arXiv preprints from January 1, 2026 through September 19, 2026 — 19:22:01 EST
The interaction of moose (Alces alces) and wolf (Canis lupus) populations in ecosystems such as Isle Royale National Park is a canonical benchmark for ecological modeling of prey-predator dynamics. Mathematical modeling is a useful tool for modeling these interactions. A central challenge in this domain is the inverse problem,...
We introduce a unified framework for supervised and unsupervised learning based on reproducing kernel Hilbert spaces (RKHSs). We introduce the notion of a nested RKHS, namely an increasing sequence of RKHSs whose union is dense in an ambient $L^2$-space. This construction makes it possible to exploit the computational structure of...
Hierarchical planning frameworks combine skills from multiple robot control policies for long-horizon task execution, where determining when to terminate the current skill and advance to the next subtask is essential. Existing approaches often rely on pre-designed completion signal checkers that are hard to obtain in real-world...
Let $M^{n+1}$ be a closed, connected smooth manifold, where $n\geq 1$. For each prescribed volume fraction $s\in(0,1)\setminus\{\frac12\}$, we prove that the isoperimetric region of volume $s \operatorname{Vol}_g(M)$ is unique for a generic set of smooth Riemannian metrics $g$. At half volume, a generic metric has exactly two...
This article introduces mutual evaluation of a replicable task worker and a critic that incentivizes truthful reporting, both modeled as strategic agents. The critic chooses a finite-valued rule that induces an evaluation score on joint report laws. Their common payoff is analyzed through regret relative to the unrestricted critic...
We prove new small-ball inequalities for boolean matrix-series. The leading example is $\mathbb E_s[{\text{det}(I-S^2)^β\,\mathbf 1_{\{\|S\|<1\}}}]\ge e^{-O(βτ)}$, which holds for boolean matrix-series $S=\sum_i s_iA_i$ formed using symmetric matrices $A_1,\dots,A_n$ and uniformly random signs $s\in\{\pm1\}^n$. Specifically, this...
Multi-turn agents trained with reinforcement learning (RL) receive a single scalar reward per trajectory, which motivates self on-policy distillation (OPD) to supply dense token-level supervision from a self-teacher with privileged task skills, letting a skill-free student internalize them. This recipe, however, is undermined by two...
For $r> 2$, we study the moduli space parameterising fixed degree morphisms $\mathbb P^r\to X$ where $X$ is a smooth hypersurface of low degree. More precisely, we prove the following result: let $n\geq 2, e\geq 1$ and $X\subset \mathbb P^{n-1}$ a smooth degree $d\geq 2$ hypersurface over an algebraically closed field of...
Research data quality is multidimensional and purpose-dependent: it emerges from the interplay of data, intended use, contextual knowledge, documentation, intervention decisions, and traceability. This concept paper presents the Data Hospital, a human-in-the-loop control and interaction model for research data quality. Using a...
Safety evaluations for large language models rely on surface-form classifiers that report declining harm scores across model generations. We provide evidence that this methodology is systematically incomplete: explicit discriminatory content is transformed rather than removed. We call this \emph{harm laundering}. Analysing 450,000...
We study a singular Dirichlet problem driven by a regularized $p(x)$-Laplacian under a prescribed modular constraint. Using growth and differentiability estimates for the regularized energy, together with coercivity and modular compactness, we construct nonnegative constrained minimizers for a family of nonsingular approximating...
Action chunking is widely used for action generation and execution in Vision-Language-Action (VLA) policies, yet existing approaches commonly use a fixed action horizon. During a rollout, different task stages may require different levels of action continuity, control precision, and closed-loop feedback, making a fixed horizon unable...
We consider the problem of testing Granger causality in time series, specifically, whether the future outcome $Y_{t+1}$ and the exposure history $\bar X_t$ are conditionally independent given the history of $\bar Y_t$ and a set of confounding variables $\bar Z_t$ up to time $t$. This testing procedure distinguishes true causal effects...
We investigate the sensitivity of solutions to multi-dimensional scalar balance laws with respect to perturbations of the initial data analytically and numerically. Reliable first-order sensitivity information is essential in gradient-based optimization and inverse problems constrained by hyperbolic balance laws. In hyperbolic...
Flow matching has emerged as the state-of-the-art generative model and has been used for plug-and-play (PnP) priors to solve inverse problems in computational imaging. However, existing flow-based inverse solvers assume linear forward models and/or make simplifying approximations in posterior sampling. To circumvent these problems, we...
We prove local regularity for axisymmetric suitable weak solutions of the 3D Navier-Stokes equations, which are smooth before the terminal time $t=0$, and satisfy Type~II pointwise bounds at a vanishing length scale $\ell(t)$. We say $\ell(t)$ is an Euler length if it is non-increasing, satisfies a doubling condition, and if...
We prove that hypercontractivity implies entropy contraction for a single quantum channel, without a detailed balance condition. For primitive quantum Markov semigroups that are KMS-symmetric with respect to a faithful invariant state \(σ\), we obtain the modified Log-Sobolev bound $α_1\geq \fracλ{(2+\log\|σ^{-1}\|_\infty)}$ where $λ$...
In this paper we study a weighted generalization of the Poisson-Voronoi tessellation called the Poisson-Laguerre tessellation, where the nuclei of the generating Poisson process additionally carry independent non-negative random weights. For each cell we can define its inradius as the radius of the largest ball centered at the nucleus...
Location estimation exhibits markedly different finite-sample behavior across noise distributions: regular families typically yield root-\(n\) rates, whereas compactly supported laws may admit faster, boundary-driven rates. We question whether a single estimator, without knowledge of the density's shape, can adapt to the instance-wise...
We introduce a new method that brings the combinatorics of hyperplane arrangements into the study of representation zeta functions of compact Lie groups. For the Witten zeta function $ζ_Φ(s)$ associated with a root system $Φ$, our method yields elegant formulas for $ζ_Φ(0)$ and $ζ_Φ'(0)$ in terms of the exponents of various parabolic...
We prove existence and uniqueness of a strong initial trace for every bounded kinetic solution of a stochastic scalar conservation law, although no initial value is prescribed and no nondegeneracy condition is imposed on the flux. The core of the proof is pathwise. After fixing a realization, the rescaled stochastic terms and kinetic...
Principal component analysis (PCA) is a fundamental tool for learning low-dimensional structure from high-dimensional data. When data are collected from multiple sources, the underlying task distributions may exhibit unknown degrees of similarity, with some tasks potentially arising from arbitrary distributions. We propose new...
Motivated by questions and results of Erdős, Sárközy and Sós (1989), and Khalfalah and Szemerédi (2006), we introduce an ergodic approach to additive problems concerning solutions of equations of the form \[ x+y=\lfloorα(n)\rfloor,\quad x,y\in A,n\in\mathbb{N} \] where $α(t)$ is a sufficiently regular function, such as a polynomial or...
We prove that for every acyclic matrix pattern $P$ it holds that $\operatorname{Ex}(n,P) \leq n^{1+O_P(1/\log\log n)}$.
We study the Anderson model on hyperbolic lattices. The graph is the Cartesian product of the Euclidean lattice with the regular hyperbolic square lattice having five squares at each vertex. We prove the existence of absolutely continuous spectrum and the absence of singular spectrum on a deterministic set of positive measure at weak...