Mathematics

We reformulate the bounded-length-distortion condition for maps between metric spaces in a certain relaxed form that requires the presence of a reference measure on the source space, which makes the new approach more natural from the…

The Chromatic Sum problem asks, given a graph $G$ and an integer $k$, whether $G$ admits a colouring $c$ with sum $\sum_{v\in V}c(v) \leq k$. We study the complexity of Chromatic Sum on graph classes defined by some set of forbidden graphs.…

This paper establishes finite-sample worst-case maximal inequalities for averages of independent centered heavy-tailed random vectors. The object of interest is the expected top-$k$ Euclidean norm of the sample average, which includes the…

Hypergraphs encode rich multiway interactions, but not all structural information is equally accessible through the dynamics. By analyzing pattern-forming instabilities in reaction-diffusion systems on directed hypergraphs, this work…

This paper focuses on identifying defective units in unbounded periodic arrays of point sources using boundary data. The study is motivated by the noninvasive evaluation of large-scale periodic source systems. Unlike classical inverse…

Let $f\colon{\mathbb Z}^2\to{\mathbb Z}$ be a Riemann function whose weight $W$ is a perfect matching. Then there is a family of sheaves of $k$-vector spaces $\{{{M}}_{W,{\bf d}}\}_{{\bf d}\in{\mathbb Z}^2}$ on a five-point topological that…

Nonlinear algebraic (polynomial) differential equations that govern fluid-structure interactions, such as those modeling vortex-induced vibrations, and shock waves, often lack analytical solutions, creating significant challenges to…

We study homology manifolds through the eyes of the six functor formalism of spectral sheaves on locally compact Hausdorff spaces. As main results, we characterize cohomologically smooth objects by adapting an argument of Scholze, deduce…

In this paper, we prove that the \'{e}tale fundamental group of the N\'{e}ron model of an abelian variety over a number field $K$ is the semidirect product of a finite group with the \'{e}tale fundamental group of the ring of integers of…

In previous work \cite{GW}, we developed a theory of modulated \(2j-k\) bi-orthogonal polynomial systems \(\{P_n(z;r),Q_n(z;r)\}\) and \(j-2k\) bi-orthogonal polynomial systems \(\{R_n(z;r),S_n(z;r)\}\), which generalize the classical…

We model an adaptive contest in which two antagonistically coupled populations continually reallocate effort among competing methods, but decisions are not fielded instantly. Each side has an intended portfolio and a deployed portfolio:…

We study weak solutions of electrodiffusion systems coupling the Nernst--Planck equations with fluid models. First, for the three-dimensional Nernst--Planck--Euler system, we establish an Onsager-type criterion for the validity of the…

Watermarking promises a statistical trace of large language model (LLM) use, but real documents, after editing or paraphrasing, rarely arrive as purely human-written or purely machine-generated. This motivates a quantitative question beyond…

Artificial intelligence (AI) systems are routinely modified after deployment through retraining and changes in their environments. These transformations raise a metaphysical question: under what conditions does an AI system remain the same…

This short review examines the primary approaches for estimating the predictive distribution of Laplace-approximated Bayesian neural networks, with particular focus on the Generalized Linear Model (GLM) formulation. We survey the landscape…

A strong majority edge-coloring of a graph is an edge-coloring in which, for every edge $e$ and every color $i$, at most half of the edges adjacent to $e$ have color $i$. Such a coloring exists only for graphs with no pendant path of length…

We develop a framework for analyzing the learning dynamics of $\ell_2$-adversarial training of single-index models on Gaussian mixtures in the high-dimensional limit under streaming stochastic gradient descent (SGD). We derive deterministic…

We study Hilbert transforms on graph products of finite von Neumann algebras, with particular interests on their boundedness on the associated noncommutative $L_p$-spaces for $1<p<\infty$. We establish a generalized Cotlar identity for…

For all Dyer groups, we find an algorithm to determine when two parabolic subgroups are conjugate. Given two conjugate standard parabolic subgroup, we fully describe the conjugating elements in terms of ribbons, showing that the ribbon…

We show that many of the standard nuclearity properties considered in the literature for the hierarchy of operator system tensor products can be expressed as approximate factorization properties, generalizing the well-known Completely…