arXiv preprints from January 1, 2026 through September 23, 2026 — 04:13:04 EST
We propose a local Legendre frame method for the accurate computation of Caputo fractional derivatives of order \(0<α<1\). On each local subinterval, the function is represented by a restricted Legendre frame obtained from scaled Legendre polynomials on an extended interval. The local coefficients are computed from equispaced samples...
Let $A$ be a commutative simple algebra in a braided finite tensor category $\mathcal{B}$. We identify the largest transparent subalgebra of $A$ as the algebra induced by a central lift of the free-module functor. This identification gives formulas for the Frobenius-Perron dimension and the Müger center of the category of local...
We describe certain finite-time singularities of the Kähler-Ricci flow arising in the analytic minimal model program. Assuming that convergence to an asymptotically conical Kähler-Ricci shrinker is realized by holomorphic maps, we prove that, in a fixed holomorphic gauge, the nearby flow is modeled on the shrinker at the level of...
We study stochastic control of multivariate Hawkes-driven stochastic differential equations with machine learning algorithms in a non-Markovian setting. Due to the path dependence of the memory of the Hawkes intensity, this problem does not fall within classical stochastic control theory outside particular Markovian kernels. We first...
We determine the critical probability for Bernoulli bond percolation on essentially any finite graph. Namely, letting $λ(G)$ denote the spectral radius (maximum eigenvalue) of $G$, we prove that the critical probability is at $1/λ(G)$: above this probability there is typically a component of order $Ω(λ(G))$, whereas below it all...
Let $π: M \to B$ be an elliptic fibration over $B = D^2$ or $B = S^2$ with $n$ nodal fibers over $Δ\subseteq B$. We study the universal liftable braids for $π$: those braids that admit a fiber-preserving lift to $M$ for all choices of coordinates on $(B,Δ)$. When $B = S^2$, we show that nontrivial universal braids do not exist by...
The goal of this paper is to prove an upper bound for the $L^4$ norm of a trigonometric polynomial whose spectrum is a nontrivial strictly monotone polynomial with integer coefficients of degree three and higher, via its $L^2$ norm. Our condition on the coefficients of the trigonometric polynomial in question is that they form a...
We consider the spherical Borel Eisenstein series induced from the trivial representation for a split semisimple linear algebraic group over a number field. We prove that its regularization at the special point corresponding to half the weighted marking of a distinguished coadjoint nilpotent orbit in the Langlands dual Lie algebra is...
The Erdős Matching Conjecture is governed by two competing ways of excluding $s+1$ disjoint edges: one may concentrate all edges on fewer than $k(s+1)$ vertices, or force every edge to meet a fixed $s$-set. We determine a near-optimal range in which the second construction is extremal. For every fixed $k\ge2$, there is $s_0(k)$ such...
We study the 4D Hessian conjecture in Lorentzian signature. For a polynomial potential $φ$ in 4 real variables whose Hessian matrix has inertia index 1 and determinant $-1$, we define a pivot of $φ$ as a direction vector $v$ such that the double derivative $D^2_vφ$ is a constant function. We then prove that the gradient mapping of...
We prove a global-in-time uniform bound for solutions to thermo-diffusive systems of reaction-diffusion equations with $L^\infty$ initial conditions.
We show that any measurable, translation and $\mathrm{SO}(n)$-invariant valuation on polytopes in $\mathbb{R}^n$ is a linear combination of the intrinsic volumes, which extends Hadwiger's classical characterization of rigid motion invariant continuous valuations on convex bodies. This result is based on a novel regularity result for...
Using the theory of complex spinorial forms, we prove that an odd-dimensional Riemannian manifold admits a pure spin-c Killing spinor with an imaginary Killing function $iμ$ if and only if it is an exact $μ$-Kenmotsu manifold, thereby obtaining an extension of a recent result by the first named author that, under the purity...
Let $G$ be an almost simple group whose socle is an alternating, classical, or sporadic group, and let $H$ be a non-parabolic maximal subgroup of $G$. We prove that any maximal subgroup $M$ of $H$ can be generated by at most $7$ elements, and that this bound is sharp when the socle of $G$ is alternating or classical; this improves the...
Let $X_1,X_2, \ldots $ be independent uniform random points in a bounded region $A \subset {\bf R}^d$ having a smooth boundary, $d \geq 1$. Let $B \subset A$ be compact. The _coverage threshold_ of $B$, $R_n$, is the smallest $r$ such that $B$ is covered by the balls of radius $r$ centred on $X_1,\ldots,X_n$. The _maximal spacing_...
This article introduces a numerical optimal control framework for minmax constrained density control for a class of noisy linear parabolic partial differential equations (PDEs), in particular the noisy heat equation. The goal is to transport an initial density to a target density while minimizing a specified cost with respect to...
Distributed target tracking is essential for scalable and robust sensing systems, as it enables multiple radar nodes to cooperatively estimate a target state without relying on a centralized fusion center. In this paper, we present a fully distributed framework for single-target tracking in frequency-modulated continuous-wave (FMCW)...
Deep reinforcement learning (DRL) has recently gained a great attention due to its real-time adaptation and effectiveness in complex optimization problems. This paper investigates the optimal deployment of millimeter-wave (mmWave) base stations (BSs) in a realistic, non-convex campus topology. The optimization problem is NP-hard, due...
Implantable neural interfaces require low-power real-time signal processing to remain within strict thermal and bandwidth constraints, motivating lightweight feature extraction methods for on-chip spike sorting. This work presents the Walsh-Hadamard Transform (WHT) as a hardware-efficient feature extraction method for neural spike...
This paper studies the problem of robust stabilization of linear input-state systems in discrete time. We prove that for any compact set of stabilizable systems, there exists a dynamic state-feedback controller that globally asymptotically stabilizes all systems in the set. In addition, we show that for some compact sets of...
The increasing penetration of power electronic converters in industrial grids introduces stability challenges at frequencies well above the electromechanical range of traditional power systems. Commercial software tools typically perform eigenvalue-based stability analysis using root-mean-square (RMS) models that assume a...
Hardware shifts, color variations, and changing patient characteristics between development and deployment routinely break trained medical image classifiers. Existing remedies fall short: standard color jittering provides insufficient diversity, while deep generative style transfer algorithms hallucinate features, destroy clinically...
Integrated sensing and communication (ISAC) enables the tracking and detection of passive objects, including the human body, by leveraging standard wireless communication signals. While already standardized in IEEE 802.11bf for Wi-Fi, ISAC is currently being defined by 3GPP for the upcoming generations of cellular networks. This...
This paper studies integrated sensing and communications (ISAC) over a hybrid system that seamlessly combines legacy cellular base stations with distributed cell-free (CF) access points (APs). We propose a hierarchical ISAC architecture where a central base station (CBS) serves its near users and simultaneously operates as a...
Scalable supervisors for multi-agent discrete-event systems control groups of isomorphic agents through a common template. Under partial observation, such a supervisor is maximally permissive if the relabeling that maps the agents onto their template is relabeling observation consistent (ROC) and a local companion condition holds....