Title: HEAP: Unsupervised Object Discovery and Localization with Contrastive Grouping
Abstract: Unsupervised object discovery and localization aims to detect or segment objects in an image without any supervision. Recent efforts have demonstrated a notable potential to identify salient foreground objects by utilizing self-supervised transformer features. However, their scopes only build upon patch-level features within an image, neglecting region/image-level and cross-image relationships at a broader scale. Moreover, these methods cannot differentiate various semantics from multiple instances. To address these problems, we introduce Hierarchical mErging framework via contrAstive grouPing (HEAP). Specifically, a novel lightweight head with cross-attention mechanism is designed to adaptively group intra-image patches into semantically coherent regions based on correlation among self-supervised features. Further, to ensure the distinguishability among various regions, we introduce a region-level contrastive clustering loss to pull closer similar regions across images. Also, an image-level contrastive loss is present to push foreground and background representations apart, with which foreground objects and background are accordingly discovered. HEAP facilitates efficient hierarchical image decomposition, which contributes to more accurate object discovery while also enabling differentiation among objects of various classes. Extensive experimental results on semantic segmentation retrieval, unsupervised object discovery, and saliency detection tasks demonstrate that HEAP achieves state-of-the-art performance.


Title: The Drinfel'd Double and Twisting in Stringy Orbifold Theory
Abstract: This paper exposes the fundamental role that the Drinfel'd double $\dkg$ of the group ring of a finite group $G$ and its twists $\dbkg$, $\beta \in Z^3(G,\uk)$ as defined by Dijkgraaf--Pasquier--Roche play in stringy orbifold theories and their twistings. The results pertain to three different aspects of the theory. First, we show that $G$--Frobenius algebras arising in global orbifold cohomology or K-theory are most naturally defined as elements in the braided category of $\dkg$--modules. Secondly, we obtain a geometric realization of the Drinfel'd double as the global orbifold $K$--theory of global quotient given by the inertia variety of a point with a $G$ action on the one hand and more stunningly a geometric realization of its representation ring in the braided category sense as the full $K$--theory of the stack $[pt/G]$. Finally, we show how one can use the co-cycles $\beta$ above to twist a) the global orbifold $K$--theory of the inertia of a global quotient and more importantly b) the stacky $K$--theory of a global quotient $[X/G]$. This corresponds to twistings with a special type of 2--gerbe.


Title: To Save Mobile Crowdsourcing from Cheap-talk: A Game Theoretic Learning Approach
Abstract: Today mobile crowdsourcing platforms invite users to provide anonymous reviews about service experiences, yet many reviews are found biased to be extremely positive or negative. The existing methods find it difficult to learn from biased reviews to infer the actual service state, as the state can also be extreme and the platform cannot verify the truthfulness of reviews immediately. Further, reviewers can hide their (positive or negative) bias types and proactively adjust their anonymous reviews against the platform's inference. To our best knowledge, we are the first to study how to save mobile crowdsourcing from cheap-talk and strategically learn from biased users' reviews. We formulate the problem as a dynamic Bayesian game, including users' service-type messaging and the platform's follow-up rating/inference. Our closed-form PBE shows that an extremely-biased user may still honestly message to convince the platform of listening to his review. Such Bayesian game-theoretic learning obviously outperforms the latest common schemes especially when there are multiple diversely-biased users to compete. For the challenging single-user case, we further propose a time-evolving mechanism with the platform's commitment inferences to ensure the biased user's truthful messaging all the time, whose performance improves with more time periods to learn from more historical data.


Title: Pursuing the double affine Grassmannian III: Convolution with affine Zastava
Abstract: This is the third paper of a series (started by arXiv:0711.2083, arXiv:0908.3390) which describes a conjectural analog of the affine Grassmannian for affine Kac-Moody groups (also known as the double affine Grassmannian). The current paper is dedicated to describing a conjectural analog of the convolution diagram for the double affine Grassmannian and affine Zastava.


Title: Enumerating m-Length Walks in Directed Graphs with Constant Delay
Abstract: In this paper, we provide a novel enumeration algorithm for the set of all walks of a given length within a directed graph. Our algorithm has worst-case constant delay between outputting succinct representations of such walks, after a preprocessing step requiring linear time relative to the size of the graph. We apply these results to the problem of enumerating succinct representations of the strings of a given length from a prefix-closed regular language (languages accepted by a finite automaton which has final states only).


Title: Global Well-posedness for 2D non-resistive MHD equations in half-space
Abstract: This paper focuses on the initial boundary value problem of two-dimensional non-resistive MHD equations in a half space. We prove that the MHD equations have a unique global strong solution around the equilibrium state $(0,\bf{e_1})$ for Dirichlet boundary condition of velocity and modified Neumann boundary condition of magnetic.


Title: Calderon-Zygmund theory for strongly coupled linear system of nonlocal equations with Holder-regular coefficient
Abstract: We extend the Calder\'on-Zygmund theory for nonlocal equations to strongly coupled system of linear nonlocal equations $\mathcal{L}^{s}_{A} u = f$, where the operator $\mathcal{L}^{s}_{A}$ is formally given by \[ \mathcal{L}^s_{A}u = \int_{\mathbb{R}^n}\frac{A(x, y)}{\vert x-y\vert ^{n+2s}} \frac{(x-y)\otimes (x-y)}{\vert x-y\vert ^2}(u(x)-u(y))dy. \] For $0 < s < 1$ and $A:\mathbb{R}^{n} \times \mathbb{R}^{n} \to \mathbb{R}$ taken to be symmetric and serving as a variable coefficient for the operator, the system under consideration is the fractional version of the classical Navier-Lam\'e linearized elasticity system. The study of the coupled system of nonlocal equations is motivated by its appearance in nonlocal mechanics, primarily in peridynamics. Our regularity result states that if $A(\cdot, y)$ is uniformly Holder continuous and $\inf_{x\in \mathbb{R}^n}A(x, x) > 0$, then for $f\in L^{p}_{loc},$ for $p\geq 2$, the solution vector $u\in H^{2s-\delta,p}_{loc}$ for some $\delta\in (0, s)$.


Title: Ramsey properties of random graphs and Folkman numbers
Abstract: For two graphs, $G$ and $F$, and an integer $r\ge2$ we write $G\rightarrow (F)_r$ if every $r$-coloring of the edges of $G$ results in a monochromatic copy of $F$. In 1995, the first two authors established a threshold edge probability for the Ramsey property $G(n,p)\to (F)_r$, where $G(n,p)$ is a random graph obtained by including each edge of the complete graph on $n$ vertices, independently, with probability $p$. The original proof was based on the regularity lemma of Szemer\'edi and this led to tower-type dependencies between the involved parameters. Here, for $r=2$, we provide a self-contained proof of a quantitative version of the Ramsey threshold theorem with only double exponential dependencies between the constants. As a corollary we obtain a double exponential upper bound on the 2-color Folkman numbers. By a different proof technique, a similar result was obtained independently by Conlon and Gowers.


Title: Learning to Generalize towards Unseen Domains via a Content-Aware Style Invariant Model for Disease Detection from Chest X-rays
Abstract: Performance degradation due to distribution discrepancy is a longstanding challenge in intelligent imaging, particularly for chest X-rays (CXRs). Recent studies have demonstrated that CNNs are biased toward styles (e.g., uninformative textures) rather than content (e.g., shape), in stark contrast to the human vision system. Radiologists tend to learn visual cues from CXRs and thus perform well across multiple domains. Motivated by this, we employ the novel on-the-fly style randomization modules at both image (SRM-IL) and feature (SRM-FL) levels to create rich style perturbed features while keeping the content intact for robust cross-domain performance. Previous methods simulate unseen domains by constructing new styles via interpolation or swapping styles from existing data, limiting them to available source domains during training. However, SRM-IL samples the style statistics from the possible value range of a CXR image instead of the training data to achieve more diversified augmentations. Moreover, we utilize pixel-wise learnable parameters in the SRM-FL compared to pre-defined channel-wise mean and standard deviations as style embeddings for capturing more representative style features. Additionally, we leverage consistency regularizations on global semantic features and predictive distributions from with and without style-perturbed versions of the same CXR to tweak the model's sensitivity toward content markers for accurate predictions. Our proposed method, trained on CheXpert and MIMIC-CXR datasets, achieves 77.32$\pm$0.35, 88.38$\pm$0.19, 82.63$\pm$0.13 AUCs(%) on the unseen domain test datasets, i.e., BRAX, VinDr-CXR, and NIH chest X-ray14, respectively, compared to 75.56$\pm$0.80, 87.57$\pm$0.46, 82.07$\pm$0.19 from state-of-the-art models on five-fold cross-validation with statistically significant results in thoracic disease classification.


Title: Higher Descent Data as a Homotopy Limit
Abstract: We define the 2-groupoid of descent data assigned to a cosimplicial 2-groupoid and present it as the homotopy limit of the cosimplicial space gotten after applying the 2-nerve in each cosimplicial degree. This can be applied also to the case of $n$-groupoids thus providing an analogous presentation of "descent data" in higher dimensions.


Title: An alternative approach to large deviations for the almost-critical Erdős-Rényi random graph
Abstract: We study the near-critical behavior of the sparse Erd\H{o}s-R\'enyi random graph $\mathcal{G}(n,p)$ on $n\gg1$ vertices, where the connection probability $p$ satisfies $np = 1+\theta(b_n^2/n)^{1/3}$, with $n^{3/10}\ll {b_n}\ll n^{1/2}$, and $\theta\in\mathbb{R}$. To this end, we introduce an empirical measure that describes connected components of $\mathcal{G}(n,p)$ of mesoscopic size $\propto (nb_n)^{2/3}$, and we characterize its large deviation behavior. The proof hinges on detailed combinatorial estimates and optimization procedures. In particular, we give precise estimates for the probability that the graph has no connected component of mesoscopic size or larger. We argue that these are a stepping stone for the analysis of more general inhomogeneous random graphs. Our proof strategy gives new and accurate estimates of the probability that the sparse Erd\H{o}s-R\'enyi graph is connected.


Title: How to Apply Markov Chains for Modeling Sequential Edit Patterns in Collaborative Ontology-Engineering Projects
Abstract: With the growing popularity of large-scale collaborative ontology-engineering projects, such as the creation of the 11th revision of the International Classification of Diseases, we need new methods and insights to help project- and community-managers to cope with the constantly growing complexity of such projects. In this paper, we present a novel application of Markov chains to model sequential usage patterns that can be found in the change-logs of collaborative ontology-engineering projects. We provide a detailed presentation of the analysis process, describing all the required steps that are necessary to apply and determine the best fitting Markov chain model. Amongst others, the model and results allow us to identify structural properties and regularities as well as predict future actions based on usage sequences. We are specifically interested in determining the appropriate Markov chain orders which postulate on how many previous actions future ones depend on. To demonstrate the practical usefulness of the extracted Markov chains we conduct sequential pattern analyses on a large-scale collaborative ontology-engineering dataset, the International Classification of Diseases in its 11th revision. To further expand on the usefulness of the presented analysis, we show that the collected sequential patterns provide potentially actionable information for user-interface designers, ontology-engineering tool developers and project-managers to monitor, coordinate and dynamically adapt to the natural development processes that occur when collaboratively engineering an ontology. We hope that presented work will spur a new line of ontology-development tools, evaluation-techniques and new insights, further taking the interactive nature of the collaborative ontology-engineering process into consideration.


Title: Jumping numbers of a unibranch curve on a smooth surface
Abstract: A formula for the jumping numbers of a curve unibranch at a singular point is established. The jumping numbers are expressed in terms of the Enriques diagram of the log resolution of the singularity, or equivalently in terms of the canonical set of generators of the semigroup of the curve at the singular point.


Title: Generalizations of quasielliptic curves
Abstract: We generalize the notion of quasielliptic curves, which have infinitesimal symmetries and exist only in characteristic two and three, to a remarkable hierarchy of regular curves having infinitesimal symmetries, defined in all characteristics and having higher genera. This relies on the study of certain infinitesimal group schemes acting on the affine line and certain compactifications. The group schemes are defined in terms of invertible additive polynomials over rings with nilpotent elements, and the compactification is constructed with the theory of numerical semigroups. The existence of regular twisted forms relies on Brion's recent theory of equivariant normalization. Furthermore, extending results of Serre from the realm of group cohomology, we describe non-abelian cohomology for semidirect products, to compute in special cases the collection of all twisted forms.


Title: Minimal surfaces with symmetries
Abstract: Let $G$ be a finite group acting on a connected open Riemann surface $X$ by holomorphic automorphisms and acting on a Euclidean space $\mathbb R^n$ $(n\ge 3)$ by orthogonal transformations. We identify a necessary and sufficient condition for the existence of a $G$-equivariant conformal minimal immersion $F:X\to\mathbb R^n$. We show in particular that such a map $F$ always exists if $G$ acts without fixed points on $X$. Furthermore, every finite group $G$ arises in this way for some open Riemann surface $X$ and $n=2|G|$. We obtain an analogous result for minimal surfaces having complete ends with finite total Gaussian curvature, and for discrete infinite groups acting on $X$ properly discontinuously and acting on $\mathbb R^n$ by rigid transformations.


Title: The bridge number of satellite knots, links, and spatial graphs in the 3-sphere and lens spaces
Abstract: Let $T$ be a satellite knot, link, or spatial graph in a 3-manifold $M$ that is either $S^3$ or a lens space. Let $b_0$ and $b_1$ denote genus 0 and genus 1 bridge number, respectively. Suppose that $T$ has a companion knot $K$ and wrapping number $\omega$ with respect to $K$. When $K$ is not a torus knot, we show that $b_1(T)\geq \omega b_1(K)$. There are previously known counter-examples if $K$ is a torus knot. Along the way, we generalize and give a new proof of Schubert's result that $b_0(T) \geq \omega b_0(K)$. We also prove versions of the theorem applicable to when $T$ is a ``lensed satellite'' or when there is a torus separating components of $T$.


Title: To Push or To Pull: On Reducing Communication and Synchronization in Graph Computations
Abstract: We reduce the cost of communication and synchronization in graph processing by analyzing the fastest way to process graphs: pushing the updates to a shared state or pulling the updates to a private state.We investigate the applicability of this push-pull dichotomy to various algorithms and its impact on complexity, performance, and the amount of used locks, atomics, and reads/writes. We consider 11 graph algorithms, 3 programming models, 2 graph abstractions, and various families of graphs. The conducted analysis illustrates surprising differences between push and pull variants of different algorithms in performance, speed of convergence, and code complexity; the insights are backed up by performance data from hardware counters.We use these findings to illustrate which variant is faster for each algorithm and to develop generic strategies that enable even higher speedups. Our insights can be used to accelerate graph processing engines or libraries on both massively-parallel shared-memory machines as well as distributed-memory systems.


Title: How Do Pedestrians' Perception Change toward Autonomous Vehicles during Unmarked Midblock Multilane Crossings: Role of AV Operation and Signal Indication
Abstract: One of the primary impediments hindering the widespread acceptance of autonomous vehicles (AVs) among pedestrians is their limited comprehension of AVs. This study employs virtual reality (VR) to provide pedestrians with an immersive environment for engaging with and comprehending AVs during unmarked midblock multilane crossings. Diverse AV driving behaviors were modeled to exhibit negotiation behavior with a yellow signal indication or non-yielding behavior with a blue signal indication. This paper aims to investigate the impact of various factors, such as AV behavior and signaling, pedestrian past behavior, etc., on pedestrians' perception change of AVs. Before and after the VR experiment, participants completed surveys assessing their perception of AVs, focusing on two main aspects: "Attitude" and "System Effectiveness." The Wilcoxon signed-rank test results demonstrated that both pedestrians' overall attitude score toward AVs and trust in the effectiveness of AV systems significantly increased following the VR experiment. Notably, individuals who exhibited a greater trust in the yellow signals were more inclined to display a higher attitude score toward AVs and to augment their trust in the effectiveness of AV systems. This indicates that the design of the yellow signal instills pedestrians with greater confidence in their interactions with AVs. Further, pedestrians who exhibit more aggressive crossing behavior are less likely to change their perception towards AVs as compared to those pedestrians with more positive crossing behaviors. It is concluded that integrating this paper's devised AV behavior and signaling within an immersive VR setting facilitated pedestrian engagement with AVs, thereby changing their perception of AVs.


Title: Longest and shortest cycles in 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 $\{1, \ldots, n\}$ with $m=m(n)$ edges. We study the cycle and block structure of $P(n,m)$ when $m\sim n/2$. More precisely, we determine the asymptotic order of the length of the longest and shortest cycle in $P(n,m)$ in the critical range when $m=n/2+o(n)$. In addition, we describe the block structure of $P(n,m)$ in the weakly supercritical regime when $n^{2/3}\ll m-n/2\ll n$.


Title: Distributed Hardware Accelerated Secure Joint Computation on the COPA Framework
Abstract: Performance of distributed data center applications can be improved through use of FPGA-based SmartNICs, which provide additional functionality and enable higher bandwidth communication. Until lately, however, the lack of a simple approach for customizing SmartNICs to application requirements has limited the potential benefits. Intel's Configurable Network Protocol Accelerator (COPA) provides a customizable FPGA framework that integrates both hardware and software development to improve computation and communication performance. In this first case study, we demonstrate the capabilities of the COPA framework with an application from cryptography -- secure Multi-Party Computation (MPC) -- that utilizes hardware accelerators connected directly to host memory and the COPA network. We find that using the COPA framework gives significant improvements to both computation and communication as compared to traditional implementations of MPC that use CPUs and NICs. A single MPC accelerator running on COPA enables more than 17Gbps of communication bandwidth while using only 1% of Stratix 10 resources. We show that utilizing the COPA framework enables multiple MPC accelerators running in parallel to fully saturate a 100Gbps link enabling higher performance compared to traditional NICs.


Title: Associators in mould theory
Abstract: By developing various techniques of mould theory, we introduce $\mathsf{GARI}(\mathscr{F})_{\mathsf{as}+\mathsf{bal}}$, a mould theoretic formulation of Drinfeld's associator set. We give a mould-theoretical generalization of the result that associator relations imply double shuffle relations, namely, we explain that $\mathsf{GARI}(\mathscr{F})_{\mathsf{as}+\mathsf{bal}}$ is embedded to Ecalle's set $\mathsf{GARI}(\mathscr{F})_{\mathsf{as}\ast\mathsf{is}}$ which is a mould theoretic version of Racinet's double shuffle set.


Title: Some remarks on combinatorial wall-crossing
Abstract: We establish a new simple explicit description of combinatorial wall-crossing for the rational Cherednik algebra applied to the trivial representation. In this way we recover a theorem of P. Dimakis and G. Yue. We also present two conjectures on combinatorial wall-crossing which were found using computer experiments.


Title: Thermodynamic Consistent Neural Networks for Learning Material Interfacial Mechanics
Abstract: For multilayer materials in thin substrate systems, interfacial failure is one of the most challenges. The traction-separation relations (TSR) quantitatively describe the mechanical behavior of a material interface undergoing openings, which is critical to understand and predict interfacial failures under complex loadings. However, existing theoretical models have limitations on enough complexity and flexibility to well learn the real-world TSR from experimental observations. A neural network can fit well along with the loading paths but often fails to obey the laws of physics, due to a lack of experimental data and understanding of the hidden physical mechanism. In this paper, we propose a thermodynamic consistent neural network (TCNN) approach to build a data-driven model of the TSR with sparse experimental data. The TCNN leverages recent advances in physics-informed neural networks (PINN) that encode prior physical information into the loss function and efficiently train the neural networks using automatic differentiation. We investigate three thermodynamic consistent principles, i.e., positive energy dissipation, steepest energy dissipation gradient, and energy conservative loading path. All of them are mathematically formulated and embedded into a neural network model with a novel defined loss function. A real-world experiment demonstrates the superior performance of TCNN, and we find that TCNN provides an accurate prediction of the whole TSR surface and significantly reduces the violated prediction against the laws of physics.


Title: Assessing the Impact of a User-Item Collaborative Attack on Class of Users
Abstract: Collaborative Filtering (CF) models lie at the core of most recommendation systems due to their state-of-the-art accuracy. They are commonly adopted in e-commerce and online services for their impact on sales volume and/or diversity, and their impact on companies' outcome. However, CF models are only as good as the interaction data they work with. As these models rely on outside sources of information, counterfeit data such as user ratings or reviews can be injected by attackers to manipulate the underlying data and alter the impact of resulting recommendations, thus implementing a so-called shilling attack. While previous works have focused on evaluating shilling attack strategies from a global perspective paying particular attention to the effect of the size of attacks and attacker's knowledge, in this work we explore the effectiveness of shilling attacks under novel aspects. First, we investigate the effect of attack strategies crafted on a target user in order to push the recommendation of a low-ranking item to a higher position, referred to as user-item attack. Second, we evaluate the effectiveness of attacks in altering the impact of different CF models by contemplating the class of the target user, from the perspective of the richness of her profile (i.e., cold v.s. warm user). Finally, similar to previous work we contemplate the size of attack (i.e., the amount of fake profiles injected) in examining their success. The results of experiments on two widely used datasets in business and movie domains, namely Yelp and MovieLens, suggest that warm and cold users exhibit contrasting behaviors in datasets with different characteristics.


Title: Near Optimal Bounds for Collision in Pollard Rho for Discrete Log
Abstract: We analyze a fairly standard idealization of Pollard's Rho algorithm for finding the discrete logarithm in a cyclic group G. It is found that, with high probability, a collision occurs in $O(\sqrt{|G|\log |G| \log \log |G|})$ steps, not far from the widely conjectured value of $\Theta(\sqrt{|G|})$. This improves upon a recent result of Miller--Venkatesan which showed an upper bound of $O(\sqrt{|G|}\log^3 |G|)$. Our proof is based on analyzing an appropriate nonreversible, non-lazy random walk on a discrete cycle of (odd) length |G|, and showing that the mixing time of the corresponding walk is $O(\log |G| \log \log |G|)$.


Title: More on Arago'n Artacho - Campoy's Algorithm
Abstract: The Arago'n Artacho-Campoy algorithm (AACA) is a new method for finding zeros of sums of monotone operators. In this paper we complete the analysis of [2] and[1] by providing study of the two possible Arago'n Artacho-Campoy operators.


Title: Notes on limits of accessible categories
Abstract: Let $\kappa$ be a regular cardinal, $\lambda<\kappa$ be a smaller infinite cardinal, and $\mathsf K$ be a $\kappa$-accessible category where colimits of $\lambda$-indexed chains exist. We show that various category-theoretic constructions applied to $\mathsf K$, such as the inserter and the equifier, produce $\kappa$-accessible categories $\mathsf E$ again, and the most obvious expected description of the full subcategory of $\kappa$-presentable objects in $\mathsf E$ in terms of $\kappa$-presentable objects in $\mathsf K$ holds true. In particular, if $\mathsf C$ is a $\kappa$-small category, then the category of functors $\mathsf C\rightarrow\mathsf K$ is $\kappa$-accessible, and its $\kappa$-presentable objects are precisely all the functors from $\mathsf C$ to the $\kappa$-presentable objects of $\mathsf K$. We proceed to discuss the preservation of $\kappa$-accessibility by conical pseudolimits, lax and oplax limits, and weighted pseudolimits. The results of this paper go back to an unpublished 1977 preprint of Ulmer. Our motivation comes from the theory of flat modules and flat quasi-coherent sheaves.


Title: Co-compact Gabor systems on locally compact abelian groups
Abstract: In this work we extend classical structure and duality results in Gabor analysis on the euclidean space to the setting of second countable locally compact abelian (LCA) groups. We formulate the concept of rationally oversampling of Gabor systems in an LCA group and prove corresponding characterization results via the Zak transform. From these results we derive non-existence results for critically sampled continuous Gabor frames. We obtain general characterizations in time and in frequency domain of when two Gabor generators yield dual frames. Moreover, we prove the Walnut and Janssen representation of the Gabor frame operator and consider the Wexler-Raz biorthogonality relations for dual generators. Finally, we prove the duality principle for Gabor frames. Unlike most duality results on Gabor systems, we do not rely on the fact that the translation and modulation groups are discrete and co-compact subgroups. Our results only rely on the assumption that either one of the translation and modulation group (in some cases both) are co-compact subgroups of the time and frequency domain. This presentation offers a unified approach to the study of continuous and the discrete Gabor frames.


Title: Gaussian Process based Stochastic Model Predictive Control for Cooperative Adaptive Cruise Control
Abstract: Cooperative driving relies on communication among vehicles to create situational awareness. One application of cooperative driving is Cooperative Adaptive Cruise Control (CACC) that aims at enhancing highway transportation safety and capacity. Model-based communication (MBC) is a new paradigm with a flexible content structure for broadcasting joint vehicle-driver predictive behavioral models. The vehicle's complex dynamics and diverse driving behaviors add complexity to the modeling process. Gaussian process (GP) is a fully data-driven and non-parametric Bayesian modeling approach which can be used as a modeling component of MBC. The knowledge about the uncertainty is propagated through predictions by generating local GPs for vehicles and broadcasting their hyper-parameters as a model to the neighboring vehicles. In this research study, GP is used to model each vehicle's speed trajectory, which allows vehicles to access the future behavior of their preceding vehicle during communication loss and/or low-rate communication. Besides, to overcome the safety issues in a vehicle platoon, two operating modes for each vehicle are considered; free following and emergency braking. This paper presents a discrete hybrid stochastic model predictive control, which incorporates system modes as well as uncertainties captured by GP models. The proposed control design approach finds the optimal vehicle speed trajectory with the goal of achieving a safe and efficient platoon of vehicles with small inter-vehicle gap while reducing the reliance of the vehicles on a frequent communication. Simulation studies demonstrate the efficacy of the proposed controller considering the aforementioned communication paradigm with low-rate intermittent communication.


Title: Maximum principal ratio of the signless Laplacian of graphs
Abstract: Let $G$ be a connected graph and $Q(G)$ be the signless Laplacian of $G$. The principal ratio $\gamma(G)$ of $Q(G)$ is the ratio of the maximum and minimum entries of the Perron vector of $Q(G)$. In this paper, we consider the maximum principal ratio $\gamma(G)$ among all connected graphs of order $n$, and show that for sufficiently large $n$ the extremal graph is a kite graph obtained by identifying an end vertex of a path to any vertex of a complete graph.


Title: Current Trends in Digital Twin Development, Maintenance, and Operation: An Interview Study
Abstract: Digital twins (DT) are often defined as a pairing of a physical entity and a corresponding virtual entity (VE), mimicking certain aspects of the former depending on the use-case. In recent years, this concept has facilitated numerous use-cases ranging from design to validation and predictive maintenance of large and small high-tech systems. Various heterogeneous cross-domain models are essential for such systems and model-driven engineering plays a pivotal role in the design, development, and maintenance of these models. We believe models and model-driven engineering play a similarly crucial role in the context of a VE of a DT. Due to the rapidly growing popularity of DTs and their use in diverse domains and use-cases, the methodologies, tools, and practices for designing, developing, and maintaining the corresponding VEs differ vastly. To better understand these differences and similarities, we performed a semi-structured interview research with 19 professionals from industry and academia who are closely associated with different lifecycle stages of digital twins. In this paper, we present our analysis and findings from this study, which is based on seven research questions. In general, we identified an overall lack of uniformity in terms of the understanding of digital twins and used tools, techniques, and methodologies for the development and maintenance of the corresponding VEs. Furthermore, considering that digital twins are software intensive systems, we recognize a significant growth potential for adopting more software engineering practices, processes, and expertise in various stages of a digital twin's lifecycle.


Title: Representative Families: A Unified Tradeoff-Based Approach
Abstract: Let $M=(E,{\cal I})$ be a matroid, and let $\cal S$ be a family of subsets of size $p$ of $E$. A subfamily $\widehat{\cal S}\subseteq{\cal S}$ represents ${\cal S}$ if for every pair of sets $X\in{\cal S}$ and $Y\subseteq E\setminus X$ such that $X\cup Y\in{\cal I}$, there is a set $\widehat{X}\in\widehat{\cal S}$ disjoint from $Y$ such that $\widehat{X}\cup Y\in{\cal I}$. Fomin et al. (Proc. ACM-SIAM Symposium on Discrete Algorithms, 2014) introduced a powerful technique for fast computation of representative families for uniform matroids. In this paper, we show that this technique leads to a unified approach for substantially improving the running times of parameterized algorithms for some classic problems. This includes, among others, $k$-Partial Cover, $k$-Internal Out-Branching, and Long Directed Cycle. Our approach exploits an interesting tradeoff between running time and the size of the representative families.


Title: Neighbourhood Evaluation Criteria for Vertex Cover Problem
Abstract: Neighbourhood Evaluation Criteria is a heuristical approximate algorithm that attempts to solve the Minimum Vertex Cover. degree count is kept in check for each vertex and the highest count based vertex is included in our cover set. In the case of multiple equivalent vertices, the one with the lowest neighbourhood influence is selected. In the case of still existing multiple equivalent vertices, the one with the lowest remaining active vertex count (the highest Independent Set enabling count) is selected as a tie-breaker.


Title: An invariant for homogeneous spaces of compact quantum groups
Abstract: The central notion in Connes' formulation of non commutative geometry is that of a spectral triple. Given a homogeneous space of a compact quantum group, restricting our attention to all spectral triples that are `well behaved' with respect to the group action, we construct a certain dimensional invariant. In particular, taking the (quantum) group itself as the homogeneous space, this gives an invariant for a compact quantum group. Computations of this invariant in several cases, including all type A quantum groups, are given.


Title: Van der Corput and metric theorems for geometric progressions for self-similar measures
Abstract: We prove a van der Corput lemma for non-atomic self-similar measures $\mu$. As an application, we show that the correlations of all finite orders of $( x^n \mod 1 )_{n\geq 1}$ converge to the Poissonian model for $\mu$-a.e. $x$, assuming $x>1$. We also complete a recent result of Algom, Rodriguez Hertz, and Wang (obtained simultaneously by Baker and Banaji), showing that any self-conformal measure with respect to a non-affine real analytic IFS has polynomial Fourier decay.


Title: Irreducibility and periodicity in $\mathbb{Z}^{2}$ symbolic systems
Abstract: We show that there exist $\mathbb{Z}^{2}$ symbolic systems that are strongly irreducible and have no (fully) periodic points


Title: On the real zeros of depth 1 quasimodular forms
Abstract: We discuss the critical points of modular forms, or more generally the zeros of quasimodular forms of depth $1$ for $\mathrm{PSL}_2(\mathbb Z)$. In particular, we consider the derivatives of the unique weight $k$ modular forms $f_k$ with the maximal number of consecutive zero Fourier coefficients following the constant $1$. Our main results state that (1) every zero of a depth $1$ quasimodular form near the derivative of the Eisenstein series in the standard fundamental domain lies on the geodesic segment $\{z \in \mathbb H: \Re(z)=1/2\}$, and (2) more than half of zeros of $f_k$ in the standard fundamental domain lie on the geodesic segment $\{z \in \mathbb H: \Re(z)=1/2\}$ for large enough $k$ with $k\equiv 0 \pmod{12}$.


Title: Local Discontinuous Galerkin Methods for Solving Convection-Diffusion and Cahn-Hilliard Equations on Surfaces
Abstract: Local discontinuous Galerkin methods are developed for solving second order and fourth order time-dependent partial differential equations defined on static 2D manifolds. These schemes are second-order accurate with surfaces triangulized by planar triangles and careful design of numerical fluxes. The schemes are proven to be energy stable. Various numerical experiments are provided to validate the new schemes.


Title: Non-existence of three non-coalescing infinite geodesics with the same direction in the directed landscape
Abstract: It is believed that for metric-like models in the KPZ class the following property holds: with probability one, starting from any point, there are at most two semi-infinite geodesics with the same direction that do not coalesce. Until now, such a result was only proved for one model - exponential LPP (Coupier 11') using its inherent connection to the totally asymmetric exclusion process. We prove that the above property holds for the directed landscape, the universal scaling limit of models in the KPZ class. Our proof reduces the problem to one on line ensembles and therefore paves the way to show similar results for other metric-like models in the KPZ class. Finally, combining our result with the ones in (Busani, Seppalainen,Sorensen 22', Bhatia 23') we obtain the full qualitative geometric description of infinite geodesics in the directed landscape.


Title: Quantum cohomology of minuscule homogeneous spaces
Abstract: We study the quantum cohomology of (co)minuscule homogeneous varieties under a unified perspective. We show that three points Gromov-Witten invariants can always be interpreted as classical intersection numbers on auxiliary varieties. Our main combinatorial tools are certain quivers, in terms of which we obtain a quantum Chevalley formula and a higher quantum Poincar\'{e} duality. In particular we compute the quantum cohomology of the two exceptional minuscule homogeneous varieties.


Title: Rigidity And Unirational Groups
Abstract: We prove a rigidity theorem for morphisms from products of open subschemes of the projective line into solvable groups not containing a copy of $\Ga$ (for example, wound unipotent groups). As a consequence, we deduce several structural results about unirational group schemes, including that unirationality for group schemes descends through separable extensions. We also apply the main result to prove that permawound unipotent groups are unirational and -- when wound -- commutative.


Title: Two Equivalent Families of Linear Fully Coupled Forward Backward Stochastic Differential Equations
Abstract: In this paper, we investigate two families of fully coupled linear Forward-Backward Stochastic Differential Equations (FBSDE). Within these families, one could get the same well-posedness of FBSDEs with totally different structures. The first family of FBSDEs are proved to be equivalent with respect to the Unified Approach. Thus one could get the well-posedness of the whole family if one member exists a unique solution. Another equivalent family of FBSDEs are investigated by introducing a linear transformation method. By reason of the fully coupling structure between the forward and backward equations, it leads to a highly interdependence in solutions. We are able to lower the coupling of FBSDEs, by virtue of the idea of transformation, without losing the well-posedness. Moreover, owing to the non-degeneracy of the transformation matrix, the solution to original FBSDE is totally determined by solutions of FBSDE after transformation. In addition, an example of optimal Linear Quadratic (LQ) problem is presented to illustrate.


Title: The Least Common Multiple of Polynomial Values over Function Fields
Abstract: Cilleruelo conjectured that for an irreducible polynomial $f \in \mathbb{Z}[X]$ of degree $d \geq 2$ one has $$\log\left[\mathrm{lcm}(f(1),f(2),\ldots f(N))\right]\sim(d-1)N\log N$$ as $N \to \infty$. He proved it in the case $d=2$ but it remains open for every polynomial with $d>2$. We investigate the function field analogue of the problem by considering polynomials over the ring $\mathbb F_q[T]$. We state an analog of Cilleruelo's conjecture in this setting: denoting by $$L_f(n) := \mathrm{lcm} \left(f\left(Q\right)\ : \ Q \in \mathbb F_q[T]\mbox{ monic},\, \mathrm{deg}\,Q = n\right)$$ we conjecture that \begin{equation}\label{eq:conjffabs}\mathrm{deg}\, L_f(n) \sim c_f \left(d-1\right) nq^n,\ n \to \infty\end{equation} ($c_f$ is an explicit constant dependent only on $f$, typically $c_f=1$). We give both upper and lower bounds for $L_f(n)$ and show that the conjectured asymptotic holds for a class of ``special" polynomials, initially considered by Leumi in this context, which includes all quadratic polynomials and many other examples as well. We fully classify these special polynomials. We also show that $\mathrm{deg}\, L_f(n) \sim \mathrm{deg}\,\mathrm{rad}\left(L_f(n)\right)$ (in other words the corresponding LCM is close to being squarefree), which is not known over $\mathbb Z$.


Title: Brown representability for directed graphs
Abstract: We prove that any contravariant functor from the homotopy category of finite directed graphs to abelian groups satisfying the additivity axiom and the Mayer-Vietoris axiom is representable.


Title: Linear inverse problems for Markov processes and their regularisation
Abstract: We study the solutions of the inverse problem \[ g(z)=\int f(y) P_T(z,dy) \] for a given $g$, where $(P_t(\cdot,\cdot))_{t \geq 0}$ is the transition function of a given Markov process, $X$, and $T$ is a fixed deterministic time, which is linked to the solutions of the ill-posed Cauchy problem \[ u_t + A u=0, \qquad u(0,\cdot)=g, \] where $A$ is the generator of $X$. A necessary and sufficient condition ensuring square integrable solutions is given. Moreover, a family of regularisations for the above problems is suggested. We show in particular that these inverse problems have a solution when $X$ is replaced by $\xi X + (1-\xi)J$, where $\xi$ is a Bernoulli random variable, whose probability of success can be chosen arbitrarily close to $1$, and $J$ is a suitably constructed jump process.


Title: Probabilistic Trajectory Design Via Approximate Gaussian Mixture Steering
Abstract: A method is presented to solve a stochastic, nonlinear optimal control problem representative of spacecraft trajectory design under uncertainty. The problem is reformulated as a chance constrained nonlinear program, or what is known as a distribution steering problem. Typical distribution steering problems rely on the underlying uncertainties to be Gaussian distributions. This work expands on previous developments by embedding Gaussian mixture distributions into the formulation to better handle the uncertainty propagation and chance constraints involved. The method is applied to a finite-thrust Earth-to-Mars transfer problem. Evaluation via Monte Carlo analysis shows a greater satisfaction of constraints under non-Gaussian distributions of the state and a statistically lower cost.


Title: Legendre-Moment Transform for Linear Ensemble Control and Computation
Abstract: Ensemble systems, pervasive in diverse scientific and engineering domains, pose challenges to existing control methods due to their massive scale and underactuated nature. This paper presents a dynamic moment approach to addressing theoretical and computational challenges in systems-theoretic analysis and control design for linear ensemble systems. We introduce the Legendre-moments and Legendre-moment transform, which maps an ensemble system defined on the $L^2$-space to a Legendre-moment system defined on the $\ell^2$-space. We show that this pair of systems is of one-to-one correspondence and shares the same controllability property. This equivalence admits the control of an ensemble system through the control of the corresponding Legendre-moment system and inspires a unified control design scheme for linear ensemble systems using structured truncated moment systems. In particular, we develop a sampling-free ensemble control design algorithm, then conduct error analysis for control design using truncated moment systems and derive error bounds with respect to the truncation orders, which are illustrated with numerical examples.


Title: Knowledge-based XAI through CBR: There is more to explanations than models can tell
Abstract: The underlying hypothesis of knowledge-based explainable artificial intelligence is the data required for data-centric artificial intelligence agents (e.g., neural networks) are less diverse in contents than the data required to explain the decisions of such agents to humans. The idea is that a classifier can attain high accuracy using data that express a phenomenon from one perspective whereas the audience of explanations can entail multiple stakeholders and span diverse perspectives. We hence propose to use domain knowledge to complement the data used by agents. We formulate knowledge-based explainable artificial intelligence as a supervised data classification problem aligned with the CBR methodology. In this formulation, the inputs are case problems composed of both the inputs and outputs of the data-centric agent and case solutions, the outputs, are explanation categories obtained from domain knowledge and subject matter experts. This formulation does not typically lead to an accurate classification, preventing the selection of the correct explanation category. Knowledge-based explainable artificial intelligence extends the data in this formulation by adding features aligned with domain knowledge that can increase accuracy when selecting explanation categories.


Title: Parametric robust structured control design
Abstract: We present a new approach to parametric robust controller design, where we compute controllers of arbitrary order and structure which minimize the worst-case $H_\infty$ norm over a pre-specified set of uncertain parameters. At the core of our method is a nonsmooth minimization method tailored to functions which are semi-infinite minima of smooth functions. A rich test bench and a more detailed example illustrate the potential of the technique, which can deal with complex problems involving multiple possibly repeated uncertain parameters.


Title: A Quasi Curtis-Tits-Phan theorem for the symplectic group
Abstract: We obtain the symplectic group as an amalgam of low rank subgroups akin to Levi components. We do this by having the group act flag-transitively on a new type of geometry and applying Tits' lemma. This provides a new way of recognizing the symplectic groups from a small collection of small subgroups. The geometry consists of all subspaces of maximal rank in a vector space of maximal rank with respect to a symplectic form. The main result holds for fields of size at least 3. We analyze the geometry over the field of size 2 and describe its simply connected cover if different from the geometry.


Title: Calculus and applications
Abstract: This is an introduction to calculus, and its applications to basic questions from physics. We first discuss the theory of functions $f:\mathbb R\to\mathbb R$, with the notion of continuity, and the construction of the derivative $f'(x)$ and of the integral $\int_a^bf(x)dx$. Then we investigate the case of the complex functions $f:\mathbb C\to\mathbb C$, and notably the holomorphic functions, and harmonic functions. Then, we discuss the multivariable functions, $f:\mathbb R^N\to\mathbb R^M$ or $f:\mathbb R^N\to\mathbb C^M$ or $f:\mathbb C^N\to\mathbb C^M$, with general theory, integration results, maximization questions, and basic applications to physics.


Title: Moduli spaces of arrangements of 12 projective lines with a sextic point
Abstract: In this paper, we try to classify moduli spaces of arrangements of $12$ lines with sextic points. We show that moduli spaces of arrangements of $12$ lines with sextic points can consist of more than two connected components. We also present defining equations of the arrangements whose moduli spaces are not irreducible taking quotients by the complex conjugation by supply some potential Zariski pairs. Through complex conjugation we take quotients and supply some potential Zariski pairs.


Title: On the Stability Functional for Conservation Laws
Abstract: This note is devoted to the explicit construction of a functional defined on all pairs of $\L1$ functions with small total variation, which is equivalent to the $\L1$ distance and non increasing along the trajectories of a given system of conservation laws. Two different constructions are provided, yielding an extension of the original stability functional by Bressan, Liu and Yang.


Title: Supervised learning on heterogeneous, attributed entities interacting over time
Abstract: Most physical or social phenomena can be represented by ontologies where the constituent entities are interacting in various ways with each other and with their environment. Furthermore, those entities are likely heterogeneous and attributed with features that evolve dynamically in time as a response to their successive interactions. In order to apply machine learning on such entities, e.g., for classification purposes, one therefore needs to integrate the interactions into the feature engineering in a systematic way. This proposal shows how, to this end, the current state of graph machine learning remains inadequate and needs to be be augmented with a comprehensive feature engineering paradigm in space and time.


Title: On the computation of coarse cohomology
Abstract: The purpose of this article is to relate coarse cohomology of metric spaces with a more computable cohomology. We introduce a notion of boundedly supported cohomology and prove that coarse cohomology of many spaces are isomorphic to the boundedly supported cohomology. Boundedly supported cohomology coincides with compactly supported Alexander--Spanier cohomology if the space is proper and contractible. Our work generalizes an earlier result of Roe which says that the coarse cohomology is isomorphic to the compactly supported Alexander-Spanier cohomology if the space is uniformly contractible. As an application of our main theorem, we obtain that coarse cohomology of the complement can be computed in terms of Alexander-Spanier cohomology for many spaces.


Title: Resonances for homoclinic trapped sets
Abstract: We study semiclassical resonances generated by homoclinic trapped sets. First, under some general assumptions, we prove that there is no resonance in a region below the real axis. Then, we obtain a quantization rule and the asymptotic expansion of the resonances when there is a finite number of homoclinic trajectories. The same kind of results is proved for homoclinic sets of maximal dimension. Next, we generalize to the case of homoclinic/heteroclinic trajectories and we study the three bump case. In all these settings, the resonances may either accumulate on curves or form clouds. We also describe the corresponding resonant states.


Title: Chiplet Cloud: Building AI Supercomputers for Serving Large Generative Language Models
Abstract: Large language models (LLMs) such as ChatGPT have demonstrated unprecedented capabilities in multiple AI tasks. However, hardware inefficiencies have become a significant factor limiting the democratization of LLMs. We propose Chiplet Cloud, an ASIC supercomputer architecture that optimizes total cost of ownership (TCO) per token for serving generative LLMs. Chiplet Cloud fits all model parameters inside the on-chip SRAMs to eliminate bandwidth limitations while moderating the die size to improve system costs while leveraging software mappings to overcome data communication overhead. We propose a comprehensive design methodology that accurately explores a spectrum of major design trade-offs in the joint space of hardware-software and generates a detailed performance-cost analysis on all valid design points. We evaluate Chiplet Cloud on four popular LLMs. Compared to GPU and TPU, our architecture can achieve up to 94x and 15x improvement in TCO/Token respectively, significantly reducing the cost for realistically serving modern LLMs.


Title: Functional central limit theorems for stick-breaking priors
Abstract: We obtain the empirical strong law of large numbers, empirical Glivenko-Cantelli theorem, central limit theorem, functional central limit theorem for various nonparametric Bayesian priors which include the Dirichlet process with general stick-breaking weights, the Poisson-Dirichlet process, the normalized inverse Gaussian process, the normalized generalized gamma process, and the generalized Dirichlet process. For the Dirichlet process with general stick-breaking weights, we introduce two general conditions such that the central limit theorem and functional central limit theorem hold. Except in the case of the generalized Dirichlet process, since the finite dimensional distributions of these processes are either hard to obtain or are complicated to use even they are available, we use the method of moments to obtain the convergence results. For the generalized Dirichlet process we use its finite dimensional marginal distributions to obtain the asymptotics although the computations are highly technical.


Title: Cosemisimple Hopf algebras are faithfully flat over Hopf subalgebras
Abstract: The question of whether or not a Hopf algebra $H$ is faithfully flat over a Hopf subalgebra $A$ has received positive answers in several particular cases: when $H$ (or more generally, just $A$) is commutative, or cocommutative, or pointed, or when $K$ contains the coradical of $H$. We prove the statement in the title, adding the class of cosemisimple Hopf algebras to those known to be faithfully flat over all Hopf subalgebras. We also show that the third term of the resulting "exact sequence" $A\to H\to C$ is always a cosemisimple coalgebra, and that the expectation $H\to A$ is positive when $H$ is a CQG algebra.


Title: Smoothing cones over K3 surfaces
Abstract: We prove that the affine cone over a general primitively polarised K3 surface of genus g is smoothable if and only if g\le 10 or g=12. We also give several examples of singularities with special behaviour, such as surfaces whose affine cone is smoothable even though the projective cone is not.


Title: Solving Almost all Systems of Random Quadratic Equations
Abstract: This paper deals with finding an $n$-dimensional solution $x$ to a system of quadratic equations of the form $y_i=|\langle{a}_i,x\rangle|^2$ for $1\le i \le m$, which is also known as phase retrieval and is NP-hard in general. We put forth a novel procedure for minimizing the amplitude-based least-squares empirical loss, that starts with a weighted maximal correlation initialization obtainable with a few power or Lanczos iterations, followed by successive refinements based upon a sequence of iteratively reweighted (generalized) gradient iterations. The two (both the initialization and gradient flow) stages distinguish themselves from prior contributions by the inclusion of a fresh (re)weighting regularization technique. The overall algorithm is conceptually simple, numerically scalable, and easy-to-implement. For certain random measurement models, the novel procedure is shown capable of finding the true solution $x$ in time proportional to reading the data $\{(a_i;y_i)\}_{1\le i \le m}$. This holds with high probability and without extra assumption on the signal $x$ to be recovered, provided that the number $m$ of equations is some constant $c>0$ times the number $n$ of unknowns in the signal vector, namely, $m>cn$. Empirically, the upshots of this contribution are: i) (almost) $100\%$ perfect signal recovery in the high-dimensional (say e.g., $n\ge 2,000$) regime given only an information-theoretic limit number of noiseless equations, namely, $m=2n-1$ in the real-valued Gaussian case; and, ii) (nearly) optimal statistical accuracy in the presence of additive noise of bounded support. Finally, substantial numerical tests using both synthetic data and real images corroborate markedly improved signal recovery performance and computational efficiency of our novel procedure relative to state-of-the-art approaches.


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


Title: Poisson summation for Hankel transforms
Abstract: In this article we study the Poisson summation for Hankel transform in the sense of Braverman-Kazhdan-Ngo in the special case of $L$-embedding $\rho: GL_1\rightarrow GL_2$. We view such a summation formula as the generalization of the classical Voronoi summation formula.


Title: A Markov Process Approach to Ensemble Control of Smart Buildings
Abstract: This paper describes a step-by-step procedure that converts a physical model of a building into a Markov Process that characterizes energy consumption of this and other similar buildings. Relative to existing thermo-physics-based building models, the proposed procedure reduces model complexity and depends on fewer parameters, while also maintaining accuracy and feasibility sufficient for system-level analyses. Furthermore, the proposed Markov Process approach makes it possible to leverage real-time data streams available from intelligent data acquisition systems, which are readily available in smart buildings, and merge it with physics-based and statistical models. Construction of the Markov Process naturally leads to a Markov Decision Process formulation, which describes optimal probabilistic control of a collection of similar buildings. The approach is illustrated using validated building data from Belgium.


Title: Failures and Fixes: A Study of Software System Incident Response
Abstract: This paper presents the results of a research study related to software system failures, with the goal of understanding how we might better evolve, maintain and support software systems in production. We have qualitatively analyzed thirty incidents: fifteen collected through in depth interviews with engineers, and fifteen sampled from publicly published incident reports (generally produced as part of postmortem reviews). Our analysis focused on understanding and categorizing how failures occurred, and how they were detected, investigated and mitigated. We also captured analytic insights related to the current state of the practice and associated challenges in the form of 11 key observations. For example, we observed that failures can cascade through a system leading to major outages; and that often engineers do not understand the scaling limits of systems they are supporting until those limits are exceeded. We argue that the challenges we have identified can lead to improvements to how systems are engineered and supported.


Title: Enhancing NOMA Networks via Reconfigurable Multi-Functional Surface
Abstract: By flexibly manipulating the radio propagation environment, reconfigurable intelligent surface (RIS) is a promising technique for future wireless communications. However, the single-side coverage and double-fading attenuation faced by conventional RISs largely restrict their applications. To address this issue, we propose a novel concept of multi-functional RIS (MF-RIS), which provides reflection, transmission, and amplification simultaneously for the incident signal. With the aim of enhancing the performance of a non-orthogonal multiple-access (NOMA) downlink multiuser network, we deploy an MF-RIS to maximize the sum rate by jointly optimizing the active beamforming and MF-RIS coefficients. Then, an alternating optimization algorithm is proposed to solve the formulated non-convex problem by exploiting successive convex approximation and penalty-based method. Numerical results show that the proposed MF-RIS outperforms conventional RISs under different settings.


Title: On the conductor of cohomological transforms
Abstract: In the analytic study of trace functions of $\ell$-adic sheaves over finite fields, a crucial issue is to control the conductor of sheaves constructed in various ways. We consider cohomological transforms on the affine line over a finite field which have trace functions given by linear operators with an additive character of a rational function in two variables as a kernel. We prove that the conductor of such a transform is bounded in terms of the complexity of the input sheaf and of the rational function defining the kernel, and discuss applications of this result, including motivating examples arising from the Polymath8 project.


Title: Reconstruction of curves from their theta hyperplanes in genera $6$ and $7$
Abstract: We derive a formula for reconstructing a generic complex canonical curve $C$ of genus 6 and 7 in terms of the theta hyperplanes of $C$. Hence, we get a generic inverse to the Torelli map, as well as a complete description of the Schottky locus in these genera. The computational part of the proof relies on a certified numerical argument.


Title: The Effects of Generative AI on Computing Students' Help-Seeking Preferences
Abstract: Help-seeking is a critical way for students to learn new concepts, acquire new skills, and get unstuck when problem-solving in their computing courses. The recent proliferation of generative AI tools, such as ChatGPT, offers students a new source of help that is always available on-demand. However, it is unclear how this new resource compares to existing help-seeking resources along dimensions of perceived quality, latency, and trustworthiness. In this paper, we investigate the help-seeking preferences and experiences of computing students now that generative AI tools are available to them. We collected survey data (n=47) and conducted interviews (n=8) with computing students. Our results suggest that although these models are being rapidly adopted, they have not yet fully eclipsed traditional help resources. The help-seeking resources that students rely on continue to vary depending on the task and other factors. Finally, we observed preliminary evidence about how help-seeking with generative AI is a skill that needs to be developed, with disproportionate benefits for those who are better able to harness the capabilities of LLMs. We discuss potential implications for integrating generative AI into computing classrooms and the future of help-seeking in the era of generative AI.


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


Title: An equivariant generalisation of McDuff-Segal's group-completion theorem
Abstract: In this short note, we prove a G-equivariant generalisation of McDuff-Segal's group-completion theorem for finite groups G. A new complication regarding genuine equivariant localisations arises and we resolve this by isolating a simple condition on the homotopy groups of E-infinity-rings in G-spectra. We check that this condition is satisfied when our inputs are a suitable variant of E-infinity-monoids in G-spaces via the existence of multiplicative norm structures, thus giving a localisation formula for their associated G-spherical group rings.


Title: Probabilistic Modeling for Sequences of Sets in Continuous-Time
Abstract: Neural marked temporal point processes have been a valuable addition to the existing toolbox of statistical parametric models for continuous-time event data. These models are useful for sequences where each event is associated with a single item (a single type of event or a "mark") -- but such models are not suited for the practical situation where each event is associated with a set of items. In this work, we develop a general framework for modeling set-valued data in continuous-time, compatible with any intensity-based recurrent neural point process model. In addition, we develop inference methods that can use such models to answer probabilistic queries such as "the probability of item $A$ being observed before item $B$," conditioned on sequence history. Computing exact answers for such queries is generally intractable for neural models due to both the continuous-time nature of the problem setting and the combinatorially-large space of potential outcomes for each event. To address this, we develop a class of importance sampling methods for querying with set-based sequences and demonstrate orders-of-magnitude improvements in efficiency over direct sampling via systematic experiments with four real-world datasets. We also illustrate how to use this framework to perform model selection using likelihoods that do not involve one-step-ahead prediction.


Title: P-TimeSync: A Precise Time Synchronization Simulation with Network Propagation Delays
Abstract: Time serves as the foundation of modern society and will continue to grow in value in the future world. Unlike previous research papers, authors delve into various time sources, ranging from atomic time and GPS time to quartz time. Specifically, we explore the time uncertainty associated with the four major Global Navigation Satellite Systems. Additionally, we provide a summary of eight metrics used to evaluate time accuracy. In existing time synchronization simulations provide partial usages. However, our research introduces a comprehensive and precise time synchronization simulation named P-TimeSync, leading to a better understanding of time synchronization in distributed environments. It is a state-of-the-art simulation tool for time because (1) it can simulate atomic clocks and quartz clocks with user-defined software clock algorithms, (2) the simulation provides nanosecond-level precision time across different network propagation paths and distances, (3) the tool offers a visualization platform with classic algorithms for distributed time synchronization, such as Cristian's algorithm and Berkeley algorithm, and (4) the simulation includes three time-sync attack functions, including distributed denial-of-service (DDoS) attack, IP spoofer, and router hijacker. The simulation easily allows for the redefinition of configurations and functions, supporting advanced research and development. The simulation tool could be downloaded via the website: https://github.com/rui5097/purdue_timesync


Title: Smooth invariant foliations and Koopman eigenfunctions about stable equilibria of semiflows
Abstract: We consider a $C^r$ semiflow $\{ \varphi_t \}_{t \geq 0}$ on a Banach space $X$ admitting a stable fixed point $x$. We show, along the lines of the parameterization method (Cabr\'e et al., 2003), the existence of a $C^r$ invariant foliation tangent to $X_1$ at $x$, for an arbitrary $D \varphi_t(x)$-invariant subspace $X_1 \subset X$ satisfying some additional spectral conditions. Uniqueness ensues in a subclass of sufficiently smooth invariant foliations tangent to $X_1$ at $x$. We then draw relations to Koopman theory, and thereby establish the existence and uniqueness, in some appropriate sense, of $C^r$ Koopman eigenfunctions. We demonstrate that these results apply to the case of the Navier-Stokes system, the archetypal example considered by the modern upheaval of applied 'Koopmanism'.


Title: Robust and Adaptive Planning under Model Uncertainty
Abstract: Planning under model uncertainty is a fundamental problem across many applications of decision making and learning. In this paper, we propose the Robust Adaptive Monte Carlo Planning (RAMCP) algorithm, which allows computation of risk-sensitive Bayes-adaptive policies that optimally trade off exploration, exploitation, and robustness. RAMCP formulates the risk-sensitive planning problem as a two-player zero-sum game, in which an adversary perturbs the agent's belief over the models. We introduce two versions of the RAMCP algorithm. The first, RAMCP-F, converges to an optimal risk-sensitive policy without having to rebuild the search tree as the underlying belief over models is perturbed. The second version, RAMCP-I, improves computational efficiency at the cost of losing theoretical guarantees, but is shown to yield empirical results comparable to RAMCP-F. RAMCP is demonstrated on an n-pull multi-armed bandit problem, as well as a patient treatment scenario.


Title: Canonical and $n$-canonical modules on a Noetherian algebra
Abstract: We define canonical and $n$-canonical modules on a module-finite algebra over a Noether commutative ring and study their basic properties. Using $n$-canonical modules, we generalize a theorem on $(n,C)$-syzygy by Araya and Iima which generalize a well-known theorem on syzygies by Evans and Griffith. Among others, we prove a non-commutative version of Aoyama's theorem which states that a canonical module descends with respect to a flat local homomorphism. We also prove the codimension two-argument for modules over a coherent sheaf of algebras with a $2$-canonical module, generalizing a result of the author.


Title: Notes on exotic and perverse-coherent sheaves
Abstract: Exotic sheaves are certain complexes of coherent sheaves on the cotangent bundle of the flag variety of a reductive group. They are closely related to perverse-coherent sheaves on the nilpotent cone. This expository article includes the definitions of these two categories, applications, and some structure theory, as well as detailed calculations for SL(2).


Title: An exact test for renewal increasing mean residual life
Abstract: In this paper, we develop an exact test for testing exponentiality against renewal increasing mean residual life class. Pitman's asymptotic efficacy value shows that our test perform well. Some numerical results are presented to demonstrate the performance of the testing method. We also discuss how the proposed method incorporates the right censored observations.


Title: Presentations of Kauffman bracket skein algebras of planar surfaces
Abstract: Let $R$ be a commutative ring with identity and a fixed invertible element $q^{\frac{1}{2}}$, and suppose $q+q^{-1}$ is invertible in $R$. For each planar surface $\Sigma_{0,n+1}$, we present its Kauffman bracket skein algebra over $R$ by explicit generators and relations. The presentation is independent of $R$, and can be considered as a quantization of the trace algebra of $n$ generic $2\times 2$ unimodular matrices.


Title: Ramsey and Turán numbers of sparse hypergraphs
Abstract: Degeneracy plays an important role in understanding Tur\'an- and Ramsey-type properties of graphs. Unfortunately, the usual hypergraphical generalization of degeneracy fails to capture these properties. We define the skeletal degeneracy of a $k$-uniform hypergraph as the degeneracy of its $1$-skeleton (i.e., the graph formed by replacing every $k$-edge by a $k$-clique). We prove that skeletal degeneracy controls hypergraph Tur\'an and Ramsey numbers in a similar manner to (graphical) degeneracy. Specifically, we show that $k$-uniform hypergraphs with bounded skeletal degeneracy have linear Ramsey number. This is the hypergraph analogue of the Burr-Erd\H{o}s conjecture (proved by Lee). In addition, we give upper and lower bounds of the same shape for the Tur\'an number of a $k$-uniform $k$-partite hypergraph in terms of its skeletal degeneracy. The proofs of both results use the technique of dependent random choice. In addition, the proof of our Ramsey result uses the `random greedy process' introduced by Lee in his resolution of the Burr-Erd\H{o}s conjecture.


Title: Manipulating Trajectory Prediction with Backdoors
Abstract: Autonomous vehicles ought to predict the surrounding agents' trajectories to allow safe maneuvers in uncertain and complex traffic situations. As companies increasingly apply trajectory prediction in the real world, security becomes a relevant concern. In this paper, we focus on backdoors - a security threat acknowledged in other fields but so far overlooked for trajectory prediction. To this end, we describe and investigate four triggers that could affect trajectory prediction. We then show that these triggers (for example, a braking vehicle), when correlated with a desired output (for example, a curve) during training, cause the desired output of a state-of-the-art trajectory prediction model. In other words, the model has good benign performance but is vulnerable to backdoors. This is the case even if the trigger maneuver is performed by a non-casual agent behind the target vehicle. As a side-effect, our analysis reveals interesting limitations within trajectory prediction models. Finally, we evaluate a range of defenses against backdoors. While some, like simple offroad checks, do not enable detection for all triggers, clustering is a promising candidate to support manual inspection to find backdoors.


Title: Affine homogeneous varieties and suspensions
Abstract: An algebraic variety $X$ is called a homogeneous variety if the automorphism group $\mathrm{Aut}(X)$ acts on $X$ transitively, and a homogeneous space if there exists a transitive action of an algebraic group on $X$. We prove a criterion of smoothness of a suspension to construct a wide class of homogeneous varieties. As an application, we give criteria for a Danielewski surface to be a homogeneous variety and a homogeneous space. Also, we construct affine suspensions of arbitrary dimension that are homogeneous varieties but not homogeneous spaces.


Title: Nonlinear Young integrals via fractional calculus
Abstract: For H\"older continuous functions $W(t,x)$ and $\varphi_t$, we define nonlinear integral $\int_a^b W(dt, \varphi_t)$ via fractional calculus. This nonlinear integral arises naturally in the Feynman-Kac formula for stochastic heat equations with random coefficients. We also define iterated nonlinear integrals.


Title: Nonconvex bundle method with application to a delamination problem
Abstract: Delamination is a typical failure mode of composite materials caused by weak bonding. It arises when a crack initiates and propagates under a destructive loading. Given the physical law characterizing the properties of the interlayer adhesive between the bonded bodies, we consider the problem of computing the propagation of the crack front and the stress field along the contact boundary. This leads to a hemivariational inequality, which after discretization by finite elements we solve by a nonconvex bundle method, where upper-$C^1$ criteria have to be minimized. As this is in contrast with other classes of mechanical problems with non-monotone friction laws and in other applied fields, where criteria are typically lower-$C^1$, we propose a bundle method suited for both types of nonsmoothness. We prove its global convergence in the sense of subsequences and test it on a typical delamination problem of material sciences.


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


Title: Hierarchical Over-the-Air Federated Learning with Awareness of Interference and Data Heterogeneity
Abstract: When implementing hierarchical federated learning over wireless networks, scalability assurance and the ability to handle both interference and device data heterogeneity are crucial. This work introduces a learning method designed to address these challenges, along with a scalable transmission scheme that efficiently uses a single wireless resource through over-the-air computation. To provide resistance against data heterogeneity, we employ gradient aggregations. Meanwhile, the impact of interference is minimized through optimized receiver normalizing factors. For this, we model a multi-cluster wireless network using stochastic geometry, and characterize the mean squared error of the aggregation estimations as a function of the network parameters. We show that despite the interference and the data heterogeneity, the proposed scheme achieves high learning accuracy and can significantly outperform the conventional hierarchical algorithm.


Title: Theta-Induced Diffusion on Tate Elliptic Curves over Non-Archimedean Local Fields
Abstract: A diffusion operator on the $K$-rational points of a Tate elliptic curve $E_q$ is constructed, where $K$ is a non-archimedean local field, as well as an operator on the Berkovich-analytification $E_q^{an}$ of $E_q$. These are integral operators for measures coming from a regular $1$-form, and kernel functions constructed via theta functions. The second operator can be described via certain non-archimedan curvature forms on $E_q^{an}$. The spectra of these self-adjoint bounded operators on the Hilbert spaces of $L^2$-functions are identical and found to consist of finitely many eigenvalues. A study of the corresponding heat equations yields a positive answer to the Cauchy problem, and induced Markov processes on the curve. Finally, some geometric information about the $K$-rational points of $E_q$ is retrieved from the spectrum.


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


Title: Efficient Continuous Relaxations for Dense CRF
Abstract: Dense conditional random fields (CRF) with Gaussian pairwise potentials have emerged as a popular framework for several computer vision applications such as stereo correspondence and semantic segmentation. By modeling long-range interactions, dense CRFs provide a more detailed labelling compared to their sparse counterparts. Variational inference in these dense models is performed using a filtering-based mean-field algorithm in order to obtain a fully-factorized distribution minimising the Kullback-Leibler divergence to the true distribution. In contrast to the continuous relaxation-based energy minimisation algorithms used for sparse CRFs, the mean-field algorithm fails to provide strong theoretical guarantees on the quality of its solutions. To address this deficiency, we show that it is possible to use the same filtering approach to speed-up the optimisation of several continuous relaxations. Specifically, we solve a convex quadratic programming (QP) relaxation using the efficient Frank-Wolfe algorithm. This also allows us to solve difference-of-convex relaxations via the iterative concave-convex procedure where each iteration requires solving a convex QP. Finally, we develop a novel divide-and-conquer method to compute the subgradients of a linear programming relaxation that provides the best theoretical bounds for energy minimisation. We demonstrate the advantage of continuous relaxations over the widely used mean-field algorithm on publicly available datasets.


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


Title: Cubic bent functions outside the completed Maiorana-McFarland class
Abstract: In this paper we prove that in opposite to the cases of 6 and 8 variables, the Maiorana-McFarland construction does not describe the whole class of cubic bent functions in $n$ variables for all $n\ge 10$. Moreover, we show that for almost all values of $n$, these functions can simultaneously be homogeneous and have no affine derivatives.


Title: Uncertainty Estimates for Ordinal Embeddings
Abstract: To investigate objects without a describable notion of distance, one can gather ordinal information by asking triplet comparisons of the form "Is object $x$ closer to $y$ or is $x$ closer to $z$?" In order to learn from such data, the objects are typically embedded in a Euclidean space while satisfying as many triplet comparisons as possible. In this paper, we introduce empirical uncertainty estimates for standard embedding algorithms when few noisy triplets are available, using a bootstrap and a Bayesian approach. In particular, simulations show that these estimates are well calibrated and can serve to select embedding parameters or to quantify uncertainty in scientific applications.


Title: Non-local games and quantum symmetries of quantum metric spaces
Abstract: We generalize Banica's construction of the quantum isometry group of a metric space to the class of quantum metric spaces in the sense of Kuperberg and Weaver. We also introduce quantum isometries between two quantum metric spaces, and we show that if a pair of quantum metric spaces are algebraically quantum isometric, then their quantum isometry groups are monoidally equivalent. Motivated by the recent work on the graph isomorphism game, we introduce a new two-player non-local game called the metric isometry game, where players can win classically if and only if the metric spaces are isometric. Winning quantum strategies of this game align with quantum isometries of the metric spaces.


Title: A New Foundation for Finitary Corecursion
Abstract: This paper contributes to a theory of the behaviour of "finite-state" systems that is generic in the system type. We propose that such systems are modeled as coalgebras with a finitely generated carrier for an endofunctor on a locally finitely presentable category. Their behaviour gives rise to a new fixpoint of the coalgebraic type functor called locally finite fixpoint (LFF). We prove that if the given endofunctor preserves monomorphisms then the LFF always exists and is a subcoalgebra of the final coalgebra (unlike the rational fixpoint previously studied by Ad\'amek, Milius and Velebil). Moreover, we show that the LFF is characterized by two universal properties: 1. as the final locally finitely generated coalgebra, and 2. as the initial fg-iterative algebra. As instances of the LFF we first obtain the known instances of the rational fixpoint, e.g. regular languages, rational streams and formal power-series, regular trees etc. And we obtain a number of new examples, e.g. (realtime deterministic resp. non-deterministic) context-free languages, constructively S-algebraic formal power-series (and any other instance of the generalized powerset construction by Silva, Bonchi, Bonsangue, and Rutten) and the monad of Courcelle's algebraic trees.


Title: Compositing with 2D Vector Fields by using Shape Maps that can represent Inconsistent, Impossible, and Incoherent Shapes
Abstract: In this paper, we present a new compositing approach to obtain stylized reflections and refractions with a simple control. Our approach does not require any mask or separate 3D rendering. Moreover, only one additional image is sufficient to obtain a composited image with convincing qualitative reflection and refraction effects. We have also developed linearized methods that are easy to compute. Although these methods do not directly correspond to the underlying physical phenomena of reflection and refraction, they can provide results that are visually similar to realistic 3D rendering. The main advantage of this approach is the ability to treat images as ``mock-3D'' shapes that can be inserted into any digital paint system without any significant structural change. The core of our approach is the shape map, which encodes 2D shape and thickness information for all visible points of an image of a shape. This information does not have to be complete or consistent to obtain interesting composites. In particular, the shape maps allow us to represent impossible and incoherent shapes with 2D non-conservative vector fields.


Title: Space reduction techniques for the $3$-wise Kemeny problem
Abstract: Kemeny's rule is one of the most studied and well-known voting schemes with various important applications in computational social choice and biology. Recently, Kemeny's rule was generalized via a set-wise approach by Gilbert et. al. This paradigm presents interesting advantages in comparison with Kemeny's rule since not only pairwise comparisons but also the discordance between the winners of subsets of three alternatives are also taken into account in the definition of the $3$-wise Kendall-tau distance between two rankings. In spite of the NP-hardness of the 3-wise Kemeny problem which consists of computing the set of $3$-wise consensus rankings, namely rankings whose total $3$-wise Kendall-tau distance to a given voting profile is minimized, we establish in this paper several generalizations of the Major Order Theorems, as obtained by Milosz and Hamel for Kemeny's rule, for the $3$-wise Kemeny voting schemes to achieve a substantial search space reduction by efficiently determining in polynomial time the relative orders of pairs of alternatives. Essentially, our theorems quantify precisely the nontrivial property that if the preference for an alternative over another one in an election is strong enough, not only in the head-to-head competition but even when taking into account one or two more alternatives, then the relative order of these two alternatives in all $3$-wise consensus rankings must be as expected. As an application, we also obtain an improvement of the Major Order Theorems for Kememy's rule. Moreover, we show that the well-known $3/4$-majority rule of Betzler et al. for Kemeny's rule is only valid in general for elections with no more than $5$ alternatives with respect to the $3$-wise Kemeny scheme. Several simulations and tests of our algorithms on real-world and uniform data are provided.


Title: Numerical Analysis for Dirichlet Optimal Control Problems on Convex Polyhedral Domains
Abstract: In this paper error analysis for finite element discretizations of Dirichlet boundary control problems is developed. For the first time, optimal discretization error estimates are established in the case of three dimensional polyhedral and convex domains. The convergence rates solely depend on the size of largest interior edge angle. These results are comparable to those for the two dimensional case. However, the approaches from the two dimensional setting are not directly extendable such that new techniques have to be used. The theoretical results are confirmed by numerical experiments.


Title: Distributed convergence detection based on global residual error under asynchronous iterations
Abstract: Convergence of classical parallel iterations is detected by performing a reduction operation at each iteration in order to compute a residual error relative to a potential solution vector. To efficiently run asynchronous iterations, blocking communication requests are avoided, which makes it hard to isolate and handle any global vector. While some termination protocols were proposed for asynchronous iterations, only very few of them are based on global residual computation and guarantee effective convergence. But the most effective and efficient existing solutions feature two reduction operations, which constitutes an important factor of termination delay. In this paper, we present new, non-intrusive, protocols to compute a residual error under asynchronous iterations, requiring only one reduction operation. Various communication models show that some heuristics can even be introduced and formally evaluated. Extensive experiments with up to 5600 processor cores confirm the practical effectiveness and efficiency of our approach.


Title: Stanley--Elder--Fine theorems for colored partitions
Abstract: We give a new proof of a partition theorem popularly known as Elder's theorem, but which is also credited to Stanley and Fine. We extend the theorem to the context of colored partitions (or prefabs). More specifically, we give analogous results for $b$-colored partitions, where each part occurs in $b$ colors; for $b$-colored partitions with odd parts (or distinct parts); for partitions where the part $k$ comes in $k$ colors; and, overpartitions.


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


Title: Approximation of polynomials from Walsh tail spaces
Abstract: We derive various bounds for the $L_p$ distance of polynomials on the hypercube from Walsh tail spaces, extending some of Oleszkiewicz's results (2017) for Rademacher sums.


Title: An Artificial Neural Network Functionalized by Evolution
Abstract: The topology of artificial neural networks has a significant effect on their performance. Characterizing efficient topology is a field of promising research in Artificial Intelligence. However, it is not a trivial task and it is mainly experimented on through convolutional neural networks. We propose a hybrid model which combines the tensor calculus of feed-forward neural networks with Pseudo-Darwinian mechanisms. This allows for finding topologies that are well adapted for elaboration of strategies, control problems or pattern recognition tasks. In particular, the model can provide adapted topologies at early evolutionary stages, and 'structural convergence', which can found applications in robotics, big-data and artificial life.


Title: Purposeful and Operation-based Cognitive System for AGI
Abstract: This paper proposes a new cognitive model, acting as the main component of an AGI agent. The model is introduced in its mature state, and as an extension of previous models, DENN, and especially AKREM, by including operational models (frames/classes) and will. In addition, it is mainly based on the duality principle in every known intelligent aspect, such as exhibiting both top-down and bottom-up model learning, generalization verse specialization, and more. Furthermore, a holistic approach is advocated for AGI designing and cognition under constraints or efficiency is proposed, in the form of reusability and simplicity. Finally, reaching this mature state is described via a cognitive evolution from infancy to adulthood, utilizing a consolidation principle. The final product of this cognitive model is a dynamic operational memory of models and instances.


Title: On the displacement of generators of free Fuchsian groups
Abstract: We prove an inequality that must be satisfied by displacement of generators of free Fuchsian groups, which is the two-dimensional version of the $\log (2k-1)$ Theorem for Kleinian groups due to Anderson-Canary-Culler-Shalen. As applications, we obtain quantitative results on the geometry of hyperbolic surfaces such as the two-dimensional Margulis constant and lengths of closed curves, which improves a result of Buser's.


Title: Ground state and nodal solutions for fractional Orlicz problems with lack of regularity and without the Ambrosetti-Rabinowitz condition
Abstract: We consider a non-local Shr\"odinger problem driven by the fractional Orlicz g-Laplace operator as follows \begin{equation}\label{PP} (-\triangle_{g})^{\alpha}u+g(u)=K(x)f(x,u),\ \ \text{in}\ \mathbb{R}^{d},\tag{P} \end{equation} where $d\geq 3,\ (-\triangle_{g})^{\alpha}$ is the fractional Orlicz g-Laplace operator, $f:\mathbb{R}^d\times\mathbb{R}\rightarrow \mathbb{R}$ is a measurable function and $K$ is a positive continuous function. Employing the Nehari manifold method and without assuming the well-known Ambrosetti-Rabinowitz and differentiability conditions on the non-linear term $f$, we prove that the problem \eqref{PP} has a ground state of fixed sign and a nodal (or sign-changing) solutions.


Title: Rigorous uniaxial limit of the Qian--Sheng inertial Q-tensor hydrodynamics for liquid crystals
Abstract: This article is concerned with the rigorous connections between the inertial Qian--Sheng model and the Ericksen--Leslie model for the liquid crystal flow, under a more general condition of coefficients. More specifically, in the framework of Hilbert expansions, we show that: (i) when the elastic coefficients tend to zero (also called the uniaxial limit), the smooth solution to the inertial Qian--Sheng model converges to that to the full inertial Ericksen--Leslie model; (ii) when the elastic coefficients and the inertial coefficient tend to zero simultaneously, the smooth solution to the inertial Qian--Sheng model converges to that to the noninertial Ericksen--Leslie model.


Title: Smoothness Estimation for Whittle-Matérn Processes on Closed Riemannian Manifolds
Abstract: The family of Mat\'ern kernels are often used in spatial statistics, function approximation and Gaussian process methods in machine learning. One reason for their popularity is the presence of a smoothness parameter that controls, for example, optimal error bounds for kriging and posterior contraction rates in Gaussian process regression. On closed Riemannian manifolds, we show that the smoothness parameter can be consistently estimated from the maximizer(s) of the Gaussian likelihood when the underlying data are from point evaluations of a Gaussian process and, perhaps surprisingly, even when the data comprise evaluations of a non-Gaussian process. The points at which the process is observed need not have any particular spatial structure beyond quasi-uniformity. Our methods are based on results from approximation theory for the Sobolev scale of Hilbert spaces. Moreover, we generalize a well-known equivalence of measures phenomenon related to Mat\'ern kernels to the non-Gaussian case by using Kakutani's theorem.


Title: Zero-one law for directional transience of one dimensional excited random walks
Abstract: The probability that a one dimensional excited random walk in stationary ergodic and elliptic cookie environment is transient to the right (left) is either zero or one. This solves a problem posed by Kosygina and Zerner [8].


Title: The weak categorical quiver minor theorem and its applications: matchings, multipaths, and magnitude cohomology
Abstract: Building upon previous works of Proudfoot and Ramos, and using the categorical framework of Sam and Snowden, we extend the weak categorical minor theorem from undirected graphs to quivers. As case of study, we investigate the consequences on the homology of multipath complexes; eg. on its torsion. Further, we prove a comparison result: we show that, when restricted to directed graphs without oriented cycles, multipath complexes and matching complexes yield functors which commute up to a blow-up operation on directed graphs. We use this fact to compute the homotopy type of matching complexes for a certain class of bipartite graphs also known as half-graphs or ladders. We complement the work with a study of the (representation) category of cones, and with analysing related consequences on magnitude cohomology of quivers.