arXiv preprints from January 1, 2026 through September 23, 2026 — 06:19:27 EST
We initiate a polyhedral study of the graph multi-separator problem proposed by Irmai et al. (2024) as an alternative to the lifted multicut problem for application to the task of image segmentation. Starting with an integer linear program (ILP) formulation and the multi-separator polytope spanned by its feasible solutions, we...
Interconnected systems have been widely studied, with a focus on interconnected systems whose subsystems are solely input-to-state stable (ISS) or passive systems. The focus of this work is on the interconnected systems that appear in adaptive gradient methods. In adaptive gradient methods, one subsystem seeks to move parameters of a...
Let $H$ and $K$ be subgroups of a virtually polycyclic group $G$. We prove the Hirsch length inequality $$h(H)+h(K) \leq h(H\cap K)+h(G).$$ We show that equality holds when the number of $(H,K)$-double cosets is finite, and that the converse holds when $G$ is nilpotent. We also apply this to twisted conjugacy, showing that for...
This paper studies generalized Hamiltonian gradient flows for contact-type Hamilton--Jacobi equations, adopting the variational framework of Herglotz's principle and its fundamental solution \(h_L(t,x,y,u)\). Two main results are presented. First, precise first-order sensitivity relations are derived, linking derivatives of \(h_L\) to...
This paper provides a complete characterization of the sign of the propagation speed in the symmetric two-species Lotka-Volterra competition-diffusion model under strong competition. The system admits a unique bistable travelling front and the sign of its speed determines which of the two species invades the other. We prove that for...
We study quadratic polynomials that are nonnegative on the non-compact set \[ F:=\{(x_1,x_2)\in\mathbb R^2:\ x_1\ge 0,\ x_2\ge 0,\ x_1x_2\le 1\}. \] All extreme rays of the cone of nonnegative quadratic polynomials are characterized on this set. The characterization allows us to study parameterized valid inequalities for quadratic...
We obtain arithmetic conditions which are satisfied by solvable groups admitting an abelian $π$-subgroup. First, we extend a previous characterization by removing the square-free hypothesis on some fixed irreducible character degree. We then show the same arithmetic conditions follow from a faithful action of an abelian $π$-subgroup...
The aim of this manuscript is to show that the group of autoequivalences of an exact Courant algebroid over a compact base manifold is a tame Fréchet Lie group. Moreover, we compute its Lie algebra. Furthermore, we show that the space of generalized almost complex structures is a tame Fréchet manifold and that the canonical action of...
Battery-swapping stations (BSSs) can shorten electric-vehicle energy replenishment while using centrally managed battery inventories as flexible grid-connected storage. Realizing both benefits requires the station to schedule charging, grid discharge, and swapping service before future customer demand and electricity prices are known....
We establish the Moran--Hutchinson formula for attractors of finite systems of surjective similitudes on semimetric spaces. More precisely, for a complete, normal semimetric space satisfying strong regularity and geometric doubling, we prove that the open set condition implies that the Hausdorff measure of the attractor at the...
We study the relation between linear stability of generated linear series on smooth curves and slope stability of their associated syzygy bundles. Motivated by conjectures of Mistretta and Stoppino, we establish new cases in which linear stability implies slope stability, focusing first on generated linear series over general curves...
Though the sharp $L^{2}$-Caffarelli--Kohn--Nirenberg (CKN) inequalities have been extensively studied in the entire Euclidean spaces, the corresponding problem on domains whose boundary contains the origin remains largely unexplored. We investigate the sharp $L^{2}$-CKN inequalities on half-spaces and orthants $\mathbb R^{n}_{k,+}$ by...
Previously we have explicitly characterized by certain linear inequalities the ${\mathfrak{k}}$-highest weight tableaux in the quantum Littlewood-Richardson (LR) rule produced by $1$-$0$-slack recording tableaux. Using the composition of promotion operators to defining the Naito-Suzuki-Watanabe bijection between...
We consider the Euclidean distance geometry problem (EDG): given a subset of the pairwise distances of an unknown cloud of $n$ points in $\mathbb{R}^\ell$, recover the point cloud up to rigid motions. When $n$ is large, a popular practical approach is to minimize a nonconvex quartic, known as the squared-stress or s-stress, over point...
The $Λ$-distribution of a compact matrix group is an invariant in algebraic probability theory that was recently introduced to study zero distributions of function field $L$-functions. It is encoded by the $σ$-moment generating function, a generalization of the Molien series of classical invariant theory. In this work, we compute the...
We study the quantum drift-diffusion, or Derrida-Lebowitz-Speer-Spohn (DLSS), equation for a nonnegative density $\varrho$ on a bounded convex domain with Neumann boundary conditions, in the square-root variable $u=\sqrt\varrho$. We show that the DLSS operator, defined and monotone on smooth strictly positive functions, admits a...
The aim of the present paper is to develop a spectral perturbation theory from a higher perspective. More precisely, we consider a one-parameter family of varying bilinear forms, each of them defined on a (possibly) different Hilbert space. Assuming the stability of the corresponding spectra, our first main result establishes a...
Long-horizon robot manipulation chains many contact-rich skills into one multi-stage task. Vision-language-action (VLA) models increasingly master the individual skills, yet the chain still fails: errors compound beyond the policy's ability to correct, and one subtask silently constrains the next. A promising recipe freezes the VLA...
The development of safe and beneficial AI requires that systems can learn and act in accordance with human preferences. However, explicitly specifying these preferences by hand is often infeasible. Inverse reinforcement learning (IRL) addresses this challenge by inferring preferences, represented as reward functions, from expert...
This paper investigates an increasingly important topic in generative modeling: pixel-space diffusion models. Although numerous studies have explored this topic, most focus on small-scale or class-conditional settings. Consequently, a practical recipe for training pixel-space models that rival or exceed well-established latent-space...
Entrepreneurs increasingly use end-user generative AI technologies such as ChatGPT for high-stakes documents like loan applications and business plans, where AI-generated errors---a wrong price, a fabricated product---can affect loan or funding outcomes. Current approaches to supporting evaluation of AI-generated text assume a single...
Long-horizon robot manipulation requires a robot to both execute individual skills reliably and sequence them coherently over extended tasks. Most hierarchical vision-language-action (VLA) models make each such decision with a single forward pass, leaving no mechanism to allocate additional computation to difficult or consequential...
The current best bounds on the matrix multiplication exponent $ω$ are obtained through a refinement of the laser method called combination loss analysis (Duan et al., 2022; Williams et al., 2024; Alman et al., 2025). In this note, we address the optimization problem at the core of this approach and propose several improvements. First,...
For $q> p$, let $T(n,q,p)$ be the minimum number of translates of the cube \(\{0,1,\dots,p-1\}^n\) required to cover the $n$-dimensional torus $(\mathbb{Z}/q\mathbb{Z})^n$. We show that for each $q$ there exists a constant $1\le Λ_q \le 2$ such that $T(n,q,2)=(Λ_q + o(1))(q/2)^n$.
Let $X_H$ denote the number of copies of a fixed graph $H$ in $G_{n, p}$. Gilmer and Kopparty conjectured that $X_H$ satisfies a local central limit theorem (LCLT) provided that $H$ is connected, $p \gg n^{-1/m(H)}$, and $n^2 (1-p) \gg 1$, where $m(H)$ is the maximum density. Following the work of Berkowitz, Sah and Sawhney...