Decentralized Multi-Task Online Convex Optimization Under Random Link Failures
Abstract: Decentralized optimization methods often entail information exchange between neighbors. Transmission failures can happen due to network congestion, hardware/software issues, communication outage, and other factors. In this paper, we investigate the random link failure problem in decentralized multi-task online convex optimization, where agents have individual decisions that are coupled with each other via pairwise constraints. Although widely used in constrained optimization, conventional saddle-point algorithms are not directly applicable here because of random packet dropping. To address this issue, we develop a robust decentralized saddle-point algorithm against random link failures with heterogeneous probabilities by replacing the missing decisions of neighbors with their latest received values. Then, by judiciously bounding the accumulated deviation stemming from this replacement, we first establish that our algorithm achieves $\mathcal{O}(\sqrt{T})$ regret and $\mathcal{O}(T^\frac{3}{4})$ constraint violations for the full information scenario, where the complete information on the local cost function is revealed to each agent at the end of each time slot. These two bounds match, in order sense, the performance bounds of algorithms with perfect communications. Further, we extend our algorithm and analysis to the two-point bandit feedback scenario, where only the values of the local cost function at two random points are disclosed to each agent sequentially. Performance bounds of the same orders as the full information case are derived. Finally, we corroborate the efficacy of the proposed algorithms and the analytical results through numerical simulations.


Title: On a Navier-Stokes-Fourier-like system capturing transitions between viscous and inviscid fluid regimes and between no-slip and perfect-slip boundary conditions
Abstract: We study a generalization of the Navier-Stokes-Fourier system for an incompressible fluid where the deviatoric part of the Cauchy stress tensor is related to the symmetric part of the velocity gradient via a maximal monotone 2-graph that is continuously parametrized by the temperature. As such, the considered fluid may go through transitions between three of the following regimes: it can flow as a Bingham fluid for a specific value of the temperature, while it can behave as the Navier-Stokes fluid for another value of the temperature or, for yet another temperature, it can respond as the Euler fluid until a certain activation initiates the response of the Navier-Stokes fluid. At the same time, we regard a generalized threshold slip on the boundary that also may go through various regimes continuously with the temperature. All material coefficients like the dynamic viscosity, friction or activation coefficients are assumed to be temperature-dependent. We establish the large-data and long-time existence of weak solutions, applying the $L^{\infty}$-truncation technique to approximate the velocity field.


Title: Local-in-time strong solutions of the homogeneous Landau-Coulomb equation with $L^p$ initial datum
Abstract: We consider the homogeneous Landau equation with Coulomb potential and general initial data $f_{in} \in L^p$, where $p$ is arbitrarily close to $3/2$. We show the local-in-time existence and uniqueness of smooth solutions for such initial data. The constraint $p > 3/2$ has appeared in several related works and appears to be the minimal integrability assumption achievable with current techniques. We adapt recent ODE methods and conditional regularity results appearing in [arXiv:2303.02281] to deduce new short time $L^p \to L^\infty$ smoothing estimates. These estimates enable us to construct local-in-time smooth solutions for large $L^p$ initial data, and allow us to show directly conditional regularity results for solutions verifying \emph{unweighted} Prodi-Serrin type conditions. As a consequence, we obtain additional stability and uniqueness results for the solutions we construct.


Title: Parameterized Verification of Disjunctive Timed Networks
Abstract: We introduce new techniques for the parameterized verification of disjunctive timed networks (DTNs), i.e., networks of timed automata (TAs) that communicate via location guards that enable a transition only if there is another process in a given location. This computational model has been considered in the literature before, example applications are gossiping clock synchronization protocols or planning problems. We address the minimum-time reachability problem (Minreach) in DTNs, and show how to efficiently solve it based on a novel zone graph algorithm. We further show that solving Minreach allows us to construct a summary TA capturing exactly the possible behaviors of a single TA within a DTN of arbitrary size. The combination of these two results enables the parameterized verification of DTNs, while avoiding the construction of an exponential-size cutoff system required by existing results. Additionally, we develop sufficient conditions for solving Minreach and parameterized verification problems even in certain cases where locations that appear in location guards can have clock invariants, a case that has usually been excluded in the literature. Our techniques are also implemented, and experiments show their practicality.


Title: The Principal Ideal Theorem in Spectral Synthesis
Abstract: In an earlier paper we solved a long-standing problem which goes back to Laurent Schwartz's work on mean-periodic functions. Namely, we completely characterised those locally compact Abelian groups having spectral synthesis. The method is based on the localisation concept. In this paper we show that localisation can be used to prove another basic result in spectral synthesis: the principal ideal theorem.


Title: Deep Recurrent Level Set for Segmenting Brain Tumors
Abstract: Variational Level Set (VLS) has been a widely used method in medical segmentation. However, segmentation accuracy in the VLS method dramatically decreases when dealing with intervening factors such as lighting, shadows, colors, etc. Additionally, results are quite sensitive to initial settings and are highly dependent on the number of iterations. In order to address these limitations, the proposed method incorporates VLS into deep learning by defining a novel end-to-end trainable model called as Deep Recurrent Level Set (DRLS). The proposed DRLS consists of three layers, i.e, Convolutional layers, Deconvolutional layers with skip connections and LevelSet layers. Brain tumor segmentation is taken as an instant to illustrate the performance of the proposed DRLS. Convolutional layer learns visual representation of brain tumor at different scales. Since brain tumors occupy a small portion of the image, deconvolutional layers are designed with skip connections to obtain a high quality feature map. Level-Set Layer drives the contour towards the brain tumor. In each step, the Convolutional Layer is fed with the LevelSet map to obtain a brain tumor feature map. This in turn serves as input for the LevelSet layer in the next step. The experimental results have been obtained on BRATS2013, BRATS2015 and BRATS2017 datasets. The proposed DRLS model improves both computational time and segmentation accuracy when compared to the the classic VLS-based method. Additionally, a fully end-to-end system DRLS achieves state-of-the-art segmentation on brain tumors.


Title: Uniform mixing and completely positive sofic entropy
Abstract: Let $G$ be a countable discrete sofic group. We define a concept of uniform mixing for measure-preserving $G$-actions and show that it implies completely positive sofic entropy. When $G$ contains an element of infinite order, we use this to produce an uncountable family of pairwise nonisomorphic $G$-actions with completely positive sofic entropy. None of our examples is a factor of a Bernoulli shift.


Title: Additive Correlation and the Inverse Problem for the Large Sieve
Abstract: Let $A\subset [1,N]$ be a set of positive integers with $|A|\gg \sqrt N$. We show that if avoids about $p/2$ residue classes modulo $p$ for each prime $p$, the $A$ must correlate additively with the squares $S=\{n^2:1\leq n\leq \sqrt N\}$, in the sense that we have the additive energy estimate $E(A,S)\gg N\log N$. This is, in a sense, optimal.


Title: On games and simulators as a platform for development of artificial intelligence for command and control
Abstract: Games and simulators can be a valuable platform to execute complex multi-agent, multiplayer, imperfect information scenarios with significant parallels to military applications: multiple participants manage resources and make decisions that command assets to secure specific areas of a map or neutralize opposing forces. These characteristics have attracted the artificial intelligence (AI) community by supporting development of algorithms with complex benchmarks and the capability to rapidly iterate over new ideas. The success of artificial intelligence algorithms in real-time strategy games such as StarCraft II have also attracted the attention of the military research community aiming to explore similar techniques in military counterpart scenarios. Aiming to bridge the connection between games and military applications, this work discusses past and current efforts on how games and simulators, together with the artificial intelligence algorithms, have been adapted to simulate certain aspects of military missions and how they might impact the future battlefield. This paper also investigates how advances in virtual reality and visual augmentation systems open new possibilities in human interfaces with gaming platforms and their military parallels.


Title: KCES: A Workflow Containerization Scheduling Scheme Under Cloud-Edge Collaboration Framework
Abstract: As more IoT applications gradually move towards the cloud-edge collaborative mode, the containerized scheduling of workflows extends from the cloud to the edge. However, given the high delay of the communication network, loose coupling of structure, and resource heterogeneity between cloud and edge, workflow containerization scheduling in the cloud-edge scenarios faces the difficulty of resource coordination and application collaboration management. To address these two issues, we propose a KubeEdge-Cloud-Edge-Scheduling scheme named KCES, a workflow containerization scheduling scheme for the KubeEdge cloud-edge framework. The KCES includes a cloud-edge workflow scheduling engine for KubeEdge and workflow scheduling strategies for task horizontal roaming and vertical offloading. Considering the scheduling optimization of cloud-edge workflows, this paper proposes a cloud-edge workflow scheduling model and cloud-edge node model and designs a cloud-edge workflow scheduling engine to maximize cloud-edge resource utilization under the constraint of workflow task delay. A cloud-edge resource hybrid management technology is used to design the cloud-edge resource evaluation and resource allocation algorithms to achieve cloud-edge resource collaboration. Based on the ideas of distributed functional roles and the hierarchical division of computing power, the horizontal roaming among the edges and vertical offloading strategies between the cloud and edges for workflow tasks are designed to realize the cloud-edge application collaboration. Through a customized IoT application workflow instance, experimental results show that KCES is superior to the baseline in total workflow duration, average workflow duration, and resource usage and has the capabilities of horizontal roaming and vertical offloading for workflow tasks.


Title: Noncentral moderate deviations for time-changed Lévy processes with inverse of stable subordinators
Abstract: In this paper we present some extensions of recent noncentral moderate deviation results in the literature. In the first part we generalize the results in \cite{BeghinMacciSPL2022} by considering a general L\'evy process $\{S(t):t\geq 0\}$ instead of a compound Poisson process. In the second part we assume that $\{S(t):t\geq 0\}$ has bounded variation and it is not a subordinator; thus, in some sense, we have the difference of two independent non-null subordinators. In this way we generalize the results in \cite{LeeMacci} for Skellam processes.


Title: Electromechanical phase-field fracture modelling of piezoresistive CNT-based composites
Abstract: We present a novel computational framework to simulate the electromechanical response of self-sensing carbon nanotube (CNT)-based composites experiencing fracture. The computational framework combines electrical-deformation-fracture finite element modelling with a mixed micromechanics formulation. The latter is used to estimate the constitutive properties of CNT-based composites, including the elastic tensor, fracture energy, electrical conductivity, and linear piezoresistive coefficients. These properties are inputted into a coupled electro-structural finite element model, which simulates the evolution of cracks based upon phase-field fracture. The coupled physical problem is solved in a monolithic manner, exploiting the robustness and efficiency of a quasi-Newton algorithm. 2D and 3D boundary value problems are simulated to illustrate the potential of the modelling framework in assessing the influence of defects on the electromechanical response of meso- and macro-scale smart structures. Case studies aim at shedding light into the interplay between fracture and the electromechanical material response and include parametric analyses, validation against experiments and the simulation of complex cracking conditions (multiple defects, crack merging). The presented numerical results showcase the efficiency and robustness of the computational framework, as well as its ability to model a large variety of structural configurations and damage patterns. The deformation-electrical-fracture finite element code developed is made freely available to download.


Title: Structural characterization of Cayley graphs
Abstract: We show that the directed labelled Cayley graphs coincide with the rooted deterministic vertex-transitive simple graphs. The Cayley graphs are also the strongly connected deterministic simple graphs of which all vertices have the same cycle language, or just the same elementary cycle language. Under the assumption of the axiom of choice, we characterize the Cayley graphs for all group subsets as the deterministic, co-deterministic, vertex-transitive simple graphs.


Title: A BDI Agent-Based Task Scheduling Framework for Cloud Computing
Abstract: Cloud computing is an attractive technology for providing computing resources over the Internet. Task scheduling is a critical issue in cloud computing, where an efficient task scheduling method can improve overall cloud performance. Since cloud computing is a large-scale and geographically distributed environment, traditional scheduling methods that allocate resources in a centralized manner are ineffective. Besides, traditional methods are difficult to make rational decisions timely when the external environment changes. This paper proposes a decentralized BDI (belief-desire-intention) agent-based scheduling framework for cloud computing. BDI agents have advantages in modelling dynamic environments because BDI agents can update their beliefs, change desires, and trigger behaviours based on environmental changes. Besides, to avoid communication stuck caused by environmental uncertainties, the asynchronous communication mode with a notify listener is employed. The proposed framework covers both the task scheduling and rescheduling stages with the consideration of uncertain events that can interrupt task executions. Two agent-based algorithms are proposed to implement the task scheduling and rescheduling processes, and a novel recommendation mechanism is presented in the scheduling stage to reduce the impact of information synchronization delays. The proposed framework is implemented by JADEX and tested on CloudSim. The experimental results show that our framework can minimize the task makespan, balance the resource utilization in a large-scale environment, and maximize the task success rate when uncertain events occur.