arXiv preprints from January 1, 2026 through September 8, 2026 — 23:34:00 EST
For matrices drawn from the standard Gaussian orthogonal ensemble (GOE) and Gaussian unitary ensemble (GUE), we prove that the normalized zero counting measure of the permanental characteristic polynomial $Per(zI_N-H_N)$ converges almost surely to the standard Wigner semicircle law on $[-2,2]$, rotated by $π/2$ onto the imaginary...
The purpose of the paper is to place Whiting's classical growing mode stability argument, extended to real frequencies by Shlapentokh-Rothman for the scalar wave equation and by Andersson, Ma, Paganini and Whiting in general, in the framework of classical PDE theory. The key steps are: a description of the dual or adjoint modes, a...
Sparse domination is a central tool in modern harmonic analysis, offering a unified approach to weighted inequalities for Calderón--Zygmund operators and related operators such as commutator operators, rough singular integrals, square functions etc. In this expository note, we briefly survey the main ideas behind sparse bounds on...
We show that every continuous and isometry invariant valuation on spherical polytopes is a linear combination of the spherical intrinsic volumes. The proof relies on a weak differentiability property satisfied by valuations on polytopes in $\mathbb{R}^n$ with a natural smoothness property with respect to the action of the affine...
Classical Nesterov acceleration employs different choices of damping and inertial parameters in the convex and strongly convex settings, both for continuous-time dynamics and for discrete algorithms. When the strong convexity parameter is small, directly using the strongly convex damping or inertial coefficient may lead to slower...
We compute the local integrals appearing in the refined Gan--Gross--Prasad conjecture for Fourier--Jacobi periods of $\mathrm{Sp}_4$ in new ramified cases and use this to formulate an explicit conjectural identity relating Petersson norms of degree 2 Siegel cusp forms and associated half-integral weight forms. We note consequences of...
We study the connectedness and enumeration of reconfiguration graphs of valid triangulations of convex polygons whose vertices are cyclically colored with $j \ge 3$ colors, where every triangle has vertices of three pairwise distinct colors. For $j = 3$, we settle a conjectural expectation of Acharya, Mütze, and Verciani: we prove...
Let $(R,\mathfrak{m})$ be a one-dimensional Cohen-Macaulay local ring. In this paper, we find the reduction number $r_{z}(\mathfrak{m}^d)$ of $\mathfrak{m}^d$ with respect to a witness $z\in \mathfrak{m}^d \setminus \mathfrak{m}^{d+1}$ to the generalized Loewy length $\text{g}\ell\ell(R)$ for several infinite families of hypersurfaces...
For surfaces of genus $g \geq 3$ with at most one boundary component, we give explicit generating sets for the kernel of the Birman-Craggs-Johnson homomorphism and the commutator subgroup of the Torelli group. As an application, we give a new proof of Johnson's calculation of the abelianization of the Torelli group.
We show that the nilpotent cone associated to a simply connected semisimple algebraic group, together with all its crepant projective partial resolutions, can be constructed as Hamiltonian reductions of the affine closure of the cotangent bundle of base affine space for suitable choices of stability parameter of a maximal torus. We...
Traditional plasticity theory is commonly organized through an elastic law, a yield condition, a flow rule, hardening relations, and loading--unloading conditions. This paper formulates these relations through directional stationarity of one scalar functional evaluated over one-sided admissible plastic paths. The first variation...
Local differential privacy (LDP) protects individuals in a dataset by perturbing each measurement before release. For real-valued data, a widely used mechanism is additive Laplace noise. We study the problem of estimating the distribution of the latent confidential data from the privatized observations via the nonparametric maximum...
Self-controlled study designs eliminate confounding by individual-level characteristics that remain constant during the observation time and are thus widely used in pharmacoepidemiology and vaccine safety research. However, existing methods remain vulnerable to time effects, including temporal trends and seasonality in the exposure or...
Grasp synthesis is a core task in robotic manipulation, for which the solution typically forms a multimodal distribution rather than a point estimate. Generative robotic grasping aims to learn this distribution with deep generative models such as diffusion and flow-based approaches. The iterative nature of such generative models makes...
We investigate the structure of interactive beliefs in networks: the epistemic state in which agents hold, revise, and act on their models of the epistemic states of other agents. What a group believes depends on what each member agent takes the others to believe, and on what each takes the others to believe about still others. We...
Intent misinterpretation during vehicle interactions causes recurring planning failures. We study a decision layer in which a language-guided intent module reads structured descriptors, computes a smoothed intent-geometry divergence score, and gates the planned maneuver before commitment, upstream of a corridor envelope. On a replayed...
This paper studies efficient and secure Rowhammer mitigation at the Memory-Controller (MC). Rowhammer mitigation faces a fundamental tradeoff between tracking storage and mitigation rate: precise trackers (such as Misra-Gries) avoid unnecessary mitigations but require large CAM structures, whereas sampling-based schemes (such as PARA)...
Test-time scaling uses extra test-time compute to improve performance, such as letting language models reason longer when solving a problem. As models keep the entire reasoning trace in memory via full attention, hard tasks that need long thinking can be prohibitively expensive. However, we find most intermediate reasoning tokens lose...
Large-kernel Convolutional Neural Networks (CNNs) deliver remarkable performance in vision tasks by significantly expanding receptive fields, yet their quadratic parameter growth critically impedes storage-efficient edge deployment. While existing efficient architectures adopt parameter-efficient depthwise separable convolution...
Vision-Language-Action (VLA) models have demonstrated effectiveness in robot manipulation, yet state-of-the-art models such as pi0.5 operate under a single-frame paradigm, limiting their ability to retain past observations and develop precise spatial perception. In this paper, we propose StreamPI, a streaming multimodal temporal...
In this paper, we present VirTooS, a Python/C# toolkit designed to implement fleet-management tasks on teams of Autonomous Mobile Robots (AMRs). VirTooS leverages the Robot Operating System (ROS) 2 and Unity game engine to provide realistic, scalable virtual experiments in a mixed-reality environment. The toolbox allows users to...
Automatic Speech Recognition (ASR) technologies have achieved remarkable performance in recent years through the use of large multilingual foundation models. However, most advances remain concentrated on high-resource languages, while indigenous languages continue to suffer from a lack of speech resources and language technologies....
Scaling generalist vision-language-action (VLA) policies is severely bottlenecked by the inherent heterogeneity of embodied data, which spans diverse robot morphologies, camera configurations, and low-level action spaces. Existing paradigms typically address this mismatch through explicit action retargeting, human-to-robot video...
Mechanical engineering (ME) requires a broad knowledge base across several disciplines. However, ME students often have insufficient training in electrical and computer engineering, complex challenges in traditional thermal system modeling, and endure heavy course loads with limited class hours. To help address these challenges, this...
Native visual reasoning treats visual generation as the medium of reasoning itself: visual states (i.e. images and videos) are not merely inputs to be understood or outputs to be rendered, but first-class substrates for problem solving beyond language. Yet progress remains bottlenecked by the lack of scalable training tasks, reliable...