diff --git "a/raw_rss_feeds/https___arxiv_org_rss_math.xml" "b/raw_rss_feeds/https___arxiv_org_rss_math.xml" --- "a/raw_rss_feeds/https___arxiv_org_rss_math.xml" +++ "b/raw_rss_feeds/https___arxiv_org_rss_math.xml" @@ -7,5348 +7,4556 @@ http://www.rssboard.org/rss-specification en-us - Wed, 10 Dec 2025 05:00:03 +0000 + Thu, 11 Dec 2025 05:00:08 +0000 rss-help@arxiv.org - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 Saturday Sunday - Decompositions of Group Algebras as a Direct Sum of Projective Indecomposable Modules and of Blocks in Positive Characteristic - https://arxiv.org/abs/2512.07835 - arXiv:2512.07835v1 Announce Type: new -Abstract: The dissertation focuses on decomposing a group algebra $kG$ over a field of positive characteristic into a direct sum of projective indecomposable modules. Such a decomposition is obtained together with the Artin--Wedderburn Theorem. The main goal of the dissertation is to explicitly decompose given group algebras as a direct sum of their projective indecomposable modules. - To achieve this, we determine the radical series of each projective indecomposable module of the given group algebras. For a group algebra over characteristic $p$, each projective indecomposable module has a simple head that is isomorphic to its socle. Projective covers and injective envelopes are used to construct these modules. A cyclic group algebra is uniserial, and a $p$-group algebra over characteristic $p$ is itself a projective indecomposable module. Using these properties, we explicitly find all projective indecomposable modules for the following group algebras over characteristic $2$: the Klein four-group, the alternating group $A_4$, and the alternating group $A_5$. Their relationships play an important role in this process. - Since $p$-group algebras have trivial head and trivial socle, the Klein four-group algebra has a corresponding radical series. Its decomposition into a direct sum of projective indecomposable modules is described explicitly, and the Cartan matrix of a group algebra is obtained by calculating the multiplicities of simples in its projective indecomposable modules. - The topic is then extended slightly by considering the unique decomposition of a group algebra into a direct sum of particular modules known as blocks. For $kA_4$, the primitive orthogonal idempotents are calculated, and since $kA_4$ has one block, it is equal to its block decomposition. For $kA_5$, we show that there are two blocks, determined by checking the nonzero entries in its Cartan matrix. - oai:arXiv.org:2512.07835v1 - math.RA - math.CT - Wed, 10 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Eun H. Park - - - Lie Theory Theorems over Positive Characteristic and Modular Lie algebras - https://arxiv.org/abs/2512.07836 - arXiv:2512.07836v1 Announce Type: new -Abstract: Sometimes, it is very important to consider what type of setting is assumed when studying a mathematical object. For example, in Galois theory, properties can completely change if we study a field extension over $F_p$ instead of a field over $\mathbb{Q}$. When we consider base fields for modules, algebras, or vector spaces, we often recall commonly used fields such as $\mathbb{C}$ and fields $F$ with char $F= p$. - Similar behavior arises in the study of Lie algebras. Properties that hold for Lie algebras over a field of characteristic zero do not necessarily hold over a field of characteristic $p$. In general, we are more familiar with studying Lie algebras and their representations over $\mathbb{C}$. However, an interesting fact is that new properties can be discovered by studying the theory over fields of positive characteristic. - Therefore, we will closely examine how theorems and properties in Lie algebra theory do not hold or behave differently when the base field has characteristic p. In fact, there is a related area of study known as modular Lie theory that deals specifically with this setting. In this theory, we study concepts such as the definition of restricted Lie algebras, that is, Lie algebras $L$ equipped with a p-mapping $[p] : L \rightarrow L$, defined as $x\mapsto x^{[p]}$, where the base field has prime characteristic. In other words, the theory introduces a new tool, the $p$-mapping, for the study of modular Lie algebras. - In this project, we aim to study Lie algebras defined over fields of positive characteristic. Specifically, the main focus will be on how Lie algebras behave over such fields and how we can develop the general framework of modular Lie theory based on the insights and structures that arise in this setting. - oai:arXiv.org:2512.07836v1 - math.RA - Wed, 10 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Eun H. Park - - - Cartan Horadam Spinors - https://arxiv.org/abs/2512.07837 - arXiv:2512.07837v1 Announce Type: new -Abstract: Number sequences with wide-ranging applications in mathematics, physics, medicine, and engineering remain an active research topic. This study examines these sequences through the general framework of Horadam numbers and their special cases associated with Cartan numbers. By defining spinor transformations on the resulting structures, new types of spinors are introduced and their key properties are analyzed. The proposed approach bridges distinct yet contemporary research areas, contributing to a broader interdisciplinary perspective. - oai:arXiv.org:2512.07837v1 - math.RA - Wed, 10 Dec 2025 00:00:00 -0500 + A Dynamical Approach to the Berezin--Li--Yau Inequality + https://arxiv.org/abs/2512.08966 + arXiv:2512.08966v1 Announce Type: new +Abstract: We develop a dynamical method for proving the sharp Berezin--Li--Yau inequality. The approach is based on the volume-preserving mean curvature flow and a new monotonicity principle for the Riesz mean $R_\Lambda(\Omega_t)$. For convex domains we show that $R_\Lambda$ is monotone non-decreasing along the flow. The key input is a geometric correlation inequality between the boundary spectral density $Q_\Lambda$ and the mean curvature $H$, established in all dimensions: in $d=2$ via circular symmetrization, and in $d\ge 3$ via the boundary Weyl expansion together with the Laugesen--Morpurgo trace minimization principle. Since the flow converges smoothly to the ball, the monotonicity implies the sharp Berezin--Li--Yau bound for every smooth convex domain. As an application, we obtain a sharp dynamical Ces\`aro--P\'olya inequality for eigenvalue averages. + oai:arXiv.org:2512.08966v1 + math.DG + math.SP + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Selime Beyza \"Oz\c{c}ev\.ik, Abdullah Dertli + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Anton Alexa - Equilateral n-gons in planar integer lattices - https://arxiv.org/abs/2512.07839 - arXiv:2512.07839v1 Announce Type: new -Abstract: We study the existence of equilateral polygons in planar integer lattices. Maehara showed that it's sufficient to work with rectangular lattices $\Lambda(m) = L[(1,0),(0,\sqrt{m})]$ with $m \equiv 3 \pmod{4}$. Building on results of Maehara and of Iino and Sakiyama, we show that for every such $m$ there exists $N$ such that for all $n \geq N$, the lattice $\Lambda(m)$ contains an equilateral $n$-gon. This extends previous classifications of equilateral polygons in planar lattices. - oai:arXiv.org:2512.07839v1 - math.MG - math.CO - Wed, 10 Dec 2025 00:00:00 -0500 + Subfield-algebraic geometry + https://arxiv.org/abs/2512.08975 + arXiv:2512.08975v1 Announce Type: new +Abstract: In this monograph, we lay the foundations for a new theory that generalizes real algebraic geometry. Let $R|K$ be a field extension, where $R$ is a real closed field and $K$ is an ordered subfield of $R$. The main objective is to study $K$-algebraic subsets of $R^n$, i.e., those subsets of $R^n$ that are the zero loci of polynomials with coefficients in $K$. Real algebraic geometry already covers the case when $K$ is also a real closed field. Our goal is to extend real algebraic geometry to the case when $K$ is not real closed, for example when $K$ is the field $\mathbb{Q}$ of rational numbers. Several new geometric phenomena appear. + There is no complex counterpart to this generalized real algebraic geometry. The reason is as follows. If $C|K$ is a field extension with $C$ algebraically closed and $X$ is a $K$-algebraic subset of $C^n$, then Hilbert's Nullstellensatz implies that the ideal of polynomials with coefficients in $C$ that vanish on~$X$ is generated by the ideal of polynomials with coefficients in $K$ that vanish on $X$. In the real realm, this is false in general, for example when we consider field extensions $R|K$ with $R$ real closed and $K=\mathbb{Q}$. + This monograph also presents some applications of the theory developed. Here is an example. The celebrated Nash-Tognoli theorem states that every compact smooth manifold $M$ is diffeomorphic to a nonsingular real algebraic set $M'$, called algebraic model of $M$. The theory developed here provides the theoretical basis to prove that the algebraic model $M'$ of $M$ can be chosen to be $\mathbb{Q}$-algebraic and $\mathbb{Q}$-nonsingular. This guarantees for the first time that, up to smooth diffeomorphisms, every compact smooth manifold can be encoded both globally and locally involving only finitely many exact data. + oai:arXiv.org:2512.08975v1 + math.AG + math.AC + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Ghaura Mahabaduge + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Jos\'e F. Fernando, Riccardo Ghiloni - The higher-order Henneberg-type minimal surfaces family in $\mathbb{R}^4$ - https://arxiv.org/abs/2512.07852 - arXiv:2512.07852v1 Announce Type: new -Abstract: We consider a higher-order Henneberg-type minimal surfaces family using the generalized Weierstrass--Enneper representation in four-dimensional space $\mathbb{R}^4$. We derive explicit parametric equations for the surface and determine its differential geometric characteristics, including the normal vector fields $\mathbf{n}_1$ and $\mathbf{n}_2$, as well as the Gauss curvature. Furthermore, by projecting these parametric forms from four to three dimensions, we generate visualizations that reveal the geometric structure of the Henneberg-type minimal surface. In addition, we examine the integral-free form and derive the corresponding algebraic function for this family of surfaces. - oai:arXiv.org:2512.07852v1 - math.DG - Wed, 10 Dec 2025 00:00:00 -0500 + Growth, Distortion, Pre-Schwarzian and Schwarzian norm estimates for Generalized Robertson class + https://arxiv.org/abs/2512.08993 + arXiv:2512.08993v1 Announce Type: new +Abstract: This paper investigates the geometric properties of functions within the generalized Robertson class which consists of alpha-starlike functions of order beta. The study's significance lies in providing a deeper understanding of the univalence and geometric behavior of these functions, which are fundamental in complex analysis and geometric function theory. The primary objective is to derive sharp bounds for the norms of the Schwarzian and pre-Schwarzian derivatives for functions in this class. These bounds are expressed in terms of the initial coefficient of the function, specifically focusing on the important case where this initial coefficient is zero. Additionally, the paper establishes sharp distortion and growth theorems for the functions belonging to this generalized class. Finally, the research addresses the radius problem for this function class by determining the sharp radius of concavity and the sharp radius of convexity. + oai:arXiv.org:2512.08993v1 + math.CV + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Erhan G\"uler, Magdalena Toda + Molla Basir Ahamed, Rajesh Hossain - Mixed Exponential Statistical Structures and Their Approximation Operators - https://arxiv.org/abs/2512.07870 - arXiv:2512.07870v1 Announce Type: new -Abstract: The paper examines the construction and analysis of a new class of mixed exponential statistical structures that combine the properties of stochastic models and linear positive operators.The relevance of the topic is driven by the growing need to develop a unified theoretical framework capable of describing both continuous and discrete random structures that possess approximation properties. The aim of the study is to introduce and analyze a generalized family of mixed exponential statistical structures and their corresponding linear positive operators, which include known operators as particular cases. We define auxiliary statistical structures B and H through differential relations between their elements, and construct the main Phillips-type structure. Recurrent relations for the central moments are obtained, their properties are established, and the convergence and approximation accuracy of the constructed operators are investigated. The proposed approach allows mixed exponential structures to be viewed as a generalization of known statistical systems, providing a unified analytical and stochastic description. The results demonstrate that mixed exponential statistical structures can be used to develop new classes of positive operators with controllable preservation and approximation properties. The proposed methodology forms a basis for further research in constructing multidimensional statistical structures, analyzing operators in weighted spaces, and studying their asymptotic characteristics. - oai:arXiv.org:2512.07870v1 - math.ST - stat.TH - Wed, 10 Dec 2025 00:00:00 -0500 + Irreducible Polynomials with Coefficients in an Affine Algebraic Set + https://arxiv.org/abs/2512.08994 + arXiv:2512.08994v1 Announce Type: new +Abstract: In this paper, we give error bounds on the number of monic irreducible polynomials $a_0+a_1x+\dots+a_{n-1}x^{n-1}+x^n$ over a finite field $\mathbb{F}_q$ of degree $n$ with $(a_0, a_1, \dots, a_{n-1}, 1)$ lying in a fixed affine algebraic set $V$ of points in $\mathbb{F}_q^{n+1}$. + oai:arXiv.org:2512.08994v1 + math.NT + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Yurii Volkov, Oleksandr Volkov + Neil Kolekar - On the discrete to continuous condensing aggregation equation: A weak convergence approach - https://arxiv.org/abs/2512.07883 - arXiv:2512.07883v1 Announce Type: new -Abstract: In this article, we study the passage of limits from discrete to continuous condensing aggregation equation which comprises of Oort-Hulst-Safronov (OHS) equation together with inverse aggregation process. We establish the relation between discrete and continuous condensing aggregation equations in its most generalized form, where kinetic-kernels with respect to OHS and inverse aggregation equations are not always equal. Convergence criterion is proved under suitable a priori estimates by approximating the continuous equation through a sequence of discrete equations, which subsequently converges towards the solution of the continuous equation by weak compactness principles. Existence of solution to the discrete model and uniform bounds on different order moments over finite time under particular conditions on kinetic-kernels are investigated. We analyze long-time dynamics and blowup of the solution leading to mass-loss or gelation for specific kernels. Three numerical experiments show the accuracy and convergence of approximated solutions to the exact solution of the continuous equation when $\varepsilon$ approaches zero. - oai:arXiv.org:2512.07883v1 - math.AP - cs.NA - math.FA - math.NA - Wed, 10 Dec 2025 00:00:00 -0500 + On the Zeros of $q$-Hankel Transform by Using P\'{o}lya-Hurwitz Partial Fraction Method + https://arxiv.org/abs/2512.09002 + arXiv:2512.09002v1 Announce Type: new +Abstract: The technique of P\'{o}lya-Hurwitz of partial fractions is implemented to investigate the zeros of finite $q$-Hankel transforms, which are defined in terms of the third $q$-Bessel function of Jackson. The new approach, which is a $q$-counterpart of P\'{o}lya-Hurwitz technique relaxes the restrictive conditions imposed on $q$ in the previously obtained results. In the present study, we use the $q$-type sampling theorems of the $q$-Hankel transforms, which lead directly to $q$-partial fractions. Various experimental examples are established. + oai:arXiv.org:2512.09002v1 + math.NT + math.CV + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Anupama Ghorai, Jitraj Saha + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Mahmoud Annaby, Shimaa Elsayed-Abdullah - Generalized Interlacing Families: New Error Bounds for CUR Matrix Decompositions - https://arxiv.org/abs/2512.07903 - arXiv:2512.07903v1 Announce Type: new -Abstract: This paper introduces the concept of generalized interlacing families of polynomials, which extends the classical interlacing polynomial method to handle polynomials of varying degrees. We establish a fundamental property for these families, proving the existence of a polynomial with a desired degree whose smallest root is greater than or equal to the smallest root of the expected polynomial. Applying this framework to the generalized CUR matrix approximation problem, we derive a theoretical upper bound on the spectral norm of a residual matrix, expressed in terms of the largest root of the expected polynomial. We then explore two important special cases: the classical CUR matrix decompositions and the row subset selection problem. For classical CUR matrix decompositions, we derive an explicit upper bound for the largest root of the expected polynomial. This yields a tighter spectral norm error bound for the residual matrix compared to many existing results. Furthermore, we present a deterministic polynomial-time algorithm for solving the classical CUR problem under certain matrix conditions. For the row subset selection problem, we establish the first known spectral norm error bound. This paper extends the applicability of interlacing families and deepens the theoretical foundations of CUR matrix decompositions and related approximation problems. - oai:arXiv.org:2512.07903v1 - math.RA - math.CO - math.FA - math.OA - Wed, 10 Dec 2025 00:00:00 -0500 + A note on lower bounds for numerical series + https://arxiv.org/abs/2512.09004 + arXiv:2512.09004v1 Announce Type: new +Abstract: This note shows that the three theorems presented in J. Math. Anal. Appl. 556 (2026), 130199, whose proofs, in their present formulation, are purely formal, follow from elementary calculus. + oai:arXiv.org:2512.09004v1 + math.CA + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jian-Feng Cai, Zhiqiang Xu, Zili Xu + R. \'Alvarez-Nodarse, K. Castillo - Inverse coefficient problem for a fully fractional diffusion equation with nonlinear and source nonlocal initial condition - https://arxiv.org/abs/2512.07914 - arXiv:2512.07914v1 Announce Type: new -Abstract: In this work, we consider an inverse problem of determining a time dependent coefficient in a fully fractional diffusion equation with a nonlinear source term. The nonlocal initial-boundary value problem refers to the forward model: the fractional diffusion equation equipped with a nonlocal initial condition and homogeneous Dirichlet boundary conditions. We first establish the existence and uniqueness of the mild solution to this nonlocal initial boundary value problem, together with the corresponding regularity properties of the solution. These results are obtained via the Fourier method, tools from fractional calculus, and key properties of the Mittag-Leffler function. - Subsequently, by applying a fixed-point argument in suitable Sobolev spaces, we prove a theorem on the local existence and uniqueness of the solution to the inverse problem. In this way, we establish the well-posedness of the problem solution. - oai:arXiv.org:2512.07914v1 - math.AP - Wed, 10 Dec 2025 00:00:00 -0500 + BISTRO - A Bi-Fidelity Stochastic Gradient Framework using Trust-Regions for Optimization Under Uncertainty + https://arxiv.org/abs/2512.09055 + arXiv:2512.09055v1 Announce Type: new +Abstract: Stochastic optimization of engineering systems is often infeasible due to repeated evaluations of a computationally expensive, high-fidelity simulation. Bi-fidelity methods mitigate this challenge by leveraging a cheaper, approximate model to accelerate convergence. Most existing bi-fidelity approaches, however, exploit either design-space curvature or random-space correlation, not both. We present BISTRO - a BI-fidelity Stochastic Trust-Region Optimizer for unconstrained optimization under uncertainty through a stochastic approximation procedure. This approach exploits the curvature information of a low-fidelity objective function to converge within a basin of a local minimum of the high-fidelity model where low-fidelity curvature information is no longer valuable. The method then switches to a variance-reduced stochastic gradient descent procedure. We provide convergence guarantees in expectation under certain regularity assumptions and ensure the best-case $\mathcal{O}(1/n)$ convergence rate for stochastic optimization. On benchmark problems and a 20-dimensional space shuttle reentry case, BISTRO converges faster than adaptive sampling and variance reduction procedures and cuts computational expense by up to 29x. + oai:arXiv.org:2512.09055v1 + math.OC + stat.CO + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - D. K. Durdiev, H. H. Turdiev + Thomas O. Dixon, Geoffrey F. Bomarito, James E. Warner, Alex A. Gorodetsky - Non-cycle triple planes with branch curve of degree at most 10 - https://arxiv.org/abs/2512.07965 - arXiv:2512.07965v1 Announce Type: new -Abstract: In this paper we classify normal non--cyclic triple covers of $\bbP^2$ with branch curve of degree at most 10. - oai:arXiv.org:2512.07965v1 - math.AG - Wed, 10 Dec 2025 00:00:00 -0500 + Cyqlone: A Parallel, High-Performance Linear Solver for Optimal Control + https://arxiv.org/abs/2512.09058 + arXiv:2512.09058v1 Announce Type: new +Abstract: We present Cyqlone, a solver for linear systems with a stage-wise optimal control structure that fully exploits the various levels of parallelism available in modern hardware. Cyqlone unifies algorithms based on the sequential Riccati recursion, parallel Schur complement methods, and cyclic reduction methods, thereby minimizing the required number of floating-point operations, while allowing parallelization across a user-configurable number of processors. Given sufficient parallelism, the solver run time scales with the logarithm of the horizon length (in contrast to the linear scaling of sequential Riccati-based methods), enabling real-time solution of long-horizon problems. Beyond multithreading on multi-core processors, implementations of Cyqlone can also leverage vectorization using batched linear algebra routines. Such batched routines exploit data parallelism using single instruction, multiple data (SIMD) operations, and expose a higher degree of instruction-level parallelism than their non-batched counterparts. This enables them to significantly outperform BLAS and BLASFEO for the small matrices that arise in optimal control. Building on this high-performance linear solver, we develop CyQPALM, a parallel and optimal-control-specific variant of the QPALM quadratic programming solver. It combines the parallel and vectorized linear algebra operations from Cyqlone with a parallel line search and parallel factorization updates, resulting in order-of-magnitude speedups compared to the state-of-the-art HPIPM solver. Open-source C++ implementations of Cyqlone and CyQPALM are available at https://github.com/kul-optec/cyqlone + oai:arXiv.org:2512.09058v1 + math.OC + cs.SY + eess.SY + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Ciro Ciliberto, Rick Miranda + Pieter Pas, Panagiotis Patrinos - Trim resolutions, stringy and Mather classes, and IC characteristic cycles - https://arxiv.org/abs/2512.07967 - arXiv:2512.07967v1 Announce Type: new -Abstract: We introduce trim resolutions of complex algebraic varieties, a strengthening of the notion of small resolution. We prove that the characteristic cycle of the intersection cohomology sheaf of a variety admitting a trim resolution is irreducible and that for such varieties the stringy and Chern-Mather classes coincide. - oai:arXiv.org:2512.07967v1 - math.AG - Wed, 10 Dec 2025 00:00:00 -0500 + Congruence permutability in quasivarieties + https://arxiv.org/abs/2512.09064 + arXiv:2512.09064v1 Announce Type: new +Abstract: It is shown that a natural notion of congruence permutability for quasivarieties already implies ``being a variety''. The result follows immediately from [3] and the sole aim of this note is to state it explicitly, together with a telegraphic proof. + oai:arXiv.org:2512.09064v1 + math.LO + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Paolo Aluffi + Luca Carai, Miriam Kurtzhals, Tommaso Moraschini - On the rational $C_2$-homotopy type of ${BSU_{\mathbb{R}}}_m$ - https://arxiv.org/abs/2512.07982 - arXiv:2512.07982v1 Announce Type: new -Abstract: Motivated by a problem in motivic homotopy theory considered by Asok-Fasel-Hopkins, we give a description of the rational $C_2$-equivariant homotopy type of the classifying space ${BSU_{\mathbb{R}}}_m$ in terms of equivariant Eilenberg-Maclane spaces. - oai:arXiv.org:2512.07982v1 - math.AT - Wed, 10 Dec 2025 00:00:00 -0500 + Geometric invariants and the Monge-Ampere equation in K\"ahler geometry + https://arxiv.org/abs/2512.09068 + arXiv:2512.09068v1 Announce Type: new +Abstract: This is a contribution to the special issue of Surveys in Differential Geometry celebrating the 75th birthday of Shing-Tung Yau. The bulk of the paper is devoted to a survey of some new geometric inequalities and estimates for the Monge-Ampere equation, obtained by the authors in the last few years in joint work with F. Tong, J. Song, and J. Sturm. These all depend in an essential way on Yau's solution of the Calabi conjecture, which is itself nearing its own 50th birthday. The opportunity is also taken to survey briefly many current directions in complex geometry, which he more recently pioneered. + oai:arXiv.org:2512.09068v1 + math.DG + math.AP + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Eunice Sukarto + Bin Guo, Duong H. Phong - On germs of mappings $\mathbb C^2\to\mathbb C^2$ - https://arxiv.org/abs/2512.07986 - arXiv:2512.07986v1 Announce Type: new -Abstract: We describe germs of mappings $(\mathbb{C}^2,0) \to (\mathbb{C}^2,0)$ ramified along a germ of irreducible curve whose image is of the form $x^p=y^q$. - oai:arXiv.org:2512.07986v1 - math.AG - Wed, 10 Dec 2025 00:00:00 -0500 + Negative Moments of Steinhaus Sums + https://arxiv.org/abs/2512.09077 + arXiv:2512.09077v1 Announce Type: new +Abstract: We prove a sharp upper bound on negative moments of sums of independent Steinhaus random variables (that is uniform on circles in the plane). Together with the series of earlier works: K\"onig-Kwapie\'n (2001), \mbox{Baernstein~II}--Culverhouse (2002), and K\"onig (2014), this closes the investigation of sharp $L_p-L_2$ Khinchin-type inequalities for the Steinhaus sums. Incidentally, we fix a mistake in an earlier paper, as well as provide an application to sharp bounds on R\'enyi entropy. + oai:arXiv.org:2512.09077v1 + math.PR + math.FA + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - S. Yu. Orevkov + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Martin Rapaport, Tomasz Tkocz, Isabella Wu - On Schauder Estimates for Fractional Hamilton-Jacobi Equations - https://arxiv.org/abs/2512.07999 - arXiv:2512.07999v1 Announce Type: new -Abstract: We prove Schauder estimates $\unicode{x2013}$ optimal regularity estimates in H\"older spaces $\unicode{x2013}$ and well-posedness results for mild and classical solutions of fractional Hamilton-Jacobi equations with subcritical nonlocal diffusions in $\mathbb{R}^d$. Due to an interplay between the regularity of the initial data and the growth of the Hamiltonian in the gradient, we focus on two canonical cases: (i) Lipschitz initial data and general Hamiltonians that are H\"older in space and merely locally Lipschitz in the gradient, and (ii) H\"older initial data and Hamiltonians that are H\"older in space and locally Lipschitz with power growth in the gradient. We compute explicit blow-up rates for $C^1$ and higher order H\"older norms as $t \to 0$. The results include short time and long time existence for mild solutions, optimal regularity in H\"older spaces and corresponding Schauder a priori estimates, and that smooth mild solutions are classical solutions. - oai:arXiv.org:2512.07999v1 - math.AP - Wed, 10 Dec 2025 00:00:00 -0500 + A classification of reduction types of curves + https://arxiv.org/abs/2512.09082 + arXiv:2512.09082v1 Announce Type: new +Abstract: The aim of this paper is to classify reduction types of algebraic curves. Reduction types capture the discrete invariants of fibres in one-dimensional families of curves, and they have been described in genus 1, 2 and 3. For fixed genus g>1, they form finitely many families, and we explain how to construct them, and introduce a naming convention. + oai:arXiv.org:2512.09082v1 + math.AG + math.NT + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Espen Robstad Jakobsen, Robin {\O}stern Lien, Artur Rutkowski + Tim Dokchitser - Relationship between the value-sharing behavior of an entire function and its derivative, and the analytic structure of a nonlinear differential equation - https://arxiv.org/abs/2512.08001 - arXiv:2512.08001v1 Announce Type: new -Abstract: In this paper, we study uniqueness problems for entire functions that partially share two values with their higher-order derivatives. The results obtained here both improve and generalize the related results of Li and Yi \cite{LYi}, L\"{u} et al. \cite{LXY1} and Sauer and Schweizer \cite{SS1}. Furthermore, we show that our results reveal a deep relationship between the value-sharing behavior of an entire function $f$ and its $k$-th derivative $f^{(k)}$, and the analytic structure of a particular type of nonlinear differential equation. Several examples are provided to illustrate the necessity of the conditions used in our results. - oai:arXiv.org:2512.08001v1 - math.CV - Wed, 10 Dec 2025 00:00:00 -0500 + Reactive Vehicle Guidance using Dynamic Maneuvering Cue + https://arxiv.org/abs/2512.09083 + arXiv:2512.09083v1 Announce Type: new +Abstract: Recent approaches for navigating among dynamic threat regions (i.e., weapon engagement zones) have focused on planning entire trajectories. Moreover, the allowance for penetration into these threat regions was based on heuristic measurements of risk. This paper offers an approach for a more reactive (i.e., feedback-based) guidance that is based on closed-form analytical expressions and thereby suitable for onboard, real-time execution. In addition, a risk measurement is formulated based upon the concept of Dynamic Maneuvering Cue (DMC) which measures the amount of turn a vehicle would need to take in its current state in order to put itself outside the threat region. This approach is then extended to handle multiple threat regions simultaneously (with minimal additional computational complexity). Finally, the DMC constraint is applied to a simple feedback controller as well as a model predictive controller (MPC). The MPC shows better performance but at the cost of having to solve an optimization problem online versus the meager computational burden associated with the simple controller. This approach, which is based on assuming the threats are adversarial, may be used as a conservative method for collision avoidance and deconfliction. + oai:arXiv.org:2512.09083v1 + math.OC + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Junfeng Xu, Sujoy Majumder, Lata Mahato + http://creativecommons.org/licenses/by-nc-nd/4.0/ + Alexander Von Moll, Isaac Weintraub - The limit joint distributions of some statistics used in testing the quality of random number generators - https://arxiv.org/abs/2512.08002 - arXiv:2512.08002v1 Announce Type: new -Abstract: The limit joint distribution of statistics that are generalizations of some statistics from the NIST STS, TestU01, and other packages is found under the following hypotheses $H_0$ and $H_1$. Hypothesis $H_0$ states that the tested sequence is a sequence of independent random vectors with a known distribution, and the simple alternative hypothesis $H_1$ converges in some sense to $H_0$ with increasing sample size. In addition, an analogue of the Berry-Esseen inequality is obtained for the statistics under consideration, and conditions for their asymptotic independence are found. - oai:arXiv.org:2512.08002v1 - math.ST - stat.AP - stat.TH - Wed, 10 Dec 2025 00:00:00 -0500 + A posteriori error estimates for mixed-dimensional Darcy flow using non-matching grids + https://arxiv.org/abs/2512.09087 + arXiv:2512.09087v1 Announce Type: new +Abstract: In this article, we extend the a posteriori error estimates for hierarchical mixed-dimensional elliptic equations developed in [Varela et al., J. Numer. Math., 48 (2023), pp. 247-280] to the setting of non-matching mixed-dimensional grids. The extension is achieved by introducing transfer grids between the planar subdomain and interface grids, together with stable discrete projection operators for primal (potential) and dual (flux) variables. The proposed non-matching estimators remain fully guaranteed and computable. Numerical experiments, including three-dimensional problems based on community benchmarks for incompressible Darcy flow in fractured porous media, demonstrate reliable performance of the estimators for the non-matching grids and effectivity that is comparable to the estimators for matching grids. + oai:arXiv.org:2512.09087v1 + math.NA + cs.NA + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - M. P. Savelov + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Jhabriel Varela, Christian E. Schaerer, Eirik Keilegavlen, Inga Berre - Structure Theorems (and Fast Algorithms) for List Recovery of Subspace-Design Codes - https://arxiv.org/abs/2512.08017 - arXiv:2512.08017v1 Announce Type: new -Abstract: List recovery of error-correcting codes has emerged as a fundamental notion with broad applications across coding theory and theoretical computer science. Folded Reed-Solomon (FRS) and univariate multiplicity codes are explicit constructions which can be efficiently list-recovered up to capacity, namely a fraction of errors approaching $1-R$ where $R$ is the code rate. - Chen and Zhang and related works showed that folded Reed-Solomon codes and linear codes must have list sizes exponential in $1/\epsilon$ for list-recovering from an error-fraction $1-R-\epsilon$. These results suggest that one cannot list-recover FRS codes in time that is also polynomial in $1/\epsilon$. In contrast to such limitations, we show, extending algorithmic advances of Ashvinkumar, Habib, and Srivastava for list decoding, that even if the lists in the case of list-recovery are large, they are highly structured. In particular, we can output a compact description of a set of size only $\ell^{O((\log \ell)/\epsilon)}$ which contains the relevant list, while running in time only polynomial in $1/\epsilon$ (the previously known compact description due to Guruswami and Wang had size $\approx n^{\ell/\epsilon}$). We also improve on the state-of-the-art algorithmic results for the task of list-recovery. - oai:arXiv.org:2512.08017v1 - cs.IT - cs.CC - math.IT - Wed, 10 Dec 2025 00:00:00 -0500 + A Taxonomy of Numerical Differentiation Methods + https://arxiv.org/abs/2512.09090 + arXiv:2512.09090v1 Announce Type: new +Abstract: Differentiation is a cornerstone of computing and data analysis in every discipline of science and engineering. Indeed, most fundamental physics laws are expressed as relationships between derivatives in space and time. However, derivatives are rarely directly measurable and must instead be computed, often from noisy, potentially corrupt data streams. There is a rich and broad literature of computational differentiation algorithms, but many impose extra constraints to work correctly, e.g. periodic boundary conditions, or are compromised in the presence of noise and corruption. It can therefore be challenging to select the method best-suited to any particular problem. Here, we review a broad range of numerical methods for calculating derivatives, present important contextual considerations and choice points, compare relative advantages, and provide basic theory for each algorithm in order to assist users with the mathematical underpinnings. This serves as a practical guide to help scientists and engineers match methods to application domains. We also provide an open-source Python package, PyNumDiff, which contains a broad suite of methods for differentiating noisy data. + oai:arXiv.org:2512.09090v1 + math.NA + cs.CE + cs.NA + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Rohan Goyal, Venkatesan Guruswami + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Pavel Komarov, Floris van Breugel, J. Nathan Kutz - Lines on K3-sextics with simple singularities - https://arxiv.org/abs/2512.08018 - arXiv:2512.08018v1 Announce Type: new -Abstract: We advance our understanding of the configurations of low degree smooth rational curves on (quasi-)polarized complex K3-surfaces. We apply our efficient approach to classify the configurations of at least 36 lines on K3-sextics with at worst A-D-E singularities. As an unexpected outcome of the further analysis of configurations of lines, we characterize a certain class of infinite dihedral groups of birational automorphisms of K3-sextics. Besides, we show that no K3-sextic can contain a Kummer configuration of lines, and we give a complete account of the line configurations on closest analogue of Kummer K3-octics or quartics, viz. the so-called Humbert K3-sextics. - oai:arXiv.org:2512.08018v1 - math.AG - Wed, 10 Dec 2025 00:00:00 -0500 + Local Banach Space Theoretic Approach to Bohr's Theorem for Vector Valued Holomorphic and Pluriharmonic Functions + https://arxiv.org/abs/2512.09091 + arXiv:2512.09091v1 Announce Type: new +Abstract: We study Bohr's theorem for vector valued holomorphic and operator valued pluriharmonic functions on complete Reinhardt domains in $\mathbb{C}^n$. Using invariants from local Banach space theory, we show that the associated Bohr radius is always strictly positive and obtain its asymptotic behavior separately in the finite- and infinite-dimensional settings. The framework developed here includes the classical Minkowski-space setting as a special case and applies to a wide class of Banach sequence spaces, including mixed Minkowski, Lorentz, and Orlicz spaces. We further establish a coefficient-type Schwarz-Pick lemma for operator valued pluriharmonic maps on complete Reinhardt domains. + oai:arXiv.org:2512.09091v1 + math.CV + math.FA + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Alex Degtyarev, S{\l}awomir Rams + Himadri Halder - Thurston's asymmetric metric on Margulis spacetimes - https://arxiv.org/abs/2512.08019 - arXiv:2512.08019v1 Announce Type: new -Abstract: In this article, we extend Thurston's asymmetric metric and the associated Finsler norm, originally defined for Teichm\"uller space, to the setting of Margulis spacetimes. We also establish several convexity properties of both the asymmetric metric and the corresponding Finsler norm. - oai:arXiv.org:2512.08019v1 - math.GT - math.DS - math.GR - Wed, 10 Dec 2025 00:00:00 -0500 + On Weighted Arboricity: Conductance-Resistance Bounds and Monoid Structure + https://arxiv.org/abs/2512.09096 + arXiv:2512.09096v1 Announce Type: new +Abstract: We study a conductance-weighted Nash--Williams density for a finite simple undirected graph $G=(V,E,c)$ with a conductance assignment $c:E\to[0,\infty)$: \[ A_c(G):=\max\bigl\{ D_c(H): H\subseteq G\text{ connected}, |V(H)|\ge 2 \bigr\},\qquad D_c(H):=\frac{\sum_{e\in E(H)}c(e)}{|V(H)|-1}. \] This functional reduces to the classical Nash--Williams density when $c\equiv 1$, isomorphism invariant, monotone under subgraphs and edge additions, positively homogeneous, and convex. We prove sharp global bounds \[ \max_{e\in E}c(e)\le A_c(G)\le\sum_{e\in E}c(e), \] with attainment by some connected subgraph. On the analytic side, we introduce a local variant and derive conductance--resistance inequalities using effective resistances in the ambient network. If $R_G(e)$ denotes the effective resistance between the endpoints of $e$ in $G$, we show that every connected $H\subseteq G$ satisfies \[ \sum_{e\in E(H)}c(e)\,R_G(e)\le |V(H)|-1, \] which in turn yields the Cauchy--Schwarz inequality \[ D_c(H)\le\sqrt{\frac{\sum_{e\in E(H)}c(e)/R_G(e)}{|V(H)|-1}} \] and hence an explicit resistance-based upper bound on $A_c(G)$. On the structural side, we describe the algebraic behavior of $A_c(G)$. We show that under edge-disjoint union, $A_c(G)$ behaves as a max invariant: for a finite disjoint union of weighted graphs one has $A_c(G)= \max_i A_{c_i}(G_i)$. In particular, disjoint union induces a commutative idempotent monoid structure at the level of isomorphism classes, with $A_c(G)$ idempotent with respect to this operation. + oai:arXiv.org:2512.09096v1 + math.CO + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Krishnendu Gongopadhyay, Neelanjan Mondal + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Rowan Moxley - Progress on Albertson's Conjecture - https://arxiv.org/abs/2512.08020 - arXiv:2512.08020v1 Announce Type: new -Abstract: Albertson conjectured that every graph with chromatic number $r$ has crossing number at least the crossing number of the complete graph $K_r$. This conjecture was proved for $r\le 12$ by Albertson, Cranston, and Fox; for $r\le 16$ by Bar\'{a}t and T\'{o}th; and for $r\le 18$ by Ackerman. Here we verify it for $r\le 24$; we also greatly restrict the possibilities for counterexamples when $r\in\{25,26\}$. In addition, we strengthen earlier work bounding the order of a minimum counterexample for each choice of $r$: we exclude the possibility that $|G|\ge 2.82r$ and exclude the possibility that $1.228r\le |G|\le 1.768r$. Finally, as $r$ grows, we extend the lower end of this range of excluded orders for a minimum counterexample. In particular: if $r\ge 125{,}000$, then we exclude the possibility that $1.10r\le |G|\le 1.768r$; and if $r\ge 825{,}000$, then we exclude the possibility that $1.05r\le |G|\le 1.768r$. - oai:arXiv.org:2512.08020v1 - math.CO - Wed, 10 Dec 2025 00:00:00 -0500 + Weyl-Type and Witt-Type Algebras with Exponential Generators:Structure, Automorphisms, and Representation Theory + https://arxiv.org/abs/2512.09102 + arXiv:2512.09102v1 Announce Type: new +Abstract: This paper introduces and systematically studies a new class of non-commutative algebras -- Weyl-type and Witt-type algebras -- generated by differential operators with exponential and generalized power function coefficients. We define the expolynomial ring $R_{p,t,\mathcal{A}} = \mathbb{F}\bigl[ e^{\pm x^{p} e^{t}},\; e^{\mathcal{A} x},\; x^{\mathcal{A}} \bigr]$ associated to an additive subgroup $\mathcal{A} \subset \mathbb{F}$, and investigate its Ore extension $A_{p,t,\mathcal{A}} = R_{p,t,\mathcal{A}}[\partial; \delta]$ (Weyl-type) and its derivation algebra $\mathfrak{g}_{p,t,\mathcal{A}} = \operatorname{Der}_{\mathbb{F}}(R_{p,t,\mathcal{A}})$ (Witt-type). Our main results establish: (1) the automorphism group of $R_{p,t,\mathcal{A}}$ is isomorphic to $(\mathbb{F}^{\times})^{2r+1} \rtimes \operatorname{GL}(2r+1,\mathbb{Z})$; (2) a Galois descent theorem showing that fixed-point subalgebras under finite Galois actions recover the original Weyl-type algebra; (3) the non-existence of finite-dimensional simple modules for $A_{p,t,\mathcal{A}}$; (4) the Zariski density of isomorphism classes in moduli spaces as transcendental parameters vary; (5) the stability of simplicity under generic quantum deformation; and (6) a complete representation-theoretic framework including the classification of irreducible weight modules, the construction of Harish--Chandra modules with BGG-type resolutions, and the structure of category $\mathcal{O}$. These results unify and extend classical theories of Weyl algebras, Witt algebras, and generalized Weyl algebras, while opening new directions in deformation theory, non-commutative geometry, and the representation theory of infinite-dimensional algebras. + oai:arXiv.org:2512.09102v1 + math.RA + math.QA + math.RT + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Daniel W. Cranston + http://creativecommons.org/licenses/by-nc-sa/4.0/ + Mohammad H. M Rashid - Non-density of nodal lines in the clamped plate problem - https://arxiv.org/abs/2512.08030 - arXiv:2512.08030v1 Announce Type: new -Abstract: We show that, in contrast to the case of Laplace eigenfunctions, the nodal set of high energy eigenfunctions of the clamped plate problem is not necessarily dense, and can in fact exhibit macroscopic "nodal voids". Specifically, we show that there are small deformations of the unit disk admitting a clamped plate eigenfunction of arbitrarily high frequency that does not vanish in a disk of radius 0.44. - oai:arXiv.org:2512.08030v1 - math.AP - math.SP - Wed, 10 Dec 2025 00:00:00 -0500 + SURA: Secure Unsourced Random Access + https://arxiv.org/abs/2512.09104 + arXiv:2512.09104v1 Announce Type: new +Abstract: This work introduces security for unsourced random access (URA) by employing wiretap-inspired physical layer techniques. To achieve confidentiality, the proposed system opportunistically exploits intrinsic features of feedback-aided URA without adding any overhead or altering its original structure or operational characteristics. As a result, the proposed system preserves the low-cost advantages of URA, including low delay and minimal signaling overhead, while providing secure communication. To secure transmission, each user generates a secret key and an artificial noise sequence from the feedback signal that the BS broadcasts in previous transmission rounds. This feedback depends on the BS-user channel, making it a private signal for each user. The secure transmission is performed by three actions: encrypting the data using the secret key, sending only the parity bits of the LDPC encoded secret key to allow the legitimate receiver to recover it, and masking these parity bits with the artificial noise. For reception, a receiver algorithm is designed for the legitimate user, and a leakage analysis is provided to quantify the information available to the eavesdropper. The simulation results show that meaningful secrecy is achieved in URA without modifying its structure and with negligible impact on standard performance. + oai:arXiv.org:2512.09104v1 + cs.IT + math.IT + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Alberto Enciso, Josef Greilhuber + Mohammad Javad Ahmadi, Rafael F. Schaefer, H. Vincent Poor - Expectations in Expectation Propagation - https://arxiv.org/abs/2512.08034 - arXiv:2512.08034v1 Announce Type: new -Abstract: Expectation Propagation (EP) is a widely used message-passing algorithm that decomposes a global inference problem into multiple local ones. It approximates marginal distributions (beliefs) using intermediate functions (messages). While beliefs must be proper probability distributions that integrate to one, messages may have infinite integral values. In Gaussian-projected EP, such messages take a Gaussian form and appear as if they have "negative" variances. Although allowed within the EP framework, these negative-variance messages can impede algorithmic progress. - In this paper, we investigate EP in linear models and analyze the relationship between the corresponding beliefs. Based on the analysis, we propose both non-persistent and persistent approaches that prevent the algorithm from being blocked by messages with infinite integral values. - Furthermore, by examining the relationship between the EP messages in linear models, we develop an additional approach that avoids the occurrence of messages with infinite integral values. - oai:arXiv.org:2512.08034v1 - cs.IT - eess.SP - math.IT - stat.CO - Wed, 10 Dec 2025 00:00:00 -0500 + On Event-Triggered Extremum Seeking via Standard and Lie-Bracket Averaging: A Hybrid Dynamical Systems Approach + https://arxiv.org/abs/2512.09113 + arXiv:2512.09113v1 Announce Type: new +Abstract: We introduce and analyze the stability of a class of event-triggered extremum-seeking algorithms designed to solve resource-aware, model-free, optimization problems. Leveraging recent advances in Lie-Bracket Averaging for hybrid systems, we demonstrate that the proposed controllers can be formulated as well-posed multi-time-scale hybrid systems that satisfy key regularity, stability, and robustness properties. In extremum-seeking systems, exploration and exploitation are inherently coupled. This coupling necessitates careful consideration in the design of the event-triggered controller. To address this challenge, we incorporate a low-pass filter into the algorithm and carefully design the flow and jump sets of the resulting hybrid system. The resulting controller renders the optimal point semi-globally practically asymptotically stable with solutions exhibiting a uniform semi-global dwell time. We also demonstrate how the proposed event-triggered scheme can be modified to allow analysis using traditional averaging tools for hybrid systems by introducing two independent tunable parameters in the controller. Numerical simulations are presented to validate and illustrate the theoretical results. + oai:arXiv.org:2512.09113v1 + math.OC + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Zilu Zhao, Fangqing Xiao, Dirk Slock + http://creativecommons.org/licenses/by/4.0/ + Mahmoud Abdelgalil, Jorge I. Poveda - Free Boundary Problem for inhomogeneous Navier-Stokes equations - https://arxiv.org/abs/2512.08039 - arXiv:2512.08039v1 Announce Type: new -Abstract: We study free boundary problems for incompressible inhomogeneous flows governed by the Navier--Stokes equations, focusing on the regularity and global-in-time well-posedness of solutions in critical functional frameworks for small initial data. - We introduce a novel analytical framework for free boundary problems formulated as perturbations of the half-space. Our approach relies on the natural Lagrangian change of coordinates and a detailed analysis of the linearized problem (the Stokes system) in the maximal regularity regime, formulated in the Lebesgue spaces $L_p(0,T; L_q)$, including time-weighted variants. The main difficulty lies in the treatment of boundary terms, for which we apply a new technique based on complex interpolation to control nonlinear terms in fractional Sobolev spaces. This strategy also allows us to handle the case of variable density, which is not easily addressed by approaches based on Besov spaces. - Using this framework and real interpolation techniques, we construct also solutions in the Lorentz class $L_{p,1}(0,T; L_q)$ in time. The method further enables a rigorous study of the stability of equilibrium configurations. In particular, we resolve the problem in two spatial dimensions, where the interplay between geometry and regularity is especially subtle. Beyond these specific applications, the proposed approach provides a powerful tool for broader classes of nonlinear PDEs and further developments in maximal regularity theory. - oai:arXiv.org:2512.08039v1 - math.AP - Wed, 10 Dec 2025 00:00:00 -0500 + High Order Numerical Methods Preserving Invariant Domain for Hyperbolic and Related Systems + https://arxiv.org/abs/2512.09116 + arXiv:2512.09116v1 Announce Type: new +Abstract: Admissible states in hyperbolic systems and related equations often form a convex invariant domain. Numerical violations of this domain can lead to loss of hyperbolicity, resulting in illposedness and severe numerical instabilities. It is therefore crucial for numerical schemes to preserve the invariant domain to ensure both physically meaningful solutions and robust computations. For complex systems, constructing invariant-domain-preserving (IDP) schemes is highly nontrivial and particularly challenging for high-order accurate methods. This paper presents a comprehensive survey of IDP schemes for hyperbolic and related systems, with a focus on the most popular approaches for constructing provable IDP schemes. We first give a systematic review of the fundamental approaches for establishing the IDP property in first-order accurate schemes, covering finite difference, finite volume, finite element, and residual distribution methods. Then we focus on two widely used and actively developed classes of high order IDP schemes as well as their recent developments, most of which have emerged in the past decade. The first class of methods seeks an intrinsic weak IDP property in high-order schemes and then designs polynomial limiters to enforce a strong IDP property at the points of interest. This generic approach applies to high-order finite volume and discontinuousGalerkin schemes. The second class is based on the flux limiting approaches, which originated from the flux-corrected transport method and can be adapted to a broader range of spatial discretizations, including finite difference and continuous finite element methods. In this survey, we elucidate the main ideas in the construction of IDP schemes, provide some new perspectives and insights, with extensive examples, and numerical experiments in gas dynamics and magnetohydrodynamics. + oai:arXiv.org:2512.09116v1 + math.NA + astro-ph.IM + cs.NA + physics.comp-ph + physics.flu-dyn + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Piotr B. Mucha, Tomasz Piasecki, Yoshihiro Shibata + Kailiang Wu, Xiangxiong Zhang, Chi-Wang Shu - Two Non--Commutative U(1)-Gauge Laplacians in the Quantum Hyperboloid - https://arxiv.org/abs/2512.08041 - arXiv:2512.08041v1 Announce Type: new -Abstract: In this paper, we will characterize the spectrum of two non--commutative U(1)-gauge Laplacians on the upper sheet of a two--sheet quantum hyperboloid. - oai:arXiv.org:2512.08041v1 - math.QA - Wed, 10 Dec 2025 00:00:00 -0500 + A Hybrid Neural Network-Finite Element Method for the Viscous-Plastic Sea-Ice Model + https://arxiv.org/abs/2512.09118 + arXiv:2512.09118v1 Announce Type: new +Abstract: We present an efficient hybrid Neural Network-Finite Element Method (NN-FEM) for solving the viscous-plastic (VP) sea-ice model. The VP model is widely used in climate simulations to represent large-scale sea-ice dynamics. However, the strong nonlinearity introduced by the material law makes VP solvers computationally expensive, with the cost per degree of freedom increasing rapidly under mesh refinement. High spatial resolution is particularly required to capture narrow deformation bands known as linear kinematic features in viscous-plastic models. To improve computational efficiency in simulating such fine-scale deformation features, we propose to enrich coarse-mesh finite element approximations with fine-scale corrections predicted by neural networks trained with high-resolution simulations. The neural network operates locally on small patches of grid elements, which is efficient due to its relatively small size and parallel applicability across grid patches. An advantage of this local approach is that it generalizes well to different right-hand sides and computational domains, since the network operates on small subregions rather than learning details tied to a specific choice of boundary conditions, forcing, or geometry. The numerical examples quantify the runtime and evaluate the error for this hybrid approach with respect to the simulation of sea-ice deformations. Applying the learned network correction enables coarser-grid simulations to achieve qualitatively similar accuracy at approximately 11 times lower computational cost relative to the high-resolution reference simulations. Moreover, the learned correction accelerates the Newton solver by up to 10% compared to runs without the correction at the same mesh resolution. + oai:arXiv.org:2512.09118v1 + math.NA + cs.NA + physics.comp-ph + physics.flu-dyn + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by-sa/4.0/ - Gustavo Amilcar Salda\~na Moncada + Nils Margenberg, Carolin Mehlmann - Spectrally symmetric orientations of graphs - https://arxiv.org/abs/2512.08049 - arXiv:2512.08049v1 Announce Type: new -Abstract: The Hermitian adjacency matrices of digraphs based on the sixth root of unity were introduced in [B. Mohar, A new kind of Hermitian matrices for digraphs, Linear Alg. Appl. (2020)]. They appear to be the most natural choice for the spectral theory of digraphs. Undirected graphs have adjacency spectrum symmetric about 0 if and only if they are bipartite. The situation is more complex for the Hermitian spectra of digraphs. In this paper we study non-bipartite oriented graphs with symmetric Hermitian spectra. Our main result concerns the extremal problem of maximizing the density of spectrally symmetric oriented graphs. The maximum possible density is shown to be between 13/18} and 10/11. Furthermore, we give a necessary condition for an oriented graph to be spectrally symmetric based on the adjacency spectrum of the underlying graph. This allows us to show that line graphs of sufficiently dense graphs do not admit spectrally symmetric orientations. We also show how to construct infinite families of spectrally symmetric graphs using 1-sums. - oai:arXiv.org:2512.08049v1 - math.CO - Wed, 10 Dec 2025 00:00:00 -0500 + Tightness and solidity in fragments of Peano Arithmetic + https://arxiv.org/abs/2512.09120 + arXiv:2512.09120v1 Announce Type: new +Abstract: It was shown by Visser that Peano Arithmetic has the property that any two bi-interpretable extensions of it (in the same language) are equivalent. Enayat proposed to refer to this property of a theory as tightness and to carry out a more systematic study of tightness and its stronger variants that he called neatness and solidity. Enayat proved that not only $\mathrm{PA}$, but also $\mathrm{ZF}$ and $\mathrm{Z}_2$ are solid. On the other hand, it was shown in later work by a number of authors that many natural proper fragments of those theories are not even tight. Enayat asked whether there is a proper solid subtheory of the theories listed above. We answer that question in the case of $\mathrm{PA}$ by proving that for every $n$, there exist both a solid theory and a tight but not neat theory strictly between $\mathrm{I}\Sigma_{n}$ and $\mathrm{PA}$. Moreover, the solid subtheories of $\mathrm{PA}$ can be required to be unable to interpret $\mathrm{PA}$. We also obtain some other separations between properties related to tightness, for example by giving an example of a sequential theory that is neat but not semantically tight in the sense of Freire and Hamkins. + oai:arXiv.org:2512.09120v1 + math.LO + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Saieed Akbari, Jonathan Aloni, Maxwell Levit, Bojan Mohar, Steven Xia + http://creativecommons.org/licenses/by/4.0/ + Piotr Gruza, Leszek Aleksander Ko{\l}odziejczyk, Mateusz {\L}e{\l}yk - Normal forms in a neighborhood of hyperbolic periodic orbits for flows in dimension 3 - https://arxiv.org/abs/2512.08051 - arXiv:2512.08051v1 Announce Type: new -Abstract: In a neighborhood of a hyperbolic periodic orbit of a volume-preserving flow on a manifold of dimension 3, we define and show the existence of a normal form for the generator of the flow that encodes the dynamics. If the flow is a contact flow, we show the existence of a normal form for the contact form what results in an improved normal form for its Reeb vector field. Additionally, we present a few rigidity results associated to periodic data for Anosov contact flows derived from the underlying normal form theory. Finally, we establish a new local rigidity result for contact flows on manifolds of dimension 3 in a neighborhood of a hyperbolic periodic point by finding a new link between the roof function and the return map to a section. - oai:arXiv.org:2512.08051v1 - math.DS - math.SG - Wed, 10 Dec 2025 00:00:00 -0500 + Fisher-Hartwig asymptotics for non-Hermitian random matrices + https://arxiv.org/abs/2512.09123 + arXiv:2512.09123v1 Announce Type: new +Abstract: We prove the two-dimensional analogue of the asymptotics for Toeplitz determinants with Fisher-Hartwig singularities, for general real symbols. This formula has applications to random normal matrices with complex spectra: (i) the characteristic polynomial converges to a Gaussian multiplicative chaos random measure on the limiting droplet, in the subcritical phase; (ii) the electric potential converges pointwise to a logarithmically correlated field; (iii) the measure of its level sets (i.e. thick points) is identified; (iv) the associated free energy undergoes a freezing transition. + This establishes emergence of the Liouville quantum gravity measure from free fermions in 2d, and universality with respect to the external potential. + oai:arXiv.org:2512.09123v1 + math.PR + math-ph + math.CA + math.FA + math.MP + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Alena Erchenko, Kurt Vinhage, Yun Yang - - - Online Ramsey turnaround numbers - https://arxiv.org/abs/2512.08053 - arXiv:2512.08053v1 Announce Type: new -Abstract: The online Ramsey turnaround game is a game between two players, Builder and Painter, on a board of $n$ vertices using $3$ colors, for a fixed graph $H$ on at most $n$ vertices. The goal of Painter is to force a monochromatic copy of $H$, the goal of Builder is to avoid this as long as possible. In each round of the game, Builder exposes one new edge and is allowed to forbid the usage of one color for Painter to color this newly exposed edge, and Painter colors the edge according to this restriction. The game is over as soon as Painter manages to achieve a monochromatic copy of $H$. For sufficiently large $n$, we consider the smallest number $f(n, H)$ of edges so that Painter can always win after $f(n, H)$ edges have been exposed by Builder. In addition, we define $f(H)$ to be the smallest $n$ such that Painter can always win on a clique with $n$ vertices. We give bounds for both functions and show that this problem is closely related to other concepts in extremal graph theory, such as polychromatic colorings, set-coloring Ramsey numbers, chromatic Ramsey numbers, and 2-color Tur\'an numbers. - oai:arXiv.org:2512.08053v1 - math.CO - Wed, 10 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - N\'ora Alm\'asi, Maria Axenovich + Paul Bourgade, Guillaume Dubach, Lisa Hartung, Ahmet Keles - Wieferich and Mersenne primes for function fields - https://arxiv.org/abs/2512.08060 - arXiv:2512.08060v1 Announce Type: new -Abstract: We study properties of recently introduced Wieferich primes for Drinfeld modules, as their relation with Fermat equations and finitess or non-finiteness of their number. We also introduce Mersenne numbers for Drinfeld modules, and study the links between these two notions. - oai:arXiv.org:2512.08060v1 - math.NT - Wed, 10 Dec 2025 00:00:00 -0500 + Topological Obstructions to Shared Priors + https://arxiv.org/abs/2512.09124 + arXiv:2512.09124v1 Announce Type: new +Abstract: Given a finite collection of probability measures defined on subsets of a measurable space, how can we determine if they are compatible, in the sense that they can be realized as conditional distributions of a single probability measure on the full space? This formulation of the consistency problem for conditional probabilities is significant in Bayesian epistemology and probabilistic reasoning, as it describes the conditions under which a collection of agents can reach agreement by sharing information. We derive a necessary and sufficient condition under which joint compatibility is equivalent to pairwise compatibility. This condition is stated in terms of the cohomology of a simplicial complex constructed from the given probability measures, exposing a novel application of algebraic topology to Bayesian reasoning. + oai:arXiv.org:2512.09124v1 + math.PR + math.AT + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Alexis Lucas + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Owen D. Biesel, Colin McSwiggen, Ted Theodosopoulos, Michael G. Titelbaum - A tentative proposal towards an equivariant mirror symmetry for Hitchin systems - https://arxiv.org/abs/2512.08062 - arXiv:2512.08062v1 Announce Type: new -Abstract: Motivated by Aganagic's equivariant mirror symmetry for certain Coulomb branches of a $3d$ $\mathcal{N}= 4$ gauge quiver theory, we would like to propose a set of ideas towards an extension of Aganagic's proposal to Hitchin systems. At the end, there are two main points in our proposal; namely, that the equivariant mirror of the Hitchin systems should be a Landau-Ginzburg model (with twisted masses) and that the dichotomy between additive and multiplicative varieties in the context of mirror symmetry for Nakajima quiver varieties should be considered in the case of Hitchin systems. - oai:arXiv.org:2512.08062v1 - math.AG - math-ph - math.MP - Wed, 10 Dec 2025 00:00:00 -0500 + Second-Order $\Lambda$-Sets and Extensions to Non-Smooth, Hybrid, and Stochastic Optimal Control + https://arxiv.org/abs/2512.09126 + arXiv:2512.09126v1 Announce Type: new +Abstract: This paper develops a comprehensive extension of the $\Lambda$-set framework for optimal control, introducing second-order $\Lambda$-sets and generalizing the theory to non-smooth, hybrid, and stochastic hybrid systems. We first establish second-order necessary conditions that incorporate curvature information of the reachable set, providing refined optimality criteria that bridge classical second-variation methods with the geometric $\Lambda$-set approach. The framework is then extended to Filippov systems with discontinuous dynamics and to hybrid dynamical systems with state-dependent switching, yielding new necessary conditions for optimality in these settings. Furthermore, we introduce stochastic $\Lambda$-sets for systems subject to both continuous diffusion and discrete random switching, connecting the framework to Peng's stochastic maximum principle. Throughout the paper, detailed examples -- including nonholonomic systems, mechanical systems with friction, and stochastic temperature control -- illustrate the theoretical developments and demonstrate the practical applicability of the extended $\Lambda$-set theory. The results unify and generalize existing maximum principles, offering a powerful geometric tool for analyzing optimal control problems across a broad spectrum of system classes, from classical smooth systems to modern stochastic hybrid systems. + oai:arXiv.org:2512.09126v1 + math.OC + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/publicdomain/zero/1.0/ - John Alexander Cruz Morales + http://creativecommons.org/licenses/by-nc-sa/4.0/ + Mohammad H. M Rashid - Power loss for the Mizohata-Takeuchi conjecture on $C^k$ convex hypersurfaces - https://arxiv.org/abs/2512.08064 - arXiv:2512.08064v1 Announce Type: new -Abstract: We find a family of compact $C^k$ hypersurfaces where the local Mizohata-Takeuchi Conjecture fails with a power loss of $R^{\alpha}$ for any $\alpha<\frac{n-1}{n-1+k}$. Moreover, this family is dense in the $C^k$ topology, and so the local Mizohata-Takeuchi conjecture fails for many convex hypersurfaces. In particular, the local Mizohata-Takeuchi Conjecture fails with a power loss of $R^\alpha$ for any $\alpha<\frac{n-1}{n+1}$ for many $C^2$ convex hypersurfaces. This power matches the best known upper bound in a paper by Tony Carbery, Marina Iliopoulou and Hong Wang up to the endpoint. For the proof, our weight is positive definite as in the first author's recent $\log(R)$-loss counterexample, and our construction is based on a projection of a higher rank lattice. As a by-product, we also construct compact convex $C^2$ hypersurfaces whose rescaling contains many lattice points in any dimension. - oai:arXiv.org:2512.08064v1 - math.CA - Wed, 10 Dec 2025 00:00:00 -0500 + A non-Hopfian ascending HNN-extension of a finitely presented Hopfian group + https://arxiv.org/abs/2512.09135 + arXiv:2512.09135v1 Announce Type: new +Abstract: We find a non-Hopfian ascending HNN-extension of a finitely presented Hopfian group by providing an explicit construction. This result addresses an analogous question to the one posed by Sapir and Wise, which asks whether there is a non-residually finite ascending HNN-extension of a finitely presented residually finite group. Such an analogy is motivated by Mal'cev's result that every finitely generated residually finite group is Hopfian. + oai:arXiv.org:2512.09135v1 + math.GR + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Hannah Cairo, Ruixiang Zhang + Jan Kim, Junseok Kim, Yoonjin Lee - Shelah Ultrafilters - https://arxiv.org/abs/2512.08081 - arXiv:2512.08081v1 Announce Type: new -Abstract: In this paper, we study a special type of ultrafilter which we call Shelah ultrafilter. We show that it is possible to add a Shelah ultrafilter using a special forcing notion. We also show that Shelah ultrafilters turn out to be I-ultrafilters for many Borel ideals. - oai:arXiv.org:2512.08081v1 - math.LO - Wed, 10 Dec 2025 00:00:00 -0500 + On the Green's functions and Martin boundary structure of a planar diffusion in a discontinuous layered medium + https://arxiv.org/abs/2512.09136 + arXiv:2512.09136v1 Announce Type: new +Abstract: We consider a two-dimensional diffusion process in a two-layered plane, governed by distinct covariance matrices in the upper and lower half-planes and by two drift vectors pointed away from the $x$-axis. We first analyze the case where the generator of the process is in divergence form, that is, when the flux is continuous across the interface. Then we extend the study to a broader class of processes whose behavior at the interface forms an oblique two-dimensional analogue of the skew Brownian motion. + We provide a detailed theoretical analysis of this transient process. Our main results are as follows: (i) we derive explicit Laplace transforms of the Green's functions; (ii) we compute exact asymptotics of the Green's functions along all possible trajectories in the plane; (iii) We determine all positive harmonic functions, identifying the full and minimal Martin boundaries, which turn out to be distinct. The nonminimality of the Martin boundary is a noteworthy phenomenon for diffusions with regular coefficients. + To obtain an analytical description of the process, we fully develop a three-variable version of the so-called kernel method by deriving and exploiting a functional equation involving unknown Laplace transforms of Green's functions and two known kernels $\gamma_+(x,y)$ and $\gamma_{-}(x,z)$. The introduction of independent auxiliary variables $y$ and $z$, associated with each half-plane, is a key idea. + oai:arXiv.org:2512.09136v1 + math.PR + Thu, 11 Dec 2025 00:00:00 -0500 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Emmanuel Balderas, David Chodounsk\'y, Osvaldo Guzm\'an + http://creativecommons.org/licenses/by/4.0/ + Sandro Franceschi, Irina Kourkova, Maxence Petit - Generalizations of the Normalized Radon Cumulative Distribution Transform for Limited Data Recognition - https://arxiv.org/abs/2512.08099 - arXiv:2512.08099v1 Announce Type: new -Abstract: The Radon cumulative distribution transform (R-CDT) exploits one-dimensional Wasserstein transport and the Radon transform to represent prominent features in images. It is closely related to the sliced Wasserstein distance and facilitates classification tasks, especially in the small data regime, like the recognition of watermarks in filigranology. Here, a typical issue is that the given data may be subject to affine transformations caused by the measuring process. To make the R-CDT invariant under arbitrary affine transformations, a two-step normalization of the R-CDT has been proposed in our earlier works. The aim of this paper is twofold. First, we propose a family of generalized normalizations to enhance flexibility for applications. Second, we study multi-dimensional and non-Euclidean settings by making use of generalized Radon transforms. We prove that our novel feature representations are invariant under certain transformations and allow for linear separation in feature space. Our theoretical results are supported by numerical experiments based on 2d images, 3d shapes and 3d rotation matrices, showing near perfect classification accuracies and clustering results. - oai:arXiv.org:2512.08099v1 + Energy-Based Modeling and Structure-Preserving Discretization of Physical Systems + https://arxiv.org/abs/2512.09138 + arXiv:2512.09138v1 Announce Type: new +Abstract: This paper develops a comprehensive mathematical framework for energy-based modeling of physical systems, with particular emphasis on preserving fundamental structural properties throughout the modeling and discretization process. The approach provides systematic methods for handling challenging system classes including high-index differential-algebraic equations and nonlinear multiphysics problems. Theoretical foundations are established for regularizing constrained systems while maintaining physical consistency, analyzing stability properties, and constructing numerical discretizations that inherit the energy dissipation structure of the continuous models. The versatility and practical utility of the framework are demonstrated through applications across multiple domains including poroelastic media, nonlinear circuits, constrained mechanics, and phase-field models. The results ensure that essential physical properties such as energy balance and dissipation are maintained from the continuous formulation through to numerical implementation, providing robust foundations for computational physics and engineering applications. + oai:arXiv.org:2512.09138v1 math.NA - cs.CV - cs.IT cs.NA - math.IT - Wed, 10 Dec 2025 00:00:00 -0500 + math.DS + Thu, 11 Dec 2025 00:00:00 -0500 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Matthias Beckmann, Robert Beinert, Jonas Bresch + http://creativecommons.org/licenses/by-nc-sa/4.0/ + M. H. M Rashid - Locally Recoverable Codes with availability from a family of fibered surfaces - https://arxiv.org/abs/2512.08100 - arXiv:2512.08100v1 Announce Type: new -Abstract: We construct Locally Recoverable Codes (LRCs) with availability $2$ from a family of fibered surfaces. To obtain the locality and availability properties, and to estimate the minimum distance of the codes, we combine techniques coming from the theory of one-variable function fields and from the theory of fibrations on surfaces. When the locality parameter is $r=3$, we obtain a sharp bound on the minimum distance of the codes. In that case, we give a geometric interpretation of our codes in terms of doubly elliptic surfaces. In particular, this provides the first instance of an error correcting code constructed using a (doubly elliptic) K3 surface. - oai:arXiv.org:2512.08100v1 - math.AG - cs.IT - math.IT - Wed, 10 Dec 2025 00:00:00 -0500 + Domination of manifolds by hypersurfaces + https://arxiv.org/abs/2512.09146 + arXiv:2512.09146v1 Announce Type: new +Abstract: In this short note we prove that any smooth, closed, oriented manifold can be dominated by a codimension 1 submanifold of the sphere. + oai:arXiv.org:2512.09146v1 + math.GT + math.AT + math.DG + Thu, 11 Dec 2025 00:00:00 -0500 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Cec\'ilia Salgado, Lara Vicino + http://creativecommons.org/licenses/by-nc-sa/4.0/ + Vasilii Rozhdestvenskii - Isometric embeddings into $C(K)$-spaces doing stable phase retrieval - https://arxiv.org/abs/2512.08110 - arXiv:2512.08110v1 Announce Type: new -Abstract: Motivated by a question posed by Freeman, Oikhberg, Pineau and Taylor, we prove that if $K$ is a compact Hausdorff space with $K^{(\alpha)}\neq\varnothing$, where $2<\alpha<\omega$, then $C[1,\omega^\alpha]$ isometrically embeds into $C(K)$ doing stable phase retrieval (SPR). We also show that the latter cannot be extended to the case $\alpha=2$. - oai:arXiv.org:2512.08110v1 - math.FA - Wed, 10 Dec 2025 00:00:00 -0500 + Coexistence for Competing Branching Random Walks with Identical Asymptotic Shape on $\mathbb{Z}^d$ + https://arxiv.org/abs/2512.09153 + arXiv:2512.09153v1 Announce Type: new +Abstract: We consider two independent branching random walks that start next to each other on the $d$-dimensional hypercubic lattice and that carry two different colors. Vertices of the lattice are colored according to the color of the walker cloud that first visits the vertex, leading to the question of possible coexistence in the sense that both colors appear on infinitely many vertices. Under mild conditions, we prove the coexistence for two independently distributed branching random walks obeying the same first- and second-order behavior for their extremal particles. To complement this result, we also exhibit examples for the almost-sure absence of coexistence, for $d=1$, in cases where the asymptotic shapes of the walker clouds are calibrated to coincide, thereby answering a question by Deijfen and Vilkas (ECP 28(15):1-11, 2023). As a main tool we employ second-order and large-deviation approximations for the position of the extremal particles in one-dimensional branching random walks. + oai:arXiv.org:2512.09153v1 + math.PR + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Enrique Garc\'ia-S\'anchez, David de Hevia + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Partha Pratim Ghosh, Benedikt Jahnel - On the existence of large subspaces of $C(K)$ that perform stable phase retrieval - https://arxiv.org/abs/2512.08114 - arXiv:2512.08114v1 Announce Type: new -Abstract: The purpose of this article is to address an open problem posed by Freeman-Oikhberg-Pineau-T.~(\textit{Math.~Ann.}~2024) regarding the existence of large subspaces of $C(K)$ that perform stable phase retrieval (SPR). We begin by proving that for both the real and complex fields, the space $C(K)$ admits an infinite-dimensional SPR subspace if and only if the second Cantor-Bendixson derivative $K{''}$ is nonempty. We then show how to construct ``large" SPR subspaces of $C(K)$, where the size of the subspace depends quantitatively on the number of non-trivial Cantor-Bendixson derivatives that the compact Hausdorff space $K$ possesses. - oai:arXiv.org:2512.08114v1 - math.FA - Wed, 10 Dec 2025 00:00:00 -0500 + Constructive Proofs of Generalized Boole--Frechet Bounds: A Dynamic Programming Approach + https://arxiv.org/abs/2512.09161 + arXiv:2512.09161v1 Announce Type: new +Abstract: Extensions of the Boole--Frechet inequalities give sharp bounds for the probabilities of compound events, particularly when only the probabilities of atomic events (that make up the compound events) are known. We present a constructive approach to obtaining generalized Boole--Frechet bounds using dynamic programming. + oai:arXiv.org:2512.09161v1 + math.PR + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Enrique Garc\'ia-S\'anchez, David de Hevia, Mitchell Taylor + Kizito Salako - Some Difference Relations for Orthogonal Polynomials of a Continuous Variable in the Askey Scheme - https://arxiv.org/abs/2512.08119 - arXiv:2512.08119v1 Announce Type: new -Abstract: Orthogonal polynomials of a continuous variable in the Askey scheme satisfying second order difference equations, such as the Askey-Wilson polynomial, can be studied by the quantum mechanical formulation, idQM (discrete quantum mechanics with pure imaginary shifts). These idQM systems have the shape invariance property, which relates the Hilbert space $\mathsf{H}_{\lambda}$ ($\lambda$ : a set of parameters) and that with shifted parameters $\mathsf{H}_{\lambda+\delta}$ ($\delta$ : shift of $\lambda$), and gives the forward and backward shift relations for the orthogonal polynomials. Based on the forward shift relation and the Christoffel's theorem with some polynomial $\check{\Phi}(x)$, which is expressed in terms of the quantities appeared in the forward and backward shift relations, we obtain some difference relations for the orthogonal polynomials. The multiplication of $\sqrt{\check{\Phi}(x)}$ gives a surjective map from $\mathsf{H}_{\lambda+2\delta}$ to $\mathsf{H}_{\lambda}$. Similarly, for the orthogonal polynomials in the Askey scheme satisfying second order differential equations, such as the Jacobi polynomial, we obtain some differential relations, and the multiplication of $\sqrt{\check{\Phi}(x)}$ in this case gives a surjective map from $\mathsf{H}_{\lambda+\delta}$ to $\mathsf{H}_{\lambda}$. - oai:arXiv.org:2512.08119v1 - math-ph - hep-th - math.CA - math.MP - Wed, 10 Dec 2025 00:00:00 -0500 + The Uniform Random Walk on graphs, loop processes and graphings + https://arxiv.org/abs/2512.09166 + arXiv:2512.09166v1 Announce Type: new +Abstract: We define the Uniform Random Walk (URW) on a connected, locally finite graph as the weak limit of the uniform walk of length $n$ starting at a fixed vertex. When the limit exists, it is necessarily Markovian and is independent of the starting point. For a finite graph, URW equals the Maximal Entropy Random Walk (MERW). + We investigate the existence and phase transitions of URW for loop perturbed regular graphs and their limits. It turns out that for a sequence of finite graphs, it is the global spectral theory of the limiting graphing that governs the behavior of the finite MERWs. + In the delocalized phase, we use a "membrane argument", showing that the principal eigenfunction of an expander graphing is stable under a small diagonal perturbation. This gives us: 1) The existence of URW on leaves; 2) The URW is a unique entropy maximizer; 3) The MERW of a finite graph sequence Benjamini-Schramm converges to the URW of the limiting graphing. + In the localized phase, the environment seen by the particle takes the role of a finite stationary measure. We show that for canopy trees, the URW exists, is transient and maximizes entropy. We also show that for large finite graphs where most vertices have a fixed degree, localization of MERW is governed by the adjacency norm. + oai:arXiv.org:2512.09166v1 + math.PR + math.CO + math.DS + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Satoru Odake + Miklos Abert, Adam Arras, Jaelin Kim - Well-posedness of a novel Lagrange multiplier formulation for fluid-poroelastic interaction - https://arxiv.org/abs/2512.08142 - arXiv:2512.08142v1 Announce Type: new -Abstract: We introduce a novel monolithic formulation that employs Lagrange multipliers (LMs) to couple a fluid flow governed by the time-dependent Stokes equations with a poroelastic structure described by the Biot equations. The formulation is developed in detail, and we establish the well-posedness of both the semi-discrete and fully discrete saddle point problems. We further prove the stability of the fully discrete system. This saddle point formulation, which utilizes three LMs, is designed to enable a partitioned approach that completely decouples the Stokes and Biot subdomains, and this approach will be explored in a subsequent work. - oai:arXiv.org:2512.08142v1 - math.NA - cs.NA - Wed, 10 Dec 2025 00:00:00 -0500 + Planar $W^{1,\,1}$-extension domains + https://arxiv.org/abs/2512.09167 + arXiv:2512.09167v1 Announce Type: new +Abstract: We show that a bounded planar simply connected domain $\Omega$ is a $W^{1,\,1}$-extension domain if and only if for every pair $x,y$ of points in $\Omega^c$ there exists a curve $\gamma \subset \Omega^c$ connecting $x$ and $y$ with $$ \int_\gamma \frac{1}{\chi_{\mathbb R^2\setminus \partial\Omega}(z)}\,ds(z) \le C|x-y|.$$ Consequently, a planar Jordan domain $\Omega$ is a $W^{1,\,1}$-extension domain if and only if it is a $BV$-extension domain, and if and only if its complementary domain $\tilde \Omega$ is a $W^{1,\,\infty}$-extension domain. + oai:arXiv.org:2512.09167v1 + math.FA + math.CV + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Amy de Castro, Hyesuk Lee + Pekka Koskela, Tapio Rajala, Yi Ru-Ya Zhang - Adversarial Barrier in Uniform Class Separation - https://arxiv.org/abs/2512.08149 - arXiv:2512.08149v1 Announce Type: new -Abstract: We identify a strong structural obstruction to Uniform Separation in constructive arithmetic. The mechanism is independent of semantic content; it emerges whenever two distinct evaluator predicates are sustained in parallel and inference remains uniformly representable in an extension of HA. Under these conditions, any putative Uniform Class Separation principle becomes a distinguished instance of a fixed point construction. The resulting limitation is stricter in scope than classical separation barriers (Baker; Rudich; Aaronson et~al.) insofar as it constrains the logical form of uniform separation within HA, rather than limiting particular relativizing, naturalizing, or algebrizing techniques. - oai:arXiv.org:2512.08149v1 - math.LO - cs.CC - cs.LO - Wed, 10 Dec 2025 00:00:00 -0500 + Magic Gems: A Polyhedral Framework for Magic Squares + https://arxiv.org/abs/2512.09170 + arXiv:2512.09170v1 Announce Type: new +Abstract: We introduce Magic Gems, a geometric representation of magic squares as three-dimensional polyhedra. By mapping an n x n magic square onto a centered coordinate grid with cell values as vertical displacements, we construct a point cloud whose convex hull defines the Magic Gem. This reveals a connection between magic square constraints and statistical structure: we prove that magic squares have vanishing covariances between position and value. We introduce a covariance energy functional -- the sum of squared covariances with row, column, and diagonal indicator variables -- and prove for n=3 (via exhaustive enumeration) that its zeros are precisely the magic squares. Large-scale sampling for n=4,5 (460+ million arrangements) provides strong numerical evidence that this characterization extends to larger orders. Perturbation analysis demonstrates that magic squares are isolated local minima. The representation is invariant under dihedral symmetry D_4, yielding canonical geometric objects for equivalence classes. + oai:arXiv.org:2512.09170v1 + math.CO + cs.CG + cs.DM + math.MG + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Milan Rosko + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Kyle Elliott Mathewson - Noise sensitivity on virtually abelian groups - https://arxiv.org/abs/2512.08151 - arXiv:2512.08151v1 Announce Type: new -Abstract: We show that aperiodic random walks with finite second moment on virtually abelian groups are noise sensitive in total variation if and only if the group admits no nonzero homomorphism onto the infinite cyclic group. - oai:arXiv.org:2512.08151v1 - math.PR - math.GR - Wed, 10 Dec 2025 00:00:00 -0500 + On the analogue of Esperet's conjecture: Characterizing hereditary classes + https://arxiv.org/abs/2512.09176 + arXiv:2512.09176v1 Announce Type: new +Abstract: In the paper [J. Graph Theory (2023) 102:458-471, the Esperet's conjecture has been posed: Every $\chi$-bounded hereditary class is poly-$\chi$-bounded]. This conjecture was first posed in [Habilitation Thesis, Universit\'e Grenoble Alpes, 24, 2017]. This is adapted from the Gy\'arf\'as--Sumner's conjecture which has been asserted in [The Theory and Applications of Graphs, (G. Chartrand, ed.), John Wiley & Sons, New York, 1981, pp. 557-576]. + Although the Esperet's conjecture is false in general, in this study we consider an analogue of Esperet's conjecture as follows: Let $C$ be a hereditary class of graphs, and $d \ge 1$. Suppose that there is a function $f$ such that $\chi(G) \le f(\tau_d(G))$ for each $G \in C$. Can we always choose $f$ to be a polynomial? We investigate this conjecture by focusing on specific classes of graphs. This work identifies hereditary graph classes that do not contain specific induced subdivisions of claws and confirms that they adhere to the stated conjecture. + oai:arXiv.org:2512.09176v1 + math.CO + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Jeremie Brieussel, Ryokichi Tanaka + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + N. Rahimi, D. A. Mojdeh - Adaptive Matched Filtering for Sensing With Communication Signals in Cluttered Environments - https://arxiv.org/abs/2512.08157 - arXiv:2512.08157v1 Announce Type: new -Abstract: This paper investigates the performance of the adaptive matched filtering (AMF) in cluttered environments, particularly when operating with superimposed signals. Since the instantaneous signal-to-clutter-plus-noise ratio (SCNR) is a random variable dependent on the data payload, using it directly as a design objective poses severe practical challenges, such as prohibitive computational burdens and signaling overhead. To address this, we propose shifting the optimization objective from an instantaneous to a statistical metric, which focuses on maximizing the average SCNR over all possible payloads. Due to its analytical intractability, we leverage tools from random matrix theory (RMT) to derive an asymptotic approximation for the average SCNR, which remains accurate even in moderate-dimensional regimes. A key finding from our theoretical analysis is that, for a fixed modulation basis, the PSK achieves a superior average SCNR compared to QAM and the pure Gaussian constellation. Furthermore, for any given constellation, the OFDM achieves a higher average SCNR than SC and AFDM. Then, we propose two pilot design schemes to enhance system performance: a Data-Payload-Dependent (DPD) scheme and a Data-Payload-Independent (DPI) scheme. The DPD approach maximizes the instantaneous SCNR for each transmission. Conversely, the DPI scheme optimizes the average SCNR, offering a flexible trade-off between sensing performance and implementation complexity. Then, we develop two dedicated optimization algorithms for DPD and DPI schemes. In particular, for the DPD problem, we employ fractional optimization and the KKT conditions to derive a closed-form solution. For the DPI problem, we adopt a manifold optimization approach to handle the inherent rank-one constraint efficiently. Simulation results validate the accuracy of our theoretical analysis and demonstrate the effectiveness of the proposed methods. - oai:arXiv.org:2512.08157v1 - cs.IT - eess.SP - math.IT - Wed, 10 Dec 2025 00:00:00 -0500 + Characterization of Jordan Vectors of Operator-Valued Functions with Applications in Differential Equations + https://arxiv.org/abs/2512.09178 + arXiv:2512.09178v1 Announce Type: new +Abstract: A well-known characterization of Jordan vectors of a matrix polynomial $L(z)$ is generalized to a characterization of Jordan vectors of the operator-valued function $Q(z)$ at an eigenvalue $\alpha \in \mathbb{C}$. The results are then applied to solve a system of nonlinear ordinary differential equations. + oai:arXiv.org:2512.09178v1 + math.FA + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Lei Xie, Hengtao He, Yifeng Xiong, Fan Liu, Shi Jin + http://creativecommons.org/licenses/by-nc-nd/4.0/ + Muhamed Borogovac - Conditions for Equivalence of Random Interlacements and Random Walk Reflected off of Infinity - https://arxiv.org/abs/2512.08166 - arXiv:2512.08166v1 Announce Type: new -Abstract: On a transient weighted graph, there are two models of random walk which continue after reaching infinity: random interlacements, and random walk reflected off of infinity, recently introduced in arXiv:2506.18827 [math.PR]. We prove these two models are equivalent if and only if all harmonic functions of the underlying graph with finite Dirichlet energy are constant functions, or equivalently, the free and wired spanning forests coincide. In particular, examples where the models are equivalent include $\mathbb{Z}^d$, cartesian products, and many Cayley graphs, while examples that fail the condition include all transient trees. - oai:arXiv.org:2512.08166v1 - math.PR - Wed, 10 Dec 2025 00:00:00 -0500 + Stability, approximable quotients, and higher property (T) + https://arxiv.org/abs/2512.09180 + arXiv:2512.09180v1 Announce Type: new +Abstract: We construct a wealth of groups that are finitely presented, Frobenius stable, have property (T), but are very far from having property (T$_2$). Our method also shows that property (T$_2$) does not pass to quotients. + oai:arXiv.org:2512.09180v1 + math.GR + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Yao Yu + Francesco Fournier-Facio - Dual Smoothing for Decentralized Optimization - https://arxiv.org/abs/2512.08167 - arXiv:2512.08167v1 Announce Type: new -Abstract: Decentralized optimization is widely used in different fields of study such as distributed learning, signal processing, and various distributed control problems. In these types of problems, nodes of the network are connected to each other and seek to optimize some objective function. In this article, we present a method for smoothing the non-smooth and non-strongly convex problems. This is done using the dual smoothing technique. We study two types of problems: consensus optimization of linear models and coupled constraints optimization. It is shown that these two problem classes are dual to each other. - oai:arXiv.org:2512.08167v1 - math.OC - Wed, 10 Dec 2025 00:00:00 -0500 + Surfaces in 4-manifolds and complex curves + https://arxiv.org/abs/2512.09181 + arXiv:2512.09181v1 Announce Type: new +Abstract: These are lecture notes from a mini-course taught at Winterbraids XIII (Montpellier, 2024). The main character of these notes are curves in the complex projective plane, viewed from a topological perspective. + oai:arXiv.org:2512.09181v1 + math.GT + math.AG + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Alexander Rogozin, Nhat Trung Nguyen, Hamed Azami Zenuzagh, Alexander Gasnikov + Marco Golla - Billey-Postnikov posets, rationally smooth Schubert varieties, and Poincar\'e duality - https://arxiv.org/abs/2512.08168 - arXiv:2512.08168v1 Announce Type: new -Abstract: Billey-Postnikov (BP) decompositions govern when Schubert varieties $X(w)$ decompose as bundles of smaller Schubert varieties. We further develop the theory of BP decompositions and show that, in finite type, they can be recognized by pattern conditions and are indexed by the order ideals of a poset $\mathsf{bp}(w)$ that we introduce; we conjecture that this holds in any Coxeter group. We then apply BP decompositions to show that, when $X(w)$ is rationally smooth and $W$ simply laced, the Schubert structure constants $c_{uv}^w$ satisfy a triangularity property, yielding a canonical involution on the Schubert cells of $X(w)$ respecting Poincar\'{e} duality. We also classify the rationally smooth Bruhat intervals in finite type (other than $E$) which admit generalized Lehmer codes, answering questions and conjectures of Billey-Fan-Losonczy, Bolognini-Sentinelli, and Bishop-Mili\'{c}evi\'{c}-Thomas. Finally, we show that rationally smooth Schubert varieties in infinite type need not have Grassmannian BP decompositions, disproving conjectures of Richmond-Slofstra and Oh-Richmond. - oai:arXiv.org:2512.08168v1 - math.CO - math.AG - Wed, 10 Dec 2025 00:00:00 -0500 + The Farey tree and embeddings of lens spaces and rational balls in $\mathbb{CP}^2$ + https://arxiv.org/abs/2512.09183 + arXiv:2512.09183v1 Announce Type: new +Abstract: Motivated by a conjecture of Koll\'ar, we study embeddings of multiple rational homology balls in $\mathbb{CP}^2$. To each node of the Farey tree, we associate such an embedding of three rational homology balls with lens space boundary, extending earlier work of the second author and of Lisca and Parma, using a recursive Kirby calculus argument. We also give further explicit constructions of embeddings of triples of rational homology balls into homotopy $\mathbb{CP}^2$s. + oai:arXiv.org:2512.09183v1 + math.GT + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Christian Gaetz, Yibo Gao + Marco Golla, Brendan Owens - Large Excursions of Reflected L\'evy Processes: Asymptotic Shapes - https://arxiv.org/abs/2512.08171 - arXiv:2512.08171v1 Announce Type: new -Abstract: This paper primarily investigates the geometric properties of excursions of L\'evy processes reflected at the past infimum with long lifetime or large height. For an oscillating process in the domain of attraction of a stable law, our results state that excursions with a long lifetime need not have a large height. After a suitable scaling, they behave like stable excursions with lifetime or height greater than one. These extend the related results in Doney and Rivero [Prob. Theory Relat. Fields, 157(1) (2013) 1-45]. In contrast, for the negative-drift case we prove that under a heavy-tailed condition, long lifetime and large height are asymptotically equivalent. Conditioned on either event, excursions converge under spatial scaling to a single-jump process with Pareto-distributed jump size and size-biased jump time. Moreover, after a suitable time rescaling, the effect of the negative drift becomes apparent. - oai:arXiv.org:2512.08171v1 - math.PR - Wed, 10 Dec 2025 00:00:00 -0500 + Towards Esperet's Conjecture: Polynomial $\chi$-Bounds for Structured Graph Classes + https://arxiv.org/abs/2512.09186 + arXiv:2512.09186v1 Announce Type: new +Abstract: In this paper, we establish that the class of $\{P_6, (2,2)\text{-broom}\}$-free graphs contains a subclass $\mathcal{L}_i$, defined by certain cutset conditions, whose chromatic number admits a linear $\chi$-bound. Building on recent results showing that broom-free graphs excluding $K_d(t)$ as a subgraph admit a polynomial bound in~$t$ on their chromatic number (A broom is obtained from a path with one end $v$ by adding leaves adjacent to $v$), we extend this result to the hereditary class $\mathcal{H}$ of $C_4$-free and \emph{$p$-flag}-free graphs (where a \emph{$p$-flag} is a triangle with an attached $p$-path). We show that if $G \in \mathcal{H}$ is $B^{+}(p+2, t-1)$-free (for $p \ge 2$ and $t \ge 3$, that is, if it excludes a generalized broom with an additional leaf), and does not contain $K_d(t)$ as a subgraph, then $\chi(G)$ is polynomially bounded in $t$. Furthermore, for the subclass of $\mathcal{H}$ excluding $K_3(t)$ as a subgraph, we prove that $\chi(G)$ is linearly $\chi$-bounded in $\omega(G)$. + oai:arXiv.org:2512.09186v1 + math.CO + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Zhi-Hao Cui, Hao Wu, Wei Xu + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + N. Rahimi, D. A. Mojdeh - The Instability of Painlev\'e Equations in Recovering Largest Eigenvalue Distributions of GUE, LUE, JUE and an Attempt of Solution to It - https://arxiv.org/abs/2512.08178 - arXiv:2512.08178v1 Announce Type: new -Abstract: The distribution of the largest eigenvalue for the three classical unitary ensembles -- GUE, LUE, and JUE -- admits two complementary exact descriptions: (i) as Fredholm determinants of their orthogonal--polynomial correlation kernels and (ii) as isomonodromic $\tau$--functions governed by Painlev\'e equations. For finite $n$, the associated Jimbo--Miwa--Okamoto $\sigma$--forms are $\PIV$ (GUE), $\mathrm{PV}$ (LUE), and $\PVI$ (JUE); under soft- or hard-edge scalings these degenerate to $\PII$ or $\PIIIp$ descriptions of the Tracy--Widom and hard-edge laws \cite{tracy1994level,forrester2003painleve,deift1999orthogonal}. - It is well known among random matrix theorists (for example Folkmar Bornemann) that the Fredholm determinant is a more numerically stable and accurate way to compute the CDF of the largest eigenvalue for GUE, LUE, JUE than direct Painlev\'e integration. The aim of this paper is not to improve on Fredholm methods, but to see to what extent one can numerically recover the \emph{correct} Painlev\'e solution from finite-$n$ data and how unstable this reconstruction is. Numerically, we verify the equality between the Fredholm- and Painlev\'e-based CDFs by combining (a) high-accuracy Nystr\"om discretizations of the finite-$n$ Fredholm determinants \cite{bornemann2010numerical} with (b) an anchored, branch-locked integration of the $\sigma$--form ODEs, where anchors are extracted from local least-squares fits to $\log\det(I-\mathsf K)$. Our results confirm agreement across GUE/LUE/JUE with precision of $O(10^{-3})$ to $O(10^{-5})$ (occasionally $O(10^{-2})$) and illustrate the finite-$n$ to scaling-limit transition. The theoretical connections to $\tau$--functions and Virasoro constraints follow the framework of \cite{adler2000random,forrester2003painleve} - oai:arXiv.org:2512.08178v1 - math.NA - cs.NA - math.PR - Wed, 10 Dec 2025 00:00:00 -0500 + Integrality of Picard-Fuchs differential equations of Kobayashi geodesics and applications + https://arxiv.org/abs/2512.09188 + arXiv:2512.09188v1 Announce Type: new +Abstract: We prove that the holomorphic solutions of Picard-Fuchs differential equations associated with one-parameter families of abelian varieties with real multiplication admit power series expansions with $S$-integral coefficients at a maximal unipotent monodromy point. This extends classical integrality results for hypergeometric functions and Bouw-M\"oller's work on Teichm\"uller curves. The integral solutions are related to the non-ordinary locus of the modulo $p$ reduction of the family, whose cardinality we bound in terms of the Euler characteristic and Lyapunov exponents of the base curve. In some cases, the non-ordinary locus can be recovered by truncating the integral solutions, as in Igusa's classical observation for the Legendre family. We also establish $S$-integrality of expansions of modular forms at cusps in terms of a modular function for (not necessarily arithmetic) Fuchsian groups with modular embeddings, and deduce congruences. These results are applied in subsequent work to construct lifts of partial Hasse invariants for rational curves in Hilbert modular varieties. + oai:arXiv.org:2512.09188v1 + math.NT + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Haonan Gu + Gabriele Bogo - Notes on the multiplier systems of $\eta(\tau)$ and $\theta(\tau)$ - https://arxiv.org/abs/2512.08187 - arXiv:2512.08187v1 Announce Type: new -Abstract: The multiplier systems of $\eta^{2k}(\tau)$ and $\theta^{2k}(\tau)$ $(k\in\mathbb{Z})$ are characters. In this paper, we determine their kernels, Ker$\,\nu_{\eta^{2k}}$ and Ker$\,\nu_{ \theta^{2k} } $. - oai:arXiv.org:2512.08187v1 + Mixed moments of twisted $L$-functions + https://arxiv.org/abs/2512.09203 + arXiv:2512.09203v1 Announce Type: new +Abstract: We establish an asymptotic formula with a power-saving error term for the twisted mixed moment of Dirichlet $L$-functions and automorphic $L$-functions twisted by all primitive characters modulo $q$, valid for all admissible moduli. As a special case, this extends the asymptotic result of Blomer, Fouvry, Kowalski, Michel, and Mili\'cevi\'c to general moduli, achieving an error term as sharp as the best bound recently proved by Khan and Zhang for prime moduli. + oai:arXiv.org:2512.09203v1 math.NT - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Kazuhide Matsuda + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Zhenpeng Tang, Xiaosheng Wu - Classification of wormhole singularities - https://arxiv.org/abs/2512.08189 - arXiv:2512.08189v1 Announce Type: new -Abstract: We classify all wormhole singularities, i.e. cyclic quotient surface singularities admitting at least two extremal P-resolutions, thereby solving an open problem posed by Urz\'ua. Our approach introduces a new combinatorial framework based on what we call the coherent graph of a framed triangulated polygon. As an application, we give an alternative proof of the Hacking-Tevelev-Urz\'ua theorem on the maximum number of extremal P-resolutions of a cyclic quotient singularity. - oai:arXiv.org:2512.08189v1 - math.AG - math.CO - math.SG - Wed, 10 Dec 2025 00:00:00 -0500 + On the Uniqueness of Best Non-decreasing Approximation in Orlicz Spaces + https://arxiv.org/abs/2512.09210 + arXiv:2512.09210v1 Announce Type: new +Abstract: Given an approximately continuous function $f$ in an Orlicz space $L^\Phi([a,b]),$ for a suitable class of convex functions $\Phi,$ we employ a characterization of the best monotone approximation set to establish its continuity, which in turn yields the uniqueness property for the best monotone approximation in $L^\Phi([a,b]).$ + oai:arXiv.org:2512.09210v1 + math.FA + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jaime Negrete + Ana Benavente, Juan Costa Ponce, Sergio Favier - On the knot types of periodic Reeb orbits of dynamically convex contact forms - https://arxiv.org/abs/2512.08190 - arXiv:2512.08190v1 Announce Type: new -Abstract: We exhibit transverse knot types on the standard contact $3$-sphere that cannot be realized as periodic Reeb orbits of a dynamically convex contact form. In particular, such transverse knot types do not arise as closed characteristics of strictly convex energy levels on a four dimensional symplectic vector space. - oai:arXiv.org:2512.08190v1 - math.SG - Wed, 10 Dec 2025 00:00:00 -0500 + Strong confluence of geodesics in Liouville quantum gravity + https://arxiv.org/abs/2512.09219 + arXiv:2512.09219v1 Announce Type: new +Abstract: $\gamma$-Liouville quantum gravity ($\gamma$-LQG) constitutes a family of planar random geometries whose geodesics exhibit intricate fractal behaviour. As is observed in various planar models of random geometry as part of the phenomenon of geodesic confluence, geodesics in $\gamma$-LQG tend to merge with each other. In particular, in Gwynne-Miller '19, it was established that in $\gamma$-LQG, geodesics targeted to a fixed point do coalesce in the sense that any two such geodesics almost surely merge before reaching their common target. However, in view of the randomness inherent to the geometry, it is a priori possible that while geodesics targeted to a fixed point do coalesce, there exists a sequence of geodesics $P_n$ converging to an exceptional geodesic $P$ as $n\rightarrow \infty$ such that $P_n$ does not overlap with $P$ for any $n$. In this paper, we prove that this is not possible, thereby establishing a strong confluence statement for $\gamma$-LQG for all $\gamma\in (0,2)$. This extends the results obtained in Miller-Qian '20 for $\gamma=\sqrt{8/3}$ to all subcritical values of $\gamma$. We discuss applications to the study of geodesic stars and geodesic networks and include a list of open questions. + oai:arXiv.org:2512.09219v1 + math.PR + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Umberto L. Hryniewicz, Pedro A. S. Salom\~ao, Richard Siefring + Manan Bhatia, Konstantinos Kavvadias - The Locally Complexified-gentle Algebras - https://arxiv.org/abs/2512.08194 - arXiv:2512.08194v1 Announce Type: new -Abstract: We call an $\mathbb{R}$-algebra locally complexified-gentle if it becomes a locally gentle $\mathbb{C}$-algebra up to Morita equivalence after complexification. We use modulated quivers to introduce two types of locally complexified-gentle algebras and show that they are Morita equivalent to some semilinear clannish algebras. - oai:arXiv.org:2512.08194v1 - math.RT - math.RA - Wed, 10 Dec 2025 00:00:00 -0500 + $L_1$ and $L_2$ embeddings of the symmetric group + https://arxiv.org/abs/2512.09226 + arXiv:2512.09226v1 Announce Type: new +Abstract: We show that the Cayley graph of the symmetric group $Sym_n$ generated by the cycle $(123...n)$ and the transposition $(12)$ embeds into $L_1$ with bi-Lipschitz distortion $O(1)$. This answers a question of Ostrovskii, and along with Kassabov's theorem gives the first example of a sequence of groups which embed bi-Lipschitzly into $L_1$ for one choice of bounded size generating sets, but not for another choice of bounded size generating sets. In particular, the Cayley graphs generated by the cycle and the transposition cannot contain coarsely any unbounded sequence of expander graphs. Moreover, within the context of the Ribe program, they are a new example of bounded degree Cayley graphs which are test spaces for Rademacher type. + oai:arXiv.org:2512.09226v1 + math.MG + math.FA + math.GR + Thu, 11 Dec 2025 00:00:00 -0500 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jie Li, Chao Zhang + http://creativecommons.org/licenses/by/4.0/ + Cosmas Kravaris - Regularity for fully nonlinear degenerate parabolic equations with strong absorption - https://arxiv.org/abs/2512.08196 - arXiv:2512.08196v1 Announce Type: new -Abstract: In this paper, we investigate dead-core problems for fully nonlinear degenerate parabolic equations with strong absorption, \begin{equation*} - |Du|^{p} F(D^{2}u) - u_{t} = \lambda_{0}(x,t)\, u^{\mu}\, \chi_{\{u>0\}}(x,t) - \qquad \text{in } \quad Q_{T} := Q \times (0,T), \end{equation*} where $0 \leq p < \infty$ and $0 < \mu < 1$. We establish a sharp and improved parabolic $C^{\alpha}$-regularity estimate along the free boundary $\partial \{ u > 0 \}$, where \[ \alpha := \frac{2+p}{1+p-\mu} > 1 + \frac{1}{1+p}. \] Moreover, we establish weak geometric properties of solutions, such as non-degeneracy and uniform positive density. As an application, we obtain a Liouville-type theorem for entire solutions and gradient bounds. Finally, as a byproduct of our approach, we derive a novel $L^{\delta}$-average estimate for fully nonlinear singular elliptic equations and present a new formulation of the gradient decay property. It is worth noting that the results presented here extend those in da Silva {\it et al.} ({\it Pacific J. Math}., \textbf{300} (2019), 179--213) and ({\it J. Differential Equations}., \textbf{264} (2018), 7270--7293) to the degenerate setting, and can be viewed as a parabolic analogue of da Silva {\it et al.} ({\it Math. Nachr}., \textbf{294} (2021), 38--55) and Teixeira ({\it Math. Ann}., \textbf{364} (2016), 1121--1134). Additionally, of independent mathematical interest, we emphasize that our manuscript establishes a comparison principle result and the compactness of viscosity solutions to fully nonlinear degenerate parabolic models with continuous and bounded forcing terms. These compactness and comparison properties serve as key ingredients in deriving enhanced regularity estimates along free boundary points for our model problem with strong absorption. - oai:arXiv.org:2512.08196v1 - math.AP - Wed, 10 Dec 2025 00:00:00 -0500 + Anabelian aspects of the outer automorphism groups of the absolute Galois groups of mixed-characteristic local fields + https://arxiv.org/abs/2512.09231 + arXiv:2512.09231v1 Announce Type: new +Abstract: In the present paper, we study the outer automorphism groups of the absolute Galois groups of mixed-characteristic local fields from the point of view of anabelian geometry. In particular, we show that, under certain mild assumptions, the image of the natural homomorphism from the automorphism group of a mixed-characteristic local field to the outer automorphism group of the associated absolute Galois group is not a normal subgroup. Furthermore, we show that, for the absolute Galois group of a mixed-characteristic local field satisfying certain assumptions, there exist a continuous representation and a continuous automorphism of the group such that the former is irreducible, abelian, and crystalline, but the continuous representation obtained as the composite of the former with the latter is not even Hodge-Tate. + These results significantly generalize previous works by Hoshi and Nishio. A key observation in obtaining these results is to focus on the analogy between the mapping class groups of topological surfaces and the outer automorphism groups of the absolute Galois groups of mixed-characteristic local fields. To the best of the author's knowledge, this is the first work applying results from the theory of mapping class groups to the anabelian geometry of mixed-characteristic local fields, going beyond a mere analogy between the two. + oai:arXiv.org:2512.09231v1 + math.NT + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jo\~ao Vitor da Silva, Feida Jiang, Jiangwen Wang + Kaiji. Kondo - Unitarity of highest weight Harish-Chandra modules and smoothness of Schubert varieties - https://arxiv.org/abs/2512.08199 - arXiv:2512.08199v1 Announce Type: new -Abstract: Let $G_{\mathbb{R}}$ be a Lie group of Hermitian type, and $L(\lambda)$ a highest weight Harish-Chandra module of $G_{\mathbb{R}}$ with highest weight $\lambda$. In this article, we exhibit a bijection between the set of connected Dynkin subdiagrams containing the noncompact simple root and the set of unitary highest weight modules $L(-w\rho-\rho)$, where $\rho$ is half the sum of positive roots. We find that $L(-w\rho-\rho)$ is unitary if and only if the Schubert variety $X(w)$ is smooth. We also give the cardinality of the set of unitary highest weight modules $L(-w\rho-\rho)$ for each Kazhdan-Lusztig right cell. - oai:arXiv.org:2512.08199v1 - math.RT - math.CO - Wed, 10 Dec 2025 00:00:00 -0500 + Embedding into Leavitt algebra $L_K(1, 2)$ + https://arxiv.org/abs/2512.09241 + arXiv:2512.09241v1 Announce Type: new +Abstract: There is a unital homomorphism from every Bergman $K$-algebra corresponding to a conical commutative monoid with an order-unit into Leavitt algebra $L_K(1,2)$, where $K$ is a field. This will be used to give a short proof that Leavitt path algebras associated with graphs with condition $(L)$ embed into $L_K(1,2)$. We then show that the Heisenberg equation $xy-yx=1$ cannot be realized in any Steinberg algebra, implying that Weyl algebras can't be embedded in $L_K(1,2)$, giving an affirmative answer to a question of Brownlowe and Sorensen on the embeddability of $K$-algebras with a countable basis inside $L_K(1,2)$. + oai:arXiv.org:2512.09241v1 + math.RA + math.OA + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Zhanqiang Bai, William Q. Erickson, Markus Hunziker, Jing Jiang + Boris Bilich, Roozbeh Hazrat, Tran Giang Nam - A multivariate generalization of Hall's theorem for Edgeworth expansions of bootstrap distributions - https://arxiv.org/abs/2512.08200 - arXiv:2512.08200v1 Announce Type: new -Abstract: Theorem 5.1 in the monograph by Hall (1992) provides rigorous in-probability justification of Edgeworth expansions of bootstrap distributions. Proving this result was rather challenging because bootstrap distributions do not satisfy the classical Cram\'er condition and therefore classical methods for justifying Edgeworth expansions, e.g. Bhattacharya and Rao (1976) and Bhattacharya and Ghosh (1978), are not available. Hall's (1992) theorem is for a univariate statistic which can be expressed as a smooth function of means, though the underlying population can be multivariate. However, there are a number of applications where a multivariate version of Hall's theorem is needed, and generalizing the proof from the univariate case to the multivariate case is not immediate. Our primary purpose in this article is to fill this gap by stating a multivariate version of the theorem and sketching the modifications to the proof of Hall's (1992) Theorem 5.1 that are needed. - oai:arXiv.org:2512.08200v1 - math.ST - stat.TH - Wed, 10 Dec 2025 00:00:00 -0500 + On the largest prime factors of shifted semiprime numbers + https://arxiv.org/abs/2512.09245 + arXiv:2512.09245v1 Announce Type: new +Abstract: A natural number $n$ is called semi-prime if it is a product of two primes or a square of a prime. We denote $\mathbb{P}_2$ the set of all semi-primes. Our goal is to prove that for fixed integer number $a$ and sufficiently large $x$ the largest prime factor of number $$ \prod_{\substack{n\in \mathbb{P}_2\\n\leq x}}(n+a) $$ exceeds $x^{\theta}$, where $\theta= 0.5-\varepsilon,$ $0<\varepsilon\leq 0.01$ is arbitrarily small. + oai:arXiv.org:2512.09245v1 + math.NT + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Andrew T. A. Wood + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Do Duc Tam - Primal-dual policy learning for mean-field stochastic LQR problem - https://arxiv.org/abs/2512.08205 - arXiv:2512.08205v1 Announce Type: new -Abstract: Integrating data-driven techniques with mechanism-driven insights has recently gained popularity as a powerful learning approach to solving traditional LQR problems for designing intelligent controllers in complex dynamic systems. However, the theoretical understanding of various reinforcement learning algorithms needs further exploration to enhance their efficiency and safety. In this article, by means of primal-dual optimization tools, we study the partially model-free design of the mean-field stochastic LQR (MF-SLQR) controller using a policy learning approach. Firstly, by designing appropriate optimizing variables, the considered MF-SLQR problem is transformed into a new static nonconvex constrained optimization problem with equivalence preserved in certain senses. After that, the equivalent formulation of the duality results is constructed via finding the solution of the generalized Lyapunov equation. Then, the strong duality is analyzed, based on which we establish a primal-dual algorithm by Karush-Kuhn-Tucker conditions. More importantly, a partially model-free implementation is also presented, which has a direct connection with the classical policy iteration algorithm. Finally, we use a high-dimensional example to validate our methods. - oai:arXiv.org:2512.08205v1 + A Benamou-Brenier Proximal Splitting Method for Constrained Unbalanced Optimal Transport + https://arxiv.org/abs/2512.09250 + arXiv:2512.09250v1 Announce Type: new +Abstract: The dynamic formulation of optimal transport, also known as the Benamou-Brenier formulation, has been extended to the unbalanced case by introducing a source term in the continuity equation. When this source term is penalized based on the Fisher-Rao metric, the resulting model is referred to as the Wasserstein-Fisher-Rao (WFR) setting, and allows for the comparison between any two positive measures without the need for equalized total mass. In recent work, we introduced a constrained variant of this model, in which affine integral equality constraints are imposed along the measure path. In the present paper, we propose a further generalization of this framework, which allows for constraints that apply not just to the density path but also to the momentum and source terms, and incorporates affine inequalities in addition to equality constraints. We prove, under suitable assumptions on the constraints, the well-posedness of the resulting class of convex variational problems. The paper is then primarily devoted to developing an effective numerical pipeline that tackles the corresponding constrained optimization problem based on finite difference discretizations and parallel proximal schemes. Our proposed framework encompasses standard balanced and unbalanced optimal transport, as well as a multitude of natural and practically relevant constraints, and we highlight its versatility via several synthetic and real data examples. + oai:arXiv.org:2512.09250v1 math.OC - Wed, 10 Dec 2025 00:00:00 -0500 + cs.NA + math.NA + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Xiushan Jiang, Dong Wang, Weihai Zhang, Daniel W. C. Ho, Yuanqing Wu + Mao Nishino, Martin Bauer, Tom Needham, Nicolas Charon - Duct boundary conditions for incompressible fluid flows: finite element discretizations and parameter estimation in coronary blood flow - https://arxiv.org/abs/2512.08207 - arXiv:2512.08207v1 Announce Type: new -Abstract: 3D-0D coupled flow models are widely used across many application fields but remain challenging to solve. Implicit coupling introduces non-local terms, whereas explicit coupling results in only conditionally stable schemes. Furthermore, incorporating inertial effects alongside viscous resistance enlarges the parameter space, making calibration more difficult. - In this work, we propose a new type of boundary condition based on the method of asymptotic partial decomposition of a domain (MAPDD), which we denote as the Duct Boundary Condition (DuBC). This approach enables the incorporation of geometrically reduced domains as a boundary term with only local coupling in the implicit case. Moreover, the DuBC accounts for both viscous and inertial effects simultaneously using a single physical parameter. Additionally, we derive a fractional-step time-marching scheme including the DuBC. We demonstrate the features of the DuBC in coronary artery blood flow simulations, including sequential parameter estimation from noisy velocity data. - oai:arXiv.org:2512.08207v1 + Higher-order multi-scale computational method and its convergence analysis for hygro-thermo-mechanical coupling problems of quasi-periodic composite structures + https://arxiv.org/abs/2512.09281 + arXiv:2512.09281v1 Announce Type: new +Abstract: This paper proposes a novel higher-order multi-scale (HOMS) computational method, which is highly targeted for efficient, high-accuracy and low-computational-cost simulation of hygro-thermo-mechanical (H-T-M) coupling problems in quasi-periodic composite structures. The first innovation of this work is that the establishment of the high-accuracy multi-scale model incorporating the higher-order correction terms for H-T-M coupling problems of quasi-periodic composite structures. The second innovation of this work is that the error analyses in the point-wise and integral senses are rigorously derived for multi-scale asymptotic solutions. Especially from the point-wise error analysis, the primary impetus for current study to develop the HOMS approach for quasi-periodic composite structures is illustrated. Furthermore, an high-accuracy multi-scale numerical algorithm is developed based on finite element method, while corresponding convergent analysis is also obtained. Finally, extensive numerical experiments are conducted to validate the computational performance of the proposed HOMS computational approach, demonstrating not only exceptional numerical accuracy, but also reduced computational cost. + oai:arXiv.org:2512.09281v1 math.NA cs.NA - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Jerem\'ias Garay, David Nolte, Crist\'obal Bertoglio + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Hao Dong, Yifei Ding, Jiale Linghu, Yufeng Nie, Yaochuang Han - Strict Elimination of Double Traversals in Outer Subaisles and Two-Block Rectangular Warehouses - https://arxiv.org/abs/2512.08235 - arXiv:2512.08235v1 Announce Type: new -Abstract: The order picking problem seeks the shortest warehouse route that visits all required item locations. Strict conditions are known for single-block rectangular layouts under which optimal routes never require double traversals, while broader results show they are avoidable only when cross-aisle connectivity is present. We strengthen these findings by proving that no double traversals are needed in the upper or lower subaisles of warehouses with at least two aisles, establishing strict conditions for both single and two-block layouts. - oai:arXiv.org:2512.08235v1 - math.OC - Wed, 10 Dec 2025 00:00:00 -0500 + Fast operator learning for mapping correlations + https://arxiv.org/abs/2512.09286 + arXiv:2512.09286v1 Announce Type: new +Abstract: We propose a fast, optimization-free method for learning the transition operators of high-dimensional Markov processes. The central idea is to perform a Galerkin projection of the transition operator to a suitable set of low-order bases that capture the correlations between the dimensions. Such a discretized operator can be obtained from moments corresponding to our choice of basis without curse of dimensionality. Furthermore, by exploiting its low-rank structure and the spatial decay of correlations, we can obtain a compressed representation with computational complexity of order $\mathcal{O}(dN)$, where $d$ is the dimensionality and $N$ is the sample size. We further theoretically analyze the approximation error of the proposed compressed representation. We numerically demonstrate that the learned operator allows efficient prediction of future events and solving high-dimensional boundary value problems. This gives rise to a simple linear algebraic method for high-dimensional rare-events simulations. + oai:arXiv.org:2512.09286v1 + math.NA + cs.NA + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - George Dunn, Elizabeth Stojanovski, Bishnu Lamichhane, Hadi Charkhgard, Ali Eshragh + Yuehaw Khoo, Yuguan Wang, Siyao Yang - The $L$-polynomial of hyperelliptic function fields and its applications - https://arxiv.org/abs/2512.08250 - arXiv:2512.08250v1 Announce Type: new -Abstract: Let $\ell$ be an odd prime, $q$ an odd prime power such that $q \not\equiv 0 \pmod \ell$, and $m$ the order of $q$ in $\F_\ell^\times$. We propose an explicit $L$-polynomial of hyperelliptic function field $K:=\F_q(T, \sqrt[\ell]{T^2+aT+b})$ with $a, b \in \F_q$ and $a^2-4b \ne 0$. Using our formula, we obtain the explicit closed formula for the class number of $K$, where $m$ is even or $m=\frac{\ell-1}{2}$.As an application, we compute the average class numbers for hyperelliptic function fields with genus up to $3$. - oai:arXiv.org:2512.08250v1 - math.NT - Wed, 10 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Peter Jaehyun Cho, Jinjoo Yoo - - - Causal inference under interference: computational barriers and algorithmic solutions - https://arxiv.org/abs/2512.08252 - arXiv:2512.08252v1 Announce Type: new -Abstract: We study causal effect estimation under interference from network data. We work under the chain-graph formulation pioneered in Tchetgen Tchetgen et. al (2021). Our first result shows that polynomial time evaluation of treatment effects is computationally hard in this framework without additional assumptions on the underlying chain graph. Subsequently, we assume that the interactions among the study units are governed either by (i) a dense graph or (ii) an i.i.d. Gaussian matrix. In each case, we show that the treatment effects have well-defined limits as the population size diverges to infinity. Additionally, we develop polynomial time algorithms to consistently evaluate the treatment effects in each case. Finally, we estimate the unknown parameters from the observed data using maximum pseudo-likelihood estimates, and establish the stability of our causal effect estimators under this perturbation. Our algorithms provably approximate the causal effects in polynomial time even in low-temperature regimes where the canonical MCMC samplers are slow mixing. For dense graphs, our results use the notion of regularity partitions; for Gaussian interactions, our approach uses ideas from spin glass theory and Approximate Message Passing. - oai:arXiv.org:2512.08252v1 + Distributional Shrinkage II: Optimal Transport Denoisers with Higher-Order Scores + https://arxiv.org/abs/2512.09295 + arXiv:2512.09295v1 Announce Type: new +Abstract: We revisit the signal denoising problem through the lens of optimal transport: the goal is to recover an unknown scalar signal distribution $X \sim P$ from noisy observations $Y = X + \sigma Z$, with $Z$ being standard Gaussian independent of $X$ and $\sigma>0$ a known noise level. Let $Q$ denote the distribution of $Y$. We introduce a hierarchy of denoisers $T_0, T_1, \ldots, T_\infty : \mathbb{R} \to \mathbb{R}$ that are agnostic to the signal distribution $P$, depending only on higher-order score functions of $Q$. Each denoiser $T_K$ is progressively refined using the $(2K-1)$-th order score function of $Q$ at noise resolution $\sigma^{2K}$, achieving better denoising quality measured by the Wasserstein metric $W(T_K \sharp Q, P)$. The limiting denoiser $T_\infty$ identifies the optimal transport map with $T_\infty \sharp Q = P$. + We provide a complete characterization of the combinatorial structure underlying this hierarchy through Bell polynomial recursions, revealing how higher-order score functions encode the optimal transport map for signal denoising. We study two estimation strategies with convergence rates for higher-order scores from i.i.d. samples drawn from $Q$: (i) plug-in estimation via Gaussian kernel smoothing, and (ii) direct estimation via higher-order score matching. This hierarchy of agnostic denoisers opens new perspectives in signal denoising and empirical Bayes. + oai:arXiv.org:2512.09295v1 math.ST - math.PR - stat.ME + cs.LG + stat.ML stat.TH - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Sohom Bhattacharya, Subhabrata Sen + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Tengyuan Liang - $0$-affine quantum groups as K-theoretic Hall algebras - https://arxiv.org/abs/2512.08272 - arXiv:2512.08272v1 Announce Type: new -Abstract: In this note, we show that the positive part of Arkhipov-Mazin's $0$-affine quantum group can be realized as the K-theoretic Hall algebra of the type $A$ Dynkin quiver. We then construct a categorical action of this positive part and demonstrate that such an action induces semiorthogonal decompositions on the corresponding weight categories. As a main example, we study the bounded derived category of coherent sheaves on $n$-step partial flag varieties. - oai:arXiv.org:2512.08272v1 - math.RT - Wed, 10 Dec 2025 00:00:00 -0500 + On the elasto-plastic filtration equation + https://arxiv.org/abs/2512.09298 + arXiv:2512.09298v1 Announce Type: new +Abstract: We study the fully nonlinear heat equation $b(\partial_tu)\partial_tu=\Delta u$ posed in a bounded domain with Dirichlet boundary conditions. Here $b(s)=b^-$ if $s<0$, $b(s)=b^+$ if $s>0$, $b^-\neq b^+$ being two positive constants. This equation models the flow of an elastic fluid in an elasto-plastic porous medium. We are interested in the existence and uniqueness of viscosity solutions and in their asymptotic behaviour as $t\to\infty$ and when $b^-\to 0^+$ or $b^+\to +\infty$. We also characterize solutions of the problem as limits of a minimization dynamic game. + oai:arXiv.org:2512.09298v1 + math.AP + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - You-Hung Hsu + Arturo de Pablo, Fernando Quiros, Julio D. Rossi - On the Bergman metric of a pseudoconvex domain with a strongly pseudoconvex polyhedral boundary point - https://arxiv.org/abs/2512.08275 - arXiv:2512.08275v1 Announce Type: new -Abstract: Let $D\subset\mathbb{C}^n$ with $n>1$ be a pseudoconvex domain, possibly unbounded, that contains a non-smooth strongly pseudoconvex polyhedral boundary point. We show that the Bergman metric of $D$ is not Einstein. - oai:arXiv.org:2512.08275v1 - math.CV - math.DG - Wed, 10 Dec 2025 00:00:00 -0500 + Infinitesimal containment and sparse factors of iid + https://arxiv.org/abs/2512.09301 + arXiv:2512.09301v1 Announce Type: new +Abstract: We introduce infinitesimal weak containment for measure-preserving actions of a countable group $\Gamma$: an action $(X,\mu)$ is infinitesimally contained in $(Y,\nu)$ if the statistics of the action of $\Gamma$ on small measure subsets of $X$ can be approximated inside $Y$. We show that the Bernoulli shift $[0,1]^\Gamma$ is infinitesimally contained in the left-regular action of $\Gamma$. For exact groups, this implies that sparse factor-of-iid subsets of $\Gamma$ are approximately hyperfinite. We use it to quantify a theorem of Chifan--Ioana on measured subrelations of the Bernoulli shift of an exact group. For the proof of infinitesimal containment we define \emph{entropy support maps}, which take a small subset $U$ of $\{0,1\}^I$ and assign weights to coordinates above every point of $U$, according to how ''important'' they are for the structure of the set. + oai:arXiv.org:2512.09301v1 + math.DS + cs.IT + math.IT + math.PR + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Xiaojun Huang, Scott James, Xiaoshan Li + Miko{\l}aj Fr\k{a}czyk - On a bound of $p$-ranks of Iwasawa modules of $\mathbb{Z}_p$-extensions over a quartic CM-field - https://arxiv.org/abs/2512.08278 - arXiv:2512.08278v1 Announce Type: new -Abstract: Let $p$ be a prime number. If a number field $k$ has at least one complex place, there are infinitely many $\mathbb{Z}_p$-extensions over $k$, and some authors studied the behavior of Iwasawa invariants of these $\mathbb{Z}_p$-extensions. In particular, Fujii studied the case where $k$ is an imaginary quadratic field and obtained some results on the boundedness of Iwasawa $\lambda$-invariants in a certain infinite family of $\mathbb{Z}_p$-extensions. In the present article, we give analogous theorems in the case where $k$ is a quartic CM-field. One of our main theorems determines all the Iwasawa invariants, including the $\nu$-invariants, of a certain infinite family of $\mathbb{Z}_p$-extensions over a quartic CM-field. - oai:arXiv.org:2512.08278v1 - math.NT - Wed, 10 Dec 2025 00:00:00 -0500 + Estimating order scale parameters of two scale mixture of exponential distributions + https://arxiv.org/abs/2512.09305 + arXiv:2512.09305v1 Announce Type: new +Abstract: Estimation of the ordered scale parameter of a two scale mixture of the exponential distribution is considered under Stein loss and symmetric loss. Under certain conditions, we prove that the inadmissibility equivariant estimator exhibits several improved estimators. Consequently, we propose various estimators that dominate the best affine equivariant estimators (BAEE). Also, we propose a class of estimators that dominates BAEE. We have proved that the boundary estimator of this class is a generalized Bayes estimator. The results are applied to the multivariate Lomax distribution and the Exponential Inverse Gaussian (E-IG) distribution. Consequently, we have obtained improved estimators for the ordered scale parameters of two multivariate Lomax distributions and the exponential inverse Gaussian distribution. For each case, we have conducted a simulation study to compare the risk performance of the improved estimators. + oai:arXiv.org:2512.09305v1 + math.ST + stat.TH + Thu, 11 Dec 2025 00:00:00 -0500 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Takuya Yanagisawa + http://creativecommons.org/licenses/by-sa/4.0/ + Somnath Mondal, Lakshmi Kanta Patra - M\"obius Transformations and the Analytic--Geometric Reconstruction of the Induction--Machine Circle Diagram - https://arxiv.org/abs/2512.08302 - arXiv:2512.08302v1 Announce Type: new -Abstract: The Heyland circle diagram is a classical graphical method for representing the steady--state behavior of induction machines using no--load and blocked--rotor test data. Despite its long pedagogical history, the traditional geometric construction has not been formalized within a closed analytic framework. This note develops a complete Euclidean reconstruction of the diagram using only the two measured phasors and elementary geometric operations, yielding a unique circle, a torque chord, a slip scale, and a maximum--torque point. We prove that this constructed circle coincides precisely with the analytic steady--state current locus obtained from the per--phase equivalent circuit. A M\"obius transformation interpretation reveals the complex--analytic origin of the diagram's circularity and offers a compact explanation of its geometric structure. - oai:arXiv.org:2512.08302v1 - math.DS - cs.SY - eess.SY - math.CV - Wed, 10 Dec 2025 00:00:00 -0500 + On asymptotic behavior of solutions to random fractional Riesz-Bessel equations with cyclic long memory initial conditions + https://arxiv.org/abs/2512.09308 + arXiv:2512.09308v1 Announce Type: new +Abstract: This paper investigates fractional Riesz-Bessel equations with random initial conditions. The spectra of these random initial conditions exhibit singularities both at zero frequency and at non-zero frequencies, which correspond to the cases of classical long-range dependence and cyclic long-range dependence, respectively. Using spectral methods and asymptotic theory, it is shown that the rescaled solutions of the equations converge to spatio-temporal Gaussian random fields. The limit fields are stationary in space and non-stationary in time. The covariance and spectral structures of the resulting asymptotic random fields are provided. The paper further establishes multiscaling limit theorems for the case of regularly varying asymptotics. A numerical example illustrating the theoretical results is also presented. + oai:arXiv.org:2512.09308v1 + math.PR + math.ST + stat.TH + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Anubhav Gupta + Maha Mosaad A. Alghamdi, Andriy Olenko - Milnor meets Hopf and Toeplitz at the K-theory of quantum projective planes - https://arxiv.org/abs/2512.08304 - arXiv:2512.08304v1 Announce Type: new -Abstract: We explore applications of the celebrated construction of the Milnor connecting homomorphism from the odd to the even K-groups in the context of Hopf--Galois theory. For a finitely generated projective module associated to any piecewise cleft principal comodule algebra, we provide an explicit formula computing the clutching $K_1$-class in terms of the representation matrix defining the module. Thus, the module is determined by an explicit Milnor idempotent. We apply this new tool to the K-theory of quantum complex projective planes to determine their $K_0$-generators in terms of modules associated to noncommutative Hopf fibrations. On the other hand, using explicit homotopy between unitaries, we express the $K_0$-class of the Milnor idempotents in terms of elementary projections in the Toeplitz C*-algebra. This allows us to infer that all our generators are in the positive cone of the $K_0$-group, which is a purely quantum phenomenon absent in the classical case. - oai:arXiv.org:2512.08304v1 - math.KT - math.OA - math.QA - Wed, 10 Dec 2025 00:00:00 -0500 + Cohomology and deformation theory of Averaging Leibniz algebras + https://arxiv.org/abs/2512.09328 + arXiv:2512.09328v1 Announce Type: new +Abstract: In this paper, we introduce the concepts of representation and dual representation for averaging Leibniz algebras. We also develop a cohomology theory for these algebras. Additionally, we explore the infinitesimal and formal deformation theories of averaging Leibniz algebras, showing that the cohomology we define is closely connected to deformation cohomology. + oai:arXiv.org:2512.09328v1 + math.RA + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Francesco D'Andrea, Piotr M. Hajac, Tomasz Maszczyk, Bartosz Zieli\'nski + Bouzid Mosbahi, Imed Basdouri, Jean Lerbet - Triality and adjoint lifting for GL(3) - https://arxiv.org/abs/2512.08307 - arXiv:2512.08307v1 Announce Type: new -Abstract: Using the stable twisted trace formula for the triality automorphism, we show the adjoint lifting (to GL(8)) of cuspidal representations of GL(3) with a discrete series local component. We also describe the possible isobaric decompositions of the resulting automorphic representations on GL(8). - oai:arXiv.org:2512.08307v1 - math.NT - math.RT - Wed, 10 Dec 2025 00:00:00 -0500 + Complex exponential integral means spectrums of univalent functions and Brennan conjecture + https://arxiv.org/abs/2512.09330 + arXiv:2512.09330v1 Announce Type: new +Abstract: In this paper we investigate the complex exponential integral means spectrums of univalent functions in the unit disk. We show that all integral means spectrum (IMS) functionals for complex exponents on the universal Teichm\"uller space, the closure of the universal Teichm\"uller curve, and the universal asymptotic Teichm\"uller space are continuous. We also show that the complex exponential integral means spectrum of any univalent function admitting a quasiconformal extension to the extended complex plane is strictly less than the universal integral means spectrum. These results extend some related ones in our recent work \cite{Jin}. Here we employ a different and more direct approach to prove the continuity of IMS functional on the universal asymptotic Teichm\"uller space. Additionally, we completely determine the integral means spectrums of all univalent rational functions in the unit disk. As a consequence, we show that the Brennan conjecture is true for this class of univalent functions. Finally, we present some remarks and raise some problems and conjectures regarding IMS functionals on Teichm\"uller spaces, univalent rational functions, and a multiplier operator whose norm is closely related to the Brennan conjecture. + oai:arXiv.org:2512.09330v1 + math.CV + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Wee Teck Gan + Jianjun Jin - Fock Space Tensor Product Categorifications and Multiplicities in Complex Rank Parabolic Category O - https://arxiv.org/abs/2512.08312 - arXiv:2512.08312v1 Announce Type: new -Abstract: We undertake the study of complex rank analogues of parabolic category O defined using Deligne categories. We regard these categories as a family over an affine space, introduce a stratification on this parameter space, and formulate conjectures on the structural constancy of fibers on each stratum. Using the theory of $\mathfrak{sl}_{\mathbb{Z}}$-categorification, we prove these conjectures for admissible strata. Namely, we axiomatize the notion of multi-Fock tensor product categorifications (MFTPCs), which are interval finite highest weight categories equipped with a compatible action of commuting copies of $\mathfrak{sl}_{\mathbb{Z}}$, categorifying an external tensor product of tensor products of highest and lowest weight Fock space representations. We prove a uniqueness theorem for admissible MFTPCs and show that complex rank parabolic categories O have the structure of MFTPCs. In turn, for suitable choices of parameters, we produce an equivalence of complex rank category O with a stable limit of classical parabolic categories O, resolving our conjecture in the admissible case. These equivalences yield multiplicities of simple objects in Verma modules in terms of stable parabolic Kazhdan--Lusztig polynomials, answering a question posed by Etingof. In particular, for the case of two Levi blocks of non-integral size, we completely describe the structure of the corresponding category O in terms of stable representation theory. As an application, we obtain multiplicities for parabolic analogs of hyperalgebra Verma modules introduced by Haboush in the large rank and large characteristic limit. - oai:arXiv.org:2512.08312v1 - math.RT - math.CT - Wed, 10 Dec 2025 00:00:00 -0500 + Oriented Hamiltonian Paths in Tournaments: Stability under Arc Deletion + https://arxiv.org/abs/2512.09332 + arXiv:2512.09332v1 Announce Type: new +Abstract: Havet and Thomass\'{e} proved that every tournament of order $n\geq 8$ contains every oriented Hamiltonian path, which was conjectured by Rosenfeld. Recently, it was shown that in any tournament $T$ of order $n\geq 8$, there exists an arc $e$ such that $T-e$ contains any oriented Hamiltonian path. A natural extension of this problem is to study the stability of this property under arbitrary arc deletion. In this paper, we prove that every arc $e$ in a tournament $T$ of order $n\geq 8$ satisfies that $T-e$ contains every oriented Hamiltonian path, except for some explicitly described exceptions. + oai:arXiv.org:2512.09332v1 + math.CO + Thu, 11 Dec 2025 00:00:00 -0500 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Hamilton Wan + http://creativecommons.org/licenses/by/4.0/ + Mahabba El Sahili, Ayman El Zein - On the Fundamental Tradeoff of Joint Communication and QCD: The Monostatic Case - https://arxiv.org/abs/2512.08332 - arXiv:2512.08332v1 Announce Type: new -Abstract: This paper investigates the fundamental tradeoff between communication and quickest change detection (QCD) in integrated sensing and communication (ISAC) systems under a monostatic setup. We introduce a novel Joint Communication and quickest Change subblock coding Strategy (JCCS) that leverages feedback to adapt coding dynamically based on real-time state estimation. The achievable rate-delay region is characterized using state-dependent mutual information and KL divergence, providing a comprehensive framework for analyzing the interplay between communication performance and detection delay. Moreover, we provide a partial converse demonstrating the asymptotic optimality of the proposed detection algorithm within the JCCS framework. To illustrate the practical implications, we analyze binary and MIMO Gaussian channels, revealing insights into achieving optimal tradeoffs in ISAC system design. - oai:arXiv.org:2512.08332v1 - cs.IT - math.IT - Wed, 10 Dec 2025 00:00:00 -0500 + An Efficient Solver to Helmholtz Equations by Recontruction Discontinuous Approximation + https://arxiv.org/abs/2512.09338 + arXiv:2512.09338v1 Announce Type: new +Abstract: In this paper, an efficient solver for the Helmholtz equation using a noval approximation space is developed. The ingradients of the method include the approximation space recently proposed, a discontinuous Galerkin scheme extensively used, and a linear system solver with a natural preconditioner. Comparing to traditional discontinuous Galerkin methods, we refer to the new method as being more efficient in the following sense. The numerical performance of the new method shows that: 1) much less error can be reached using the same degrees of freedom; 2) the sparse matrix therein has much fewer nonzero entries so that both the storage space and the solution time cost for the iterative solver are reduced; 3) the preconditioner is proved to be optimal with respect to the mesh size in the absorbing case. Such advantage becomes more pronounced as the approximation order increases. + oai:arXiv.org:2512.09338v1 + math.NA + cs.NA + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Sung Hoon Lim, Daewon Seo + Shuhai Zhao - Limit absorption and Green function estimates for matrix-valued periodic operators - https://arxiv.org/abs/2512.08335 - arXiv:2512.08335v1 Announce Type: new -Abstract: The boundary value of the resolvent of a generic periodic tight-binding Hamiltonian with matrix symbols is shown to satisfy a limit absorption principle which is continuous in energy in dimensions $d=3$, and in dimension $d=2$ away from critical points of the energy bands corresponding to van Hove singularities. The analysis away from critical points of the energy bands is based on the coarea formula, while at the critical points it involves a parametric Morse lemma and stationary phase arguments. In particular, at Weyl points a new type of oscillatory integrals is dealt with. - oai:arXiv.org:2512.08335v1 - math-ph - math.MP - Wed, 10 Dec 2025 00:00:00 -0500 + Hochschild cohomology groups of 5-dimensional complex nilpotent associative algebras + https://arxiv.org/abs/2512.09346 + arXiv:2512.09346v1 Announce Type: new +Abstract: This paper explores the structure of low-dimensional cohomology groups in the context of complex nilpotent associative algebras. Specifically, we study 5-dimensional complex nilpotent associative algebras satisfying $\mathcal{A}^4 = 0$ and $\mathcal{A}^3 \neq 0$. Using their isomorphism invariants, we compute and present the zeroth and first Hochschild cohomology groups, $H^0(\mathcal{A}, \mathcal{A})$ and $H^1(\mathcal{A}, \mathcal{A})$, in explicit matrix form. These results show how cohomology helps to identify and classify different associative algebras. + oai:arXiv.org:2512.09346v1 + math.RA + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Miguel Ballesteros, Gerardo Franco Cordova, Hermann Schulz-Baldes + Bouzid Mosbahi, Imed Basdouri, Jean Lerbet - Chern Conjecture on Minimal Willmore Hypersurfaces with Constant Scalar Curvature - https://arxiv.org/abs/2512.08342 - arXiv:2512.08342v1 Announce Type: new -Abstract: In this paper, we prove that for an $n$-dimensional closed minimal Willmore hypersurface $M^n$ with constant scalar curvature in the unit sphere $\mathbb{S}^{n+1}$, the squared norm $S$ of the second fundamental form of $M^n$ satisfies $S\geqslant n+\frac{4n+9-\sqrt{4 n^{2}+60 n+81}}{2}$ if $S>n$. This proves, in the approximate sense, the Chern conjecture about the second gap ($S\geqslant 2n$ if $S>n$), which will be fully verified under a further inequality condition about the 4-th mean curvature. - oai:arXiv.org:2512.08342v1 - math.DG - Wed, 10 Dec 2025 00:00:00 -0500 + A higher-order three-scale computational method for efficient nonlinear thermo-mechanical coupling simulation of heterogeneous structures with multiple spatial scales + https://arxiv.org/abs/2512.09357 + arXiv:2512.09357v1 Announce Type: new +Abstract: Classical multi-scale methods involving two spatial scales face significant challenges when simulating heterogeneous structures with complicated three-scale spatial configurations. This study proposes an innovative higher-order three-scale (HOTS) computational method, aimed at accurately and efficiently computing the transient nonlinear thermo-mechanical coupling problems of heterogeneous structures with multiple spatial scales. In these heterogeneous structures, temperature-dependent material properties have an important impact on the thermo-mechanical coupling responses, which is the particular interest in this work. At first, the detailed macro-meso-micro correlative model with higher-order correction terms is established by recursively two-scale analysis between macro-meso and meso-micro scales, which enables high-accuracy analysis of temperature-dependent nonlinear thermo-mechanical behaviors of heterogeneous structures with complicated three-scale configurations. The local error analysis mathematically illustrates the well-balanced property of HOTS computational model, endowing it with high computational accuracy. In addition, a two-stage numerical algorithm with off-line and on-line stages is proposed in order to efficiently simulate the nonlinear thermo-mechanical responses of heterogeneous structures with three-level spatial scales and accurately capture their highly oscillatory information at micro-scale. Finally, the high computational efficiency, high numerical accuracy and low computational cost of the presented higher-order three-scale computational approach are substantiated via representative numerical experiments. It can be summarized that this scalable and robust HOTS computational approach offers a reliably numerical tool for nonlinear multiphysics simulation of large-scale heterogeneous structures in real-world applications. + oai:arXiv.org:2512.09357v1 + math.NA + cs.NA + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jianquan Ge, Huixin Tan, Wenjiao Yan, Yunheng Zhang + Hao Dong, Yanqi Wang, Jiale Linghu, Qiang Ma - Hydrodynamic limit of the Vlasov-Poisson-Fokker-Planck system in low-field regime - https://arxiv.org/abs/2512.08346 - arXiv:2512.08346v1 Announce Type: new -Abstract: In this paper, we study the hydrodynamic limit of the scaled Vlasov-Poisson-Fokker-Planck (VPFP) system in the low-field regime. By employing the moment method, we formally derive the corresponding Drift-Diffusion-Poisson (DDP) system. Furthermore, we rigorously justify the pointwise convergence from the VPFP system to the DDP system through delicate high-order energy estimates based on the Macro-Micro decomposition. The main difficulty lies in controlling the nonlinear coupling between the kinetic and electrostatic fields and establishing uniform bounds with respect to the scaling parameter. These challenges are overcome by developing refined high-order energy methods that yield uniform energy estimates and ensure the global well-posedness of smooth solutions, without relying on any a priori assumptions for the limiting DDP system. - oai:arXiv.org:2512.08346v1 - math.AP - Wed, 10 Dec 2025 00:00:00 -0500 + Finite axiomatization of $\textbf{GL}\times\textbf{S5}$ and $\textbf{Grz}\times\textbf{S5}$ + https://arxiv.org/abs/2512.09381 + arXiv:2512.09381v1 Announce Type: new +Abstract: We prove that $\mathbf{GL} \times \mathbf{S5}$ is product matching, and that $\mathbf{Grz} \times \mathbf{S5}$ is axiomatizable by adding to $[\mathbf{Grz},\mathbf{S5}]$ the G\"odel translation of the monadic Casari formula. This settles the question of finite axiomatization these logics. + oai:arXiv.org:2512.09381v1 + math.LO + Thu, 11 Dec 2025 00:00:00 -0500 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Zhendong Fang, Kunlun Qi + http://creativecommons.org/licenses/by/4.0/ + Guram Bezhanishvili, Mashiath Khan - A constrained approximation theorem for integral functionals on $L^p$ - https://arxiv.org/abs/2512.08347 - arXiv:2512.08347v1 Announce Type: new -Abstract: Let $(T,{\cal F},\mu)$ be a $\sigma$-finite measure space, $E$ a separable real Banach space and $p\geq 1$. Given a sequence of functions $f, f_1, f_2,...$ from $T\times E$ to ${\bf R}$, under general assumptions, we prove that, for each closed hyperplane $V$ of $L^p(T,E)$, for each $u\in V$, and for each sequence $\{\lambda_n\}$ converging to $\int_Tf(t,u(t))d\mu$, there exists a sequence $\{u_n\}$ in $V$ converging to $u$ and such that $\int_Tf_n(t,u_n(t))d\mu=\lambda_n$ for all $n$ large enough. - oai:arXiv.org:2512.08347v1 - math.FA - math.CA - Wed, 10 Dec 2025 00:00:00 -0500 + The Dirac and Rarita-Schwinger equations on scalar flat metrics of Taub-NUT type + https://arxiv.org/abs/2512.09382 + arXiv:2512.09382v1 Announce Type: new +Abstract: We construct a scalar flat metric of Taub-NUT type whose total mass can be negative. The standard Taub-NUT metric and its negative NUT charge counterpart serve as particular examples, for which the complex 2-dimensional space of parallel spinors gives rise to $L^2$ harmonic spinors and Rarita-Schwinger fields. For the scalar flat Taub-NUT type metric, we study the Dirac and Rarita-Schwinger equations by separating them into angular and radial equations, and obtain explicit solutions in certain special cases. + oai:arXiv.org:2512.09382v1 + math-ph + math.MP + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Biagio Ricceri + http://creativecommons.org/licenses/by-nc-nd/4.0/ + Xiaoman Xue, Chuxiao Liu - On Discrete Ambiguity Functions of Random Communication Waveforms - https://arxiv.org/abs/2512.08352 - arXiv:2512.08352v1 Announce Type: new -Abstract: This paper provides a fundamental characterization of the discrete ambiguity functions (AFs) of random communication waveforms under arbitrary orthonormal modulation with random constellation symbols, which serve as a key metric for evaluating the delay-Doppler sensing performance in future ISAC applications. A unified analytical framework is developed for two types of AFs, namely the discrete periodic AF (DP-AF) and the fast-slow time AF (FST-AF), where the latter may be seen as a small-Doppler approximation of the DP-AF. By analyzing the expectation of squared AFs, we derive exact closed-form expressions for both the expected sidelobe level (ESL) and the expected integrated sidelobe level (EISL) under the DP-AF and FST-AF formulations. For the DP-AF, we prove that the normalized EISL is identical for all orthogonal waveforms. To gain structural insights, we introduce a matrix representation based on the finite Weyl-Heisenberg (WH) group, where each delay-Doppler shift corresponds to a WH operator acting on the ISAC signal. This WH-group viewpoint yields sharp geometric constraints on the lowest sidelobes: The minimum ESL can only occur along a one-dimensional cut or over a set of widely dispersed delay-Doppler bins. Consequently, no waveform can attain the minimum ESL over any compact two-dimensional region, leading to a no-optimality (no-go) result under the DP-AF framework. For the FST-AF, the closed-form ESL and EISL expressions reveal a constellation-dependent regime governed by its kurtosis: The OFDM modulation achieves the minimum ESL for sub-Gaussian constellations, whereas the OTFS waveform becomes optimal for super-Gaussian constellations. Finally, four representative waveforms, namely, SC, OFDM, OTFS, and AFDM, are examined under both frameworks, and all theoretical results are verified through numerical examples. - oai:arXiv.org:2512.08352v1 - cs.IT - eess.SP - math.IT - Wed, 10 Dec 2025 00:00:00 -0500 + A Survey of the Kakeya conjecture, 2000-2025 + https://arxiv.org/abs/2512.09397 + arXiv:2512.09397v1 Announce Type: new +Abstract: We survey progress on the Kakeya conjecture in Euclidean space, with an emphasis on developments that have occurred since the previous surveys by Wolff and Katz-Tao. + oai:arXiv.org:2512.09397v1 + math.CA + Thu, 11 Dec 2025 00:00:00 -0500 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Ying Zhang, Fan Liu, Yifeng Xiong, Weijie Yuan, Shuangyang Li, Le Zheng, Tony Xiao Han, Christos Masouros, Shi Jin + http://creativecommons.org/licenses/by/4.0/ + Joshua Zahl - A reconstructed discontinuous approximation for distributed elliptic control problems - https://arxiv.org/abs/2512.08353 - arXiv:2512.08353v1 Announce Type: new -Abstract: In this paper, we present and analyze an internal penalty discontinuous Galerkin method for the distributed elliptic optimal control problems. It is based on a reconstructed discontinuous approximation which admits arbitrarily high-order approximation space with only one unknown per element. Applying this method, we develop a proper discretization scheme that approximates the state and adjoint variables in the approximation space. Our main contributions are twofold: (1) the derivation of both a priori and a posteriori error estimates of the $L^2$-norm and the energy norms, and (2) the implementation of an efficiently solvable discrete system, which is solved via a linearly convergent projected gradient descent method. Numerical experiments are provided to verify the convergence order in a priori estimate and the efficiency of a posteriori error estimate. - oai:arXiv.org:2512.08353v1 - math.NA - cs.NA + Geometric properties of optimizers for the maximum gradient of the torsion function + https://arxiv.org/abs/2512.09400 + arXiv:2512.09400v1 Announce Type: new +Abstract: Consider $J(\Omega):= \|\nabla u_\Omega\|_\infty/\sqrt{|\Omega|} $ and $J_P(\Omega):= \|\nabla u_\Omega\|_\infty/P(\Omega) $, where $\Omega$ is a planar convex domain, $u_\Omega$ is the torsion function, $P(\Omega)$ is the perimeter of $\Omega$ and $|\Omega|$ its area. We prove that there exist planar convex domains that maximize the functionals $J$ and $J_P$, and any maximizer has a $C^1$ boundary that contains a line segment on which $|\nabla u_\Omega|$ attains its maximum. + oai:arXiv.org:2512.09400v1 + math.AP math.OC - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/publicdomain/zero/1.0/ - Ruo Li, Haoyang Liu, Jun Yin + http://creativecommons.org/licenses/by/4.0/ + Krzysztof Burdzy, Ilias Ftouhi, Xuefeng Liu, Phanuel Mariano - Multiple cover formulas for abelian surfaces via correlated invariants - https://arxiv.org/abs/2512.08357 - arXiv:2512.08357v1 Announce Type: new -Abstract: We prove the multiple cover formula conjecture for abelian surfaces for a large class of insertions, including all stationary invariants. The proof uses the reduced degeneration formula expressing the invariants in terms of the correlated Gromov--Witten invariants previously introduced by the authors. - oai:arXiv.org:2512.08357v1 - math.AG - Wed, 10 Dec 2025 00:00:00 -0500 + Inverse problems for ZS-operators and their isomorphisms + https://arxiv.org/abs/2512.09413 + arXiv:2512.09413v1 Announce Type: new +Abstract: Consider two inverse problems for ZS-operators problems on the + unit interval. It means that there are two corresponding mappings $F, f$ from a Hilbert space of potentials $H$ into their spectral data. They are called isomorphic if $F$ is a composition of $f$ and some isomorphism $U$ of $H$ onto itself. We consider isomorphic inverse problems for ZS-operators on the unit interval under basic boundary conditions and on the circle. The proof is based on the non-linear analysis and properties of the 4-spectra mapping constructed in our paper. + oai:arXiv.org:2512.09413v1 + math.SP + Thu, 11 Dec 2025 00:00:00 -0500 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Thomas Blomme, Francesca Carocci + http://creativecommons.org/licenses/by/4.0/ + Evgeny Korotyaev, Zongfeng Zhang - Generalized Discrepancy of Random Points - https://arxiv.org/abs/2512.08364 - arXiv:2512.08364v1 Announce Type: new -Abstract: We study the $L_p$-discrepancy of random point sets in high dimensions, with emphasis on small values of $p$. Although the classical $L_p$-discrepancy suffers from the curse of dimensionality for all $p \in (1,\infty)$, the gap between known upper and lower bounds remains substantial, in particular for small $p \ge 1$. To clarify this picture, we review the existing results for i.i.d.\ uniformly distributed points and derive new upper bounds for \emph{generalized} $L_p$-discrepancies, obtained by allowing non-uniform sampling densities and corresponding non-negative quadrature weights. - Using the probabilistic method, we show that random points drawn from optimally chosen product densities lead to significantly improved upper bounds. For $p=2$ these bounds are explicit and optimal; for general $p \in [1,\infty)$ we obtain sharp asymptotic estimates. The improvement can be interpreted as a form of importance sampling for the underlying Sobolev space $F_{d,q}$. - Our results also reveal that, even with optimal densities, the curse of dimensionality persists for random points when $p\ge 1$, and it becomes most pronounced for small $p$. This suggests that the curse should also hold for the classical $L_1$-discrepancy for deterministic point sets. - oai:arXiv.org:2512.08364v1 - math.NA - cs.NA - math.NT - math.PR - Wed, 10 Dec 2025 00:00:00 -0500 + Some model theory of the Heisenberg group + https://arxiv.org/abs/2512.09414 + arXiv:2512.09414v1 Announce Type: new +Abstract: We show that a field $K$ is model complete (in the language of rings) if and only if the Heisenberg group $H(K)$ is model complete (in the language of groups). To show that, we extend Levchuk's result about automorphisms of $H(K)$ to the case of monomorphisms $H(K)\to H(L)$. We also show that $H(K)$ does not have quantifier elimination and that it is not bi-interpretable with $K$. + oai:arXiv.org:2512.09414v1 + math.LO + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Erich Novak, Friedrich Pillichshammer + Maciej Fr\k{a}cek, Piotr Kowalski - A unified planar network approach to total positivity of combinatorial matrices and real-rootedness of polynomials - https://arxiv.org/abs/2512.08369 - arXiv:2512.08369v1 Announce Type: new -Abstract: We present a common sufficient condition for the total positivity of combinatorial triangles and their reversals, as well as the real-rootedness of generating functions of the rows. The proof technique is to construct a unified planar network that represent the matrix, its reversal, and the Toeplitz matrices of rows, respectively, when selecting different sets of sources and sinks. These results can be applied to the exponential Riordan arrays, the iteration matrices and the $n$-recursive matrices. As consequences, we prove the total positivity and real-rootedness properties associated to many well-known combinatorial numbers, including the Stirling numbers of both kinds (of type A and type B), the Lah numbers, the idempotent numbers, the Delannoy numbers, and the derangement numbers of type A and type B. - oai:arXiv.org:2512.08369v1 - math.CO - Wed, 10 Dec 2025 00:00:00 -0500 + Asymptotics of lowlying Dirichlet eigenvalues of Witten Laplacians on domains in pinned path groups + https://arxiv.org/abs/2512.09419 + arXiv:2512.09419v1 Announce Type: new +Abstract: Let $G$ be a compact Lie group and $P_{e,a}(G)=C([0,1]\to G~|~\gamma(0)=e, \gamma(1)=a)$ be the pinned path space with a pinned Brownian motion measure $\nu_{\lambda,a}$ defined by the heat kernel $p(\lambda^{-1}t,x,y)$, where $\lambda$ is a positive parameter. We consider a Witten Laplacian $-L_{\lambda,\mathcal{D}}$ with the Dirichlet boundary condition on a certain domain $\mathcal{D}\subset P_{e,a}(G)$ which includes finitely many geodesics $\{l_1,\ldots,l_N\}$ between $e$ and $a$. $\nu_{\lambda,a}$ has the formal path integral expression $\nu_{\lambda,a}(d\gamma)=Z_{\lambda}^{-1}\exp \left(-\lambda E(\gamma)\right)d\gamma$, where $E(\gamma)=\frac{1}{2}\int_0^1|\dot{\gamma}(t)|^2dt$ and $E$ is a Morse function when $a$ is not a point of the set of cut-locus of $e$. Hence, by the analogy of finite dimensional cases, one may expect that the lowlying spectrum of $-\lambda^{-1}L_{\lambda,\mathcal{D}}$ can be approximated by the spectral sets of Ornstein-Uhlenbeck type operators which approximate $-\lambda^{-1}L_{\lambda,\mathcal{D}}$ at each critical points $\{l_i\}$ when $\lambda\to\infty$. However, differently from finite dimensional cases, the spectral sets of the approximate Ornstein-Uhlenbeck type operators contain essential spectrum. It may be difficult to analyze the behavior of the spectrum of $-\lambda^{-1}L_{\lambda,\mathcal{D}}$ near the set of the essential spectrum. In this paper, we study the asymptotic behavior of the lowlying discrete spectrum of $-\lambda^{-1}L_{\lambda,\mathcal{D}}$ in the complement of the neighborhood of the set of essential spectrum of the approximate Ornstein-Uhlenbeck type operators at $\{l_i\}$. + oai:arXiv.org:2512.09419v1 + math.PR + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Xi Chen, Lang Fu, Jiajie Ruan + Shigeki Aida - A Characterization of Functional Affine Surface Areas - https://arxiv.org/abs/2512.08375 - arXiv:2512.08375v1 Announce Type: new -Abstract: A characterization of valuations on the space of convex Lipschitz functions whose domain is a polytope in $\mathbb{R}^n$ is obtained. It is shown that every upper semicontinuous, equi-affine and dually epi-translation invariant valuation can be written as a linear combination of a constant term, the volume of the domain, and a functional affine surface area. In addition, dual statements for finite-valued convex functions are established. - oai:arXiv.org:2512.08375v1 - math.MG - math.FA - Wed, 10 Dec 2025 00:00:00 -0500 + Factorisability in K-theory + https://arxiv.org/abs/2512.09420 + arXiv:2512.09420v1 Announce Type: new +Abstract: We revisit and give a detailed proof of a lemma of Okounkov showing that, for a scheme X with a torus action, the Euler characteristic generating function associated with a "factorisable" sequence of torus-equivariant coherent sheaves on the symmetric powers $\operatorname{Sym}^n X$ equals the plethystic exponential of the generating function of Euler characteristics of some sequence of sheaves on X. + oai:arXiv.org:2512.09420v1 + math.AG + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Fernanda M. Ba\^eta + J{\o}rgen Vold Rennemo - The 1/4-phenomenon of placement probabilities of tilings in the Aztec diamond - https://arxiv.org/abs/2512.08377 - arXiv:2512.08377v1 Announce Type: new -Abstract: We consider domino tilings of the Aztec diamond. Using the Domino Shuffling algorithm introduced by Elkies, Kuperberg, Larsen, and Propp in arXiv:math/9201305, we are able to generate domino tilings uniformly at random. In this paper, we investigate the probability of finding a domino at a specific position in such a random tiling. We prove that this placement probability is always equal to $1/4$ plus a rational function, whose shape depends on the location of the domino, multiplied by a position-independent factor that involves only the size of the diamond. This result leads to significantly more compact explicit counting formulas compared to previous findings. As a direct application, we derive explicit counting formulas for the domino tilings of Aztec diamonds with $2\times 2$-square holes at arbitrary positions. - oai:arXiv.org:2512.08377v1 - math.CO + Nonequilibrium fluctuations for the occupation time of the SSEP in $d \geq 2$ + https://arxiv.org/abs/2512.09424 + arXiv:2512.09424v1 Announce Type: new +Abstract: We study the symmetric simple exclusion process in two or higher dimensions. We prove the invariance principles for the occupation time when the process starts from nonequilibrium measures. Our proof combines the martingale method and correlation estimates for the exclusion process. + oai:arXiv.org:2512.09424v1 math.PR - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Marcus Sch\"onfelder + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Tiecheng Xu, Linjie Zhao - Sharp Regularizing Effect of the Cauchy Problem for the Inhomogeneous Non-Cutoff Kac Equation - https://arxiv.org/abs/2512.08380 - arXiv:2512.08380v1 Announce Type: new -Abstract: In this work, we study the spatially inhomogeneous Kac equation with a non-cutoff cross section in a setting close to equilibrium. We prove that the solution to the Cauchy problem exhibits a sharp Gevrey-Gelfand-Shilov smoothing effect with an optimal radius. We employ a well-chosen exponential-type Fourier multiplier to establish the smoothing effect for position and velocity variables. - oai:arXiv.org:2512.08380v1 + Fractional calculus approach to models of adsorption: Barrier-diffusion control + https://arxiv.org/abs/2512.09426 + arXiv:2512.09426v1 Announce Type: new +Abstract: The mathematical model of surfactant adsorption under mixed barrier-diffusion control is analyzed using techniques from fractional calculus. The kinetic models of Henry, Langmuir, Frumkin, Volmer and van der Waals are considered. First, treating the Ward-Tordai integral equation as a fractional order one, the partial differential model is transformed into a single fractional ordinary differential equation for the adsorption. A transformation of the obtained equation is proposed that reduces the number of parameters to two dimensionless groups (at Frumkin and van der Waals models a third parameter appears). In the simplest case of Henry adsorption isotherm the fractional differential model depends on a single dimensionless group and an exact solution exists, represented in terms of Mittag-Leffler functions. Based on this solution, second order asymptotes (at small values of the adsorption) are derived for the other models. The asymptotes of the adsorption result in a higher order asymptotes for the surface pressure (surface tension). For small surface coverage, all considered models converge to the Henry model's predictions, making it a universal first-order approximation for the surface tension. Next, the fractional differential model is written as an integral equation %of fractional order that can be considered as a generalization of the well-known Ward-Tordai equation to the case of barrier-diffusion control. For computer simulation of the obtained integral equation a predictor-corrector numerical method is developed and numerical results are presented and discussed. + oai:arXiv.org:2512.09426v1 math.AP - Wed, 10 Dec 2025 00:00:00 -0500 + math-ph + math.MP + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Xinzhi Cai, Hongmei Cao, Chao-jiang Xu + Ivan Bazhlekov, Emilia Bazhlekova - A Class of Non-linear Anisotropic Elliptic problems with Unbounded Coefficients and Singular Quadratic Lower Order Terms - https://arxiv.org/abs/2512.08391 - arXiv:2512.08391v1 Announce Type: new -Abstract: In this work, we study the existence and regularity results of anisotropic elliptic equations with a singular lower order term that grows naturally with respect to the gradient and unbounded coefficients. We take up the following model problem \begin{equation*} \left\{\begin{array}{ll}-\displaystyle\sum\limits_{j\in J} D_{j}\left(\left[ 1+ u^{q}\right]\vert D_{j}u\vert^{p_{j}-2} D_{j}u\right)+\sum\limits_{j\in J}\frac{\vert D_{j}u\vert^{p_{j}}}{ u^{\theta}}=f& \hbox{in}\;\Omega, \\ u>0& \hbox{in}\;\Omega, - u =0 & \hbox{on}\; \partial\Omega, \end{array} - \right. \end{equation*} $\Omega$ is a bounded domain in $\mathbb{R}^{N}$, $j\in J=\{1,2,\ldots,N\},$ $q>0$, $0< \theta<1$, $2\leq p_{1}\leq p_{2}\leq... \leq p_{N}$ and $f\in L^{1}(\Omega)$. Our study's conclusions will depend on the values of $q$ and $\theta$. - oai:arXiv.org:2512.08391v1 - math.AP - Wed, 10 Dec 2025 00:00:00 -0500 + Components of Hilbert Schemes of low degree and smoothable algebras + https://arxiv.org/abs/2512.09428 + arXiv:2512.09428v1 Announce Type: new +Abstract: In this article, we describe the irreducible components of the Hilbert scheme of $d$ points on $\mathbb{A}^n$ for $d=9,10$. The main techniques we use are the variety of commuting matrices and analyzing loci of local algebras with a specific Hilbert function. We further prove that any finite local algebra of degrees $9,10$ and the socle dimension $2$ is smoothable. As the main consequence, we establish the equality of the cactus Grassmann and the secant Grassmann variety in the corresponding cases. + oai:arXiv.org:2512.09428v1 + math.AG + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Fessel Achhoud, Hichem Khelifi + Maciej Ga{\l}\k{a}zka, Hanieh Keneshlou, Klemen \v{S}ivic - Global optimization of low-rank polynomials - https://arxiv.org/abs/2512.08394 - arXiv:2512.08394v1 Announce Type: new -Abstract: This work considers polynomial optimization problems where the objective admits a low- rank canonical polyadic tensor decomposition. We introduce LRPOP (low-rank polynomial optimization), a new hierarchy of semidefinite programming relaxations for which the size of the semidefinite blocks is determined by the canonical polyadic rank rather than the number of variables. As a result, LRPOP can solve low-rank polynomial optimization problems that are far beyond the reach of existing sparse hierarchies. In particular, we solve problems with up to thousands of variables with total degree in the thousands. Numerical conditioning for problems of this size is improved by using the Bernstein basis. The LRPOP hierarchy converges from below to the global minimum of the polynomial under standard assumptions. - oai:arXiv.org:2512.08394v1 - math.OC - Wed, 10 Dec 2025 00:00:00 -0500 + Normalized solutions of $L^2$ supercritical NLS equations in exterior domains with inhomogeneous nonlinearities + https://arxiv.org/abs/2512.09437 + arXiv:2512.09437v1 Announce Type: new +Abstract: This paper establishes the existence of normalized mountain pass solutions to the $L^2$-supercritical nonlinear Schr\"odinger equation with inhomogeneous nonlinearity $|x|^{-\alpha}|u|^{p-2}u$ in exterior domains. In contrast, for the autonomous case ($\alpha=0$), Appolloni \& Molle (2025) and Zhang \& Zhang (2022) showed that potential mountain pass solutions share the same energy levels as in $\mathbb{R}^N$, causing non-existence due to energy leakage to infinity. This work demonstrates that the physically motivated decaying term $|x|^{-\alpha}$ breaks the scaling symmetry inherent in the autonomous case. Such breaking energetically separates the exterior domain problem from the whole space one and thereby prevents energy leakage. Using a novel min-max argument that combines monotonicity trick, Morse index estimates, and blow-up analysis, we prove the existence of a positive mountain pass solution for sufficiently small mass, revealing a new phenomenon of non-autonomous nonlinearities in non-compact domains. + oai:arXiv.org:2512.09437v1 + math.AP + math-ph + math.MP + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Lloren\c{c} Balada Gaggioli, Didier Henrion, Milan Korda + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Xiaojun Chang, Cong-Mei Li - Holomorphic one-forms without zeros on K\"ahler manifolds of Kodaira codimension one - https://arxiv.org/abs/2512.08395 - arXiv:2512.08395v1 Announce Type: new -Abstract: We give a bimeromorphic classification of compact K\"ahler manifolds of Kodaira codimension one that admit a holomorphic one form without zeros. - oai:arXiv.org:2512.08395v1 - math.CV - math.AG - Wed, 10 Dec 2025 00:00:00 -0500 + Parameter-Free Accelerated Quasi-Newton Method for Nonconvex Optimization + https://arxiv.org/abs/2512.09439 + arXiv:2512.09439v1 Announce Type: new +Abstract: We propose a quasi-Newton-type method for nonconvex optimization with Lipschitz continuous gradients and Hessians. The algorithm finds an $\varepsilon$-stationary point within $\tilde{\mathrm{O}}(d^{1/4} \varepsilon^{-13/8})$ gradient evaluations, where $d$ is the problem dimension. Although this bound includes an additional logarithmic factor compared with the best known complexity, our method is parameter-free in the sense that it requires no prior knowledge of problem-dependent parameters such as Lipschitz constants or the optimal value. Moreover, it does not need the target accuracy $\varepsilon$ or the total number of iterations to be specified in advance. The result is achieved by combining several key ideas: momentum-based acceleration, quartic regularization for subproblems, and a scaled variant of the Powell-symmetric-Broyden (PSB) update. + oai:arXiv.org:2512.09439v1 + math.OC + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Simon Pietig + Naoki Marumo - The Jordan canonical form of the Fr\'{e}chet derivative of a matrix function - https://arxiv.org/abs/2512.08399 - arXiv:2512.08399v1 Announce Type: new -Abstract: Let $\F$ be an algebraically closed field of characteristic $0$. Given a square matrix $A \in \F^{n \times n}$ and a polynomial $f \in \F[w]$, we determine the Jordan canonical form of the formal Fr\'{e}chet derivative of $f(A)$, in terms of that of $A$ and of $f$. When $\F\subseteq \C$, via Hermite interpolation, our result provides a full solution to [N.J. Higham, \emph{Functions of Matrices: Theory and Computation}, Research Problem 3.11]. A generalization consists of finding the Jordan canonical form of linear combinations of Kronecker products of powers of two square matrices, i.e., $\sum_{i,j} a_{ij} (X^i \otimes Y^j)$. For this generalization, we provide some new partial results, including a partial solution under certain assumptions and general bounds on the number and the sizes of Jordan blocks. - oai:arXiv.org:2512.08399v1 - math.RA - Wed, 10 Dec 2025 00:00:00 -0500 + $t$-Fold $s$-Blocking Sets and $s$-Minimal Codes + https://arxiv.org/abs/2512.09457 + arXiv:2512.09457v1 Announce Type: new +Abstract: Blocking sets and minimal codes have been studied for many years in projective geometry and coding theory. In this paper, we provide a new lower bound on the size of $t$-fold $s$-blocking sets without the condition $t \leq q$, which is stronger than the classical result of Beutelspacher in 1983. Then a lower bound on lengths of projective $s$-minimal codes is also obtained. It is proved that $(s+1)$-minimal codes are certainly $s$-minimal codes. We generalize the Ashikhmin-Barg condition for minimal codes to $s$-minimal codes. Many infinite families of $s$-minimal codes satisfying and violating this generalized Ashikhmin-Barg condition are constructed. We also give several examples which are binary minimal codes, but not $2$-minimal codes. + oai:arXiv.org:2512.09457v1 + cs.IT + math.IT + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Vanni Noferini + http://creativecommons.org/publicdomain/zero/1.0/ + Hao Chen, Xu Pan, Conghui Xie - Another view on smooth prime Fano threefolds of degree 22 with infinite automorphism groups - https://arxiv.org/abs/2512.08409 - arXiv:2512.08409v1 Announce Type: new -Abstract: We give a self-contained alternative proof of the classification of smooth prime Fano threefolds of degree 22 with infinite automorphism groups established by Kuznetsov, Prokhorov and Shramov. - oai:arXiv.org:2512.08409v1 - math.AG - Wed, 10 Dec 2025 00:00:00 -0500 + The Complex-Step Integral Transform + https://arxiv.org/abs/2512.09459 + arXiv:2512.09459v1 Announce Type: new +Abstract: Building on the well-established connection between the Hilbert transform and derivative operators, and motivated by recent developments in complex-step differentiation, we introduce the Complex-Step Integral Transform (CSIT): a generalized integral transform that combines analytic continuation, derivative approximation, and multi-scale smoothing within a unified framework. A spectral analysis shows that the CSIT preserves phase while suppressing high-wavenumber noise, offering advantages over conventional Fourier derivatives. We discuss the roles of the real and imaginary step parameters, compare FFT-based and interpolation-based implementations, and demonstrate the method on the advection equation and instantaneous-frequency computation. Results show that the CSIT yields smoother, more robust attributes than Hilbert-based methods and provides built-in stabilization for PDE solvers. The CSIT thus represents a flexible alternative for numerical differentiation, spectral analysis, and seismic signal processing. The method opens several avenues for future work, including non-periodic implementations, adaptive parameter selection, and integration with local interpolation frameworks such as high-order Finite-Element methods. + oai:arXiv.org:2512.09459v1 + math.NA + cs.NA + physics.geo-ph + Thu, 11 Dec 2025 00:00:00 -0500 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Adrien Dubouloz (LMA), Kento Fujita, Takashi Kishimoto + http://creativecommons.org/licenses/by/4.0/ + Rafael Abreu, Stephanie Durand, Jochen Kamm, Christine Thomas, Monika Pandey - Global Leray-Schauder continuation for Fredholm operators - https://arxiv.org/abs/2512.08412 - arXiv:2512.08412v1 Announce Type: new -Abstract: This paper ascertains the global behavior of the forward and backward branches of solutions provided by the Leray-Schauder continuation theorem for orientable $\mathcal{C}^1$ Fredholm maps, as developed by the authors in [54]. Under properness on bounded sets and a nonzero local index at the given base solution, each branch satisfies the following alternative: either it is unbounded, or it reaches the boundary of the domain, or it accumulates at a different solution on the base parameter level. When the component is bounded and stays in the interior, there is a degree balance on the base slice entailing a vanishing sum of local indices and, in particular, the existence of an even number of non-degenerate contact points. For real-analytic maps we construct locally injective parameterizations that exhibit blow-up, approach to the boundary, or return to the base level. An application to a quasilinear boundary value problem driven by the mean-curvature and Minkowski operators illustrates the global results. - oai:arXiv.org:2512.08412v1 - math.AP - math.FA - Wed, 10 Dec 2025 00:00:00 -0500 + Some Remarks on Positive/Negative Feedback + https://arxiv.org/abs/2512.09474 + arXiv:2512.09474v1 Announce Type: new +Abstract: In the context of unstable systems with control, a commonly-held precept is that negative and positive feedback cannot both be stabilizing. The canonical linear prototype is the scalar system $\dot x=u$ which, under negative linear feedback $u=-kx$ ($k >0$) is exponentially stable for all $k >0 $, whereas the inherent lack of exponential instability of the uncontrolled system is amplified by positive feedback $u=kx$ ($k >0)$. By contrast, for nonlinear systems it is shown that this intuitively-appealing dichotomy may fail to hold. + oai:arXiv.org:2512.09474v1 + math.OC + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Juli\'an L\'opez-G\'omez, Juan Carlos Sampedro - - - Weighted projective lines and Hochschild cohomology - https://arxiv.org/abs/2512.08414 - arXiv:2512.08414v1 Announce Type: new -Abstract: We describe the dimensions of Hochschild (co)homology groups of weighted projective curves over complex numbers. Surprisingly, all but one of those numbers depend only on the genus of the underlying non-weighted curve and the number of exceptional points. Our proof involves revising a classical representation-theoretic argument of Happel together with more recent results of Lenzing and Arinkin, C\u{a}ld\u{a}raru and Hablicsek. We give concrete realizations of a large class of weighted projective lines as quotient stacks. This paper conicides with the author's master's thesis submitted to the University of Bonn in 2019. - oai:arXiv.org:2512.08414v1 - math.AG - math.RT - Wed, 10 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Felix Schremmer + Thomas Berger, Achim Ilchmann, Eugene P. Ryan - Optimal Operation and Valuation of Electricity Storages in Intraday Markets - https://arxiv.org/abs/2512.08422 - arXiv:2512.08422v1 Announce Type: new -Abstract: This paper applies computational techniques of convex stochastic optimization to optimal operation and valuation of electricity storages in the face of uncertain electricity prices. Our valuations are based on the indifference pricing principle, which builds on optimal trading strategies and calibrates to the user's financial position, market views and risk preferences. The underlying optimization problem is solved with the Stochastic Dual Dynamic Programming algorithm which is applicable to various specifications of storages, and it allows for e.g. hard constraints on storage capacity and charging speed. We illustrate the approach in intraday trading where the agent charges or discharges a battery over a finite number of delivery periods, and the electricity prices are subject to bid-ask spreads and significant uncertainty. Optimal strategies are found in a matter of minutes on a regular PC. We find that the corresponding trading strategies and battery valuations vary consistently with respect to the agent's risk preferences as well as the physical characteristics of the battery. - oai:arXiv.org:2512.08422v1 + Suboptimal open-loop solution of a Stackelberg linear-quadratic differential game with cheap control of a follower: analytical/numerical study + https://arxiv.org/abs/2512.09476 + arXiv:2512.09476v1 Announce Type: new +Abstract: A two-player finite horizon linear-quadratic Stackelberg differential game is considered. The feature of this game is that the control cost of a follower in the cost functionals of both players is small, which means that the game under consideration is a cheap control game. The open-loop solution of this game is studied. Using the game's solvability conditions, obtaining such a game's solution is reduced to the solution of a proper boundary-value problem. Due to the smallness of the follower's control cost, this boundary-value problem is singularly perturbed. The asymptotic behaviour of the solution to this problem is analysed. Based on this analysis, the asymptotic behaviour of the open-loop optimal players' controls and the optimal values of the cost functionals is studied. Using these results, asymptotically suboptimal players' controls are designed. An illustrative example of a supply chain problem with a small control cost of a retailer is presented. + oai:arXiv.org:2512.09476v1 math.OC - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jean-Philippe Chancelier (CERMICS), Michel de Lara (CERMICS), Fran\c{c}ois Pacaud (LMU), Tanguy Lindegaard (LMU), Teemu Pennanen (LMU), Ari-Pekka Perkki\"o (LMU) + Valery Y. Glizer, Vladimir Turetsky - Optimal coefficients for elliptic PDEs - https://arxiv.org/abs/2512.08431 - arXiv:2512.08431v1 Announce Type: new -Abstract: We consider an optimization problem related to elliptic PDEs of the form $-{\rm div}(a(x)\nabla u)=f$ with Dirichlet boundary condition on a given domain $\Omega$. The coefficient $a(x)$ has to be determined, in a suitable given class of admissible choices, in order to optimize a given criterion. We first deal with the case when the cost is the so-called elastic compliance, and then we discuss the more general case when the problem is written as an optimal control problem. - oai:arXiv.org:2512.08431v1 - math.OC - Wed, 10 Dec 2025 00:00:00 -0500 + Mathematical and numerical studies on ground states of trapped unitary Fermi gases + https://arxiv.org/abs/2512.09479 + arXiv:2512.09479v1 Announce Type: new +Abstract: We mathematically and numerically study the ground states of unitary Fermi gases. Starting from the three-dimensional nonlinear Schr\"{o}dinger equation that contains a quantum pressure term and an angular momentum rotation term, we first nondimensionalize the equation and then obtain its one-dimensional and two-dimensional counterparts in some limit regimes of the external potentials. Existence and uniqueness of the ground states of the unitary Fermi gases are studied with/without the angular momentum rotation term. We present a regularized normalized gradient flow method to compute the ground states of trapped unitary Fermi gases. Our numerical results show that the quantum pressure term has a significant effect on the ground state properties. Specifically, with the presence of the quantum pressure term, the vortex lattices are very different from those obtained in conventional Bose-Einstein condensation. + oai:arXiv.org:2512.09479v1 + math-ph + math.MP + Thu, 11 Dec 2025 00:00:00 -0500 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Giuseppe Buttazzo, Juan Casado-D\'iaz, Faustino Maestre + http://creativecommons.org/licenses/by-nc-nd/4.0/ + Yongyong Cai, Xinran Ruan, Yanzhi Zhang - An Overview of Sensitivity-Based Distributed Optimization and Model Predictive Control - https://arxiv.org/abs/2512.08446 - arXiv:2512.08446v1 Announce Type: new -Abstract: This paper presents a concise overview of sensitivity-based methods for solving large-scale optimization problems in distributed fashion. The approach relies on sensitivities and primal decomposition to achieve coordination between the subsystems while requiring only local computations with neighbor-to-neighbor communication. We give a brief historical synopsis of its development and apply it to both static and dynamic optimization problems. Furthermore, a real-time capable distributed model predictive controller is proposed which is experimentally validated on a coupled watertank system. - oai:arXiv.org:2512.08446v1 - math.OC - Wed, 10 Dec 2025 00:00:00 -0500 + Isoperimetric Regions in Anisotropically Scaled Product Manifolds + https://arxiv.org/abs/2512.09490 + arXiv:2512.09490v1 Announce Type: new +Abstract: Let $M, N$ be compact Riemannian manifolds. Then, for fixed volume fraction, in the product of a sufficiently small homothetic copy of $M$ with $N$, every isoperimetric region is the product of $M$ with an isoperimetric region in $N$, provided the boundaries of the isoperimetric regions in $N$ are smooth. + oai:arXiv.org:2512.09490v1 + math.DG + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Maximilian Pierer von Esch, Andreas V\"olz, Knut Graichen + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Efstratios Vernadakis - On the stochastic proof of the Blaschke-Santal\'o inequality - https://arxiv.org/abs/2512.08454 - arXiv:2512.08454v1 Announce Type: new -Abstract: In 2024, Courtade, Fathi and Mikulincer gave a proof of the symmetrized Talagrand inequality based on stochastic calculus, in the spirit of Borell's proof of the Pr\'ekopa-Leindler inequality. The symmetrized Talagrand inequality can be seen as a dual form of the functional Santal\'o inequality. The modest purpose of this note is to give a simplified version of the Courtade, Fathi and Mikulincer argument. Namely we first recall briefly Borell's original argument, and we then explain a simple twist in his proof that allows to recover the functional Santal\'o inequality directly, rather than in its dual form. - oai:arXiv.org:2512.08454v1 + Kesten's criterion for discrete probability measure-preserving groupoids + https://arxiv.org/abs/2512.09507 + arXiv:2512.09507v1 Announce Type: new +Abstract: Inspired by Kesten's criterion for the amenability of groups, we establish a characterization of the amenability of discrete probability measure-preserving groupoids in terms of the operator norms of symmetric invariant Markov operators. + oai:arXiv.org:2512.09507v1 math.FA + math.DS + math.GR math.PR - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Joseph Lehec + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Soham Chakraborty, Milan Donvil, Felipe Flores, Mario Klisse - Roth-type theorems in additive combinatroics - https://arxiv.org/abs/2512.08455 - arXiv:2512.08455v1 Announce Type: new -Abstract: In this article we will introduce a central problem in additive combinatorics, which arised from the famous van der Waerden theorem and an early conjecture of Erd\H{o}s and Tur\'{a}n. The first important theorem was due to Roth in 1953. There were a number of generalized or improved results afterwards, which we call Roth-type theorems. We will list them and try to give concise expositions to the ideas in some of the proofs without much prior knowledge. - oai:arXiv.org:2512.08455v1 + Coloring Geometric Hypergraphs: A Survey + https://arxiv.org/abs/2512.09509 + arXiv:2512.09509v1 Announce Type: new +Abstract: The \emph{chromatic number} of a hypergraph is the smallest number of colors needed to color the vertices such that no edge of at least two vertices is monochromatic. Given a family of geometric objects $\mathcal{F}$ that covers a subset $S$ of the Euclidean space, we can associate it with a hypergraph whose vertex set is $\mathcal F$ and whose edges are those subsets ${\mathcal{F}'}\subset \mathcal F$ for which there exists a point $p\in S$ such that ${\mathcal F}'$ consists of precisely those elements of $\mathcal{F}$ that contain $p$. The question whether $\mathcal F$ can be split into 2 coverings is equivalent to asking whether the chromatic number of the hypergraph is equal to 2. + There are a number of competing notions of the chromatic number that lead to deep combinatorial questions already for abstract hypergraphs. In this paper, we concentrate on \emph{geometrically defined} (in short, \emph{geometric}) hypergraphs, and survey many recent coloring results related to them. In particular, we study and survey the following problem, dual to the above covering question. Given a set of points $S$ in the Euclidean space and a family $\mathcal{F}$ of geometric objects of a fixed type, define a hypergraph ${\mathcal H}_m$ on the point set $S$, whose edges are the subsets of $S$ that can be obtained as the intersection of $S$ with a member of $\mathcal F$ and have at least $m$ elements. Is it true that if $m$ is large enough, then the chromatic number of ${\mathcal H}_m$ is equal to 2? + oai:arXiv.org:2512.09509v1 math.CO - math.NT - Wed, 10 Dec 2025 00:00:00 -0500 + cs.CG + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Weiwen Zhang + G\'abor Dam\'asdi, Bal\'azs Keszegh, J\'anos Pach, D\"om\"ot\"or P\'alv\"olgyi, G\'eza T\'oth - Elliptic functions, Floquet transform and Bergman spaces on doubly periodic domains - https://arxiv.org/abs/2512.08460 - arXiv:2512.08460v1 Announce Type: new -Abstract: We study Bergman spaces A^2(D), their kernels and Toeplitz operators on unbounded, doubly periodic domains D in the complex plane. We establish the mapping properties of the Floquet transform operator defined in A^2(D) and derive a general formula connecting the Bergman kernel and projection of the domain D to a kernel and projection on the bounded periodic cell B. As an application, we prove, for Toeplitz operators T_a with doubly periodic symbols, a spectral band formula, which describes the spectrum and essential spectrum of T_a in terms of the spectra of a family of Toeplitz-type operators on the cell B. Technical challenges arise from the fact that double quasiperiodic boundary conditions have to be taken into account in the definitions of the spaces and operators on the periodic cell B. This requires novel operator theoretic tools, which are based on modifications of certain elliptic functions, e.g. the Weierstrass p-function. - oai:arXiv.org:2512.08460v1 - math.CV - math.FA - Wed, 10 Dec 2025 00:00:00 -0500 + A parallelogram height inequality for Drinfeld modules + https://arxiv.org/abs/2512.09526 + arXiv:2512.09526v1 Announce Type: new +Abstract: We prove inequalities relating the Taguchi heights, respectively the graded heights, of four Drinfeld modules arranged in a ``parallelogram of isogenies''. This inequality is the analogue for Drinfeld modules of the parallelogram inequality of R\'emond (2022) for abelian varieties over number fields and of Griffon--Le Fourn--Pazuki (2025) for abelian varieties over function fields. + oai:arXiv.org:2512.09526v1 + math.NT + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Jari Taskinen, Zhan Zhang + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Liam Baker, Richard Griffon, Fabien Pazuki - Fields of dp-Rank 2 and their W_2-Topologies: The Characteristic 2 Case - https://arxiv.org/abs/2512.08468 - arXiv:2512.08468v1 Announce Type: new -Abstract: In this note we reproduce Johnson's analysis of $W_2$-topologies on fields of characteristic 2, which was originally stated for fields of characteristic different than 2. Following his framework, we prove that the canonical topology of an unstable field of characteristic 2 and dp-rank 2 is a $V$-topology. Additionally, we show that any $W_2$-topology on a field of characteristic 2 is either induced by the intersection of two valuation rings or it is induced by dense pre-diffeo-valuation data, completing the picture for all positive characteristic fields. - oai:arXiv.org:2512.08468v1 - math.LO - Wed, 10 Dec 2025 00:00:00 -0500 + Hyperbolic foliated entropy of suspensions + https://arxiv.org/abs/2512.09528 + arXiv:2512.09528v1 Announce Type: new +Abstract: We study the hyperbolic entropies of foliations obtained by suspensions of a representation, in the sense of Dinh, Nguy\^en and Sibony (topological and measure-theoretic). We establish a link between this type of entropy and an adapted version of an entropy defined by Ghys, Langevin and Walczak for pseudo-groups of homeomorphisms. + Such a link has various consequences. Among them, it implies that the hyperbolic entropy of foliations is not invariant by diffeomorphisms, and that a minimal entropy suspension admits an invariant measure. Finally, this allows us to study thoroughly the simple case in which the image of the representation is isomorphic to~$\mathbb{Z}$. In that case, we give the first exact estimate of the hyperbolic entropy, and prove a Brin--Katok type theorem and a variational principle, relying strongly on the standard ones for the entropy of maps. + oai:arXiv.org:2512.09528v1 + math.DS + math.CV + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Paulo Andr\'es Soto Moreno + Fran\c{c}ois Bacher - Quasiconformal symbols and projected composition operators - https://arxiv.org/abs/2512.08473 - arXiv:2512.08473v1 Announce Type: new -Abstract: We study projected composition operators K_g with quasiconformal symbols g on weighted Bergman spaces on the open unit disc D. If the symbol were conformal, i.e.a M\"obius transform of D, the corresponding composition operator would be automatically invertible at least in standard weighted spaces. We show that the invertibility remains, if the Beltrami coefficient is small enough, in particular, it satisfies a certain vanishing condition at the boundary of the disc. We also consider the invertibility of K_g for symbols g which are conformal in an annulus { R < |z| < 1 }. The weight classes in our considerations include both standard and exponentially decreasing weights. - oai:arXiv.org:2512.08473v1 - math.FA - Wed, 10 Dec 2025 00:00:00 -0500 + Bochner's technique in Einstein's non-symmetric geometry + https://arxiv.org/abs/2512.09532 + arXiv:2512.09532v1 Announce Type: new +Abstract: A. Einstein considered a manifold with a non-symmetric (0,2)-tensor $G$ and a linear connection $\nabla=(\Gamma^k_{ij})$ satisfying the condition $\dfrac{\partial G_{ij}}{\partial x^k} = \Gamma^p_{ik}G_{pj} +\Gamma^p_{kj}G_{ip}$. Guided by the construction of an almost Lie algebroid (on a vector bundle), we define the following concepts of Bochner's technique for the Einstein's non-symmetric geometry: the $\nabla^{f}$-connection, Bochner and Hodge $f$-Laplacians on tensors, the $f$-curvature operator and the Weitzenb\"{o}ck type curvature operator of Einstein's connection. We prove Weitzenb\"{o}ck type decomposition formula and obtain vanishing results about the null space of the Bochner and Hodge $f$-Laplacians. + oai:arXiv.org:2512.09532v1 + math.DG + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Sinem S\"onmez, Jari Taskinen + http://creativecommons.org/licenses/by/4.0/ + Vladimir Rovenski - Construction and Performance of Kinetic Schemes for Linear Systems of Conservation Laws - https://arxiv.org/abs/2512.08479 - arXiv:2512.08479v1 Announce Type: new -Abstract: We describe a methodology to build vectorial kinetic schemes, targetting the numerical solution of linear symmetric-hyperbolic systems of conservation laws -a minimal application case for those schemes. Precisely, we fully detail the construction of kinetic schemes that satisfy a discrete equivalent to a convex extension (an additional non-trivial conservation law) of the target system -the (linear) acoustic and elastodynamics systems, specifically -. Then, we evaluate numerically the convergence of various possible kinetic schemes toward smooth solutions, in comparison with standard finite-difference and finite-volume discretizations on Cartesian meshes. Our numerical results confirm the interest of ensuring a discrete equivalent to a convex extension, and show the influence of remaining parameter variations in terms of error magnitude, both for ''first-order'' and ''second-order'' kinetic schemes\,: the parameter choice with largest CFL number (equiv., smallest spurious diffusion in the equivalent equation analysis) has the smallest discretization error. - oai:arXiv.org:2512.08479v1 - math.NA - cs.NA - Wed, 10 Dec 2025 00:00:00 -0500 + Trajectory Optimization by Successive Pseudospectral Convexification on Riemannian Manifolds + https://arxiv.org/abs/2512.09551 + arXiv:2512.09551v1 Announce Type: new +Abstract: This paper proposes an intrinsic pseudospectral convexification framework for optimal control problems with manifold constraints. While successive pseudospectral convexification combines spectral collocation with successive convexification, classical pseudospectral methods are not geometry-consistent on manifolds. This is because interpolation and differentiation are performed in Euclidean coordinates. We introduce a geometry-consistent transcription that enables pseudospectral collocation without imposing manifold constraints extrinsically. The resulting method solves nonconvex manifold-constrained problems through a sequence of convex subproblems. A six-degree-of-freedom landing guidance example with unit quaternions and unit thrust-direction vectors demonstrates the practicality of the approach and preserves manifold feasibility to machine precision. + oai:arXiv.org:2512.09551v1 + math.OC + Thu, 11 Dec 2025 00:00:00 -0500 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Emmanuel Audusse (LAGA), S\'ebastien Boyaval (MATHERIALS, LHSV), Virgile Dubos (UMA), Minh-Hoang Le (LHSV) + http://creativecommons.org/licenses/by-nc-nd/4.0/ + Tatsuya Narumi, Shin-ichiro Sakai - Scattering from a random thin coating of nanoparticles: the Dirichlet case - https://arxiv.org/abs/2512.08487 - arXiv:2512.08487v1 Announce Type: new -Abstract: We study the time-harmonic scattering by a heterogeneous object covered with a thin layer of randomly distributed sound-soft nanoparticles. The size of the particles, their distance between each other and the layer's thickness are all of the same order but small compared to the wavelength of the incident wave. Solving the Helmholtz equation in this context can be very costly and the simulation depends on the given distribution of particles. To circumvent this, we propose, via a multi-scale asymptotic expansion of the solution, an effective model where the layer of particles is replaced by an equivalent boundary condition. The coefficients that appear in this equivalent boundary condition depend on the solutions to corrector problems of Laplace type defined on unbounded random domains. Under the assumption that the particles are distributed given a stationary and mixing random point process, we prove that those problems admit a unique solution in the proper space. We then establish quantitative error estimates for the effec tive model and present numerical simulations that illustrate our theoretical results. - oai:arXiv.org:2512.08487v1 - math.AP - Wed, 10 Dec 2025 00:00:00 -0500 + A tensor phase theory with applications in multilinear control + https://arxiv.org/abs/2512.09559 + arXiv:2512.09559v1 Announce Type: new +Abstract: The purpose of this paper is to initiate a phase theory for tensors under the Einstein product, and explore its applications in multilinear control systems. Firstly, the sectorial tensor decomposition for sectorial tensors is derived, which allows us to define phases for sectorial tensors. A numerical procedure for computing phases of a sectorial tensor is also proposed. Secondly, the maximin and minimax expressions for tensor phases are given, which are used to quantify how close the phases of a sectorial tensor are to those of its compressions. Thirdly, the compound spectrum, compound numerical ranges and compound angular numerical ranges of two sectorial tensors $A,B$ are defined and characterized in terms of the compound numerical ranges and compound angular numerical ranges of the sectorial tensors $A,B$. Fourthly, it is shown that the angles of eigenvalues of the product of two sectorial tensors are upper bounded by the sum of their individual phases. Finally, based on the tensor phase theory developed above, a tensor version of the small phase theorem is presented, which can be regarded as a natural generalization of the matrix case, recently proposed in Ref. [10]. The results offer powerful new tools for the stability and robustness analysis of multilinear feedback control systems. + oai:arXiv.org:2512.09559v1 + math.OC + cs.SY + eess.SY + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Amandine Boucart, Sonia Fliss, Laure Giovangigli + Chengdong Liu, Yimin Wei, Guofeng Zhang - On iterated universal extensions and Nori's fundamental group of nilpotent bundles - https://arxiv.org/abs/2512.08494 - arXiv:2512.08494v1 Announce Type: new -Abstract: Let $k$ be a field of characteristic $0$, $X$ be a geometrically connected, smooth and proper variety over $k$ and $x\in X(k)$ be a base point. Using the notion of an iterated universal extension, we show that Nori's fundamental group $\pi_{1}^{N}(X,x)$ of nilpotent bundles is uniquely determined by the coherent cohomology groups $\mathrm{H}^{i}(X)=\mathrm{H}^{i}(X,\mathcal{O}_{X})$, $i=1,2$, and the cup product $\cup: \mathrm{H}^{1}(X)\otimes\mathrm{H}^{1}(X) \rightarrow \mathrm{H}^{2}(X)$. This can be seen as an analogy of a classical fact on the de Rham fundamental group of compact K\"ahler manifolds. We also prove a homotopy exact sequence for Nori's fundamental group. - oai:arXiv.org:2512.08494v1 - math.AG - Wed, 10 Dec 2025 00:00:00 -0500 + Reductive monoids and cluster algebras + https://arxiv.org/abs/2512.09564 + arXiv:2512.09564v1 Announce Type: new +Abstract: We show that the coordinate ring of the Vinberg monoid of a simply connected semisimple complex group is an upper cluster algebra. As an application, we construct cluster structures on a large class of flat reductive monoids. After localization, we obtain cluster structures on any connected reductive group whose commutator group is simply connected. + oai:arXiv.org:2512.09564v1 + math.RT + math.RA + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Xiaodong Yi + Jinfeng Song, Jeff York Ye - Fractional Homogenization of Parabolic Equations with Long-Range Random Potentials - https://arxiv.org/abs/2512.08496 - arXiv:2512.08496v1 Announce Type: new -Abstract: This paper establishes a complete homogenization theory for the one-dimensional parabolic equation with long-range correlated random potential: \[ \partial_t u_\varepsilon(t,x) = \frac{1}{2} \partial_{xx} u_\varepsilon(t,x) + \varepsilon^{-\alpha/2} a\left(\frac{x}{\varepsilon}\right) u_\varepsilon(t,x), \] where the random field $a$ has covariance decaying as $|x|^{-\alpha}$ with $\alpha \in (0,1)$. Contrary to classical homogenization where rapid decorrelation leads to deterministic limits, the non-integrable covariance preserves macroscopic randomness. - We prove that under the critical scaling $\varepsilon^{-\alpha/2}$, the solution converges in distribution to a stochastic limit described by a fractional Gaussian field with Hurst index $H = 1-\alpha/2 > 1/2$: \[ u(t,x) = \mathbb{E}^B\left[\varphi(x+B_t) \exp\left(\beta\int_{\mathbb{R}} L_t^x(y) dW^H(y)\right)\right], \] where $W^H$ is fractional Brownian motion and the integral is a Young integral. Our contributions include: (i) functional convergence of the integrated potential to fBm, (ii) quantitative convergence rates in Wasserstein distance $W_2(u_\varepsilon, u) \leq C\varepsilon^{\min(\alpha,1-\alpha)/4}$, (iii) a central limit theorem for rescaled fluctuations with scaling $\varepsilon^{-\alpha/4}$, and (iv) superdiffusive transport $\mathbb{E}[X_t^2] \sim t^{2H}$. - The results reveal a new homogenization mechanism driven by long-range dependence, connecting stochastic homogenization, fractional calculus, and anomalous diffusion theory. - oai:arXiv.org:2512.08496v1 - math.PR - Wed, 10 Dec 2025 00:00:00 -0500 + Equiaffine immersions and pseudo-Riemannian space forms + https://arxiv.org/abs/2512.09569 + arXiv:2512.09569v1 Announce Type: new +Abstract: We introduce an explicit construction that produces immersions into the pseudosphere $\mathbb{S}^{n,n+1}$ and the pseudohyperbolic space $\mathbb{H}^{n+1,n}$ starting from equiaffine immersions in $\mathbb{R}^{n+1}$, and conversely. We describe how these immersions interact with a para-Sasaki metric defined on $\mathbb{H}^{n+1,n}$ via a principal $\mathbb{R}$-bundle structure over a para-K\"ahler manifold. In the case where the immersion in $\mathbb{R}^{n+1}$ is an $n$-dimensional hyperbolic affine sphere, we obtain spacelike maximal immersions in $\mathbb{H}^{n+1,n}$ that satisfy a transversality condition with respect to the principal $\mathbb{R}$-bundle structure. As a first application, we show that, given a certain boundary set $\Lambda_\Omega \subset \partial_\infty \mathbb{H}^{n+1,n}$, associated with a properly convex subset $\Omega \subset \mathbb{RP}^n$ and homeomorphic to an $(n-1)$-sphere, there exists an $n$-dimensional maximal spacelike submanifold in $\mathbb{H}^{n+1,n}$ whose boundary is precisely $\Lambda_\Omega$. As a second application, we show that the Blaschke lift of the hyperbolic affine sphere, introduced by Labourie for $n=2$, into the symmetric space of $\mathrm{SL}(n+1,\mathbb{R})$ is a harmonic map. + oai:arXiv.org:2512.09569v1 + math.DG + math.GT + math.SG + Thu, 11 Dec 2025 00:00:00 -0500 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Atef Lechiheb + http://creativecommons.org/licenses/by/4.0/ + Nicholas Rungi - Weak disjointness of hypercyclic operators - https://arxiv.org/abs/2512.08519 - arXiv:2512.08519v1 Announce Type: new -Abstract: We study the weak disjointness of hypercyclic operators to advance the classifications of hypercyclic operators. We establish an analogue of the Weiss-Akin-Glasner Theorem from topological dynamics within the framework of linear dynamics, which gives a characterization of the weak disjointness of each class of mixing operators with respect to a given Furstenberg family. The key ingredient is the analogues of Weiss-Akin-Glasner Lemma from topological dynamics, which gives a characterization of subsets of non-negative integers which can be realized by the return time sets of mixing operators with respect to a given Furstenberg family. We also provide several examples to distinguish some classes of hypercyclic operators and end with the characterization of the weak disjointness of backward shifts on Fr\'echet sequence spaces. - oai:arXiv.org:2512.08519v1 - math.DS + Fractional weighted Sobolev spaces associated to the Riesz fractional gradient + https://arxiv.org/abs/2512.09575 + arXiv:2512.09575v1 Announce Type: new +Abstract: In this work, we introduce a new family of functions spaces, the weighted fractional Sobolev spaces $X^{s,p}_{0,w}(\Omega)$, where $w$ is a weight in the Muckenhoupt class $A_p$. This space is a natural extension of the fractional Sobolev spaces $H^{s,p}_0$, obtained by means of the Riesz fractional gradient $D^s$, to the setting of the weighted Lebesgue spaces $L^p_w$. As it happened in the unweighted space, the spaces $X^{s,p}_{0,w}(\Omega)$ coincide with the weighted version of the Bessel potential space. We obtaien several structural properties for these spaces, as well as continuous and compact embeddings. We conclude with the study of a family of degenerate fractional elliptic partial differential equations. + oai:arXiv.org:2512.09575v1 + math.AP math.FA - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jian Li, Qijing Liao, Yonghang Ruan + Guillermo Garc\'ia-S\'aez - Decomposable semigroups on C*-algebras and D-divisible dynamical maps - https://arxiv.org/abs/2512.08525 - arXiv:2512.08525v1 Announce Type: new -Abstract: We analyze semigroups of decomposable maps on C*-algebras in context of the algebraic structure of associated infinitesimal generators. Case of von Neumann algebras, including $B(\mathcal{H})$ for $\mathcal{H}$ a Hilbert space, is also addressed. We then elaborate on D-divisible (decomposably divisible) dynamical maps on the Banach space of trace class operators. Our analysis extends earlier results on decomposable dynamical maps on matrix algebras (J. Phys. A: Math. Theor. 56 485202) and provides a partial generalization of the seminal work of Lindblad (Commun. Math. Phys. 48 119-130) on completely positive semigroups. - oai:arXiv.org:2512.08525v1 + New insights into linear maps which are anti-derivable at zero + https://arxiv.org/abs/2512.09578 + arXiv:2512.09578v1 Announce Type: new +Abstract: Let $A$ be a Banach algebra admitting a bounded approximate unit and satisfying property $\mathbb{B}$. Suppose $T: A \rightarrow X$ is a continuous linear map, where $X$ is an essential Banach $A$-bimodule. We prove that the following statements are equivalent: + $(i)$ $T$ is anti-derivable at zero (i.e., $a b =0$ in $A$ $\Rightarrow T(b)\cdot a + b\cdot T(a) =0$); + $(ii)$ There exist an element $\xi \in X^{**}$ and a linear map (actually a bounded Jordan derivation) $d: A\to X$ satisfying $\xi \cdot a = a \cdot \xi \in X$, $T(a) = d(a) +\xi \cdot a$, and $d(b)\cdot a + b\cdot d(a)= - 2 \xi \cdot (b a),$ for all $a,b\in A$ with $a b =0$. + Assuming that $A$ is a C$^*$-algebra we show that a bounded linear mapping $T: A\to X$ is anti-derivable at zero if, and only if, there exist an element $\eta \in X^{**}$ and an anti-derivation $d: A \rightarrow X$ satisfying $\eta \cdot a = a \cdot \eta \in X$, $\eta \cdot [a,b] = 0$ {\rm(}i.e., $L_{\eta}: A \to A$, $L_{\eta} (a) = \eta \cdot a$ vanishes on commutators{\rm)}, and $T(a) = d(a) +\eta \cdot a$, for all $a,b \in A$. The results are also applied for some special operator algebras. + oai:arXiv.org:2512.09578v1 math.OA - math-ph - math.MP - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Krzysztof Szczygielski + http://creativecommons.org/licenses/by-nc-nd/4.0/ + Jiankui Li, Antonio M. Peralta, Shanshan Su - A Lie-theoretic generalization of some Hilbert schemes - https://arxiv.org/abs/2512.08532 - arXiv:2512.08532v1 Announce Type: new -Abstract: We define several versions of a class of varieties $X_{\mathfrak{g}}$ attached to a complex reductive Lie algebra $\mathfrak{g}$, generalizing the Hilbert scheme of points on the plane. These include trigonometric and elliptic versions attached to the corresponding groups. We also define the corresponding isospectral varieties $Y_{\mathfrak{g}}$. We prove a Gordon-Stafford localization theorem for $X_{\mathfrak{g}}$ and the corresponding equal-parameter rational Cherednik algebras, relate these varieties to the affine Springer fiber-sheaf correspondence of arXiv:2204.00303, and discuss examples. We conjecture that the torus-fixed points of our varieties are in bijection with two-sided cells in the finite Weyl group and prove this in types $ABC$. We relate these results to known results about Calogero-Moser spaces. - oai:arXiv.org:2512.08532v1 - math.AG - math.RT - Wed, 10 Dec 2025 00:00:00 -0500 + Concentration of Truncated Signatures of Gaussian Rough Paths + https://arxiv.org/abs/2512.09588 + arXiv:2512.09588v1 Announce Type: new +Abstract: This paper establishes a comprehensive concentration theory for truncated signatures of Gaussian rough paths. The signature of a path, defined as the collection of all iterated integrals, provides a complete description of its geometric structure and has emerged as a powerful tool in machine learning and stochastic analysis. Despite growing applications in finance, healthcare, and engineering, the non-asymptotic concentration properties of signature features remain largely unexplored. + We prove that level-$k$ signature coordinates exhibit optimal $\exp(-c t^{2/k})$ tail decay and establish dimension-free concentration inequalities for the full truncated signature vector. Our results reveal a fundamental trade-off: higher truncation levels capture more complex path properties but exhibit heavier tails. For Brownian motion and fractional Brownian motion with Hurst parameter $H > 1/4$, we derive explicit variance formulas and sharp constants. + The technical contributions combine rough path theory with Gaussian analysis, leveraging Wiener chaos decomposition, hypercontractivity, and the algebraic structure of tensor algebras. We further establish concentration for log-signatures, lead-lag transformations, and provide sample complexity bounds for statistical learning with signature features. + This work bridges advanced probability theory with practical applications, offering both theoretical guarantees and computational methods for signature-based approaches in sequential data analysis. + oai:arXiv.org:2512.09588v1 + math.PR + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Oscar Kivinen + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Atef Lechiheb - The Smith form of Sylvester and B\'ezout matrices for zero-dimensional ideals - https://arxiv.org/abs/2512.08550 - arXiv:2512.08550v1 Announce Type: new -Abstract: Let $\mathbb{K}$ be a field and let $f,g \in \mathbb{K}[x,y]$ be such that the ideal $\ideal{f,g}$ is zero-dimensional. We study the Sylvester and B\'{e}zout resultant polynomial matrices, built by interpreting $f$ and $g$ as univariate polynomials in $x$ with coefficients in $\mathbb{K}[y]$. We characterize their Smith forms over $\mathbb{K}[y]$ in terms of the dual spaces of differential operators, that were defined and studied by H. M. M\"{o}ller et al. In particular, we show that, if the leading coefficients of $f$ and $g$ are coprime over $\mathbb{K}[y]$, then the partial multiplicities of the Sylvester and B\'{e}zout resultant matrices coincide with certain integers, that we call M\"{o}ller indices. These indices are uniquely determined by $\ideal{f,g}$, and can be easily computed from a Gauss basis, as defined in [M. G. Marinari, H. M. M\"{o}ller, T. Mora, Trans. Amer. Math. Soc. 348(8):3283--3321, 1996], of the dual spaces. We then generalize this result to the case of common factors in the leading coefficients, which correspond to intersections at $x=\infty$, again describing all the invariant factors of Sylvester and B\'{e}zout resultant matrices. As a corollary, this fully characterizes the algebraic multiplicity of all the roots of the resultant $\Res_x(f,g) \in \mathbb{K}[y]$ in terms of the intersection multiplicities for $f$ and $g$, including those arising from infinite intersections. We discuss both algebraic and computational implications of our results. - oai:arXiv.org:2512.08550v1 - math.AC - math.AG - Wed, 10 Dec 2025 00:00:00 -0500 + On Inhomogeneous Affine Volterra Processes: Stationarity and Applications to the Volterra Heston Model + https://arxiv.org/abs/2512.09590 + arXiv:2512.09590v1 Announce Type: new +Abstract: True Volterra equations are inherently non stationary and therefore do not admit $\textit{genuine stationary regimes}$ over finite horizons. This motivates the study of the finite-time behavior of the solutions to scaled inhomogeneous affine Stochastic Volterra equations through the lens of a weaker notion of stationarity referred to as $\textit{fake stationary regime}$ in the sense that all marginal distributions share the same expectation and variance. As a first application, we introduce the $\textit{Fake stationary Volterra Heston model}$ and derive a closed-form expression for its characteristic function. Having established this finite-time proxy for stationarity, we then investigate the asymptotic (long-time) behavior to assess whether genuine stationary regimes emerge in the limit. Using an extension of the exponential-affine transformation formula for those processes, we establish in the long run the existence of limiting distributions, which (unlike in the case of classical affine diffusion processes) may depend on the initial state of the process, unless the Volterra kernel coincides with the $\alpha-$ fractional integration kernel, for which the dependence on the initial state vanishes. We then proceed to the construction of stationary processes associated with these limiting distributions. However, the dynamics in this long-term regime are analytically intractable, and the process itself is not guaranteed to be stationary in the classical sense over finite horizons. This highlights the relevance of finite-time analysis through the lens of the aforementioned $\textit{fake stationarity}$, which offers a tractable approximation to stationary behavior in genuinely non-stationary Volterra systems. + oai:arXiv.org:2512.09590v1 + math.PR + q-fin.MF + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Etna Lindy, Vanni Noferini + http://creativecommons.org/licenses/by/4.0/ + Emmanuel Gnabeyeu, Gilles Pag\`es, Mathieu Rosenbaum - Mixed Hessian inequalities on Hermitian manifolds and applications - https://arxiv.org/abs/2512.08552 - arXiv:2512.08552v1 Announce Type: new -Abstract: Let $(X,\omega)$ be a compact Hermitian manifold of complex dimension $n$. In this paper we establish a Ko\l odziej-Nguyen type weak convergence theorem of complex Hessian operators. Utilizing this result, we prove a general mixed Hessian inequality with respect to a background Hermitian metric, covering both local and global case. As an application, we prove the existence of bounded solutions of complex Hessian equations where the right-hand side measure is well dominated by capacities. - oai:arXiv.org:2512.08552v1 - math.DG - Wed, 10 Dec 2025 00:00:00 -0500 + Quasi self-adjoint extensions of a class of formally non-self-adjoint discrete Hamiltonian systems + https://arxiv.org/abs/2512.09594 + arXiv:2512.09594v1 Announce Type: new +Abstract: This paper is concerned with the characterizations of quasi self-adjoint extensions of a class of formally non-self-adjoint discrete Hamiltonian systems. Some properties of the solutions and the characterization of the minimal linear relations of the non-self-adjoint systems are obtained. A bijective projection between all the quasi self-adjoint extensions of non-self-adjoint systems and all the self-adjoint extensions of the self-adjoint systems generated by the non-self-adjoint Hamiltonian systems is established in the general case. When the system is in the limit point case and $\I=[a,\infty)$, a complete characterization of all the quasi self-adjoint extensions is obtained by a subspace $Q\subset \C^{2n}$ with $\dim Q=n$ in terms of boundary conditions. + oai:arXiv.org:2512.09594v1 + math.SP + Thu, 11 Dec 2025 00:00:00 -0500 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Haoyuan Sun + http://creativecommons.org/licenses/by-nc-nd/4.0/ + Guojing Ren, Guixin Xu - A scalable high-order multigrid-FFT Poisson solver for unbounded domains on adaptive multiresolution grids - https://arxiv.org/abs/2512.08555 - arXiv:2512.08555v1 Announce Type: new -Abstract: Multigrid solvers are among the most efficient methods for solving the Poisson equation, which is ubiquitous in computational physics. For example, in the context of incompressible flows, it is typically the costliest operation. The present document expounds upon the implementation of a flexible multigrid solver that is capable of handling any type of boundary conditions within murphy, a multiresolution framework for solving partial differential equations (PDEs) on collocated adaptive grids. The utilization of a Fourier-based direct solver facilitates the attainment of flexibility and enhanced performance by accommodating any combination of unbounded and semi-unbounded boundary conditions. The employment of high-order compact stencils contributes to the reduction of communication demands while concurrently enhancing the accuracy of the system. The resulting solver is validated against analytical solutions for periodic and unbounded domains. In conclusion, the solver has been demonstrated to demonstrate scalability to 16,384 cores within the context of leading European high-performance computing infrastructures. - oai:arXiv.org:2512.08555v1 - math.NA - cs.DC - cs.NA - Wed, 10 Dec 2025 00:00:00 -0500 + Sums, products, and exponents in two-colorings of the naturals + https://arxiv.org/abs/2512.09598 + arXiv:2512.09598v1 Announce Type: new +Abstract: We prove that for any coloring of the naturals using two colors there are monochromatic sets of the form $\{x,y,xy,x+iy:i\leq k\}$ and $\{x,y,x^y,xy^i:i\leq k\}$ for any $k$. + oai:arXiv.org:2512.09598v1 + math.CO + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Gilles Poncelet, Jonathan Lambrechts, Thomas Gillis, Philippe Chatelain + Ryan Alweiss, Matthew Bowen, Marcin Sabok - Stability of $n$-soliton solutions for the Intermediate Long Wave equation - https://arxiv.org/abs/2512.08562 - arXiv:2512.08562v1 Announce Type: new -Abstract: In this work, we focus on the stability of $n$-soliton solutions ($n\in \mathbb{N}, n\geq 1$) to the completely integrable intermediate long wave equation (ILW), which models long internal gravity waves in a stratified fluid of finite depth. We show that the $n$-soliton solutions of the ILW equation form non-isolated constrained minimizers of a variational problem associated with a non-local elliptic equation. To establish this result, we construct a suitable Lyapunov functional and utilize the inverse scattering transform to relate the infinite sequence of conservation laws to the scattering data. Furthermore, we employ the recursion operator derived from the bi-Hamiltonian structure to optimize our analysis. Our analysis demonstrates that the $n$-soliton solutions of the ILW equation are dynamically stable in the space $H^{\frac{n}{2}}(\mathbb{R})$ ($n\in \mathbb{N}, n\geq 1$). Additionally, we establish the orbital stability of double soliton solutions in $H^1(\mathbb{R})$. - oai:arXiv.org:2512.08562v1 + On a large deviation principle for 1d cubic NLS with optimal decaying data + https://arxiv.org/abs/2512.09599 + arXiv:2512.09599v1 Announce Type: new +Abstract: In this article, we revisit the work of \cite{garrido2023large}, and prove large deviation principles for more general random initial data for cubic NLS. The Fourier coefficient of our random data admits an optimal polynomial decay. + oai:arXiv.org:2512.09599v1 math.AP - Wed, 10 Dec 2025 00:00:00 -0500 + math.PR + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Zhen Lu, Shou-Fu Tian + Chenjie Fan, Feng Ye - Realization of relational presheaves - https://arxiv.org/abs/2512.08566 - arXiv:2512.08566v1 Announce Type: new -Abstract: Relational presheaves generalize traditional presheaves by going to the category of sets and relations (as opposed to sets and functions) and by allowing functors which are lax. This added generality is useful because it intuitively allows one to encode situations where we have representables without boundaries or with multiple boundaries at once. In particular, the relational generalization of precubical sets has natural application to modeling concurrency. In this article, we study categories of relational presheaves, and construct realization functors for those. We begin by observing that they form the category of set-based models of a cartesian theory, which implies in particular that they are locally finitely presentable categories. By using general results from categorical logic, we then show that the realization of such presheaves in a cocomplete category is a model of the theory in the opposite category, which allows characterizing situations in which we have a realization functor. Finally, we explain that our work has applications in the semantics of concurrency theory. The realization namely allows one to compare syntactic constructions on relational presheaves and geometric ones. Thanks to it, we are able to provide a syntactic counterpart of the blowup operation, which was recently introduced by Haucourt on directed geometric semantics, as way of turning a directed space into a manifold. - oai:arXiv.org:2512.08566v1 - math.CT - cs.LO - Wed, 10 Dec 2025 00:00:00 -0500 + Explicit valuation of elliptic nets for elliptic curves with complex multiplication + https://arxiv.org/abs/2512.09601 + arXiv:2512.09601v1 Announce Type: new +Abstract: Division polynomials associated to an elliptic curve $E/K$ are polynomials $\phi_n, \psi_n^2$ that arise from the sequence of points $\{nP\}_{n \in \mathbb{N}}$ on this curve. If one wishes to study $\mathbb{Z}$--linear combination of points on $E(K)$, we can use net polynomials $\Phi_{v}, \Psi_{v}^2$ which are higher--dimensional analogue of division polynomials. It turns out they are also elliptic nets, an $n$--dimensional array with values in $K$ satisfying the same nonlinear recurrence relation that division polynomials do as well. Now further assume the elliptic curve $E/K$ has complex multiplication by an order of a quadratic imaginary field $F \subseteq K$, we will prove a formula for the common valuation of $\Phi_{v}$ and $\Psi_{v}^2$ associated to multiples of points by elements of an order in $F$. As an application, we will use the formula to show that elliptic divisibility sequences associated to multiples of points indexed by elements of an order also satisfy a recurrence relation when indexed by elements of an order, subject to certain conditions on the indices. Additionally, we also expect that the formula may also be used in computing $\mathcal{O}_K$--integral points of an elliptic curve of rank $2$ with complex multiplication (this is future work). + oai:arXiv.org:2512.09601v1 + math.NT + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Yorgo Chamoun, Samuel Mimram + Edison H L Au-Yeung - Enhancing Kernel Search with Pattern Recognition: the Single-Source Capacitated Facility Location Problem - https://arxiv.org/abs/2512.08576 - arXiv:2512.08576v1 Announce Type: new -Abstract: We introduce Pattern-based Kernel Search (PaKS), a two-phase matheuristic for the solution of the Single-Source Capacitated Facility Location Problem (SSCFLP). In the first phase, PaKS employs a pattern recognition technique to identify an implicit spatial separation of potential locations and customers into subsets, called regions, within which location and assignment decisions are strongly interdependent. In the second phase, PaKS employs an enhanced Kernel Search (KS) heuristic that leverages the interdependencies among the decision variables identified in the first phase. On a set of 112 benchmark instances, consisting of up to 1,000 locations and 1,000 customers, computational results show that PaKS consistently outperforms both a standard KS implementation and the current state-of-the-art heuristic for solving the SSCFLP, as well as CPLEX when run with a time limit. For these instances, PaKS achieved an average gap compared to the best known solution of 0.02%. Experimental results conducted on a large set of new very large test problems, comprising up to 2,000 locations and 2,000 customers, demonstrate that PaKS outperforms both the standard KS heuristic and CPLEX in terms of quality of the solution found, finding the largest number of best solutions, and achieving the smallest average gap. - oai:arXiv.org:2512.08576v1 - math.OC - Wed, 10 Dec 2025 00:00:00 -0500 + Enlarge Greedy Sums in Greedy-Type Properties by Different Factors + https://arxiv.org/abs/2512.09604 + arXiv:2512.09604v1 Announce Type: new +Abstract: It was previously known that the almost greedy (AG) property essentially remains the same when we enlarge greedy sums in the classical definition by a factor $\lambda \geqslant 1$. The present paper shows that if instead, we enlarge greedy sums in a reformulation of the AG property, we obtain a weaker one. However, the new property is essentially independent of the enlarging factor $\lambda$ once $\lambda > 1$. In contrast, we observe a continuum of partially greedy-like properties by varying $\lambda\in [1,\infty)$. Last but not least, under a threshold for $\lambda$, we characterize the isometric version of the weakened AG property. Specifically, the characterization holds if and only if $\lambda\in [1, 2]$. + oai:arXiv.org:2512.09604v1 + math.FA + Thu, 11 Dec 2025 00:00:00 -0500 + new + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Hung Viet Chu + + + Extensions and Applications of Stein-Weiss Operators to Traceless Symmetric Tensor + https://arxiv.org/abs/2512.09605 + arXiv:2512.09605v1 Announce Type: new +Abstract: First-order differential operators arising from the representation-theoretic decomposition of the covariant derivative play a central role in Riemannian geometry. In this paper, we study Stein-Weiss $O(n)$-gradients acting on covariant symmetric trace-free tensors of arbitrary rank $p \ge 2$. By analyzing the decomposition of $T^*M \otimes S_0^p(M)$ into its $O(n)$-irreducible components, we explicitly describe the corresponding generalized gradients and compute Weitzenbock formulas for their adjoint compositions. These results extend Bouguignon four-dimensional formulas for $p = 2$ and generalize previous work of other authors to higher-rank symmetric tensors. The formulas obtained provide a unified framework for understanding second-order Stein-Weiss operators and yield tools applicable to deformation complexes, curvature estimates, and stability problems in geometric analysis. The article continues the authors' earlier investigations of Stein-Weiss operators on natural tensor bundles. + oai:arXiv.org:2512.09605v1 + math.DG + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Hannah Bakker, Gianfranco Guastaroba, Stefan Nickel, M. Grazia Speranza + Sergey Stepanov, Irina Tsyganok - L-algebras and their ideals: from simplicity to semidirect products - https://arxiv.org/abs/2512.08579 - arXiv:2512.08579v1 Announce Type: new -Abstract: In this paper, we investigate the ideals of semidirect products of L-algebras and the structure of simple L-algebras. We provide a precise characterization of the ideals of semidirect products and describe the structure of their prime spectrum. Furthermore, we introduce a family of finite simple L-algebras and prove that every simple linear L-algebra belongs to this family. We also show that the family we construct coincides with the class of simple algebras in a certain subclass of finite CKL-algebras. As an application, we use these results to give a clear description of linear Hilbert algebras and their symmetric semidirect products. - oai:arXiv.org:2512.08579v1 - math.RA - math.CO + Some results on the $\pi$-weight of countable Fr\'echet-Urysohn spaces + https://arxiv.org/abs/2512.09614 + arXiv:2512.09614v1 Announce Type: new +Abstract: The $\pi$-weight spectrum for countable regular Fr\'echet-Urysohn spaces is the set of uncountable cardinals that are equal to the $\pi$-weight for some such space. We determine this $\pi$-weight spectrum in the standard Miller rational perfect set model and in the Random real model. + oai:arXiv.org:2512.09614v1 math.LO - math.QA - Wed, 10 Dec 2025 00:00:00 -0500 + math.GN + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Silvia Properzi, Yufei Qin + Alan Dow - Improved Local Well-Posedness in Sobolev Spaces for Two-Dimensional Compressible Euler Equations - https://arxiv.org/abs/2512.08581 - arXiv:2512.08581v1 Announce Type: new -Abstract: We establish the local existence and uniqueness of solutions to the two-dimensional compressible Euler equations with initial velocity $\bv_0$, logarithmic density $\rho_0$, and specific vorticity \(w_0\), which satisfy $(\bv_0, \rho_0, w_0, \nabla w_0)\in H^{\frac74+}(\mathbb{R}^2)\times H^{\frac74+}(\mathbb{R}^2) \times H^{\frac32}(\mathbb{R}^2) \times L^{8}(\mathbb{R}^2)$. - The proof applies Smith-Tataru method \cite{ST} and the inherent wave-transport structure of the two-dimensional compressible Euler equations. The key observation is that Strichartz estimates hold when the regularity requirement for vorticity is lower than that for velocity and density, even though the gradient of vorticity appears as a source term in the velocity wave equation. Furthermore, our result presents an improvement of $\frac{1}{4}$-order regularity compared to previous results \cite{Z1} and \cite{Z2}. - oai:arXiv.org:2512.08581v1 - math.AP - Wed, 10 Dec 2025 00:00:00 -0500 + Preprojective categories of type A + https://arxiv.org/abs/2512.09618 + arXiv:2512.09618v1 Announce Type: new +Abstract: We introduce a continuous version of preprojective algebras of type $A$. In particular, we are interested in the preprojective category over an open, bounded subinterval $\mathbb{I}$ of $\mathbb{R}$, denoted $\Lambda_{\mathbb{I}}$. We study the representable projective modules and define a useful type of sub- and quotient module called decorous modules. These are completely described by a function from the closure $\overline{\mathbb{I}}$ of $\mathbb{I}$ to $\mathbb{R}$ whose 'slopes' are not too steep anywhere. We later use these to describe permuton ideals, a generalization of the support $\tau$-tilting ideals of preprojective algebras of type $A_n$, which we call permutation ideals. Once we have our generalization, we show that permutation ideals can be recovered from permuton ideals. Moreover, permutation ideals are $\tau$-rigid and we show an analogous property for our permuton ideals. Along the way, we classify all the brick $\Lambda_{\mathbb{I}}$-modules. + oai:arXiv.org:2512.09618v1 + math.RT + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Huali Zhang + Job Daisie Rock, Hugh Thomas - On essential simplicial maps $S^3 \rightarrow S^2$ - https://arxiv.org/abs/2512.08584 - arXiv:2512.08584v1 Announce Type: new -Abstract: A fiber-uniform bound on the complexity of an essential simplicial map $S^3\rightarrow S^2$ is proven, and the tightness of the bound is investigated. It follows that the triangulation of the Hopf map constructed by Madahar and Sarkaria is minimal in its homotopy class in terms of the number of 3-simplices in the triangulation of $S^3$. - oai:arXiv.org:2512.08584v1 - math.AT - Wed, 10 Dec 2025 00:00:00 -0500 + Inverse SRB measures for endomorphisms on surfaces + https://arxiv.org/abs/2512.09624 + arXiv:2512.09624v1 Announce Type: new +Abstract: We extend D. Burguet's construction of SRB measures for the non invertible scenario obtaining hyperbolic invariant measures with absolutely continuous disintegrations on stable manifolds for a certain class of endomorphisms on the two torus. The constructed measures maximize the folding entropy, in particular, one may obtain such SRB measures for conservative perturbations of the examples given by M. Andersson, P. Carrasco and R. Saghin for which the Lebesgue measure does not maximize the folding entropy. This way, we obtain examples of topologically mixing maps with at least two inverse SRB measures. In the case of inverse SRB measures that maximize the folding entropy, we give criteria for uniqueness. + oai:arXiv.org:2512.09624v1 + math.DS + Thu, 11 Dec 2025 00:00:00 -0500 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Mikhail V. Bludov, Sergei Vad. Fomin, Oleg R. Musin + http://creativecommons.org/licenses/by/4.0/ + Victor Janeiro, Radu Saghin - Poisson bivectors on infinite dimensional manifolds - https://arxiv.org/abs/2512.08590 - arXiv:2512.08590v1 Announce Type: new -Abstract: We show that, on a smoothly paracompact convenient manifold $M$ modeled on a convenient space with the bornological approximation property, the dual map of a Poisson bracket factors as a smooth section of the vector bundle $L_{skew}^2(T^*M,\mathbb R)$. - oai:arXiv.org:2512.08590v1 - math.DG - Wed, 10 Dec 2025 00:00:00 -0500 + Classification of real and imaginary modules of quantum affine algebras in monoidal categorifications of affine cluster algebras + https://arxiv.org/abs/2512.09631 + arXiv:2512.09631v1 Announce Type: new +Abstract: Recently, Kashiwara-Kim-Oh-Park introduced a wide family of monoidal categories of finite-dimensional representations of quantum affine algebras, which provide monoidal categorifications of cluster algebras. In this paper, we prove that, for types $ADE$, some of these categories provide monoidal categorifications of cluster algebras of affine type. Moreover, by means of the combinatorial theory of affine type cluster algebras, we give a complete classification of real and imaginary simple modules in these categories. In particular, we show that, in these cases, the conjecture asserting that real simple modules correspond exactly to cluster monomials holds. + oai:arXiv.org:2512.09631v1 + math.RT + math.QA + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Peter W. Michor, Praful Rahangdale + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Heizo Sakamoto - A conceptual model for growth by Capital-Education investments - https://arxiv.org/abs/2512.08594 - arXiv:2512.08594v1 Announce Type: new -Abstract: Economic growth depends on capital investments and on investments in education and innovation. The model introduced here will specifiy aggregate output as determined by aggregate supply of capital and education investment. After formulating and analysing such a model in section 2 we will consider the effectiveness of education for the growth of the National Product. It turns out that small changes of the quality of education has a considerable impact on economic growth. Secondly we consider the influence of chaotic fluctuations of capital investments caused by hype-cycles or erratic policies. In section 3 we introduce a continuous control on education investments depending on consumption. In this 3-dimensional macro-economic model it turns out that a tipping point exists where increase of consumption affecting the amount of education and innovation leads to decline of economic growth. - oai:arXiv.org:2512.08594v1 + Baker domains and orbits disappearing to infinity + https://arxiv.org/abs/2512.09632 + arXiv:2512.09632v1 Announce Type: new +Abstract: We study attracting orbits escaping to infinity in natural families of transcendental entire functions. We show that, if an attracting fixed point escapes to infinity while its multiplier tends to one, then the limiting function has a doubly parabolic Baker domain. Conversely, we show that any function with an invariant doubly parabolic Baker domain can be approximated locally uniformly by functions in its quasiconformal equivalence class having an attracting fixed point whose multiplier tends to one. + oai:arXiv.org:2512.09632v1 math.DS - Wed, 10 Dec 2025 00:00:00 -0500 + math.CV + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Ferdinand Verhulst + Gustavo R. Ferreira - Small time asymptotics of spectral heat content of isotropic processes - https://arxiv.org/abs/2512.08595 - arXiv:2512.08595v1 Announce Type: new -Abstract: We provide a general approach for proving small time asymptotic of spectral heat content for any translation invariant isotropic process satisfying negligible tail probability condition. As a consequence, we recover several existing results in the context of L\'evy processes and Gaussian processes, and provide spectral heat content asymptotic for a class of time-changed Brownian motions. - oai:arXiv.org:2512.08595v1 - math.PR - Wed, 10 Dec 2025 00:00:00 -0500 + Inexact Gauss Seidel and Coarse Solvers for AMG and s-step CG + https://arxiv.org/abs/2512.09642 + arXiv:2512.09642v1 Announce Type: new +Abstract: Communication-avoiding Krylov methods require solving small dense Gram systems at each outer iteration. We present a low-synchronization approach based on Forward Gauss--Seidel (FGS), which exploits the structure of Gram matrices arising from Chebyshev polynomial bases. We show that a single FGS sweep is mathematically equivalent to Modified Gram--Schmidt (MGS) orthogonalization in the $A$-norm and provide corresponding backward error bounds. For weak scaling on AMD MI-series GPUs, we demonstrate that 20--30 FGS iterations preserve scalability up to 64 GPUs with problem sizes exceeding 700 million unknowns. We further extend this approach to Algebraic MultiGrid (AMG) coarse-grid solves, removing the need to assemble or factor dense coarse operators + oai:arXiv.org:2512.09642v1 + math.NA + cs.NA + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/publicdomain/zero/1.0/ - Rohan Sarkar + http://creativecommons.org/licenses/by/4.0/ + Stephen Thomas, Pasqua D'Ambra - A fourth-order multi-scale computational method and its convergence analysis for composite Kirchhoff plates with microscopic periodic configurations - https://arxiv.org/abs/2512.08597 - arXiv:2512.08597v1 Announce Type: new -Abstract: The Kirchhoff plate model plays a vital role in modeling, computing and analyzing the mechanical behaviors of thin plate structures. This study propose a novel fourth-order multi-scale (FOMS) computational method for high-accuracy and efficient simulation of composite Kirchhoff plates with highly periodic heterogeneities. At first, two-scale asymptotic expansion theory is employed to establish the high-accuracy fourth-order multi-scale computation model with novel fourth-order correctors for composite Kirchhoff plates, which are governed by fourth-order partial differential equation (PDE) with periodically oscillatory and highly discontinuous coefficients. Then, the locally point-wise error analysis is derived to theoretically illustrate the local balance preserving of fourth-order multi-scale model enabling high-accuracy multi-scale computation. Furthermore, a global error estimation with an explicit order for fourth-order multi-scale solutions is first demonstrated under appropriate assumptions. In contrast to the second- and third-order multi-scale solutions, only the fourth-order one is capable of providing an explicit error order estimate. Additionally, an efficient numerical algorithm is developed to conduct high-accuracy simulation for heterogeneous plate structures. Extensive numerical examples are provided to confirm the theoretical results for the computational convergence and accuracy of the proposed method. This work offers a higher-order (fourth-order) multi-scale computational framework that enables robust simulation and high-accuracy analysis to composite Kirchhoff plates. - oai:arXiv.org:2512.08597v1 - math.NA - cs.NA - Wed, 10 Dec 2025 00:00:00 -0500 + Relaxation limit and asymptotic stability for the Euler-Navier-Stokes equations + https://arxiv.org/abs/2512.09650 + arXiv:2512.09650v1 Announce Type: new +Abstract: The Euler-Navier-Stokes (E-NS) system arises as a macroscopic description of kinetic-fluid interactions, derived from the local-Maxwellian closure of the Vlasov-Fokker-Planck-Navier-Stokes flow. In this paper, we investigate the singular limit of the system in $\mathbb{R}^d$ ($d\ge2$) when the relaxation parameter $\varepsilon>0$ tends to zero. In contrast to the Euler system with velocity damping, the E-NS model features only a weaker relaxation of the relative velocity, which makes it challenging to analyze its dynamics as $\varepsilon\rightarrow 0$. We develop an energy argument to show global-in-time error estimates between the E-NS system and its limit system, the so-called Kramers-Smoluchowski-Navier-Stokes (KS-NS) system. These error estimates enable us to prove the global existence and uniform-in-$\varepsilon$ regularity of the strong solution to the E-NS system in a hybrid critical Besov space with a sharp frequency threshold of order $\mathcal{O}(\varepsilon^{-1})$ separating the low- and high-frequency regimes. Moreover, the large-time asymptotic stability of the global solution to the E-NS system is established. More precisely, we derive the optimal decay rates of the solution uniformly in $\varepsilon$, and the enhanced decay rates for the difference between the densities of the E-NS system and the KS-NS system. + oai:arXiv.org:2512.09650v1 + math.AP + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Hao Dong, Liqun Cao + Mingwen Fei, Ling-Yun Shou, Houzhi Tang - Comparison of canonical periods under base change - https://arxiv.org/abs/2512.08599 - arXiv:2512.08599v1 Announce Type: new -Abstract: In this paper we prove the canonical period of a Hilbert modular form with respect to the base change of a real quadratic extension differs from the square of its own canonical period only by a $p$-adic unit under some conditions. We prove this by proving a specific version of anticyclotomic Iwasawa main conjecture for Hilbert modular forms. - oai:arXiv.org:2512.08599v1 + The de Jong fundamental group of $\mathbb{P}^1_C$ depends on $C$ and is not always topologically countably generated + https://arxiv.org/abs/2512.09651 + arXiv:2512.09651v1 Announce Type: new +Abstract: For $C/\mathbb{Q}_p$ a complete algebraically closed field, we construct a collection of non-isomorphic rank two $\mathbb{Q}_p$-local systems on $\mathbb{P}^1_C$ indexed by $C$. This implies that the de Jong fundamental group $\pi_{1,\mathrm{dJ}}(\mathbb{P}^1_C)$ depends on $C$ and, if $C$ has cardinality $>2^{\mathbb{N}}$, that $\pi_{1,\mathrm{dJ}}(\mathbb{P}^1_C)$ is not topologically countably generated. The argument in fact applies to any connected rigid analytic variety over $C$ with a non-constant function to $\mathbb{P}^1_C$. + oai:arXiv.org:2512.09651v1 + math.AG math.NT - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Qingshen Lv, Bingyong Xie + Sean Howe - Skew polynomial representations of matrix algebras and applications to coding theory - https://arxiv.org/abs/2512.08602 - arXiv:2512.08602v1 Announce Type: new -Abstract: We extend the existing skew polynomial representations of matrix algebras which are direct sum of matrix spaces over division rings. In this representation, the sum-rank distance between two tuples of matrices is captured by a weight function on their associated skew polynomials, defined through degrees and greatest common right divisors with the polynomial that defines the representation. We exploit this representation to construct new families of maximum sum-rank distance (MSRD) codes over finite and infinite fields, and over division rings. These constructions generalize many of the known existing constructions of MSRD codes as well as of optimal codes in the rank and in the Hamming metric. As a byproduct, in the case of finite fields we obtain new families of MDS codes which are linear over a subfield and whose length is close to the field size. - oai:arXiv.org:2512.08602v1 - cs.IT - math.IT - math.RA - Wed, 10 Dec 2025 00:00:00 -0500 + Remarks on potential functions of noncompact quasi-Einstein manifolds + https://arxiv.org/abs/2512.09653 + arXiv:2512.09653v1 Announce Type: new +Abstract: In this article, we study the set of potential functions on noncompact quasi-Einstein manifolds. We show that the space of all positive potential functions on a three-dimensional noncompact quasi-Einstein manifold has dimension at most two, and that equality holds if and only if the manifold is isometric to a product $B\times\mathbb{R}$, where $B$ is a $\lambda$-Einstein surface or one of the examples obtained by L. Berard Bergery and described in Besse's book. Moreover, we prove that any asymptotically flat $n$-dimensional quasi-Einstein manifold with $\lambda=0$ is necessarily Ricci-flat. + oai:arXiv.org:2512.09653v1 + math.DG + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Alessandro Neri, Paolo Santonastaso + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Jaciane Gon\c{c}alves - Compact Runge-Kutta flux reconstruction methods for non-conservative hyperbolic equations - https://arxiv.org/abs/2512.08611 - arXiv:2512.08611v1 Announce Type: new -Abstract: Compact Runge-Kutta (cRK) Flux Reconstruction (FR) methods are a variant of RKFR methods for hyperbolic conservation laws with a compact stencil including only immediate neighboring finite elements. We extend cRKFR methods to handle hyperbolic equations with stiff source terms and non-conservative products. To handle stiff source terms, we use IMplicit EXplicit (IMEX) time integration schemes such that the implicitness is local to each solution point, and thus does not increase inter-element communication. Although non-conservative products do not correspond to a physical flux, we formulate the scheme using numerical fluxes at element interfaces. We use similar numerical fluxes for a lower order finite volume scheme on subcells of each element, which is then blended with the high order cRKFR scheme to obtain a robust scheme for problems with non-smooth solutions. Combined with a flux limiter at the element interfaces, the subcell based blending scheme preserves the physical admissibility of the solution, e.g., positivity of density and pressure for compressible Euler equations. The procedure thus leads to an admissibility preserving IMEX cRKFR scheme for hyperbolic equations with stiff source terms and non-conservative products. The capability of the scheme to handle stiff terms is shown through numerical tests involving Burgers' equations, reactive Euler's equations, and the ten moment problem. The non-conservative treatment is tested using variable advection equations, shear shallow water equations, the GLM-MHD, and the multi-ion MHD equations. - oai:arXiv.org:2512.08611v1 - math.NA - cs.NA - Wed, 10 Dec 2025 00:00:00 -0500 + Binary and Non-Binary Self-Dual Sequences and Maximum Period Single-Track Gray Codes + https://arxiv.org/abs/2512.09655 + arXiv:2512.09655v1 Announce Type: new +Abstract: Binary self-dual sequences have been considered and analyzed throughout the years, and they were used for various applications. Motivated by a construction for single-track Gray codes, we examine the structure and recursive constructions for binary and non-binary self-dual sequences. The feedback shift registers that generate such sequences are discussed. The connections between these sequences and maximum period single-track codes are discussed. Maximum period non-binary single-track Gray codes of length $p^t$ and period $p^{p^t}$ are constructed. These are the first infinite families of maximum period codes presented in the literature. + oai:arXiv.org:2512.09655v1 + cs.IT + math.IT + Thu, 11 Dec 2025 00:00:00 -0500 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Arpit Babbar, Hendrik Ranocha + http://creativecommons.org/licenses/by/4.0/ + Tuvi Etzion - Flat Vector Bundles on Very General Curves and Codimension of Non-Abelian Hodge Loci - https://arxiv.org/abs/2512.08620 - arXiv:2512.08620v1 Announce Type: new -Abstract: We bound the codimension of components of the nonabelian Hodge loci in the relative de Rham moduli space over $\shm_{g,n}$ in terms of the rank and level of a complex variation of Hodge structure. If the rank is $r$ and the level is $\ell$, then the codimension must be positive if $r$ and $\ell$ are small relative to $g$. The key input is a generalization of a bound on the rank of flat vector bundles by Landesman and Litt, which we apply to the isomonodromy foliation on the relative de Rham space. As an auxiliary result, we are able to bound the rank of the Lie algebra of the algebraic monodromy group of the isomonodromic deformation of a flat bundle to a nearby curve. - oai:arXiv.org:2512.08620v1 + The de Jong fundamental group of a non-trivial abelian variety is non-abelian + https://arxiv.org/abs/2512.09661 + arXiv:2512.09661v1 Announce Type: new +Abstract: We show the de Jong fundamental group of any non-trivial abelian variety over a complete algebraically closed extension of $\mathbb{Q}_p$ is non-abelian. + oai:arXiv.org:2512.09661v1 math.AG - Wed, 10 Dec 2025 00:00:00 -0500 + math.NT + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Nathan H. Morris + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Sean Howe - Fluctuations from a random fractional averaging limit - https://arxiv.org/abs/2512.08621 - arXiv:2512.08621v1 Announce Type: new -Abstract: We consider a system of multiscale stochastic differential equations whose slow component is drivenby a fractional Brownian motion with Hurst parameter H greater than 1/2. Under ergodic assumptions ensuring the applicability of the fractional averaging and fractional homogenization theorems of Hairer and Li (arXiv:1902.11251, arXiv:2109.06948), we establish a fluctuation result. The deviation of the slow motion, scaled by epsilon^{1/2-H}, from its effective, time-dependent random limit converges, as the time-separation scale epsilon tends to zero, to the solution of a stochastic differential equation driven by a fractional Brownian motion and influenced by an additional space--time Gaussian field. Since the averaging principle and the fractional homogenization hold in different modes of convergence, obtaining the required joint convergence is a delicate matter. Moreover, neither the continuity of the Ito--Lyons solution map nor the martingale method is directly applicable for our purposes, so the proof requires several innovations. To establish the fluctuation theorem, we combine cumulant methods with a residue lemma and formulate the enlarged system as a rough differential equation in a suitable space. - oai:arXiv.org:2512.08621v1 - math.PR - Wed, 10 Dec 2025 00:00:00 -0500 + Persistent Cycle Representatives and Generalized Landscapes for Codimension 1 Persistent Homology + https://arxiv.org/abs/2512.09668 + arXiv:2512.09668v1 Announce Type: new +Abstract: For a filtered simplicial complex $K$ embedded in $\mathbb{R}^{d+1}$, the merge tree of the complement of $K$ induces a forest structure on the persistent homology $H_d(K)$ via Alexander duality. We prove that the connected components of $\mathbb{R}^{d+1}\setminus K_r$ correspond to representative cycles for a basis of $H_d(K_r)$ which are volume-optimal. By keeping track of how these representatives evolve with the filtration of $K$, we can equip each interval $I$ in the barcode of $H_d(K)$ with a sequence of canonical representative cycles. We develop and implement an efficient algorithm to compute the progression of cycles in time $\mathcal{O}((\#K)^2)$. We apply functionals to these representatives, such as path length, enclosed volume, or total curvature. This way, we obtain a real-valued function for each interval, which captures geometric information about~$K$. Deriving from this construction, we introduce the \emph{generalized persistence landscapes}. Using the constant one-function as the functional, this construction gives back the standard persistence landscapes. Generalized landscapes can distinguish point clouds with similar persistent homology but distinct shape, which we demonstrate by concrete examples. + oai:arXiv.org:2512.09668v1 + math.AT + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Xue-Mei Li, Colin Piernot, Szymon Sobczak, Kexing Ying + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Fabian Lenzen, Leon Renkin - The St\'ephanois theorem with only prime isogenies - https://arxiv.org/abs/2512.08631 - arXiv:2512.08631v1 Announce Type: new -Abstract: We present a strengthening of the proof of the St\'ephanois theorem. We follow the modular version by Waldschmidt, which is based in a suggestion by Daniel Bertrand, but it also applies to the original proof. The improvement is not in the result or the conditions, but in the need of weaker tools on the proof itself. More precisely, we only employ modular polynomials of prime degree, instead of polynomials of arbitrary level. Furthermore, one can restrict to primes in fixed arithmetic sequence. - On the proof itself, the only crucial difference appears in Cinqui\`eme pas and on the final contradiction in Septi\`eme pas of Waldschmidt's proof, but for readability, we present a complete proof with this modification. - This is part of a larger project to generalize the St\'ephanois theorem to the Igusa invariants of curves of genus two, as the Siegel modular polynomials in the literature are usually only considered for prime levels. - The material is part of Chapter 7 of the author's PhD thesis. - oai:arXiv.org:2512.08631v1 + The geometric Sen morphism is the unique lift of the Kodaira--Spencer morphism + https://arxiv.org/abs/2512.09669 + arXiv:2512.09669v1 Announce Type: new +Abstract: We show that the geometric Sen morphism of a de Rham torsor over a smooth rigid analytic variety over a $p$-adic field is the unique lift, along a natural map, of the Kodaira--Spencer morphism of the associated filtered torsor with integrable connection. This extends previous computations in the minuscule case, and implies that the geometric Sen morphism is the derivative of the lattice Hodge period map. The computation applies, in particular, to non-minuscule period domains generalizing local Shimura varieties, furnishing new examples of towers satisfying He's stalkwise perfectoidness. + oai:arXiv.org:2512.09669v1 + math.AG math.NT - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Desir\'ee Gij\'on G\'omez + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Sean Howe - Higher walks and squares - https://arxiv.org/abs/2512.08633 - arXiv:2512.08633v1 Announce Type: new -Abstract: We continue the development of the theory of higher dimensional walks on ordinals began recently by Bergfalk. In particular we identify natural coherence conditions on higher dimensional $C$-sequences that entail coherence of the resultant higher rho-functions. We also introduce various higher square principles by adding non-triviality conditions to these coherent higher $C$-sequences and investigate basic properties of said square principles. For example, in analogy with the classical case, we prove that these higher square principles abound in the constructible universe but can be forced to fail, modulo large cardinals. Finally, we prove that certain higher rho-functions obtained by walking along higher square sequences exhibit non-triviality in addition to coherence. In particular, it follows that higher square principles on a cardinal $\lambda$ entail certain non-vanishing \v{C}ech cohomology groups for $\lambda$ considered with the order topology. - oai:arXiv.org:2512.08633v1 - math.LO - Wed, 10 Dec 2025 00:00:00 -0500 + A Monotone--Operator Proof of Existence and Uniqueness for a Simple Stationary Mean Field Game + https://arxiv.org/abs/2512.09671 + arXiv:2512.09671v1 Announce Type: new +Abstract: We study a stationary first--order mean field game on the $d$--dimensional torus. The system couples a Hamilton--Jacobi equation for the value function with a transport equation for the density of players. Our goal is to give a detailed and friendly exposition of the monotone--operator argument that yields existence and uniqueness of solutions. + We first present a general framework in a Hilbert space and prove existence of a strong solution by adding a simple coercive regularisation and applying Minty's method. Then we specialise to the explicit Hamiltonian \[ H(p,m)=|p|^2-m, \] check all assumptions, and show how the abstract theorem gives existence and uniqueness for this concrete mean field game. The exposition is written in a slow and elementary way so that a motivated undergraduate can follow each step. + oai:arXiv.org:2512.09671v1 + math.FA + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Chris Lambie-Hanson, Pedro Marun + http://creativecommons.org/publicdomain/zero/1.0/ + Hikmatullo Ismatov - Linearity and virtual poly-freeness of the fundamental group of plane curves of degree at most five - https://arxiv.org/abs/2512.08642 - arXiv:2512.08642v1 Announce Type: new -Abstract: We prove that for any algebraic plane curve $C$ of degree at most $5$, the fundamental group $\pi_1(\mathbb CP^2\setminus C)$ is linear and virtually polyfree. As a consequence, we answer positively the open question on the residual finiteness of these groups for all plane curves of degree at most $5$. - oai:arXiv.org:2512.08642v1 - math.AG - math.GR - Wed, 10 Dec 2025 00:00:00 -0500 + Neighborhood Complexes of induced $k$-independent graphs + https://arxiv.org/abs/2512.09674 + arXiv:2512.09674v1 Announce Type: new +Abstract: This paper is devoted to the neighborhood complexes of the induced $k$-independent graphs. Inspired by the surprising correspondence between total $k$-cut complex of $n$-cycle $C_n$ and neighborhood complex of stable Kneser graph $SG(n,k)$, we anticipate that the homotopy type of total cut complexes may have some relationships with the neighborhood complexes of induced $k$-independent graphs. We investigated the homotopy type of some total cut complexes and neighborhood complexes of some other graphs, using techniques from algebraic topology and discrete Morse theory. + oai:arXiv.org:2512.09674v1 + math.CO + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Shengkui Ye, Kejia Zhu + Yufeng Shen, Zhiyu Song, Feneglin Yu, Leopold Wuhan Zhou, Jingqi Zhuang - Weakly $\mathcal U(d)$-homogeneous commuting tuple of bounded operators - https://arxiv.org/abs/2512.08649 - arXiv:2512.08649v1 Announce Type: new -Abstract: We introduce and study the weakly $\mathcal U(d)$-homogeneous commuting tuple of operators. We provide a sufficient condition under which a weakly $\mathcal U(d)$-homogeneous tuple is similar to a $\mathcal U(d)$-homogeneous tuple. Further, we focus our attention to multishifts and completely characterize weakly $\mathcal U(d)$-homogeneous multishifts. In particular, we show that a multishift is weakly $\mathcal U(d)$-homogeneous if and only if it similar to a $\mathcal U(d)$-homogeneous multishift. The results for multishifts are further refined for the class of spherically balanced multishifts. - oai:arXiv.org:2512.08649v1 - math.FA - Wed, 10 Dec 2025 00:00:00 -0500 + The Ky Fan Norms and Beyond: Dual Norms and Combinations for Matrix Optimization + https://arxiv.org/abs/2512.09678 + arXiv:2512.09678v1 Announce Type: new +Abstract: In this article, we explore the use of various matrix norms for optimizing functions of weight matrices, a crucial problem in training large language models. Moving beyond the spectral norm underlying the Muon update, we leverage duals of the Ky Fan $k$-norms to introduce a family of Muon-like algorithms we name Fanions, which are closely related to Dion. By working with duals of convex combinations of the Ky Fan $k$-norms with either the Frobenius norm or the $l_\infty$ norm, we construct the families of F-Fanions and S-Fanions, respectively. Their most prominent members are F-Muon and S-Muon. We complement our theoretical analysis with an extensive empirical study of these algorithms across a wide range of tasks and settings, demonstrating that F-Muon and S-Muon consistently match Muon's performance, while outperforming vanilla Muon on a synthetic linear least squares problem. + oai:arXiv.org:2512.09678v1 + math.OC + cs.AI + cs.LG + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Soumitra Ghara, Surjit Kumar, Shailesh Trivedi + Alexey Kravatskiy, Ivan Kozyrev, Nikolai Kozlov, Alexander Vinogradov, Daniil Merkulov, Ivan Oseledets - L-equivalence and Fourier--Mukai partners of cubic fourfolds - https://arxiv.org/abs/2512.08651 - arXiv:2512.08651v1 Announce Type: new -Abstract: We study L-equivalence in the Grothendieck ring of varieties and its interaction with categorical invariants of cubic fourfolds. Assuming a Derived Torelli-type criterion for Kuznetsov components and a mild condition on the discriminant of the transcendental lattice, we prove a counting formula for Fourier--Mukai partners of such cubic fourfolds. As an application, we exhibit cubic fourfolds with a fixed algebraic lattice admitting a unique non-trivial Fourier--Mukai partner and which are trivially L-equivalent. Finally, we show that L-equivalence classes of cubic fourfolds are finite. - oai:arXiv.org:2512.08651v1 - math.AG - Wed, 10 Dec 2025 00:00:00 -0500 + The non-existence of some Moore polygons and spectral Moore bounds + https://arxiv.org/abs/2512.09680 + arXiv:2512.09680v1 Announce Type: new +Abstract: In this paper, we study the maximum order $v(k,\theta)$ of a connected $k$-regular graph whose second largest eigenvalue is at most $\theta$. From Alon-Boppana and Serre, we know that $v(k,\theta)$ is finite when $\theta < 2\sqrt{k-1}$ while the work of Marcus, Spielman, and Srivastava implies that $v(k,\theta)$ is infinite if $\theta\geq 2\sqrt{k-1}$. Cioab\u{a}, Koolen, Nozaki, and Vermette obtained a general upper bound on $v(k, \theta)$ via Nozaki's linear programming bound and determined many values of $v(k,\theta)$. The graphs attaining this bound are distance-regular and are called Moore polygons. Damerell and Georgiacodis proved that there are no Moore polygons of diameter $6$ or more. For smaller diameters, there are infinitely many Moore polygons. + We complement these results by proving two nonexistence results for Moore polygons with specific parameters. We also determine new values of $v(k,\theta)$: $v(4, \sqrt{2}) = 14$ and $v(5, \sqrt{2}) = v(5,\sqrt{5}-1)=16$. The former is achieved by the co-Heawood graph, and the latter by the folded $5$-cube. We verify that any connected $5$-regular graph with second eigenvalue $\lambda_2$ exceeding $1$ satisfies $\lambda_2 \geq \sqrt{5} - 1$, and that the unique $5$-regular graph attaining equality in this bound has $10$ vertices. We prove a stronger form of a 2015 conjecture of Kolokolnikov related to the second eigenvalue of cubic graphs of given order, and observe that other recent results on the second eigenvalue of regular graphs are consequences of the general upper bound theorem on $v(k,\theta)$ mentioned above. + oai:arXiv.org:2512.09680v1 + math.CO + cs.DM + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Reinder Meinsma, Riccardo Moschetti + Sebastian M. Cioab\u{a}, Vishal Gupta, Hiroshi Nozaki, Ziqing Xiang - Fast free resolutions of bifiltered chain complexes - https://arxiv.org/abs/2512.08652 - arXiv:2512.08652v1 Announce Type: new -Abstract: In a $k$-critical bifiltration, every simplex enters along a staircase with at most $k$ steps. Examples with $k>1$ include degree-Rips bifiltrations and models of the multicover bifiltration. We consider the problem of converting a $k$-critical bifiltration into a $1$-critical (i.e. free) chain complex with equivalent homology. This is known as computing a free resolution of the underlying chain complex and is a first step toward post-processing such bifiltrations. - We present two algorithms. The first one computes free resolutions corresponding to path graphs and assembles them to a chain complex by computing additional maps. The simple combinatorial structure of path graphs leads to good performance in practice, as demonstrated by extensive experiments. However, its worst-case bound is quadratic in the input size because long paths might yield dense boundary matrices in the output. Our second algorithm replaces the simplex-wise path graphs with ones that maintain short paths which leads to almost linear runtime and output size. - We demonstrate that pre-computing a free resolution speeds up the task of computing a minimal presentation of the homology of a $k$-critical bifiltration in a fixed dimension. Furthermore, our findings show that a chain complex that is minimal in terms of generators can be asymptotically larger than the non-minimal output complex of our second algorithm in terms of description size. - oai:arXiv.org:2512.08652v1 - math.AT - Wed, 10 Dec 2025 00:00:00 -0500 + Backbone probability of planar Brownian motion + https://arxiv.org/abs/2512.09683 + arXiv:2512.09683v1 Announce Type: new +Abstract: Motivated by critical planar percolation, we investigate a ``backbone'' event of planar Brownian motion, i.e.~the existence of two disjoint subpaths on the Brownian trajectory connecting the $\varepsilon$-neighborhood of the starting point to a macroscopic distance. We show that the probability of~this event is $(\log|\log\varepsilon|)^{-1}$ up to a multiplicative constant. + oai:arXiv.org:2512.09683v1 + math.PR + math-ph + math.MP + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Ulrich Bauer, Tamal K. Dey, Michael Kerber, Florian Russold, Matthias S\"ols + Gefei Cai, Zhuoyan Xie - Global Weak Solutions for the High--Friction Quantum Navier--Stokes--Poisson Model - https://arxiv.org/abs/2512.08655 - arXiv:2512.08655v1 Announce Type: new -Abstract: In [1], the Authors rigorously establish the relaxation limit from the Quantum Navier Stokes Poisson (QNSP) system to the Quantum Drift Diffusion (QDD) equation, while providing only a brief outline of the global existence theory for weak solutions to QNSP in the high friction regime (see Appendix A therein). In this manuscript, we present a complete and fully self contained proof of global existence. - More precisely, we prove the global existence of finite energy weak solutions to the QNSP system with high friction and large initial data on the three-dimensional torus. The model describes a compressible, viscous quantum fluid with Korteweg type capillarity effects, and allows for degenerate viscosity and vacuum regions. - The construction proceeds in two main steps. First, it is introduced a Faedo Galerkin approximation endowed with suitable damping mechanisms, which yields smooth approximate solutions through compactness arguments. Then, it will be justify the convergence of the approximating sequence by combining a truncation of the momentum equation with DiPerna Lions commutator estimates, providing the required control over the nonlinear transport structure. - oai:arXiv.org:2512.08655v1 - math.AP - Wed, 10 Dec 2025 00:00:00 -0500 + A Simple Weak Galerkin Finite Element Method for the Reissner-Mindlin Plate Model on Non-Convex Polytopal Meshes + https://arxiv.org/abs/2512.09688 + arXiv:2512.09688v1 Announce Type: new +Abstract: This paper presents a simple weak Galerkin (WG) finite element method for the Reissner-Mindlin plate model that partially eliminates the need for traditionally employed stabilizers. The proposed approach accommodates general, including non-convex, polytopal meshes, thereby offering greater geometric flexibility. It utilizes bubble functions without imposing the restrictive conditions required by existing stabilizer-free WG methods, which simplifies implementation and broadens applicability to a wide range of partial differential equations (PDEs). Moreover, the method allows for flexible choices of polynomial degrees in the discretization and can be applied in any spatial dimension. We establish optimal-order error estimates for the WG approximation in a discrete H^1 norm, and present numerical experiments that validate the theoretical results. + oai:arXiv.org:2512.09688v1 + math.NA + cs.NA + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Giada Cianfarani Carnevale + Chunmei Wang, Shangyou Zhang - Interpreting the Ehrhart coefficients of cross-polytopes - https://arxiv.org/abs/2512.08669 - arXiv:2512.08669v1 Announce Type: new -Abstract: It is known that the Ehrhart polynomials of cross-polytopes, as well as of pyramids over them, have positive coefficients. We give a combinatorial proof of this fact by showing that a scaled version of the Ehrhart polynomials are generating functions for certain colored permutations. This answers a question posed by Stanley. - oai:arXiv.org:2512.08669v1 - math.CO - Wed, 10 Dec 2025 00:00:00 -0500 + Regularity and pointwise convergence for dispersive equations on Riemannian symmetric spaces of compact type + https://arxiv.org/abs/2512.09689 + arXiv:2512.09689v1 Announce Type: new +Abstract: In this article, we first prove that for general dispersive equations on Riemannian symmetric spaces of compact type $\mathbb{X}=U/K$, of rank $1$ and $2$, the Sobolev regularity threshold $\alpha >1/2$ for the initial data, is sufficient to obtain pointwise convergence of the solution a.e. on $\mathbb{X}$. We next focus on $K$-biinvariant initial data for certain special cases of rank $1$, depending on geometric and topological considerations, and prove that the sufficiency of the regularity threshold can be improved down to $\alpha>1/3$, whereas the phenomenon fails for $\alpha<1/4$ for the Schr\"odinger equation. We also obtain the same results for other dispersive equations: the Boussinesq equation and the Beam equation, also known as the fourth order Wave equation, by a novel transference principle, which seems to be new even for the circle $\mathbb{T} \cong SO(2)$ and may be of independent interest. Our arguments involve harmonic analysis arising from the representation theory of compact semi-simple Lie groups and also number theory. + oai:arXiv.org:2512.09689v1 + math.AP + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Krishna Menon, Emil Verkama + Utsav Dewan, Sanjoy Pusti - A constant rank theorem for linear elliptic equations on the sphere with applications to the mixed Christoffel problem - https://arxiv.org/abs/2512.08670 - arXiv:2512.08670v1 Announce Type: new -Abstract: We study the mixed Christoffel problem for $C^{2,+}$ convex bodies providing sufficient conditions for its solution. Key to our approach is a constant rank theorem, following the approach developed in \cite{Guan-Ma-2003} to address the Christoffel problem, in order to ensure that the solution to a related second order linear PDE on the sphere is indeed geometric, that is, it is the support functions of a $C^{2,+}$ convex body. - oai:arXiv.org:2512.08670v1 - math.AP - math.MG - Wed, 10 Dec 2025 00:00:00 -0500 + A recollement approach to Brieskorn-Pham singularities + https://arxiv.org/abs/2512.09692 + arXiv:2512.09692v1 Announce Type: new +Abstract: In this paper, we construct recollements and ladders for Brieskorn-Pham singularities via reduction/insertion functors, and study the singularity categories of the Brieskorn-Pham singularities using these ladders. + In particular, we construct a class of tilting objects, called the extended tilting $n$-cuboids, whose endomorphism algebras are $n$-fold tensor products of certain Nakayama algebras. Moreover, we show that such an endomorphism algebra is derived equivalent to a certain replicated algebra. This generalizes the Happel-Seidel symmetry to the context of Brieskorn-Pham singularities. + oai:arXiv.org:2512.09692v1 + math.RT + math.AG + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - A. Colesanti, M. Focardi, P. Guan, P. Salani + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Weikang Weng - Raimi's theorem for manifolds with circle symmetry - https://arxiv.org/abs/2512.08676 - arXiv:2512.08676v1 Announce Type: new -Abstract: Raimi's classical theorem establishes a partition of the natural numbers with a remarkable unavoidability property: for every finite coloring of $\mathbb{N}$, there is a color class whose translate meets both parts of the partition in infinitely many points. Recently, Kang, Koh, and Tran have extended this phenomenon to the circle group, proving that there exists a measurable partition of the circle such that every finite measurable cover admits a rotation whose image meets each part of the partition in positive measure. This paper shows that this phenomenon extends beyond compact abelian groups to a wide class of non-group geometric surfaces that still exhibit \textit{a hidden one-dimensional symmetry}. Specifically, we establish analogs of Raimi's theorem for three families of surfaces (with their natural surface measures): the unit sphere $S^{n-1} \subset \mathbb{R}^n$, rotational power surfaces (such as cones and paraboloids), and circular cylindrical surfaces. The common feature is that each of these surfaces carries a natural measure-preserving action of the circle group by rotation in a fixed plane and admits a measurable trivialization as a product $C \times Y$. This circle-bundle structure allows the measurable Raimi partition on the base circle to be lifted to an unavoidable partition on the manifold. Our approach is unified through a general circle-bundle theorem, which reduces all three geometric cases to verifying suitable equivariance and product disintegration properties of the surface measure. - oai:arXiv.org:2512.08676v1 + Minuscule Coxeter Dressians + https://arxiv.org/abs/2512.09703 + arXiv:2512.09703v1 Announce Type: new +Abstract: In this extended abstract, we study special tropical prevarieties which we call Coxeter Dressians. They arise from equations capturing a generalization of valuated symmetric basis exchange for Coxeter matroids. In particular, we study subdivisions of the associated Coxeter matroid polytopes. We show that the subdivisions induced by points of the Coxeter Dressian consist of cells which are strong Coxeter matroidal. This generalizes well-known results in type $A$ to other Lie types. Finally, we implement explicit computations of Coxeter Dressians in OSCAR. + oai:arXiv.org:2512.09703v1 math.CO - math.CA - math.NT - Wed, 10 Dec 2025 00:00:00 -0500 + math.AG + math.RT + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Dung The Tran + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Andreas Gross, Kevin Kuehn, Dante Luber - L-shadowing for the induced hyperspace homeomorphism - https://arxiv.org/abs/2512.08677 - arXiv:2512.08677v1 Announce Type: new -Abstract: We prove that a homeomorphism f of a compact metric space X satisfies the L-shadowing property if and only if its induced hyperspace homeomorphism also satisfies the L-shadowing property. In the proof, assuming only the L-shadowing property, we obtain the existence of points in the asymptotic local-product-structure with iterates approaching in a uniform rate of convergence to zero. This contrasts with the lack of uniformity of contraction on local stable/unstable sets on many homeomorphisms with the L-shadowing property. - oai:arXiv.org:2512.08677v1 - math.DS - Wed, 10 Dec 2025 00:00:00 -0500 + A simple geometric proof for the characterisation of e-merging functions + https://arxiv.org/abs/2512.09708 + arXiv:2512.09708v1 Announce Type: new +Abstract: E-values offer a powerful framework for aggregating evidence across different (possibly dependent) statistical experiments. A fundamental question is to identify e-merging functions, namely mappings that merge several e-values into a single valid e-value. A simple and elegant characterisation of this function class was recently obtained by Wang(2025), though via technically involved arguments. This note gives a short and intuitive geometric proof of the same characterisation, based on a supporting hyperplane argument applied to concave envelopes. We also show that the result holds even without imposing monotonicity in the definition of e-merging functions, which was needed for the existing proof. This shows that any non-monotone merging rule is automatically dominated by a monotone one, and hence extending the definition beyond the monotone case brings no additional generality. + oai:arXiv.org:2512.09708v1 + math.ST + stat.TH + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Mayara Antunes, Bernardo Carvalho, Welington Cordeiro + Eugenio Clerico - Moduli space of complete stable pairs - https://arxiv.org/abs/2512.08678 - arXiv:2512.08678v1 Announce Type: new -Abstract: We define complete stable pairs on a smooth projective variety, and construct their moduli space. These moduli spaces have natural morphisms to the moduli of stable pairs and Quot-schemes. As an example, we show that the moduli of complete stable pairs on $\mathbb P^1$ is an iterated blowing-up of the moduli of stable pairs, similar to the construction of the space of complete collineations. - oai:arXiv.org:2512.08678v1 - math.AG - Wed, 10 Dec 2025 00:00:00 -0500 + Computer-Assisted Search for Differential Equations Corresponding to Optimization Methods and Their Convergence Rates + https://arxiv.org/abs/2512.09712 + arXiv:2512.09712v1 Announce Type: new +Abstract: Let $f:\mathbb{R}^n \to \mathbb{R}$ be a continuously differentiable convex function with its minimizer denoted by $x_*$ and optimal value $f_* = f(x_*)$. Optimization algorithms such as the gradient descent method can often be interpreted in the continuous-time limit as differential equations known as continuous dynamical systems. Analyzing the convergence rate of $f(x) - f_*$ in such systems often relies on constructing appropriate Lyapunov functions. However, these Lyapunov functions have been designed through heuristic reasoning rather than a systematic framework. Several studies have addressed this issue. In particular, Suh, Roh, and Ryu (2022) proposed a constructive approach that involves introducing dilated coordinates and applying integration by parts. Although this method significantly improves the process of designing Lyapunov functions, it still involves arbitrary choices among many possible options, and thus retains a heuristic nature in identifying Lyapunov functions that yield the best convergence rates. In this study, we propose a systematic framework for exploring these choices computationally. More precisely, we propose a brute-force approach using symbolic computation by computer algebra systems to explore every possibility. By formulating the design of Lyapunov functions for continuous dynamical systems as an optimization problem, we aim to optimize the Lyapunov function itself. As a result, our framework successfully reproduces many previously reported results and, in several cases, discovers new convergence rates that have not been shown in the existing studies. + oai:arXiv.org:2512.09712v1 + math.OC + cs.NA + math.CA + math.DS + math.NA + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Baosen Wu + Atsushi Tabei, Ken'ichiro Tanaka - Resolvable Triple Arrays - https://arxiv.org/abs/2512.08681 - arXiv:2512.08681v1 Announce Type: new -Abstract: We present a new construction of triple arrays by combining a symmetric 2-design with a resolution of another 2-design. This is the first general method capable of producing non-extremal triple arrays. We call the triple arrays which can be obtained in this way resolvable. We employ the construction to produce the first examples of $(21 \times 15, 63)$-triple arrays, and enumerate all resolvable $(7 \times 15, 35)$-triple arrays, of which there was previously only a single known example. An infinite subfamily of Paley triple arrays turns out to be resolvable. - We also introduce a new intermediate object, unordered triple arrays, that are to triple arrays what symmetric 2-designs are to Youden rectangles, and propose a strengthening of Agrawal's long-standing conjecture on the existence of extremal triple arrays. For small parameters, we completely enumerate all unordered triple arrays, and use this data to corroborate the new conjecture. We construct several infinite families of resolvable unordered triple arrays, and, in particular, show that all $((q + 1) \times q^2, q(q + 1))$-triple arrays are resolvable and are in correspondence with finite affine planes of order $q$. - oai:arXiv.org:2512.08681v1 - math.CO - cs.DM - Wed, 10 Dec 2025 00:00:00 -0500 + Weak-Strong Uniqueness and Relaxation Limit for a Navier-Stokes-Korteweg Model + https://arxiv.org/abs/2512.09719 + arXiv:2512.09719v1 Announce Type: new +Abstract: We consider a parabolic relaxation model for the compressible Navier-Stokes-Korteweg equations in the isothermal framework. This system depends on the relaxation parameters $\alpha,\beta>0$ and approximates formally solutions of the compressible Navier-Stokes-Korteweg equations in the relaxation limit $\alpha \to \infty$ and $\beta\to 0$. Introducing the class of finite energy weak solutions for the initial-boundary value problem corresponding to the relaxation model in spatial dimension three, we show that the weak-strong uniqueness principle holds. It asserts that a weak solution and a strong solution emanating from the same initial data coincide as long as the strong solution exists. Furthermore, we contribute a rigorous convergence result for the relaxation limit $\alpha \to \infty$ and $\beta\to 0$ and thus justify the relaxation model as an approximate model for the compressible Navier-Stokes-Korteweg equations from a mathematical point of view. Our results hold for general non-monotone pressure-density relations. + oai:arXiv.org:2512.09719v1 + math.AP + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Alexey Gordeev, Lars-Daniel \"Ohman + Nilasis Chaudhuri, Christian Rohde, Florian Wendt - On the Number of Posets - https://arxiv.org/abs/2512.08686 - arXiv:2512.08686v1 Announce Type: new -Abstract: This paper presents combinatorial facts dealing with the number of unlabeled partially ordered sets (posets) refined by the number of arcs in the Hasse diagram (sequence A342447 in OEIS). The main result is that the differences with respect to the number of points in this sequence become stationary if the number of points is sufficiently high. These differences are proposed as the new sequence A376894. In addition, the underlying combinatorial and graph theoretical arguments were used to extend some further OEIS sequences. - oai:arXiv.org:2512.08686v1 - math.CO - Wed, 10 Dec 2025 00:00:00 -0500 + A Smooth Approximation Framework for Weakly Convex Optimization + https://arxiv.org/abs/2512.09720 + arXiv:2512.09720v1 Announce Type: new +Abstract: Standard complexity analyses for weakly convex optimization rely on the Moreau envelope technique proposed by Davis and Drusvyatskiy (2019). The main insight is that nonsmooth algorithms, such as proximal subgradient, proximal point, and their stochastic variants, implicitly minimize a smooth surrogate function induced by the Moreau envelope. Meanwhile, explicit smoothing, which directly minimizes a smooth approximation of the objective, has long been recognized as an efficient strategy for nonsmooth optimization. In this paper, we generalize the notion of smoothable functions, which was proposed by Beck and Teboulle (2012) for nonsmooth convex optimization. This generalization provides a unified viewpoint on several important smoothing techniques for weakly convex optimization, including Nesterov-type smoothing and Moreau envelope smoothing. Our theory yields a framework for designing smooth approximation algorithms for both deterministic and stochastic weakly convex problems with provable complexity guarantees. Furthermore, our theory extends to the smooth approximation of non-Lipschitz functions, allowing for complexity analysis even when global Lipschitz continuity does not hold. + oai:arXiv.org:2512.09720v1 + math.OC + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Rico Z\"ollner, Konrad Handrich + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Qi Deng, Wenzhi Gao - Bootstrapping Noncommutative Geometry with Dirac Ensembles - https://arxiv.org/abs/2512.08694 - arXiv:2512.08694v1 Announce Type: new -Abstract: This paper surveys a bootstrap framework for random Dirac operators arising from finite spectral triples in noncommutative geometry. Motivated by a toy model for quantum gravity to replace integration over metrics by integration over Dirac operators, we give an overview of multitrace and multimatrix random matrix models built from spectral triples and analyze them in the large $N$ limit using positivity constraints on Hankel moment matrices. In this setting, the bootstrap philosophy, originating in the S-matrix program and revived in modern conformal bootstrap theory, reappears as a rigorous analytic tool for extracting spectral data from consistency alone, without solving the model explicitly. - We explain how Schwinger-Dyson equations, factorization at large $N$, and the noncommutative moment problem lead to finite-dimensional semidefinite programs whose feasible regions encode the allowed pairs of coupling constants and moments. Connections with spectral geometry, in particular the study of Laplace eigenvalues, are also discussed, illustrating how bootstrapping provides a unified mechanism for deriving bounds in both commutative and noncommutative settings. - oai:arXiv.org:2512.08694v1 - math-ph - hep-th - math.MP - math.QA - Wed, 10 Dec 2025 00:00:00 -0500 + Extrapolation for bilinear compact operators in the variable exponent setting + https://arxiv.org/abs/2512.09721 + arXiv:2512.09721v1 Announce Type: new +Abstract: We establish extrapolation of compactness for bilinear operators in the scale of weighted variable exponent Lebesgue spaces. First, we prove an abstract principle relying on the Cobos--Fern\'{a}ndez--Cabrera--Mart\'{i}nez theorem. Then, as an application we deduce new compactness results for the commutators of bilinear $\omega$-Calder\'{o}n--Zygmund operators and bilinear fractional integrals acting on weighted variable exponent Lebesgue spaces. Our work extends and unifies among others earlier works of the second named author together with Hyt\"{o}nen as well as Oikari. + oai:arXiv.org:2512.09721v1 + math.CA + math.FA + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Masoud Khalkhali, Nathan Pagliaroli + Spyridon Kakaroumpas, Stefanos Lappas - Multifractal Analysis of Equilibrium States of Endomorphisms of $\mathbb{P}^k$ - https://arxiv.org/abs/2512.08696 - arXiv:2512.08696v1 Announce Type: new -Abstract: Let $f$ be a holomorphic endomorphism of $\mathbb{C}\mathbb{P}^k$ of algebraic degree at least $2$ and let $X \subseteq \mathbb{C}\mathbb{P}^k$ be an uniformly expanding set. In this paper, we study multifractal analysis of equilibrium states of H\"older continuous functions for the non-conformal dynamical system $f : X \to X$. In lieu of Hausdorff dimensions, we use a new dimension theory (i.e., the volume dimension theory) to define various local dimension multifractal spectra and show that each of these spectra form a Legendre transform pair with the temperature function as in the conformal case. As an application of our main theorems, we also prove a conditional variational principle for such dimension multifractal spectra. - oai:arXiv.org:2512.08696v1 - math.DS - Wed, 10 Dec 2025 00:00:00 -0500 + A tree bijection for the moduli space of genus-0 hyperbolic surfaces with boundaries + https://arxiv.org/abs/2512.09722 + arXiv:2512.09722v1 Announce Type: new +Abstract: The Weil-Petersson volume of genus-g hyperbolic surfaces with geodesic boundaries is known since work of Mirzakhani to be polynomial in the boundary lengths. We provide a bijective proof of this fact in the genus-0 case in the presence of a distinguished cusp. It is based on a generalization of a recent tree bijection, by the first author and Curien, to the setting with geodesic boundaries, requiring an extension of the Bowditch-Epstein-Penner spine construction. As an application of our tree bijection we establish an explicit formula for the distance-dependent three-point function, which records an exact metric statistic measuring the difference of two geodesic distances among a triple of distinguished cusps in a Weil-Petersson random surface. We conclude with a discussion of the relevance of this function to the topological recursion of Weil-Petersson volumes and metric properties of Weil-Petersson random surfaces with many boundaries or cusps. + oai:arXiv.org:2512.09722v1 + math.GT + math-ph + math.CO + math.MP + math.PR + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Nathan Dalaklis, Yan Mary He + Timothy Budd, Thomas Meeusen, Bart Zonneveld - On the Homotopy Type of Balanced subsets - https://arxiv.org/abs/2512.08707 - arXiv:2512.08707v1 Announce Type: new -Abstract: For a finite set of points $V=\{v_1, \dots, v_m\}$ in Euclidean space $\mathbb{R}^d$ and a point $r \in \mathbb{R}^d$, a subset $S \subset V$ is called $r$-balanced if $\mathrm{relint}(\mathrm{conv}(S)) \cap r \neq \emptyset$. In the case when $r$ is a point in the relative interior of the whole set $\mathrm{conv}(V)$, we prove that the poset of all balanced subsets, excluding the whole set $V$, is homotopy equivalent to the sphere of dimension $m-k-2$, where $k$ is the dimension of the affine hull of $V$. - oai:arXiv.org:2512.08707v1 - math.CO - Wed, 10 Dec 2025 00:00:00 -0500 + PrIncipal quiver Grassmannians: conjectures + https://arxiv.org/abs/2512.09731 + arXiv:2512.09731v1 Announce Type: new +Abstract: Let $P$ and $I$ be a projective and an injective representations of a Dynkin quiver. We consider quiver Grassmannians of subrepresentations of dimension $\dim P$ inside representations of dimension $\dim P + \dim I$. Based on extensive computer experiments, we formulate several conjectures about the algebro-geometric properties of these quiver Grassmannians. + oai:arXiv.org:2512.09731v1 + math.AG + math.RT + Thu, 11 Dec 2025 00:00:00 -0500 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Mikhail V. Bludov + http://creativecommons.org/licenses/by/4.0/ + Stanislav Fedotov, Evgeny Feigin - Bruhat Preclosure - https://arxiv.org/abs/2512.08711 - arXiv:2512.08711v1 Announce Type: new -Abstract: In 2011, Dyer published a series of conjectures on the weak order of Coxeter groups. One of these conjectures stated that the inversion set of the join of two elements in a Coxeter group is equal to some "closure" of the union of their inversion sets. In this paper we show that this "closure" is in fact a preclosure, which we call the Bruhat preclosure, but is a closure whenever our underlying set is an inversion set. By performing the Bruhat preclosure an infinite number of times we obtain a closure which we call the infinite Bruhat closure. We show in a uniform way that Dyer's conjecture is true when using the infinite Bruhat closure (instead of Bruhat preclosure) if the join exists between two elements. Finally, we end by showing in type A, the Bruhat preclosure is a closure thus giving a (second) proof that Dyer's conjecture is true in type A. - oai:arXiv.org:2512.08711v1 - math.CO - Wed, 10 Dec 2025 00:00:00 -0500 + Analysis of splitting schemes for stochastic evolution equations with non-Lipschitz nonlinearities driven by fractional noise + https://arxiv.org/abs/2512.09733 + arXiv:2512.09733v1 Announce Type: new +Abstract: We propose a novel time-splitting scheme for a class of semilinear stochastic evolution equations driven by cylindrical fractional noise. The nonlinearity is decomposed as the sum of a one-sided, non-globally, Lipschitz continuous function, and of a globally Lipschitz continuous function. The proposed scheme is based on a splitting strategy, where the first nonlinearity is treated using the exact flow of an associated differential equation, and the second one is treated by an explicit Euler approximation. We prove mean-square, strong error estimates for the proposed scheme and show that the order of convergence is $H-1/4$, where $H\in(1/4,1)$ is the Hurst index. For the proof, we establish new regularity results for real-valued and infinite dimensional fractional Ornstein-Uhlenbeck process depending on the value of the Hurst parameter $H$. Numerical experiments illustrate the main result of this manuscript. + oai:arXiv.org:2512.09733v1 + math.NA + cs.NA + math.PR + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Aram Dermenjian + Xiao-Li Ding, Charles-Edouard Br\'ehier, Dehua Wang - Stabilized symplectic embeddings of higher-dimensional ellipsoids - https://arxiv.org/abs/2512.08720 - arXiv:2512.08720v1 Announce Type: new -Abstract: We provide a lower bound for the embedding capacity of higher-dimensional symplectic ellipsoids, formulated in terms of the Lagrangian capacity of ellipsoids. Our approach relies on examining the Borman--Sheridan class of a Weinstein neighborhood of a suitable monotone Lagrangian torus, using Tonkonog's string topology-based computation of the gravitational descendants of the torus. - oai:arXiv.org:2512.08720v1 - math.SG - Wed, 10 Dec 2025 00:00:00 -0500 + Well-posedness of the motion of a rigid body immersed in a compressible inviscid fluid + https://arxiv.org/abs/2512.09741 + arXiv:2512.09741v1 Announce Type: new +Abstract: We consider a rigid body freely moving in a compressible inviscid fluid within a bounded domain $\Omega\subset\mathbb{R}^3$. The fluid is thereby governed by the non necessarily isentropic compressible Euler equations, while the rigid body obeys the conservation of linear and angular momentum. This forms a coupled system comprising an ODE and the initial boundary value problem (IBVP) of a hyperbolic system with characteristic boundary in a moving domain, where the fluid velocity matches the solid velocity along the normal direction of the solid boundary. We establish the existence of a unique local classical solution to this coupled system. To construct the solution, we first perform a change of variables to reformulate the problem in a fixed spatial domain, and then analyze an approximate system with a non-characteristic boundary. For this nonlinear approximate system, we use the better regularity for the trace of the pressure on the boundary to contruct a solution by a fixed-point argument in which the fluid motion and the solid motion are updated in successive steps. We are then able to derive estimates independent of the regularization parameter and to pass to the limit by a strong compactness arguments. + oai:arXiv.org:2512.09741v1 + math.AP + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Shah Faisal + Fr\'ed\'eric Rousset, Pei Su - Exponential blow-up of mild solutions to the fractional Boussinesq equations in the Gevrey class - https://arxiv.org/abs/2512.08726 - arXiv:2512.08726v1 Announce Type: new -Abstract: This work establishes conditions for the existence and uniqueness of local mild solutions to the Boussinesq equations with fractional dissipations in Sobolev-Gevrey spaces. We prove that a unique mild solution exists in an appropriate Sobolev-Gevrey class and analyze its behavior up to the maximal time of existence. In particular, we derive quantitative lower bounds describing how the norm of the solution must blow up as it approaches a finite maximal time. As a corollary, we deduce that the solution exhibits exponential growth. - oai:arXiv.org:2512.08726v1 - math.AP - Wed, 10 Dec 2025 00:00:00 -0500 + Anti-Ramsey Number of Stars in 3-uniform hypergraphs + https://arxiv.org/abs/2512.09747 + arXiv:2512.09747v1 Announce Type: new +Abstract: An edge-colored hypergraph is called \emph{a rainbow hypergraph} if all the colors on its edges are distinct. Given two positive integers $n,r$ and an $r$-uniform hypergraph $\mathcal{G}$, the anti-Ramsey number $ar_r(n,\mathcal{G})$ is defined to be the minimum number of colors $t$ such that there exists a rainbow copy of $\mathcal{G}$ in any exactly $t$-edge-coloring of the complete $r$-uniform hypergraph of order $n$. Let $ \mathcal{F}_k $ denote the 3-graph ($k$-star) consisting of $k$ edges sharing exactly one vertex. Tang, Li and Yan \cite{YTG} determined the value of $ar_3(n,\mathcal{F}_3)$ when $n\geq 20$. In this paper, we determine the anti-Ramsey number $ar_3(n,\mathcal{F}_{k+1})$, where $k\geq 3$ and $n> \frac{5}{2}k^3+\frac{15}{2}k^2+26k-3$. + oai:arXiv.org:2512.09747v1 + math.CO + Thu, 11 Dec 2025 00:00:00 -0500 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Wilberclay G. Melo, Cilon Perusato, Thyago S. R. Santos + http://creativecommons.org/publicdomain/zero/1.0/ + Hongliang Lu, Xinyue Luo, Xinxin Ma - Conditional traffic-like rules for particle-flow simulation in cellular automata - https://arxiv.org/abs/2512.08727 - arXiv:2512.08727v1 Announce Type: new -Abstract: This paper presents a novel approach to the description and understanding of two-dimensional binary cellular automata with the Moore neighborhood that preserve the number of active cells. Such dynamical systems are known to successfully capture particle dynamics and are often used as theoretical models of physical processes where some conservation laws have to be taken into account. Unfortunately, to date, there are no tools for designing such non-trivial cellular automata or for studying their properties, not to mention finding them all and describing their dynamics (even the order of magnitude of their number is unknown). We believe that the novel framework unfolded in this paper will make it possible to overcome all these challenges. - oai:arXiv.org:2512.08727v1 - math.DS - Wed, 10 Dec 2025 00:00:00 -0500 + The real analytic structure of the Teichm\"uller space of circle diffeomorphisms with Zygmund continuous derivatives + https://arxiv.org/abs/2512.09749 + arXiv:2512.09749v1 Announce Type: new +Abstract: We apply the methods of simultaneous uniformization and composition operators on Besov spaces to the Teichm\"uller space $T^Z$ of circle diffeomorphisms with Zygmund continuous derivatives. As consequences, we obtain the following: (1) a new proof of the correspondence between quasiconformal self-homeomorphisms of the unit disk with complex dilatations of linear decay order and their quasisymmetric extensions to the unit circle with regularity in the Zygmund continuously differentiable class; (2) a real-analytic equivalence of $T^Z$ with the real Banach space of Zygmund continuous functions on the unit circle. + oai:arXiv.org:2512.09749v1 + math.CV + Thu, 11 Dec 2025 00:00:00 -0500 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - B. Wolnik, D. M. Falkiewicz, W. Bo{\l}t, A. Rutkowski, B. De Baets + http://creativecommons.org/licenses/by/4.0/ + Katsuhiko Matsuzaki - A Task Parallel Orthonormalization Multigrid Method For Multiphase Elliptic Problems - https://arxiv.org/abs/2512.08728 - arXiv:2512.08728v1 Announce Type: new -Abstract: Multigrid methods have been a popular approach for solving linear systems arising from the discretization of partial differential equations (PDEs) for several decades. They are particularly effective for accelerating convergence rates with optimal complexity in terms of both time and space. K-cycle orthonormalization multigrid is a robust variant of the multigrid method that combines the efficiency of multigrid with the robustness of Krylov-type residual minimalizations for problems with strong anisotropies. However, traditional implementations of K-cycle orthonormalization multigrid often rely on bulk-synchronous parallelism, which can limit scalability on modern high-performance computing (HPC) systems. This paper presents a task- parallel variant of the K-cycle orthonormalization multigrid method that leverages asynchronous execution to improve scalability and performance on large-scale parallel systems. - oai:arXiv.org:2512.08728v1 + Trace inequalities for piecewise $W^{1,p}$ functions over general polytopic meshes + https://arxiv.org/abs/2512.09752 + arXiv:2512.09752v1 Announce Type: new +Abstract: Trace inequalities are crucial tools to derive the stability of partial differential equations with inhomogeneous, natural boundary conditions. In the analysis of corresponding Galerkin methods, they are also essential to show convergence of sequences of discrete solutions to the exact one for data with minimal regularity under mesh refinements and/or degree of accuracy increase. In nonconforming discretizations, such as Crouzeix-Raviart and discontinuous Galerkin, the trial and test spaces consists of functions that are only piecewise continuous: standard trace inequalities cannot be used in this case. In this work, we prove several trace inequalities for piecewise $W^{1,p}$ functions. Compared to analogous results already available in the literature, our inequalities are established: (i) on fairly general polytopic meshes (with arbitrary number of facets and arbitrarily small facets); (ii) without the need of finite dimensional arguments (e.g., inverse estimates, approximation properties of averaging operators); (iii) for different ranges of maximal and nonmaximal Lebesgue indices. + oai:arXiv.org:2512.09752v1 math.NA - cs.DC cs.NA - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Teoman Toprak, Florian Kummer + http://creativecommons.org/licenses/by/4.0/ + Michele Botti, Lorenzo Mascotto - Variance strikes back: sub-game--perfect Nash equilibria in time-inconsistent $N$-player games, and their mean-field sequel - https://arxiv.org/abs/2512.08745 - arXiv:2512.08745v1 Announce Type: new -Abstract: We investigate a time-inconsistent, non-Markovian finite-player game in continuous time, where each player's objective functional depends non-linearly on the expected value of the state process. As a result, the classical Bellman optimality principle no longer applies. To address this, we adopt a two-layer game-theoretic framework and seek sub-game--perfect Nash equilibria both at the intra-personal level, which accounts for time inconsistency, and at the inter-personal level, which captures strategic interactions among players. We first characterise sub-game--perfect Nash equilibria and the corresponding value processes of all players through a system of coupled backward stochastic differential equations. We then analyse the mean-field counterpart and its sub-game--perfect mean-field equilibria, described by a system of McKean-Vlasov backward stochastic differential equations. Building on this representation, we finally prove the convergence of sub-game--perfect Nash equilibria and their corresponding value processes in the $N$-player game to their mean-field counterparts. - oai:arXiv.org:2512.08745v1 - math.PR - econ.TH + On Parameter Identification in Three-Dimensional Elasticity and Discretisation with Physics-Informed Neural Networks + https://arxiv.org/abs/2512.09754 + arXiv:2512.09754v1 Announce Type: new +Abstract: Physics-informed neural networks have emerged as a powerful tool in the scientific machine learning community, with applications to both forward and inverse problems. While they have shown considerable empirical success, significant challenges remain -- particularly regarding training stability and the lack of rigorous theoretical guarantees, especially when compared to classical mesh-based methods. In this work, we focus on the inverse problem of identifying a spatially varying parameter in a constitutive model of three-dimensional elasticity, using measurements of the system's state. This setting is especially relevant for non-invasive diagnosis in cardiac biomechanics, where one must also carefully account for the type of boundary data available. To address this inverse problem, we adopt an all-at-once optimisation framework, simultaneously estimating the state and parameter through a least-squares loss that encodes both available data and the governing physics. For this formulation, we prove stability estimates ensuring that our approach yields a stable approximation of the underlying ground-truth parameter of the physical system independent of a specific discretisation. We then proceed with a neural network-based discretisation and compare it to traditional mesh-based approaches. Our theoretical findings are complemented by illustrative numerical examples. + oai:arXiv.org:2512.09754v1 math.OC - Wed, 10 Dec 2025 00:00:00 -0500 + cs.NA + math.NA + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Dylan Possama\"i, Chiara Rossato + Federica Caforio, Martin Holler, Matthias H\"ofler - Saturation-based robustly optimal hierarchical operation control of microgrids - https://arxiv.org/abs/2512.08757 - arXiv:2512.08757v1 Announce Type: new -Abstract: This paper studies the problem of robustly optimal operation control of microgrids with a high share of renewable energy sources. The main goal is to ensure optimal operation under a wide range of circumstances, given the highly intermittent and uncertain nature of renewable sources and load demand. We formally state this problem, and, in order to solve it, we make effective use of the hierarchical power system control approach. We consider an enhanced primary control layer including droop control and autonomous limitation of power and energy. We prove that this enables the use of constant power setpoints to achieve optimal operation under certain conditions. In order to relax these conditions, the approach is combined with an energy management system, which solves a robust unit commitment problem within a model predictive control framework. Finally, a case study demonstrates the viability of the control design. - oai:arXiv.org:2512.08757v1 + The tangent space to the Wasserstein space: parallel transport and other applications + https://arxiv.org/abs/2512.09763 + arXiv:2512.09763v1 Announce Type: new +Abstract: We propose a new notion of the formal tangent space to the Wasserstein space $\mathcal{P}(X)$ at a given measure. Modulo an integrability condition, we say that this tangent space is made of functions over $X$ which are valued in the probability measures over the tangent bundle to $X$. This generalization of previous concepts of tangent spaces allows us to define appropriate notions of parallel transport, $\mathcal{C}^{1,\alpha}$ regularity over $\mathcal{P}(X)$ and translation of a curve over $\mathcal{P}(X)$. + oai:arXiv.org:2512.09763v1 + math.AP + math.MG math.OC - cs.SY - eess.SY - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Ujjwal Pratap, Steffen Hofmann + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Charles Bertucci (CEREMADE) - Explainable Learning Based Regularization of Inverse Problems - https://arxiv.org/abs/2512.08758 - arXiv:2512.08758v1 Announce Type: new -Abstract: Machine learning techniques for the solution of inverse problems have become an attractive approach in the last decade, while their theoretical foundations are still in their infancy. In this chapter we want to pursue the study of regularization properties, robustness, convergence rates, and structure of regularizers for inverse problems obtained from different learning paradigms. For this sake we study simple architectures that are explainable in the sense that they allow for a theoretical analysis also in the infinite-dimensional limit. In particular we will advance the study of spectral architectures with new results on convergence rates highlighting the role of the smoothness in the training data set, and a study of adversarial robustness. We can show that adversarial training is actually a convergent regularization method. Moreover, we discuss extensions to frame systems and CNN-type architectures for variational regularizers, where we obtain some results on their structure by carefully designed numerical experiments. - oai:arXiv.org:2512.08758v1 - math.NA - cs.NA - Wed, 10 Dec 2025 00:00:00 -0500 + Stochastic Fleet Size and Mix Consistent Vehicle Routing Problem for Last Mile Delivery + https://arxiv.org/abs/2512.09764 + arXiv:2512.09764v1 Announce Type: new +Abstract: In this paper, we address the joint optimization of fleet size and mix, along with vehicle routing, under uncertain customer demand. We propose a two-stage stochastic mixed-integer programming model, where first-stage decisions concern the composition of the delivery fleet and the design of consistent baseline routes. In the second stage, approximate recourse actions are introduced to adapt the initial routes in response to realized customer demands. The objective is to minimize the total delivery cost, including vehicle acquisition, travel distance, and penalty costs for unserved demand. To tackle the computational challenges arising in realistic problem instances, we develop a path-based reformulation of the model and design a Kernel Search-based heuristic to enhance scalability. Computational experiments on small synthetic instances, generated through a population-density-based sampling approach, are conducted to validate the formulation and assess the effects of demand stochasticity through standard stochastic measures, after applying a scenario reduction technique. Additional tests on large-scale real-world instances, based on data from the Italian postal company, demonstrate the effectiveness of the proposed approach and provide managerial and practical insights. + oai:arXiv.org:2512.09764v1 + math.OC + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Martin Burger, Samira Kabri, Gitta Kutyniok, Yunseok Lee, Lukas Weigand + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Paolo Beatrici, Sebastian Birolini, Francesca Maggioni, Paolo Malighetti - Computing normalized Nash equilibria for generalized Nash games with nonconvex players - https://arxiv.org/abs/2512.08770 - arXiv:2512.08770v1 Announce Type: new -Abstract: Generalized Nash equilibrium (GNE) is a solution concept for complete information games, in which each player's objective function and feasible region depend on other players' actions. While numerical methods for finding GNE when players possess convex structure are relatively mature, the same cannot be said when players optimize nonconvex objective functions over nonconvex feasible regions. Drawing inspiration from the notion of a normalized (or variational) Nash equilibrium, which is a more restrictive class of solutions to generalized Nash games, we extend the ideas of Harwood et al. ("Equilibrium modeling and solution approaches inspired by nonconvex bilevel programming." Computational Optimization and Applications, 87(2):641-676, 2024) to develop an exact method that can find a normalized Nash equilibrium (NNE) of a problem, when such an NNE exists. By adapting the framework of Harwood et al., we are able to find NNE without any convexity assumptions. We demonstrate the effectiveness of our method on several nonconvex games. - oai:arXiv.org:2512.08770v1 - math.OC - Wed, 10 Dec 2025 00:00:00 -0500 + A family of trivial ozone algebras + https://arxiv.org/abs/2512.09766 + arXiv:2512.09766v1 Announce Type: new +Abstract: We study a family of Calabi--Yau algebras that include the quadratic Artin--Schelter regular algebras associated to a nodal cubic. It is shown that these algebras have trivial ozone group, that is, the identity is the only automorphism that fixes the center pointwise. The graded members of this family of algebras are shown to be rigid in the sense that the invaraint ring under a nontrivial group of graded automorphisms is not Artin--Schelter regular. + oai:arXiv.org:2512.09766v1 + math.RA + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - 10.1007/s10479-025-06968-z - Stuart M. Harwood, Dimitri J. Papageorgiou + Jason Gaddis, Daniel Yee - Scaling Limits of a Weakly Perturbed Random Interface Model - https://arxiv.org/abs/2512.08771 - arXiv:2512.08771v1 Announce Type: new -Abstract: We consider a random interface model on the discrete torus with $2n$ sites, obtained from the classical corner flip dynamics but with a weak global perturbation, namely an asymmetry of order $n^{-\gamma}$ of the direction of growth that switches direction based on the sign of the total area under the interface. The slopes of this model can be viewed as a non-simple exclusion process at half filling with globally dependent rates. We show that, for $\gamma=1$, the hydrodynamic equation of the empirical density is given by a time concatenation of the viscous Burgers equation and the heat equation. Moreover, for $n$ prime and $\gamma>\frac{6}{7}$, we establish convergence in law of the equilibrium fluctuations to an infinite-dimensional Ornstein-Uhlenbeck process. - oai:arXiv.org:2512.08771v1 - math.PR - Wed, 10 Dec 2025 00:00:00 -0500 + Multiplicity Bounds for Arbitrary Eigenvalues of Connected Signed Graphs + https://arxiv.org/abs/2512.09768 + arXiv:2512.09768v1 Announce Type: new +Abstract: The study of eigenvalue multiplicities plays a central role in the spectral theory of signed graphs, extending several classical results from the unsigned setting. While most existing work focuses on the nullity of a signed graph (the multiplicity of the eigenvalue $0$), much less is known for arbitrary eigenvalues. In this paper, we establish a sharp upper bound for the multiplicity $m(G_\sigma, \lambda)$ of any real eigenvalue $\lambda$ of a connected signed graph $G_\sigma$ in terms of its girth. Our main result shows that \[ m(G_\sigma, \lambda) \le n - g(G_\sigma) + 2, \] where $n$ is the number of vertices and $g(G_\sigma)$ is the girth. We prove that equality holds if and only if $G_\sigma$ is switching equivalent to one of the following extremal families: \begin{itemize} + \item[(i)] a balanced complete graph with $\lambda = -1$; + \item[(ii)] an antibalanced complete graph with $\lambda = 1$; or + \item[(iii)] a balanced complete bipartite graph with $\lambda = 0$. \end{itemize} This fully extends and generalizes the known result for the nullity case ($\lambda = 0$), originally due to Wu et al.\ (2022), to the entire eigenvalue spectrum. Our approach combines Cauchy interlacing, switching equivalence, and a structural analysis of induced cycles in signed graphs. We also provide a characterization of eigenvalues with multiplicity $1$ and $2$ for signed cycles, and include examples illustrating the sharpness and spectral behavior of the extremal families. + oai:arXiv.org:2512.09768v1 + math.CO + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Patr\'icia Gon\c{c}alves, Martin Hairer, Maria Chiara Ricciuti + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Monther R. Alfuraidan, Suliman Khan - Adaptive Regularized Newton Method with Inexact Hessian - https://arxiv.org/abs/2512.08775 - arXiv:2512.08775v1 Announce Type: new -Abstract: Newton's method is the most widespread high-order method, demanding the gradient and the Hessian of the objective function. However, one of the main disadvantages of Newtons method is its lack of global convergence and high iteration cost. Both these drawbacks are critical for modern optimization motivated primarily by current applications in machine learning. In this paper, we introduce a novel algorithm to deal with these disadvantages. Our method can be implemented with various Hessian approximations, including methods that use only the first-order information. Thus, computational costs might be drastically reduced. Also, it can be adjusted to problems' geometries via the usage of different Bregman divergences. The proposed method converges for nonconvex and convex problems globally and it has the same rates as other well-known methods that lack mentioned properties. We present experiments validating our method performs according to the theoretical bounds and shows competitive performance among other Newton-based methods. - oai:arXiv.org:2512.08775v1 - math.OC - Wed, 10 Dec 2025 00:00:00 -0500 + Calder{\'o}n splitting and weak solutions for Navier-Stokes equations with initial data in weighted L p spaces + https://arxiv.org/abs/2512.09770 + arXiv:2512.09770v1 Announce Type: new +Abstract: We show the existence of global weak solutions of the 3D Navier-Stokes equations with initial velocity in the weighted spaces , using Calder{\'o}n splitting L p $\Phi$$\gamma$ $\subset$ L 2 $\Phi$ 2 + L r (with some r $\in$ (3, +$\infty$)) and energy controls in L 2 $\Phi$ 2 . + oai:arXiv.org:2512.09770v1 + math.AP + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Aleksandr Shestakov, Nail Bashirov, Andrei Semenov, Alexander Gasnikov, Martin Tak\'a\v{c}, Aleksandr Beznosikov, Dmitry Kamzolov + Pierre Gilles Lemari\'e-Rieusset (LaMME) - Character Formulas for Kirillov-Reshetikhin Modules via Folding of Supercharacters of $\mathfrak{gl}(M|N)$ - https://arxiv.org/abs/2512.08791 - arXiv:2512.08791v1 Announce Type: new -Abstract: We derive decomposition formulas for supercharacters of quantum affine ortho-symplectic superalgebras and twisted quantum affine superalgebras into supercharacters of their finite-type quantum sub-superalgebras, by employing Cauchy-type identities for supersymmetric Schur functions. These formulas are obtained via a folding (reduction) procedure applied to the supercharacters of the finite-dimensional general linear Lie superalgebra $\mathfrak{gl}(M|N)$. As a special case, our results provide explicit character formulas for a class of Kirillov--Reshetikhin modules of quantum affine algebras (and their Yangian counterparts), thereby proving a previously proposed conjecture derived from Bethe ansatz analysis (arXiv:2309.16660). - oai:arXiv.org:2512.08791v1 - math-ph - math.MP - Wed, 10 Dec 2025 00:00:00 -0500 + Diophantine approximation with mixed powers of Piatetski-Shapiro primes + https://arxiv.org/abs/2512.09771 + arXiv:2512.09771v1 Announce Type: new +Abstract: Let $[\,\cdot\,]$ denote the floor function. In this paper, we show that whenever $\eta$ is real and the constants $\lambda _i$ satisfy some necessary conditions, then for any fixed $\frac{63}{64}<\gamma<1$ and $\theta>0$, there exist infinitely many prime triples $p_1,\, p_2,\, p_3$ satisfying the inequality \begin{equation*} |\lambda _1p_1 + \lambda _2p_2 + \lambda _3p^2_3+\eta|<\big(\max \{p_1, p_2, p^2_3\}\big)^{{\frac{63-64\gamma}{52}}+\theta} \end{equation*} and such that $p_i=[n_i^{1/\gamma}]$,\;\;$i=1,\,2,\,3$. + oai:arXiv.org:2512.09771v1 + math.NT + Thu, 11 Dec 2025 00:00:00 -0500 + new + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + S. I. Dimitrov + + + Mostow Rigidity Made Easier + https://arxiv.org/abs/2512.09774 + arXiv:2512.09774v1 Announce Type: new +Abstract: This article gives a self-contained proof of Mostow Rigidity that has no analytic black boxes. The proof should be accessible to grad students interested in geometry and topology. It has no new research, but I think that this is an unusually clean and analytically light proof of this famous result. I am posting this because I think it will be useful to geometry/topology students. + oai:arXiv.org:2512.09774v1 + math.GT + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Zengo Tsuboi + Richard Evan Schwartz - Persistent Homology for Labeled Datasets: Gromov-Hausdorff Stability and Generalized Landscapes - https://arxiv.org/abs/2512.08794 - arXiv:2512.08794v1 Announce Type: new -Abstract: Techniques from metric geometry have become fundamental tools in modern mathematical data science, providing principled methods for comparing datasets modeled as finite metric spaces. Two of the central tools in this area are the Gromov-Hausdorff distance and persistent homology, both of which yield isometry-invariant notions of distance between datasets. However, these frameworks do not account for categorical labels, which are intrinsic to many real-world datasets, such as labeled images, pre-clustered data, and semantically segmented shapes. In this paper, we introduce a general framework for labeled metric spaces and develop new notions of Gromov-Hausdorff distance and persistent homology which are adapted to this setting. Our main result shows that our persistent homology construction is stable with respect to our novel notion of Gromov-Hausdorff distance, extending a classic result in topological data analysis. To facilitate computation, we also introduce a labeled version of persistence landscapes and show that the landscape map is Lipschitz. - oai:arXiv.org:2512.08794v1 - math.AT + The number of ends of big mapping class groups + https://arxiv.org/abs/2512.09776 + arXiv:2512.09776v1 Announce Type: new +Abstract: We analyze the number of ends of the mapping class group of a stable avenue surface. We prove that the mapping class group is one-ended whenever the stable avenue surface has at least one end of discrete type. Our method is to show that the associated translatable curve graph, which is quasi-isometric to the mapping class group, is one-ended. + oai:arXiv.org:2512.09776v1 + math.GT + math.GR math.MG - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/publicdomain/zero/1.0/ - Yaoying Fu, Evgeniya Lagoda, Shiying Li, Tom Needham, Lander Ver Hoef, Morgan Weiler + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Josiah Oh, Yulan Qing, Xiaolei Wu - Dubrovin duality for open Hurwitz flat F-manifolds - https://arxiv.org/abs/2512.08795 - arXiv:2512.08795v1 Announce Type: new -Abstract: We prove that the Dubrovin dual of a Hurwitz Frobenius manifold extends naturally to an F-manifold with compatible flat connection on the universal curve, in the sense of the open WDVV equations. A similar result is proven for the Frobenius manifold itself in arXiv:2503.09258 . This equips the universal curve with two F-manifolds with compatible flat structure, and we study their duality. We show that they combine into a bi-flat F-manifold. Conditions on open WDVV solutions imposed in previous work are retrieved in this setting, thus providing them with a geometrical meaning. Finally, explicit examples are computed. For Saito Frobenius manifolds of types $A$ and $D$, the extended prepotentials coincide with open WDVV solutions computed independently, whereas even the existence of the solution in type $E$ had not been previously discussed. On the other hand, new non-homogeneous solutions are constructed by duality. - oai:arXiv.org:2512.08795v1 - math-ph - math.DG - math.MP - nlin.SI - Wed, 10 Dec 2025 00:00:00 -0500 + Quasi-isometric rigidity for a product of lattices + https://arxiv.org/abs/2512.09782 + arXiv:2512.09782v1 Announce Type: new +Abstract: We demonstrate quasi-isometric rigidity for the product of a non-uniform rank one lattice and a nilpotent lattice. Specifically, we show that any finitely-generated group quasi-isometric to such a product is, up to finite noise, an extension of a non-uniform rank one lattice by a nilpotent lattice. Furthermore, we show under extra conditions that this extension is nilcentral, a notion which generalizes central extensions to extensions by a nilpotent group. + oai:arXiv.org:2512.09782v1 + math.GT + math.GR + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Alessandro Proserpio, Ian A. B. Strachan + Josiah Oh - Graph Quantum Magic Squares and Free Spectrahedra - https://arxiv.org/abs/2512.08797 - arXiv:2512.08797v1 Announce Type: new -Abstract: Recently De les Coves, Drescher and Netzer showed that an analogue of the Birkhoff--von Neumann theorem fails in the quantum setting. Motivated by this and questions arising in the study of quantum automorphisms of graphs, we introduce a graph-based variant of quantum magic squares and show that the analogue already fails for the cycle \(C_4\), via an explicit counterexample. We also show that they admit monic linear matrix inequality descriptions, hence form compact free spectrahedra. - oai:arXiv.org:2512.08797v1 - math-ph - math.MP - math.OA - Wed, 10 Dec 2025 00:00:00 -0500 + A general class of continuous asymmetric distributions with positive support + https://arxiv.org/abs/2512.09787 + arXiv:2512.09787v1 Announce Type: new +Abstract: In order to better fit real-world datasets, studying asymmetric distribution is of great interest. In this work, we derive several mathematical properties of a general class of asymmetric distributions with positive support which shows up as a unified framework for Extreme Value Theory asymptotic results. The new model generalizes some well-known distribution models such as Generalized Gamma, Inverse Gamma, Weibull, Fr\'echet, Half-normal, Modified half-normal, Rayleigh, and Erlang. To highlight the applicability of our results, the performance of the analytical models is evaluated through real-life dataset modeling. + oai:arXiv.org:2512.09787v1 + math.ST + stat.AP + stat.TH + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Francesca La Piana + Felipe S. Quintino, Pushpa N. Rathie, Luan C. S. M. Ozelim, Tiago A. da Fonseca, Roberto Vila - Three views on the thinned Bernoulli field on the line - https://arxiv.org/abs/2512.08800 - arXiv:2512.08800v1 Announce Type: new -Abstract: This paper investigates the thinned Bernoulli field (TBF) on the one-dimensional integer lattice, where isolated occupied sites are removed from a standard Bernoulli configuration with density $p$. Our present work complements previous findings in higher dimensions and on trees by focusing on the detailed behavior on the line, particularly as $p$ approaches $1.$ First we show that while the TBF on the line is always quasilocally Gibbs, it displays a growing sensitivity to boundary conditions as $p$ increases, indicating an incipient loss of quasilocality. We provide precise asymptotics for this phenomenon, which is an echo of non-quasilocality happening in higher dimensions. Second, we turn to the one-sided point of view and prove that the TBF is a g-measure in the sense of dynamical systems and ergodic theory. The corresponding g-function is quasilocal but becomes long-range again for large $p$. From that we finally develop our third view, in which we provide a transparent construction of the process in terms of a driving Markov chain on the integers of generalized house of cards type, offering a novel perspective on the TBF. - oai:arXiv.org:2512.08800v1 - math.PR - math-ph - math.MP - Wed, 10 Dec 2025 00:00:00 -0500 + Optimal strategy against straightforward bidding in clock auctions + https://arxiv.org/abs/2512.09788 + arXiv:2512.09788v1 Announce Type: new +Abstract: We study a model of auction representative of the 5G auction in France. We determine the optimal strategy of a bidder, assuming that the valuations of competitors are unknown to this bidder and that competitors adopt the straightforward bidding strategy. Our model is based on a Partially Observable Markov Decision Process (POMDP). This POMDP admits a concise statistics, avoiding the solution of a dynamic programming equation in the space of beliefs. In addition, under this optimal strategy, the expected gain of the bidder does not decrease if competitors deviate from straightforward bidding. We illustrate our results by numerical experiments, comparing the value of the bidder with the value of a perfectly informed one. + oai:arXiv.org:2512.09788v1 + math.OC + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Christof Kuelske, Niklas Schubert + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Performance Evaluation, 2025, 169, pp.102502 + Jad Zeroual (TROPICAL), Marianne Akian (TROPICAL), Aur\'elien Bechler (TROPICAL), Matthieu Chardy (TROPICAL), St\'ephane Gaubert (TROPICAL) - The Cahill-Casazza-Daubechies problem on H\"older stable phase retrieval - https://arxiv.org/abs/2512.08806 - arXiv:2512.08806v1 Announce Type: new -Abstract: Phase retrieval using a frame for a finite-dimensional Hilbert space is known to always be Lipschitz stable. However, phase retrieval using a frame or a continuous frame for an infinite-dimensional Hilbert space is always unstable. In order to bridge the gap between the finite and infinite dimensional phenomena, Cahill-Casazza-Daubechies (Trans.Amer.Math.Soc. 2016) gave a construction of a family of nonlinear subsets of an infinite-dimensional Hilbert space where phase retrieval could be performed with a H\"older stability estimate. They then posed the question of whether these subsets satisfied Lipschitz stable phase retrieval. We solve this problem both by giving examples which fail Lipschitz stability and by giving examples which satisfy Lipschitz stability. - oai:arXiv.org:2512.08806v1 - math.FA - cs.NA - math.NA - Wed, 10 Dec 2025 00:00:00 -0500 + A mixed local-nonlocal H\'enon problem in $\mathbb{R}^N$ + https://arxiv.org/abs/2512.09794 + arXiv:2512.09794v1 Announce Type: new +Abstract: In this article, we study a H\'enon-type equation in $\mathbb{R}^N$ driven by a nonlinear operator given by the combination of a local and a nonlocal term. This equation was originally proposed to model spherically symmetric stellar clusters. Here, we prove that, under a suitable relation among the parameters, there exists a threshold separating the existence and non-existence of solutions. Moreover, we establish regularity properties of the solutions. + oai:arXiv.org:2512.09794v1 + math.AP + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Daniel Freeman, Mitchell A. Taylor + Pablo Ochoa, Ariel Salort - Norm Inflation For The Critical SQG Equation - https://arxiv.org/abs/2512.08816 - arXiv:2512.08816v1 Announce Type: new -Abstract: We consider the critical dissipative surface quasi-geostrophic (SQG) equation on $\mathbb{R}^2$ or $\mathbb{T}^2$. Despite global regularity of the equation, we show that the data-to-solution map at the critical level $H^1$ is not uniformly bounded. We construct solutions that experience $H^1$ norm inflation from smooth, compactly supported initial data with large $H^1$ norm. We also demonstrate small-data norm inflation in supercritical Sobolev spaces $W^{\beta,p}$ for $1<p<2$ and $1\le\beta<\tfrac{2}{p}$. - oai:arXiv.org:2512.08816v1 - math.AP - Wed, 10 Dec 2025 00:00:00 -0500 + Stabilization of a chain of 3 hyperbolic PDEs with 2 inputs in arbitrary position + https://arxiv.org/abs/2512.09799 + arXiv:2512.09799v1 Announce Type: new +Abstract: This paper addresses the stabilization of a chain of three coupled hyperbolic partial differential equations actuated by two control inputs applied at arbitrary nodes of the network. With the exception of configurations where one input is located at an endpoint, cases already well studied in the literature, all admissible two-inputs configurations are treated in this paper within a unified framework. The proposed approach relies on a backstepping transformation combined with a reformulation of the closed-loop dynamics as an Integral Difference Equation (IDE). This IDE representation reveals a common structural pattern across configurations and clarifies the role played by delayed dynamics in the stability analysis. Within this formulation, the stabilization problem can be handled using existing IDE control techniques. For most configurations, the stabilization of the PDE system requires an approximate spectral controllability assumption. Remarkably, one specific configuration can be stabilized without imposing any additional spectral condition. In contrast, we also provide an explicit example of a configuration for which the required spectral controllability property fails to hold. + oai:arXiv.org:2512.09799v1 + math.OC + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Dengjun Guo, Xiaoyutao Luo + Adam Braun (L2S), Jean Auriol (L2S), Lucas Brivadis (L2S) - Clasped web bases from hourglass plabic graphs - https://arxiv.org/abs/2512.08817 - arXiv:2512.08817v1 Announce Type: new -Abstract: G.-Pechenik-Pfannerer-Striker-Swanson applied hourglass plabic graphs to construct web bases for spaces of tensor invariants of fundamental representations of $U_q(\mathfrak{sl}_4)$, extending Kuperberg's celebrated basis for $U_q(\mathfrak{sl}_3)$. We give several combinatorial characterizations of basis webs in the kernel of the projection to invariants in a tensor product of arbitrary (type $1$) irreducibles. We apply this to show that the nonzero images of basis webs form a basis (a property shared with Lusztig's dual canonical basis) yielding distinguished clasped web bases for each such tensor product. - oai:arXiv.org:2512.08817v1 - math.CO - math.RT - Wed, 10 Dec 2025 00:00:00 -0500 + Meromorphic maps from ${\Bbb C}^{p}$ into semi-abelian varieties and general projective varieties + https://arxiv.org/abs/2512.09805 + arXiv:2512.09805v1 Announce Type: new +Abstract: In 1953, W. Stoll proposed a method of studying holomorphic functions of several complex variables by reducing them to one variable through fiber integration. In this paper, we use this method to extend some important Nevanlinna-type results for holomorphic curves into projective varieties to meromorphic maps from ${\Bbb C}^{p}$ to projective varieties. This includes Bloch's theorem and Noguchi-Winklemann-Yamanoi's Second Main Theorem for holomorphic maps into semi-abelian varieties intersecting an effective divisor, as well as Huynh-Vu-Xie's Second Main Theorem for meromorphic maps into projective space intersecting with a generic hypersurface with sufficiently high degree. + oai:arXiv.org:2512.09805v1 + math.CV + math.AG + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Pranav Enugandla, Christian Gaetz + Zhe Wang - Point and interval estimators of a changepoint in stochastical dominance between two distributions - https://arxiv.org/abs/2512.08823 - arXiv:2512.08823v1 Announce Type: new -Abstract: For differences between means of continuous data from independent groups, the customary scale-free measure of effect is the standardized mean difference (SMD). To justify use of SMD, one should be reasonably confident that the group-level variances are equal. Empirical evidence often contradicts this assumption. Thus, we have investigated an alternate approach, based on stochastic ordering of the treatment and control distributions, that takes into account means and variances. For applying stochastic ordering, our development yields a key quantity, $\mathsf{A}$, the outcome value at which the direction of the ordering of the treatment and control distributions changes. - Using an extensive simulation, we studied relative bias of point estimators of $\mathsf{A}$ and coverage and relative width of bootstrap confidence intervals. - oai:arXiv.org:2512.08823v1 - math.ST - stat.TH - Wed, 10 Dec 2025 00:00:00 -0500 + Jacob's ladders, our old formula (1985) and new $\zeta$-equivalent of the Fermat-Wiles theorem on two-parametric set of lemniscates of Bernoulli + https://arxiv.org/abs/2512.09812 + arXiv:2512.09812v1 Announce Type: new +Abstract: In our paper from 1985 we have constructed two integrals of the Riemann's function $Z^2(t)$ over two disconnected sets with asymptotically equal measures such that these two integrals differ by considerably big excess. In the present paper we use the formula for that excess to construct a new $\zeta$-equivalent of the Fermat-Wiles theorem on a two-parametric set of lemniscates of Bernoulli. + oai:arXiv.org:2512.09812v1 + math.NT + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Elena Kulinskaya, David C. Hoaglin + Jan Moser - R-harmonious groups - https://arxiv.org/abs/2512.08830 - arXiv:2512.08830v1 Announce Type: new -Abstract: A group is R-harmonious if there exists a permutation $g_1,g_2,\ldots, g_{n-1}$ of the non-identity elements of $G$ such that the consecutive products $g_1g_2$, $g_2g_3$, $\ldots, g_{n-1}g_1$ also form a permutation of the non-identity elements, where $n=|G|$. We investigate R-harmonious groups via cyclic and split extensions. Among our results, we prove that every group of odd-order not divisible by 3 is R-harmonious. - oai:arXiv.org:2512.08830v1 - math.GR - math.CO - Wed, 10 Dec 2025 00:00:00 -0500 + Bounding shears of spiralling triangulations on hyperbolic surfaces + https://arxiv.org/abs/2512.09818 + arXiv:2512.09818v1 Announce Type: new +Abstract: We show that all hyperbolic surfaces admit an ideal triangulation with bounded shear parameters. This upper bound depends logarithmically on the topology of the surface. + oai:arXiv.org:2512.09818v1 + math.GT + Thu, 11 Dec 2025 00:00:00 -0500 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Mohammad Javaheri + http://creativecommons.org/licenses/by-sa/4.0/ + Marie Abadie - A Generalisation of the Munn Semigroup - https://arxiv.org/abs/2512.08835 - arXiv:2512.08835v1 Announce Type: new -Abstract: To each meet-semilattice $E$ is associated an inverse semigroup $T_{E}$ called the Munn semigroup of $E$. We generalise this construction by replacing the meet-semilattice $E$ by a presheaf of sets $X$ over a meet-semilattice. The inverse semigroup $T_{X}$ that results is called the generalised Munn semigroup. Our construction can be viewed as a generalisation of one due to Zhitomirskiy as well as a restriction of one due to Reilly. We prove that idempotent-separating representations in to the generalised Munn semigroup characterise \'etale actions of inverse semigroups. - oai:arXiv.org:2512.08835v1 - math.RA - math.CT - Wed, 10 Dec 2025 00:00:00 -0500 + A Relaxed Randomized Averaging Block Extended Bregman-Kaczmarz Method for Combined Optimization Problems + https://arxiv.org/abs/2512.09825 + arXiv:2512.09825v1 Announce Type: new +Abstract: Randomized Kaczmarz-type methods are widely used for their simplicity and efficiency in solving large-scale linear systems and optimization problems. However, their applicability is limited when dealing with inconsistent systems or incorporating structural information such as sparsity. In this work, we propose a \emph{relaxed randomized averaging block extended Bregman-Kaczmarz} (rRABEBK) method for solving a broad class of combined optimization problems. The proposed method integrates an averaging block strategy with two relaxation parameters to accelerate convergence and enhance numerical stability. We establish a rigorous convergence theory showing that rRABEBK achieves linear convergence in expectation, with explicit constants that quantify the effect of the relaxation mechanism, and a provably faster rate than the classical randomized extended Bregman-Kaczmarz method. Our method can be readily adapted to sparse least-squares problems and extended to both consistent and inconsistent systems without modification. Complementary numerical experiments corroborate the theoretical findings and demonstrate that rRABEBK significantly outperforms the existing Kaczmarz-type algorithms in terms of both iteration complexity and computational efficiency, highlighting both its practical and theoretical advantages. + oai:arXiv.org:2512.09825v1 + math.NA + cs.NA + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Francesco Tesolin + Zeyu Dong, Aqin Xiao, Guojian Yin, Junfeng Yin - Dynamics on Hyperspace of Pointwise Periodic Homeomorphisms - https://arxiv.org/abs/2512.08836 - arXiv:2512.08836v1 Announce Type: new -Abstract: In this paper, we consider the dynamics of induced map $2^f$ of a given pointwise periodic homeomorphism $f:X\to X$ of a compact metric space $X$. First, we show that the topological entropy of $2^f$ is zero, i.e. $h_{top}(2^f)=0$ and that the set of almost periodic points coincides with the set of uniformly recurrent points, i.e. $AP(2^f)=UR(2^f)$. Furthermore, we prove that inside any infinite $\omega$-limit set $\omega_{2^f}(A)$ there is a unique minimal set and this minimal set is an adding machine. As a consequence, $(2^X,2^f)$ has no Devaney chaotic subsystems. In contrast to these rigidity properties, we obtain some results with chaotic flavor. In fact, we prove the following dichotomy, the hyperspace system $(2^X,2^f)$ is either equicontinuous or choatic with respect to Li-Yorke chaos and $\omega$-chaos. It is shown that the later case occurs if and only if $R(2^f)\setminus AP(2^f)\neq\emptyset$. This enables us to provide simple examples of pointwise periodic homeomorphisms with chaotic induced systems. - oai:arXiv.org:2512.08836v1 - math.DS - Wed, 10 Dec 2025 00:00:00 -0500 + Dichotomy results for classes of countable graphs + https://arxiv.org/abs/2512.09832 + arXiv:2512.09832v1 Announce Type: new +Abstract: We study classes of countable graphs where every member does not contain a given finite graph as an induced subgraph -- denoted by $\mathsf{Free}(\mathcal{G})$ for a given finite graph $\mathcal{G}$. Our main results establish a structural dichotomy for such classes: If $\mathcal{G}$ is not an induced subgraph of $\mathcal{P}_4$, then $\mathsf{Free}(\mathcal{G})$ is on top under effective bi-interpretability, implying that the members of $\mathsf{Free}(\mathcal{G})$ exhibit the full range of structural and computational behaviors. In contrast, if $\mathcal{G}$ is an induced subgraph of $\mathcal{P}_4$, then $\mathsf{Free}(\mathcal{G})$ is structurally simple, as witnessed by the fact that every member satisfies the computable embeddability condition. This dichotomy is mirrored in the finite setting when one considers combinatorial and complexity-theoretic properties. Specifically, it is known that $\mathsf{Free}(\mathcal{G})^{fin}$ is complete for graph isomorphism and not a well-quasi-order under embeddability whenever $\mathcal{G}$ is not an induced subgraph of $\mathcal{P}_4$, while in all other cases $\mathsf{Free}(\mathcal{G})^{fin}$ forms a well-quasi-order and the isomorphism problem for $\mathsf{Free}(\mathcal{G})^{fin}$ is solvable in polynomial time. + oai:arXiv.org:2512.09832v1 + math.LO + cs.CC + Thu, 11 Dec 2025 00:00:00 -0500 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Issam Naghmouchi + http://creativecommons.org/licenses/by/4.0/ + Vittorio Cipriani, Ekaterina Fokina, Matthew Harrison-Trainor, Liling Ko, Dino Rossegger - Loose Hamiltonicity - https://arxiv.org/abs/2512.08837 - arXiv:2512.08837v1 Announce Type: new -Abstract: We study the appearance of Hamilton $\ell$-cycles in dense $k$-uniform hypergraphs when $\ell \leq k-2$ and $k-\ell$ does not divide $k$. Our main result reduces this problem to the robust existence of a connected $\ell$-cycle tiling in host graph families that are approximately closed under subsampling. As an application, we determine the minimum $d$-degree threshold for $d=k-2$ and all $1 \leq \ell \leq k-2$ when $k - \ell$ does not divide $k$. We also reduce the case $\ell < d$ entirely to the corresponding (non-connected) $\ell$-cycle tiling problem. In addition, our outcomes lead to counting and random robust versions of these results. The proofs are based on the recently introduced method of blow-up covers and thus avoid the use of the Regularity Lemma and the Absorption Method. - oai:arXiv.org:2512.08837v1 - math.CO - Wed, 10 Dec 2025 00:00:00 -0500 + On Landis' conjecture in the plane for real-valued potentials with decay + https://arxiv.org/abs/2512.09839 + arXiv:2512.09839v1 Announce Type: new +Abstract: We investigate the quantitative unique continuation properties of real-valued solutions to planar Schr\"odinger equations with potential functions that exhibit pointwise decay at infinity. That is, for equations of the form $-\Delta u + V u = 0$ in $\mathbb{R}^2$, where $|V(z)| \lesssim \langle z \rangle^{-N}$ for some $N > 0$, we prove that real-valued solutions satisfy exponential decay estimates with a rate that depends explicitly on $N$. Examples show that the estimates established here are essentially sharp. The case of $N = 0$ corresponds to the Landis conjecture, which was proved for real-valued solutions in the plane in [LMNN20], while the case of $N < 0$ was previously investigated by the author in [Dav24]. Here, the proof techniques rely on the ideas presented in [LMNN20] combined with conformal transformations and an iteration scheme. + oai:arXiv.org:2512.09839v1 + math.AP + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Richard Lang, Nicol\'as Sanhueza-Matamala + Blair Davey - Holonomic D-cap-modules on rigid analytic spaces - https://arxiv.org/abs/2512.08838 - arXiv:2512.08838v1 Announce Type: new -Abstract: We adapt Caro's notion of overholonomicity to give a definition of holonomic D-cap-modules on rigid analytic spaces. We prove stability under five of the six operations (both inverse image functors, duality, and both direct image functors for projective morphisms), as well as base change results. Up to the open problem of stability under tensor products, we obtain an analogue of the usual six-functor formalism for holonomic D-modules. - oai:arXiv.org:2512.08838v1 - math.AG - math.NT - Wed, 10 Dec 2025 00:00:00 -0500 + The Kakeya Conjecture: where does it come from and why is it important? + https://arxiv.org/abs/2512.09842 + arXiv:2512.09842v1 Announce Type: new +Abstract: Roughly speaking, the Kakeya Conjecture asks to what extent lines which point in different directions can be packed together in a small space. In $\R^2$, the problem is relatively straightforward and was settled in the 1970s. In $\R^3$ it is much more difficult and was only recently resolved in a monumental and groundbreaking work of Hong Wang and Joshua Zahl. This note describes the origins of the Kakeya Conjecture, with a particular focus on its classical connections to Fourier analysis, and concludes with a discussion of elements of the Wang--Zahl proof. The goal is to give a sense of why the problem is considered so central to mathematical analysis, and thereby underscore the importance of the Wang--Zahl result. + oai:arXiv.org:2512.09842v1 + math.CA + Thu, 11 Dec 2025 00:00:00 -0500 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Andreas Bode + http://creativecommons.org/licenses/by/4.0/ + Jonathan Hickman - Orbital stability of kinks in the NLS equation with competing nonlinearities - https://arxiv.org/abs/2512.08840 - arXiv:2512.08840v1 Announce Type: new -Abstract: Kinks connecting zero and nonzero equilibria in the NLS equation with competing nonlinearities occur at the special values of the frequency parameter. Since they are minimizers of energy, they are expected to be orbitally stable in the time evolution of the NLS equation. However, the stability proof is complicated by the degeneracy of kinks near the nonzero equilibrium. The main purpose of this work is to give a rigorous proof of the orbital stability of kinks. We give details of analysis for the cubic--quintic NLS equation and show how the proof is extended to the general case. - oai:arXiv.org:2512.08840v1 - math.AP - nlin.PS - Wed, 10 Dec 2025 00:00:00 -0500 + On ortho and disjointly compact operators acting to Frechet spaces + https://arxiv.org/abs/2512.09857 + arXiv:2512.09857v1 Announce Type: new +Abstract: We study compactness along orthonormal (disjoint bounded) sequences for operators from Hilbert spaces (Banach lattices) to Frechet spaces. + oai:arXiv.org:2512.09857v1 + math.FA + Thu, 11 Dec 2025 00:00:00 -0500 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Justin Holmer, Panayotis G. Kevrekidis, Dmitry E. Pelinovsky + http://creativecommons.org/licenses/by/4.0/ + Svetlana Gorokhova - Space-time discretization for barotropic flow stemming from a multisymplectic variational formulation - https://arxiv.org/abs/2512.08841 - arXiv:2512.08841v1 Announce Type: new -Abstract: This study proposes and analyses a novel higher-order, structure preserving discretization method for inviscid barotropic flows from a Lagrangian perspective. The method is built on a multisymplectic variational principle discretized over a full space-time domain. Flow variables are encoded on a staggered space-time mesh, leveraging the principles of mimetic spectral element discretization. Unlike standard Lagrangian methods, which are prone to mesh distortion, this framework computes fluid deformations in a fixed reference configuration and systematically maps them to the physical domain via the Piola-Kirchhoff stress. Further, the structure preserving design ensures that the discrete analogues of the fundamental conservation laws for mass, momentum, and energy are satisfied up to machine precision. The formulation also inherently handles low-Mach number flows without specialized preconditioning. Numerical experiments on expansion and compression flows confirm the accuracy, stability, and exact conservation properties of the discretization. - oai:arXiv.org:2512.08841v1 - math.NA - cs.NA - physics.flu-dyn - Wed, 10 Dec 2025 00:00:00 -0500 + Typical Solutions of Multi-User Linearly-Decomposable Distributed Computing + https://arxiv.org/abs/2512.09858 + arXiv:2512.09858v1 Announce Type: new +Abstract: We solve, in the typical-case sense, the multi-sender linearly-decomposable distributed computing problem introduced by tessellated distributed computing. We model real-valued encoders/decoders and demand matrices, and assess structural fidelity via a thresholded graph edit distance between the demand support and the two-hop support of the computed product. Our analysis yields: a closed-form second-moment (Frobenius) risk under spike-and-slab ensembles; deterministic links between thresholded GED and norm error; a Gaussian surrogate with sub-exponential tails that exposes explicit recall lines; concentration of GED and operator-norm control; and a compute-capped design with a visible knee. We map the rules to aeronautical and satellite networks. + oai:arXiv.org:2512.09858v1 + cs.IT + math.IT + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Mukthesh Mahadev, Marc Gerritsma + http://creativecommons.org/licenses/by-nc-nd/4.0/ + Ali Khalesi, Mohammad Reza Deylam Salehi - Monadic reconstruction of unitary Drinfeld centers and Factorization Homology - https://arxiv.org/abs/2512.08848 - arXiv:2512.08848v1 Announce Type: new -Abstract: We prove that the unitary Drinfeld center of a unitary tensor category is equivalente to the category of unitary bimodules for the canonical W*-algebra object, generalizing M\"uger's result to the non-fusion case. This is then used to express factorization homology in terms of C*-algebraic extensions of symmetric enveloping algebras and actions of Drinfeld dobules of compact quantum groups. - oai:arXiv.org:2512.08848v1 - math.QA + Colouring Graphs Without a Subdivided H-Graph: A Full Complexity Classification + https://arxiv.org/abs/2512.09859 + arXiv:2512.09859v1 Announce Type: new +Abstract: We consider Colouring on graphs that are $H$-subgraph-free for some fixed graph $H$, i.e., graphs that do not contain $H$ as a subgraph. It is known that even $3$-Colouring is NP-complete for $H$-subgraph-free graphs whenever $H$ has a cycle; or a vertex of degree at least $5$; or a component with two vertices of degree $4$, while Colouring is polynomial-time solvable for $H$-subgraph-free graphs if $H$ is a forest of maximum degree at most $3$, in which each component has at most one vertex of degree $3$. For connected graphs $H$, this means that it remains to consider when $H$ is tree of maximum degree $4$ with exactly one vertex of degree $4$, or a tree of maximum degree $3$ with at least two vertices of degree $3$. We let $H$ be a so-called subdivided "H"-graph, which is either a subdivided $\mathbb{H}_0$: a tree of maximum degree $4$ with exactly one vertex of degree $4$ and no vertices of degree $3$, or a subdivided $\mathbb{H}_1$: a tree of maximum degree $3$ with exactly two vertices of degree $3$. In the literature, only a limited number of polynomial-time and NP-completeness results for these cases are known. We develop new polynomial-time techniques that allow us to determine the complexity of Colouring on $H$-subgraph-free graphs for all the remaining subdivided "H"-graphs, so we fully classify both cases. As a consequence, the complexity of Colouring on $H$-subgraph-free graphs has now been settled for all connected graphs $H$ except when $H$ is a tree of maximum degree $4$ with exactly one vertex of degree $4$ and at least one vertex of degree $3$; or a tree of maximum degree $3$ with at least three vertices of degree $3$. We also employ our new techniques to obtain the same new polynomial-time results for another classic graph problem, namely Stable Cut. + oai:arXiv.org:2512.09859v1 + math.CO + cs.CC + cs.DM + cs.DS + Thu, 11 Dec 2025 00:00:00 -0500 + new + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Tala Eagling-Vose, Jorik Jooken, Felicia Lucke, Barnaby Martin, Dani\"el Paulusma + + + Effective Operators in the Theory of Composites: Hilbert Space Framework + https://arxiv.org/abs/2512.09860 + arXiv:2512.09860v1 Announce Type: new +Abstract: In this chapter, the Hilbert space framework in the mathematical theory of composite materials is introduced for studying the properties of effective operators. The goal is to introduce some of the key concepts and fundamental theorems in this area while showing that they follow naturally from using only basic results in operator theory on Hilbert spaces. These concepts include the $Z$-problem as an abstraction of a constitutive equation defined in terms of a bounded linear operator on a Hilbert space with a Hodge decomposition, direct and dual $Z$-problems with the duality interpretation of the inverse of an effective operator, and the notion of an $n$-phase composite with orthogonal $Z(n)$-subspace collection. These theorems include sufficient conditions for the existence and uniqueness of both the solution of a $Z$-problem and the effective operator of a $Z$-problem, a representation formula for the effective operator as an operator Schur complement, the Dirichlet and Thomson minimization principles for the effective operator, the result on monotonicity and concavity of the effective operator map, and the Keller-Dykhne-Mendelson duality relations. Moreover, another important theorem given here (which may also be of independent interest to systems theorists) says that an effective operator of an $n$-phase composite with orthogonal $Z(n)$-subspace collection is the Schur complement of a normalized homogeneous semidefinite operator pencil (in particular, has a Bessmertny\u{\i} realization) and, up to a unitary equivalence, the converse is also true. Finally, the general theory presented here is shown to recover classical results dealing with effective conductivity but can also be applied to many other important problems involving composites in physics and engineering, e.g., in elasticity and electromagnetism. + oai:arXiv.org:2512.09860v1 math-ph + math.FA math.MP math.OA - Wed, 10 Dec 2025 00:00:00 -0500 + physics.class-ph + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Lucas Hataishi + Aaron Welters - Rationally Simply Connected Hypersurfaces in Orthogonal Grassmannians - https://arxiv.org/abs/2512.08849 - arXiv:2512.08849v1 Announce Type: new -Abstract: In this paper, we study the moduli space of rational curves in a general low degree hypersurface in the Orthogonal Grassmanian $OG(k,n+1)$ of $k$-dimensional isotropic subspaces of an $n+1$-dimensional vector space equipped with a symmetric, non-degenerate, bilinear form. We prove rationally simply connectedness for such a general hypersurface of degree $d$ where $d$ satisfies $n+1-8k-4\ge (3k-1)d^2-d$. - oai:arXiv.org:2512.08849v1 - math.AG - Wed, 10 Dec 2025 00:00:00 -0500 + Symmetry for the wave equation on torus: sharp unique continuation and observability conditions for spacetime regions + https://arxiv.org/abs/2512.09873 + arXiv:2512.09873v1 Announce Type: new +Abstract: In this work, we discover a new symmetry structure for the 1D wave equations associated with spacetime observable regions: observable symmetry condition. This structure yields a new conservation law for forced wave equations and provides a necessary condition for unique continuation, observability, and controllability. Building on this symmetry, we establish a necessary and sufficient condition for unique continuation by introducing a weak GCC. Moreover, this symmetry serves as an essential complement to the classical GCC, allowing us to derive a necessary and sufficient characterization of observability and controllability through spacetime geometric regions. + oai:arXiv.org:2512.09873v1 + math.AP + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Srijan Ghosh + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Jingrui Niu, Ming Wang, Shengquan Xiang - A Weaker Notion of Atomicity in Integral Domains - https://arxiv.org/abs/2512.08850 - arXiv:2512.08850v1 Announce Type: new -Abstract: In classical factorization theory, an integral domain is called \emph{atomic} if every nonzero nonunit element can be written as a finite product of irreducible elements. Here, we introduce and study a weaker notion of atomicity, which relaxes the requirement that all elements admit a factorization into irreducibles. Namely, we say that an integral domain is \emph{completely atomic} if every nonunit divisor of an atomic element is also atomic. We further consider several factorization properties associated with this notion. Then, we investigate the basic properties of such domains, provide examples, and explore the behavior of the completely atomic property under standard constructions such as localization, polynomial rings, and $D+M$ constructions. Our results highlight the independence of the completely atomic property from other classical factorization properties and introduce an important class of integral domains that lies between atomic and non-atomic domains. - oai:arXiv.org:2512.08850v1 - math.AC - Wed, 10 Dec 2025 00:00:00 -0500 + Topological median algebra structures on ER homology manifolds I: local cubulation + https://arxiv.org/abs/2512.09875 + arXiv:2512.09875v1 Announce Type: new +Abstract: We study topological median algebra structures on Euclidean spaces + and, more generally, ER homology manifolds. We show that all such + median structures have a local CAT(0) cubulation structure. We also + show that topological median algebra structures are completely metrizable as + median metric spaces if and only if intervals are compact. We give + examples of both metrizable and non-metrizable such structures, as + well as provide a construction for producing many non-locally + cubulated topological median algebra structures on the unit ball in + Euclidean space. + oai:arXiv.org:2512.09875v1 + math.GT + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Mohamed Benelmekki, Brahim Boulayat + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Mladen Bestvina, Kenneth Bromberg, Michah Sageev - Speeding up the Goemans-Williamson randomized procedure by difference-of-convex optimization - https://arxiv.org/abs/2512.08852 - arXiv:2512.08852v1 Announce Type: new -Abstract: We present a novel approach to accelerate the Goemans-Williamson (GW) randomized rounding procedure for quadratic unconstrained binary optimization (QUBO) problems. Instead of solving the conventional semi-definite programming (SDP) relaxation, which is computationally expensive, we employ a difference-of-convex (DC) optimization framework to efficiently approximate the SDP solution. The DC optimization produces candidate vectors that are then used within the GW randomized rounding scheme to generate high-quality binary solutions. Furthermore, we perform direct expectation minimization over manifolds of matrices with limited rank to further enhance the solution quality. Our method is benchmarked on real-world QUBO instances, including inverse kinematics problems, and compared against state-of-the-art solvers, such as quantum-inspired algorithms, demonstrating competitive approximation guarantees alongside substantial computational gains. - oai:arXiv.org:2512.08852v1 - math.OC - Wed, 10 Dec 2025 00:00:00 -0500 + Homological Milnor-Witt modules and Chow-Witt groups over general bases + https://arxiv.org/abs/2512.09876 + arXiv:2512.09876v1 Announce Type: new +Abstract: We introduce a general theory of homological Milnor-Witt cycle modules over an excellent base scheme equipped with a dimension function, extending both Rost's cycle modules and Feld's theory over fields. To any such module we associate a Rost-Schmid type complex whose homology defines a Borel-Moore intersection theory with quadratic coefficients, satisfying homotopy invariance, localization, proper pushforwards, smooth pullbacks, and Gysin morphisms for essentially smoothable lci morphisms. + Using duality data induced by pinning structures, we define cohomological Milnor-Witt modules and establish a duality equivalence between homological and cohomological theories. As applications, we extend Chow-Witt groups to schemes over general (possibly singular or arithmetic) bases, prove generalized Bloch formulas and representability results, and compute graded Chow-Witt groups over Dedekind schemes of finite type over the integers. In particular, we obtain finiteness results for Chow-Witt and related Milnor-Witt invariants in dimension at most one. + oai:arXiv.org:2512.09876v1 + math.AG + math.AT + math.KT + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Hadi Salloum, Roland Hildebrand, Nhat Trung Nguyen, Vitali Pirau, Amer Al Badr, Mohammad Alkousa, Alexander Gasnikov + Fr\'ed\'eric D\'eglise, Niels Feld, Fangzhou Jin - Segre classes and integral dependence - https://arxiv.org/abs/2512.08863 - arXiv:2512.08863v1 Announce Type: new -Abstract: A fundamental property of Segre classes is their birational invariance. This invariance implies that the Segre class of a closed subscheme only depends on the integral closure of the defining ideal sheaf. - In this paper, we show that, conversely, the Segre class of a closed subscheme encodes an integral dependence criterion for its defining ideal sheaf. As an application, we prove that Aluffi's Segre zeta function provides an integral dependence criterion for homogeneous ideals in polynomial rings. - oai:arXiv.org:2512.08863v1 - math.AG - math.AC - Wed, 10 Dec 2025 00:00:00 -0500 + Gehring-Hayman Inequality for Meromorphic Univalent Mappings + https://arxiv.org/abs/2512.09877 + arXiv:2512.09877v1 Announce Type: new +Abstract: Let $f$ be a meromorphic univalent function on the open unit disk having a simple pole at $p\in (0,1)$ that extends continuously to the left half $\IT^{-}$ of the unit circle. In this article, we prove that the ratio of the length of the image of the vertical diameter $\IA$ of the unit disk to the length of the image of $\IT^{-}$ under the mapping $f$ is bounded by a constant depending only on $p.$ Next, we extend this result by considering any hyperbolic geodesic and any Jordan curve in $\D$ sharing the same endpoints. These results extend the classical Gehring-Hayman inequality to meromorphic univalent functions and also prove a conjecture posed by Bhowmik and Maity [Bull. Sci. Math. \textbf{199} (2025), \# 103583]. + oai:arXiv.org:2512.09877v1 + math.CV + Thu, 11 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Yairon Cid-Ruiz + Bappaditya Bhowmik, Deblina Maity, Toshiyuki Sugawa - Curves on Frobenius nonclassical loci of hypersurfaces - https://arxiv.org/abs/2512.08874 - arXiv:2512.08874v1 Announce Type: new -Abstract: Let $\mathcal{S} \subset \mathbb{P}^n$ be an absolutely irreducible projective hypersurface defined over a finite field $\mathbb{F}_q$, equipped with the $\mathbb{F}_q$-Frobenius map $\Phi_q$. In this paper, we investigate irreducible curves $\mathcal{X} \subset \mathcal{S}_{\Phi_q}$, where $\mathcal{S}_{\Phi_q}$ is the $\mathbb{F}_q$-Frobenius nonclassical locus of $\mathcal{S}$. In particular, we show that every curve $\mathcal{X} \subset \mathcal{S}_{\Phi_q}$ such that the restriction of the Gauss map of $\mathcal{S}$ to $\mathcal{X}$ is inseparable is $\mathbb{F}_q$-Frobenius nonclassical. This provides a way to construct new Frobenius nonclassical curves, which are curves that tend to have many $\mathbb{F}_q$-rational points. We also prove that a certain type of Frobenius nonclassical hypersurfaces $\mathcal{S}$ defined by separated variables are such that their Gauss maps restricted to any curve contained in $\mathcal{S}$ is inseparable. Finally, in parallel with the plane curve cases, we show that if the strict Gauss map $\Gamma$ of a $\mathbb{F}_q$-Frobenius nonclassical hypersurface $\mathcal{S}$ is given by $p$ powers, then $\Gamma$ is purely inseparable. - oai:arXiv.org:2512.08874v1 - math.AG - math.AC - Wed, 10 Dec 2025 00:00:00 -0500 + An Ehresmann-Schein-Nambooripad-type theorem for left restriction semigroupoids + https://arxiv.org/abs/2512.09881 + arXiv:2512.09881v1 Announce Type: new +Abstract: We introduce the concept of locally inductive constellations and establish isomorphisms between the categories of left restriction semigroupoids and locally inductive constellations. This construction offers an alternative to the celebrated Ehresmann-Schein-Nambooripad (ESN) Theorem and, in particular, generalizes results for one-sided restriction semigroups. We also obtain ESN-type theorems for one-sided restriction categories and inverse semigroupoids. + oai:arXiv.org:2512.09881v1 + math.RA + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Nazar Arakelian, Pietro Speziali + Rafael Haag, Wesley G. Lautenschlaeger, Tha\'isa Tamusiunas - On the Prague dimension of sparse random graphs - https://arxiv.org/abs/2512.08899 - arXiv:2512.08899v1 Announce Type: new -Abstract: The Prague dimension of a graph $G$ is defined as the minimum number of complete graphs whose direct product contains $G$ as an induced subgraph. Introduced in the 1970s by Ne\v{s}et\v{r}il, Pultr, and R\"odl -- and motivated by the work of Dushnik and Miller, as well as by the induced Ramsey theorem -- determining the Prague dimension of a graph is a notoriously hard problem. In this paper, we show that for all $\varepsilon > 0$ and $p$ such that $ n^{-1+\varepsilon} \le p \le n^{-\varepsilon}$, with high probability the Prague dimension of $G_{n,p}$ is $\Theta_{\varepsilon}(pn)$, which improves upon a recent result by Molnar, R\"odl, Sales and Schacht. - Inspired by the work of Bennett and Bohman, our approach centres on analysing a random greedy process that builds an independent set of size $\Omega(p^{-1}\log pn)$ by iteratively selecting vertices uniformly at random from the common non-neighbourhood of those already chosen. Using the differential equation method, we show that every non-edge is essentially equally likely to be covered by this process, which is key to establishing our bound. - oai:arXiv.org:2512.08899v1 - math.CO - Wed, 10 Dec 2025 00:00:00 -0500 + Berezin transform of Toeplitz operators on Bergman space with Bekolle and Bonami weights + https://arxiv.org/abs/2512.09885 + arXiv:2512.09885v1 Announce Type: new +Abstract: In this paper, we obtain some interesting reproducing kernel estimates and some Carleson properties that play an important role. + We completely characterized every case of the bounded and compact Toeplitz operators on the weighted Bergman spaces with B\'{e}koll\'{e}-Bonami + weights in terms of Berezin transforms. + oai:arXiv.org:2512.09885v1 + math.CV + math.FA + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Felix Joos, Let\'icia Mattos + Hicham Arroussi, Zhan Zhang - Family of hyperbolic manifolds with exponential homology torsion growth - https://arxiv.org/abs/2512.08915 - arXiv:2512.08915v1 Announce Type: new -Abstract: In this note, we construct a family of hyperbolic manifolds with exponentially growing torsion in their homology groups. This demonstrates that the recent bound on homological torsion, established by Bader, Gelander, and Sauer, is asymptotically sharp and cannot be improved. - oai:arXiv.org:2512.08915v1 + Crosscap numbers of alternating links via state codes + https://arxiv.org/abs/2512.09887 + arXiv:2512.09887v1 Announce Type: new +Abstract: We describe a way of encoding a Kauffman state as a set of tuples, similar to a Gauss code. Then we describe a procedure for using these state codes to determine the unoriented genus and crosscap number of any prime alternating knot or link. Finally, we compute these values for all such links through 14 crossings and all such knots through 19 crossings (this data is new for links with 10-14 crossings and knots with 14-19 crossings), and we identify several intriguing patterns in the resulting data. + oai:arXiv.org:2512.09887v1 math.GT - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Stepan Alexandrov + Isaias Bahena, Thomas Kindred, Jason Parsley - Reddening sequences and mutation of infinite quivers - https://arxiv.org/abs/2512.08916 - arXiv:2512.08916v1 Announce Type: new -Abstract: Cluster algebras, introduced by Fomin and Zelevinsky through the process of quiver mutation, have become central objects in modern algebra and geometry, linking combinatorial constructions with diverse mathematical domains such as Teichmuller theory, total positivity, and even theoretical physics. Building on foundational work by Fomin, Shapiro, and Thurston connecting cluster algebras to triangulated surfaces, recent research has extended mutation theory to infinite settings, including the infinity-gon and more general marked surfaces. In this paper, we develop a purely combinatorial framework for mutation of infinite quivers, independent of but compatible with these topological constructions. By formalizing infinite quivers as limits of embedded finite quivers, we establish a consistent definition of mutation that generalizes prior surface-based results. We then apply this framework to extend the notion of reddening sequences, special mutation sequences with significant algebraic consequences, from the finite to the infinite setting. Our approach not only unifies previous topological and combinatorial perspectives but also provides a technical foundation for further generalizations of cluster algebra theory in the infinite case. - oai:arXiv.org:2512.08916v1 - math.CO - math.RT - Wed, 10 Dec 2025 00:00:00 -0500 + Random walks on cocompact Fuchsian and Kleinian groups + https://arxiv.org/abs/2512.09900 + arXiv:2512.09900v1 Announce Type: new +Abstract: The question of the singularity at infinity of the hitting measure of random walks has a long history, originating from the work of Furstenberg in the 1960s. In 2011, Kaimanovich and Le Prince conjectured that the hitting measure of any finitely supported random walk on a discrete subgroup $\Gamma$ of $\mathrm{SL}_N(\mathbb R)$ is singular at infinity with respect to the Lebesgue measure. Using algebraic and geometric convergence and hyperbolic Dehn filling, we prove the singularity conjecture for certain measures on ``most'' cocompact Fuchsian and Kleinian groups. + oai:arXiv.org:2512.09900v1 + math.DS + math.GR + math.GT + math.PR + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Eric Bucher, Elizabeth Howard + Nikolay Bogachev, Peter Kosenko, Giulio Tiozzo - The Maxwell equations on full sub-extremal and extremal Kerr spacetimes - https://arxiv.org/abs/2512.08917 - arXiv:2512.08917v1 Announce Type: new -Abstract: We study the Cauchy problem for the Maxwell equations in the exterior region of Kerr black hole spacetimes. The equations are formulated for components of the Maxwell field relative to the algebraically special frame of Kerr, with the unknowns treated as tensorial quantities associated with a non-integrable horizontal distribution. The extremal Maxwell components decouple into Teukolsky equations, whereas the middle Maxwell components form a coupled system of transport and elliptic equations. Assuming control over the extremal components, we prove uniform boundedness (without loss of derivatives) and decay estimates for the middle components in the full |a|<=M range of spacetime parameters. Our analysis relies on (i) deriving a decoupled system of transport and elliptic equations for two modified middle Maxwell components and (ii) decomposing general solutions into a dynamical and stationary part, the latter determined by two real (electric and magnetic) charges which are entirely read off from the initial data at the event horizon. - In the sub-extremal |a|<M case, works of Shlapentokh-Rothman and the second author provide the necessary control over the extremal components, yielding unconditional boundedness and decay results for all the unknowns in the equations. - In the extremal |a|=M case, we formulate a conjectural boundedness and decay statement for the extremal components, motivated by work of Casals, Gralla and Zimmerman on fixed azimuthal mode solutions compactly supported away from the event horizon. Our boundedness and decay results for all the unknowns in the equations remain, therefore, conditional. We show that the complicated dynamics of the extremal components at the event horizon is inherited by the middle components; in particular, we uncover novel conservation laws for the middle components of axisymmetric solutions. - oai:arXiv.org:2512.08917v1 - math.AP - gr-qc - math-ph - math.MP - Wed, 10 Dec 2025 00:00:00 -0500 + Connecting orbits in quasiaffine spherical varieties via $B$-root subgroups + https://arxiv.org/abs/2512.09906 + arXiv:2512.09906v1 Announce Type: new +Abstract: Given a connected reductive algebraic group $G$ with a Borel subgroup $B$ and a quasiaffine spherical $G$-variety $X$, we prove that every $G$-orbit $Y$ contained in the regular locus of $X$ can be connected by a $B$-normalized additive one-parameter group action with any minimal $G$-orbit in $X$ containing $Y$ in its closure. As a consequence, we show that the regular locus of $X$ is transitive for the subgroup in the automorphism group of $X$ generated by $G$ and all $B$-normalized additive one-parameter subgroups. + oai:arXiv.org:2512.09906v1 + math.AG + Thu, 11 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Gabriele Benomio, Rita Teixeira da Costa + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Roman Avdeev, Vladimir Zhgoon - Gaussian approximation on the Skorokhod space via Malliavin calculus and regularization - https://arxiv.org/abs/2512.08919 - arXiv:2512.08919v1 Announce Type: new -Abstract: We introduce a carr\'e du champ operator for Banach-valued random elements, taking values in the projective tensor product, and use it to control the bounded Lipschitz distance between a Malliavin-smooth random element satisfying mild regularity assumptions and a Radon Gaussian taking values in the Skorokhod space equipped with the uniform topology. In the case where the random element is a Banach-valued multiple integral, the carr\'e du champ expression is further bounded by norms of the contracted integral kernel. The main technical tool is an integration by parts formula, which might be of independent interest. - As a by-product, we recover a bound obtained recently by D\"uker and Zoubouloglou in the Hilbert space setting and complement it by providing contraction bounds. - oai:arXiv.org:2512.08919v1 - math.PR + Multiplicative Renormalization in Causal Perturbation Theory + https://arxiv.org/abs/2512.09918 + arXiv:2512.09918v1 Announce Type: new +Abstract: We construct multiplicative renormalization for the Epstein--Glaser renormalization scheme in perturbative Algebraic Quantum Field Theory: To this end, we fully combine the Connes--Kreimer renormalization framework with the Epstein--Glaser renormalization scheme. In particular, in addition to the already established position-space renormalization Hopf algebra, we also construct the renormalized Feynman rules and the counterterm map via an algebraic Birkhoff decomposition. This includes a discussion about the appropriate target algebra of regularized distributions and the renormalization scheme as a Rota--Baxter operator thereon. In particular, we show that the Hadamard singular part satisfies the Rota--Baxter property and thus relate factorization in Epstein--Glaser with multiplicativity in Connes--Kreimer. Next, we define $Z$-factors as the images of the counterterm map under the corresponding combinatorial Green's functions. This allows us to define the multiplicatively renormalized Lagrange density, for which we show that the corresponding Feynman rules are regular. Finally, we exemplify the developed theory by working out the specific case of $\phi^3_6$-theory. + oai:arXiv.org:2512.09918v1 + math-ph + hep-th math.FA - Wed, 10 Dec 2025 00:00:00 -0500 + math.MP + Thu, 11 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Solesne Bourguin, Simon Campese + Jonah Epstein, Arne Hofmann, David Prinz - Toward Practical Forecasts of Public Sentiments via Convexification for Mean Field Games: Evidence from Real World COVID-19 Discussion Data - https://arxiv.org/abs/2512.08925 - arXiv:2512.08925v1 Announce Type: new -Abstract: We apply a convexification-based numerical method to forecast public sentiment dynamics using Mean Field Games (MFGs). The theoretical foundation for the convexification approach, established in our prior work, guarantees global convergence to the unique solution to the MFG system. The present work demonstrates the practical potential of this framework using real-world sentiment data extracted from social media public discussion during the COVID-19 pandemic. The results show that the MFG model with appropriate parameters and convexification yields sentiment density predictions that align closely with observed data and satisfy the governing equations. While current parameter selection relies on manual calibration, our findings establish the first proof-of-concept evidence that MFG models can capture complex temporal patterns in public sentiment, laying the groundwork for future work on systematic parameter identification methods, i.e. solutions of coefficient inverse problems for the MFG system. - oai:arXiv.org:2512.08925v1 - math.NA - cs.NA - Wed, 10 Dec 2025 00:00:00 -0500 - new + Online Inference of Constrained Optimization: Primal-Dual Optimality and Sequential Quadratic Programming + https://arxiv.org/abs/2512.08948 + arXiv:2512.08948v1 Announce Type: cross +Abstract: We study online statistical inference for the solutions of stochastic optimization problems with equality and inequality constraints. Such problems are prevalent in statistics and machine learning, encompassing constrained $M$-estimation, physics-informed models, safe reinforcement learning, and algorithmic fairness. We develop a stochastic sequential quadratic programming (SSQP) method to solve these problems, where the step direction is computed by sequentially performing a quadratic approximation of the objective and a linear approximation of the constraints. Despite having access to unbiased estimates of population gradients, a key challenge in constrained stochastic problems lies in dealing with the bias in the step direction. As such, we apply a momentum-style gradient moving-average technique within SSQP to debias the step. We show that our method achieves global almost-sure convergence and exhibits local asymptotic normality with an optimal primal-dual limiting covariance matrix in the sense of H\'ajek and Le Cam. In addition, we provide a plug-in covariance matrix estimator for practical inference. To our knowledge, the proposed SSQP method is the first fully online method that attains primal-dual asymptotic minimax optimality without relying on projection operators onto the constraint set, which are generally intractable for nonlinear problems. Through extensive experiments on benchmark nonlinear problems, as well as on constrained generalized linear models and portfolio allocation problems using both synthetic and real data, we demonstrate superior performance of our method, showing that the method and its asymptotic behavior not only solve constrained stochastic problems efficiently but also provide valid and practical online inference in real-world applications. + oai:arXiv.org:2512.08948v1 + stat.ML + cs.LG + math.OC + math.ST + stat.TH + Thu, 11 Dec 2025 00:00:00 -0500 + cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Shi Chen, Michael V. Klibanov, Kevin McGoff, Trung Truong, Wangjiaxuan Xin, Shuhua Yin + Yihang Gao, Michael K. Ng, Michael W. Mahoney, Sen Na - Failure of the Markov property for stochastic Volterra equations - https://arxiv.org/abs/2512.08926 - arXiv:2512.08926v1 Announce Type: new -Abstract: Memory-driven stochastic dynamics arise naturally in many applications, and stochastic Volterra equations (SVEs) offer a flexible framework for modeling such systems. Their convolution structure with Volterra kernels endows the dynamics with a formal path-dependency, which suggests the failure of the Markov property. While this has previously been rigorously established only for Gaussian Volterra processes, by constructing nondegenerate admissible perturbations through Markovian lifts, we prove that also general SVEs with H\"older-continuous coefficients do not possess the Markov property for a broad class of Volterra kernels. Moreover, we show that the associated Markovian lift is, in general, necessarily infinite-dimensional. These observations reflect the intrinsic infinite-dimensionality of memory effects in SVEs and underscore the need for analytical and probabilistic tools beyond the classical Markovian framework. - oai:arXiv.org:2512.08926v1 - math.PR - Wed, 10 Dec 2025 00:00:00 -0500 - new + Hill's Lunar Equations, Series, Convergence, Motion of the Perigee + https://arxiv.org/abs/2512.08961 + arXiv:2512.08961v1 Announce Type: cross +Abstract: We investigate Hill's lunar equations, series and the motion of the perigee, and we use computers to go farther than has previously been known, calculating the coefficients of Hill's series up to order 24 in m, and the coefficients that do not depend on a_0 up to order 30. Numerical calculations indicate that the radius of convergence of Hill's series is somewhere near the value of m of the cusped orbit (0.560958), which we formulate as a conjecture. We calculate the motion of the perigee using a linearization of the equation for the anomalistic period, as in Hill's documentation, but with some discrepancies. + oai:arXiv.org:2512.08961v1 + nlin.CD + math.SG + Thu, 11 Dec 2025 00:00:00 -0500 + cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Martin Friesen, Stefan Gerhold, Kristof Wiedermann + Thomas Ligon - On a cross-diffusion hybrid model: Cancer Invasion Tissue with Normal Cell Involved - https://arxiv.org/abs/2512.08929 - arXiv:2512.08929v1 Announce Type: new -Abstract: In this paper, we study a well-posedness problem on a new mathematical model for cancer invasion within the plasminogen activation system, which explicitly incorporates cooperation with host normal cells. Key biological mechanisms--including chemotaxis, haptotaxis, recruitment, logistic growth, and natural degradation of normal cells--along with other primary components (cancer cells, vitronectin, uPA, uPAI-1 and plasmin) are modeled via a continuum framework of cancer cell invasion of the extracellular matrix. The resulting model constitutes a strongly coupled, cross-diffusion hybrid system of differential equations. The primary mathematical challenges arise from the strongly coupled cross-diffusion terms, the parabolic operators of divergence form, and the interaction between the cross-diffusion fluxes and the ODE components. We address these by deriving several a priori estimates for dimensions d less or equal to 3. Subsequently, we employ a decoupling strategy to split the system into proper sub-problems, establishing the existence (and uniqueness) for each subsystem. Finally, we demonstrate the global existence and uniqueness of the solution for dimensions d less or equal to 2 and the global existence of a solution for dimension d = 3. - oai:arXiv.org:2512.08929v1 - math.AP - Wed, 10 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Guanjun Pan, Hong-Ming Yin + The ${\cal N}=1$ supersymmetric Pati-Salam models with extra $SU(2)_{L_2/R_2}$ gauge symmetry from intersecting D6-branes + https://arxiv.org/abs/2512.09057 + arXiv:2512.09057v1 Announce Type: cross +Abstract: By introducing an extra stack of D6-branes to standard ${\cal N}=1$ supersymmetric Pati-Salam models, we extend the landscape of its complete search. In this construction, the $d$-stack of D6-branes is introduced besides the standard $a,~b,~c$-stacks. More intersections from the extra stacks of D6-branes appear, and thus Higgs/Higgs-like particles arise from more origins. Among these models, we find eight new classes of ${\cal N}=1$ supersymmetric Pati-Salam models with gauge symmetries $SU(4)_C\times SU(2)_L\times SU(2)_{R_1}\times SU(2)_{R_2}$ and $SU(4)_C\times SU(2)_{L_1}\times SU(2)_{R}\times SU(2)_{L_2}$, where $d$-stack of D6-branes carries the gauge symmetries $SU(2)_{R_2}$ and $SU(2)_{L_2}$, respectively. The $SU(2)_{L_1/R_1} \times SU(2)_{L_2/R_2}$ can be broken down to the diagonal $SU(2)_{L/R}$ gauge symmetry via bifundamental Higgs fields. In such a way, we for the first time successfully constructed three-family supersymmetric Pati-Salam models from non-rigid D6-branes with extra $d$-stacks of D6-branes as visible sectors. Interestingly, by introducing extra stack of D6-branes to the standard supersymmetric Pati-Salam models, the number of filler brane reduces in general, and eventually the models without any $USp(N)$ gauge symmetry present. This reduces the exotic particles from filler brane intersection yet provides more vector-like particles from ${\cal N}=2$ subsector that are useful in renormalization group equation evolution as an advantage. Moreover, interesting degeneracy behavior with the same gauge coupling ratio exists in certain class of models. + oai:arXiv.org:2512.09057v1 + hep-th + hep-ph + math-ph + math.MP + Thu, 11 Dec 2025 00:00:00 -0500 + cross + http://creativecommons.org/licenses/by/4.0/ + Haotian Huangfu, Tianjun Li, Qi Sun, Rui Sun, Lina Wu - Fast and Robust Diffusion Posterior Sampling for MR Image Reconstruction Using the Preconditioned Unadjusted Langevin Algorithm - https://arxiv.org/abs/2512.05791 - arXiv:2512.05791v1 Announce Type: cross -Abstract: Purpose: The Unadjusted Langevin Algorithm (ULA) in combination with diffusion models can generate high quality MRI reconstructions with uncertainty estimation from highly undersampled k-space data. However, sampling methods such as diffusion posterior sampling or likelihood annealing suffer from long reconstruction times and the need for parameter tuning. The purpose of this work is to develop a robust sampling algorithm with fast convergence. - Theory and Methods: In the reverse diffusion process used for sampling the posterior, the exact likelihood is multiplied with the diffused prior at all noise scales. To overcome the issue of slow convergence, preconditioning is used. The method is trained on fastMRI data and tested on retrospectively undersampled brain data of a healthy volunteer. - Results: For posterior sampling in Cartesian and non-Cartesian accelerated MRI the new approach outperforms annealed sampling in terms of reconstruction speed and sample quality. - Conclusion: The proposed exact likelihood with preconditioning enables rapid and reliable posterior sampling across various MRI reconstruction tasks without the need for parameter tuning. - oai:arXiv.org:2512.05791v1 - physics.med-ph - cs.CV + Natural Geometry of Robust Data Attribution: From Convex Models to Deep Networks + https://arxiv.org/abs/2512.09103 + arXiv:2512.09103v1 Announce Type: cross +Abstract: Data attribution methods identify which training examples are responsible for a model's predictions, but their sensitivity to distributional perturbations undermines practical reliability. We present a unified framework for certified robust attribution that extends from convex models to deep networks. For convex settings, we derive Wasserstein-Robust Influence Functions (W-RIF) with provable coverage guarantees. For deep networks, we demonstrate that Euclidean certification is rendered vacuous by spectral amplification -- a mechanism where the inherent ill-conditioning of deep representations inflates Lipschitz bounds by over $10{,}000\times$. This explains why standard TRAK scores, while accurate point estimates, are geometrically fragile: naive Euclidean robustness analysis yields 0\% certification. Our key contribution is the Natural Wasserstein metric, which measures perturbations in the geometry induced by the model's own feature covariance. This eliminates spectral amplification, reducing worst-case sensitivity by $76\times$ and stabilizing attribution estimates. On CIFAR-10 with ResNet-18, Natural W-TRAK certifies 68.7\% of ranking pairs compared to 0\% for Euclidean baselines -- to our knowledge, the first non-vacuous certified bounds for neural network attribution. Furthermore, we prove that the Self-Influence term arising from our analysis equals the Lipschitz constant governing attribution stability, providing theoretical grounding for leverage-based anomaly detection. Empirically, Self-Influence achieves 0.970 AUROC for label noise detection, identifying 94.1\% of corrupted labels by examining just the top 20\% of training data. + oai:arXiv.org:2512.09103v1 cs.LG - math.PR - Wed, 10 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Moritz Blumenthal, Tina Holliber, Jonathan I. Tamir, Martin Uecker - - - Bianchi Cosmologies in a Thurston-Based Theory of Gravity - https://arxiv.org/abs/2512.07708 - arXiv:2512.07708v1 Announce Type: cross -Abstract: The strong interplay between Bianchi--Kantowski--Sachs (BKS) spacetimes and Thurston geometries motivates the exploration of the role of topology in our understanding of gravity. As such, we study non-tilted BKS solutions of a theory of gravity that explicitly depends on Thurston geometries. We show that shear-free solutions with perfect fluid, as well as static vacuum solutions, exist for all topologies. Moreover, we prove that, aside from non-rotationally-symmetric Bianchi II models, all BKS metrics isotropize in the presence of a positive cosmological constant, and that recollapse is never possible when the weak energy condition is satisfied. This contrasts with General Relativity (GR), where these two properties fail for Bianchi IX and KS metrics. No additional parameters compared to GR are required for these results. We discuss, in particular, how this framework might allow for simple inflationary models in any topology. - oai:arXiv.org:2512.07708v1 - gr-qc - math-ph - math.MP - Wed, 10 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Quentin Vigneron, Hamed Barzegar - - - State and Parameter Estimation for a Neural Model of Local Field Potentials - https://arxiv.org/abs/2512.07842 - arXiv:2512.07842v1 Announce Type: cross -Abstract: The study of cortical dynamics during different states such as decision making, sleep and movement, is an important topic in Neuroscience. Modelling efforts aim to relate the neural rhythms present in cortical recordings to the underlying dynamics responsible for their emergence. We present an effort to characterize the neural activity from the cortex of a mouse during natural sleep, captured through local field potential measurements. Our approach relies on using a discretized Wilson--Cowan Amari neural field model for neural activity, along with a data assimilation method that allows the Bayesian joint estimation of the state and parameters. We demonstrate the feasibility of our approach on synthetic measurements before applying it to a dataset available in literature. Our findings suggest the potential of our approach to characterize the stimulus received by the cortex from other brain regions, while simultaneously inferring a state that aligns with the observed signal. - oai:arXiv.org:2512.07842v1 - q-bio.NC - math.DS - math.PR - stat.CO - Wed, 10 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Daniele Avitabile, Gabriel J. Lord, Khadija Meddouni - - - Normal form computation of nonlinear dispersion relationship for locally resonant metamaterial - https://arxiv.org/abs/2512.07861 - arXiv:2512.07861v1 Announce Type: cross -Abstract: This article is devoted to the application of the parametrisation method for invariant manifold with a complex normal form style (CNF), for the derivation of high-order approximations of underdamped nonlinear dispersion relationships for periodic structures, more specifically by considering the case of a locally resonant metamaterial chain incorporating damping and various nonlinear stiffnesses. Two different strategies are proposed to solve the problem. In the first one, Bloch's assumption is first applied to the equations of motion, and then the nonlinear change of coordinates provided by the complex normal form style in the parametrisation method is applied. This direct procedure, which applies first the wave dependency to the original physical coordinates of the problem, is referred to as CNF-BP (for CNF applied with Bloch's assumption on physical coordinates). In the second strategy, the nonlinear change of coordinates provided by the parametrisation method, which relates the physical coordinates to the so-called normal coordinates, is first applied. Then the periodic assumption is used, thus imposing a Bloch wave ansatz on the normal coordinates. This method will be referred to as CNF-PN (for CNF with a periodic assumption on normal coordinates). In the conservative case, the CNF-PN strategy exhibits superior capability in capturing complex wave propagation phenomena, whereas the CNF-BP strategy encounters limitations in handling non-fundamental harmonics and the nonlinear interactions between host oscillators. For underdamped systems, the CNF-PN is rigorously validated and systematically compared against numerical techniques, a classical analytical perturbation technique (the method of multiple scales), and direct numerical time integration of annular chain structures. - oai:arXiv.org:2512.07861v1 - physics.optics - math.DS - physics.app-ph - physics.class-ph - Wed, 10 Dec 2025 00:00:00 -0500 + math.OC + Thu, 11 Dec 2025 00:00:00 -0500 cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Tao Wang, Cyril Touz\'e, Haiqin Li, Qian Ding + Shihao Li, Jiachen Li, Dongmei Chen - Finding core subgraphs of directed graphs via discrete Ricci curvature flow - https://arxiv.org/abs/2512.07899 - arXiv:2512.07899v1 Announce Type: cross -Abstract: Ricci curvature and its associated flow offer powerful geometric methods for analyzing complex networks. While existing research heavily focuses on applications for undirected graphs such as community detection and core extraction, there have been relatively less attention on directed graphs. - In this paper, we introduce a definition of Ricci curvature and an accompanying curvature flow for directed graphs. Crucially, for strongly connected directed graphs, this flow admits a unique global solution. We then apply this flow to detect strongly connected subgraphs from weakly connected directed graphs. (A weakly connected graph is connected overall but not necessarily strongly connected). Unlike prior work requiring graphs to be strongly connected, our method loosens this requirement. We transform a weakly connected graph into a strongly connected one by adding edges with very large artificial weights. This modification does not compromise our core subgraph detection. Due to their extreme weight, these added edges are automatically discarded during the final iteration of the Ricci curvature flow. - For core evaluation, our approach consistently surpasses traditional methods, achieving better results on at least two out of three key metrics. The implementation code is publicly available at https://github.com/12tangze12/Finding-core-subgraphs-on-directed-graphs. - oai:arXiv.org:2512.07899v1 - cs.SI - math.CO - Wed, 10 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Juan Zhao, Jicheng Ma, Yunyan Yang, Liang Zhao - - - Symmetry-Based Quantum Codes Beyond the Pauli Group - https://arxiv.org/abs/2512.07908 - arXiv:2512.07908v1 Announce Type: cross -Abstract: Typical stabilizer codes aim to solve the general problem of fault-tolerance without regard for the structure of a specific system. By incorporating a broader representation-theoretic perspective, we provide a generalized framework that allows the code designer to take this structure into account. For any representation of a finite group, we produce a quantum code with a code space invariant under the group action, providing passive error mitigation against errors belonging to the image of the representation. Furthermore, errors outside this scope are detected and diagnosed by performing a projective measurement onto the isotypic components corresponding to irreducible representations of the chosen group, effectively generalizing syndrome extraction to symmetry-resolved quantum measurements. We show that all stabilizer codes are a special case of this construction, including qudit stabilizer codes, and show that there is a natural one logical qubit code associated to the dihedral group. Thus we provide a unifying framework for existing codes while simultaneously facilitating symmetry-aware codes tailored to specific systems. - oai:arXiv.org:2512.07908v1 - quant-ph - math-ph - math.MP - Wed, 10 Dec 2025 00:00:00 -0500 + Semantic Trajectory Generation for Goal-Oriented Spacecraft Rendezvous + https://arxiv.org/abs/2512.09111 + arXiv:2512.09111v1 Announce Type: cross +Abstract: Reliable real-time trajectory generation is essential for future autonomous spacecraft. While recent progress in nonconvex guidance and control is paving the way for onboard autonomous trajectory optimization, these methods still rely on extensive expert input (e.g., waypoints, constraints, mission timelines, etc.), which limits the operational scalability in real rendezvous missions.This paper introduces SAGES (Semantic Autonomous Guidance Engine for Space), a trajectory-generation framework that translates natural-language commands into spacecraft trajectories that reflect high-level intent while respecting nonconvex constraints. Experiments in two settings -- fault-tolerant proximity operations with continuous-time constraint enforcement and a free-flying robotic platform -- demonstrate that SAGES reliably produces trajectories aligned with human commands, achieving over 90\% semantic-behavioral consistency across diverse behavior modes. Ultimately, this work marks an initial step toward language-conditioned, constraint-aware spacecraft trajectory generation, enabling operators to interactively guide both safety and behavior through intuitive natural-language commands with reduced expert burden. + oai:arXiv.org:2512.09111v1 + cs.RO + cs.AI + math.OC + Thu, 11 Dec 2025 00:00:00 -0500 cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Zachary P. Bradshaw, Margarite L. LaBorde, Dillon Montero + Yuji Takubo, Arpit Dwivedi, Sukeerth Ramkumar, Luis A. Pabon, Daniele Gammelli, Marco Pavone, Simone D'Amico - Quantum algorithms for viscosity solutions to nonlinear Hamilton-Jacobi equations based on an entropy penalisation method - https://arxiv.org/abs/2512.07919 - arXiv:2512.07919v1 Announce Type: cross -Abstract: We present a framework for efficient extraction of the viscosity solutions of nonlinear Hamilton-Jacobi equations with convex Hamiltonians. These viscosity solutions play a central role in areas such as front propagation, mean-field games, optimal control, machine learning, and a direct application to the forced Burgers' equation. Our method is based on an entropy penalisation method proposed by Gomes and Valdinoci, which generalises the Cole-Hopf transform from quadratic to general convex Hamiltonians, allowing a reformulation of viscous Hamilton-Jacobi dynamics by a discrete-time linear dynamics which approximates a linear heat-like parabolic equation, and can also extend to continuous-time dynamics. This makes the method suitable for quantum simulation. The validity of these results hold for arbitrary nonlinearity that correspond to convex Hamiltonians, and for arbitrarily long times, thus obviating a chief obstacle in most quantum algorithms for nonlinear partial differential equations. We provide quantum algorithms, both analog and digital, for extracting pointwise values, gradients, minima, and function evaluations at the minimiser of the viscosity solution, without requiring nonlinear updates or full state reconstruction. - oai:arXiv.org:2512.07919v1 - quant-ph - math-ph - math.MP - Wed, 10 Dec 2025 00:00:00 -0500 + Bayesian Optimization of Laser-Wakefield Acceleration via Spectral Pulse Shaping + https://arxiv.org/abs/2512.09125 + arXiv:2512.09125v1 Announce Type: cross +Abstract: In this paper, we investigate the effect of spectral pulse shaping of the laser driver on the performance of channel-guided, laser-plasma accelerators. The study was carried out with the assistance of Bayesian optimization using particle-in-cell simulations. We used a realistic plasma profile based on a novel optical-field-ionized channel technique with ionization injection and low on-axis plasma densities to maximize the energy gain of the electron bunch trailing the laser. Spectral shaping allows us to modify the temporal profile of the laser driver while keeping the laser energy constant, affecting the acceleration and injection processes. Given the complexity and breadth of the parameter space in question, we used numerical optimization to identify high performers. In particular, we found laser profiles with additional spectral content that, when used with optimal plasma channel parameters, result in charge content an order of magnitude higher than the baseline Gaussian case while also increasing the mean energy of the electron bunch. + oai:arXiv.org:2512.09125v1 + physics.plasm-ph + math.OC + physics.acc-ph + Thu, 11 Dec 2025 00:00:00 -0500 cross http://creativecommons.org/licenses/by/4.0/ - Shi Jin, Nana Liu + B. Z. Djordjevi\'c, C. Benedetti, A. D. McNaughton, C. B. Schroeder, R. Lehe, H. -E. Tsai, S. C. Wilks, B. A. Reagan, G. J. Williams, J. van Tilborg - On semantics of first-order justification logic with binding modalities - https://arxiv.org/abs/2512.07994 - arXiv:2512.07994v1 Announce Type: cross -Abstract: We introduce the first order logic of proofs $FOLP^\Box$ in the joint language combining justification terms and binding modalities. The main issue is Kripke--style semantics for this logic. We describe models for $FOLP^\Box$ in terms of valuations of individual variables instead of introducing constants to the language. This approach requires a new format of the evidence function. This allows us to assign semantic meaning to formulas that contain free variables. The main results are soundness and completeness of $FOLP^\Box$ with respect to the described semantics. - oai:arXiv.org:2512.07994v1 - cs.LO - math.LO - Wed, 10 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Tatiana Yavorskaya (Steklov Mathematical Institute of Russian Academy of Science), Elena Popova (Steklov Mathematical Institute of Russian Academy of Science) - - - On the accuracy of population level approximation of network processes - https://arxiv.org/abs/2512.07995 - arXiv:2512.07995v1 Announce Type: cross -Abstract: The individual-based model of simple contagion processes is considered on regular graphs. This model explicitly incorporates the adjacency matrix of the network enabling us to study the effect of network structure on the dynamic of the propagation process. While the asymptotic behaviour of the model is well known, the transient behaviour has been less studied. Our goal in this paper is to give a theoretical estimate on the accuracy of the one-dimensional population-level approximation. This is carried out for arbitrary simple contagion processes and regular Tur\'an graphs. Numerical evidence is shown that the theoretical estimate is rather sharp for dense graphs. - oai:arXiv.org:2512.07995v1 - physics.soc-ph - math.DS - Wed, 10 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by-nc-nd/4.0/ - No\'emi Nagy, S\'andor Horv\'ath, Bal\'azs Maga, P\'eter L. Simon - - - Learning Dynamics from Infrequent Output Measurements for Uncertainty-Aware Optimal Control - https://arxiv.org/abs/2512.08013 - arXiv:2512.08013v1 Announce Type: cross -Abstract: Reliable optimal control is challenging when the dynamics of a nonlinear system are unknown and only infrequent, noisy output measurements are available. This work addresses this setting of limited sensing by formulating a Bayesian prior over the continuous-time dynamics and latent state trajectory in state-space form and updating it through a targeted marginal Metropolis-Hastings sampler equipped with a numerical ODE integrator. The resulting posterior samples are used to formulate a scenario-based optimal control problem that accounts for both model and measurement uncertainty and is solved using standard nonlinear programming methods. The approach is validated in a numerical case study on glucose regulation using a Type 1 diabetes model. - oai:arXiv.org:2512.08013v1 - eess.SY - cs.LG - cs.SY - math.OC - Wed, 10 Dec 2025 00:00:00 -0500 + Inhomogeneous Branching Random Walks: Incorporating Genealogy and Density Effects + https://arxiv.org/abs/2512.09145 + arXiv:2512.09145v1 Announce Type: cross +Abstract: In this paper, we introduce a novel framework using inhomogeneous Branching Random Walks (BRWs) to model growth processes, specifically introducing genealogy-dependence in branching rates and displacement distributions to model phenomena like bacterial colony growth. Current stochastic models often either assume independent and identical behavior of individual agents or incorporate only spatiotemporal inhomogeneity, ignoring the effect of genealogy-based inhomogeneity on the long-time behavior of these processes. Such long-time asymptotics are of independent mathematical interest and are crucial in understanding the effect of patterns. We propose several inhomogeneous BRW models in 2D space where displacement distributions and branching rates vary with time, space, and genealogy. A combined model then uses a weighted average of positions given by these separate models to study the shape of the growth patterns. Using computer simulations, we tune parameters from these models, which are based on genealogical and spatiotemporal factors, observe the resulting structures, and compare them with images of real bacterial colonies. + oai:arXiv.org:2512.09145v1 + q-bio.PE + math.PR + Thu, 11 Dec 2025 00:00:00 -0500 cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Robert Lefringhausen, Theodor Springer, Sandra Hirche + http://creativecommons.org/licenses/by/4.0/ + Lauren Ajax, Beatrice Durham, Pratima Hebbar, Cade Johnson, Jiayi Zhang - Classical and quantum dynamics of a particle confined in a paraboloidal cavity - https://arxiv.org/abs/2512.08021 - arXiv:2512.08021v1 Announce Type: cross -Abstract: We present a classical and quantum analysis of a particle confined in a three-dimensional paraboloidal cavity formed by two confocal paraboloids. Classically, the system is integrable and presents three independent constants of motion, namely, the energy, the $z$-component of the angular momentum, and a third dynamical constant associated with the paraboloidal geometry, which can be derived from the separability of the Hamilton--Jacobi equation. We derive closed-form analytical expressions for the actions, which allow us to determine the two conditions to get periodic closed trajectories. We classify these trajectories through the indices $(s,t,\ell)$. The caustic paraboloids that bound the motion provide a complete geometric characterization of admissible trajectories. Quantum mechanically, separability of the Schr\"odinger equation in parabolic coordinates yields eigenmodes described by Whittaker functions. We determine the energy spectrum and identify degeneracies arising not only from azimuthal symmetry but also from specific cavity deformations. A direct correspondence between classical trajectories and quantum eigenstates reveals that probability densities concentrate in the classically allowed region with controlled penetration into forbidden zones. - oai:arXiv.org:2512.08021v1 - quant-ph + About possible measures in Quantum Gravity + https://arxiv.org/abs/2512.09191 + arXiv:2512.09191v1 Announce Type: cross +Abstract: Possible measures for Quantum Gravity are considered. Choices that are invariant under diffeomorphisms are analyzed, but the possibility of employing non invariant measures is also taken into account. The last possibility may be accepted if the anomaly in the measure is compensated by counter term redefinitions of the model under analysis. Particular attention is paid to some concrete examples of non covariant looking measures, which may be useful for generalizing the Veltmann identities when quantizing around curved space times. The results are specified for the Stelle gravity model [1]-[2], which is known to be renormalizable in flat space, although not known to be so in curved ones. + oai:arXiv.org:2512.09191v1 + gr-qc + hep-th math-ph math.MP - physics.class-ph - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - \'Angel E. Reyna-Cruz, Julio C. Guti\'errez-Vega + O. P. Santill\'an - Provable Diffusion Posterior Sampling for Bayesian Inversion - https://arxiv.org/abs/2512.08022 - arXiv:2512.08022v1 Announce Type: cross -Abstract: This paper proposes a novel diffusion-based posterior sampling method within a plug-and-play (PnP) framework. Our approach constructs a probability transport from an easy-to-sample terminal distribution to the target posterior, using a warm-start strategy to initialize the particles. To approximate the posterior score, we develop a Monte Carlo estimator in which particles are generated using Langevin dynamics, avoiding the heuristic approximations commonly used in prior work. The score governing the Langevin dynamics is learned from data, enabling the model to capture rich structural features of the underlying prior distribution. On the theoretical side, we provide non-asymptotic error bounds, showing that the method converges even for complex, multi-modal target posterior distributions. These bounds explicitly quantify the errors arising from posterior score estimation, the warm-start initialization, and the posterior sampling procedure. Our analysis further clarifies how the prior score-matching error and the condition number of the Bayesian inverse problem influence overall performance. Finally, we present numerical experiments demonstrating the effectiveness of the proposed method across a range of inverse problems. - oai:arXiv.org:2512.08022v1 - stat.ML - cs.LG - cs.NA - math.NA - math.PR - math.ST - stat.TH - Wed, 10 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jinyuan Chang, Chenguang Duan, Yuling Jiao, Ruoxuan Li, Jerry Zhijian Yang, Cheng Yuan - - - Analytical Study for Primordial Non-Gaussianity in the gravity 4D Einstein-scalar-Gauss-Bonnet Inflation - https://arxiv.org/abs/2512.08047 - arXiv:2512.08047v1 Announce Type: cross -Abstract: An inflationary model can be constrained by non-gaussian statistics as a parameter in the LSS (Large Scale Structure) distribution, and in the radiation of CMB (Cosmic Microwave Background) fluctuating temperature. Data on the CMB from Planck Collaboration provide up-to-date constraints on the parameters controlling the degree of non-Gaussianity in certain inflationary models, thus supporting or not supporting the model. Setting the non-Gaussianity parameter investigated in this study can be a reference whether or not it is a good parameter in constraining cosmological inflation models. This study attempts to examine the non-Gaussianity of the 3+1-dimensional 4DEGB gravitational cosmological inflation model starting from random field statistics. The non-Gaussian signature generated by the model is quantified, and the parameters controlling the degree of non-Gaussianity are constrained using data observation of Planck Collaboration. The method used in investigating non-Gaussianity is the in-in formalism, applied after obtaining the 3-point of $\zeta$ (curvature perturbation) terms of the perturbation expansion to the third order. The 3-point correlation function helps to create a bispectrum used to investigate the non-gaussinity of the inflation model. The results of this study show that the model tested is the slow roll pressed in the squeezed limit, because it witnesses a dominant local shape function. It has such as the non-gaussianity possessed by the single scalar field inflation as confirmation that Gauss-Bonnet term within Einstein-Hilbert action is topologically invariant, and no influence gravitational field equations in $D<5$ spacetimes. - oai:arXiv.org:2512.08047v1 + Spontaneous Decoherence from Imaginary-Order Spectral Deformations + https://arxiv.org/abs/2512.09236 + arXiv:2512.09236v1 Announce Type: cross +Abstract: We examine a mechanism of spontaneous decoherence in which the generator of quantum dynamics is replaced by the imaginary-order spectral deformation $H^{1+i\beta}$ of a positive Hamiltonian $H$. The deformation modifies dynamical phases through the factor $E^{i\beta} = e^{i\beta \log E}$, whose rapid oscillation suppresses interference between distinct energies. A non-stationary-phase analysis yields quantitative estimates showing that oscillatory contributions to amplitudes or decoherence functionals decay at least as $O(1/|\beta|)$. The Born rule and the Hilbert-space inner product remain unchanged; the modification is entirely dynamical. + The physical motivation for the deformation arises from clock imperfections, renormalization-group and effective-action corrections that introduce logarithmic spectral terms, and semiclassical quantum-gravity analyses in which complex actions produce spectral factors of the form $E^{i\beta}$. Examples including FRW minisuperspace, quartic potentials, curved-background Hamiltonians, and a Schwarzschild interior-type model illustrate how the mechanism yields explicit decoherence rates. The parameter $\beta$ may be experimentally constrained through precision coherence measurements in low-noise quantum platforms. The mechanism contrasts with Milburn-type intrinsic decoherence, Diosi-Penrose gravitational collapse, and real-order fractional dynamics in that it acts purely through deterministic spectral phases of a single Hamiltonian. The analysis positions the framework as a compact and testable phenomenological representation of logarithmic spectral corrections appearing in quantum-gravity-motivated effective theories. + oai:arXiv.org:2512.09236v1 + quant-ph gr-qc hep-th math-ph math.MP - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 cross http://creativecommons.org/licenses/by/4.0/ - A. Agung, U. Sambiri, G. Hikmawan, F. P. Zen + Sridhar Tayur - Multi-agent learning under uncertainty: Recurrence vs. concentration - https://arxiv.org/abs/2512.08132 - arXiv:2512.08132v1 Announce Type: cross -Abstract: In this paper, we examine the convergence landscape of multi-agent learning under uncertainty. Specifically, we analyze two stochastic models of regularized learning in continuous games -- one in continuous and one in discrete time with the aim of characterizing the long-run behavior of the induced sequence of play. In stark contrast to deterministic, full-information models of learning (or models with a vanishing learning rate), we show that the resulting dynamics do not converge in general. In lieu of this, we ask instead which actions are played more often in the long run, and by how much. We show that, in strongly monotone games, the dynamics of regularized learning may wander away from equilibrium infinitely often, but they always return to its vicinity in finite time (which we estimate), and their long-run distribution is sharply concentrated around a neighborhood thereof. We quantify the degree of this concentration, and we show that these favorable properties may all break down if the underlying game is not strongly monotone -- underscoring in this way the limits of regularized learning in the presence of persistent randomness and uncertainty. - oai:arXiv.org:2512.08132v1 - cs.GT - cs.LG - math.OC - Wed, 10 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Kyriakos Lotidis, Panayotis Mertikopoulos, Nicholas Bambos, Jose Blanchet - - - Robust equilibria in continuous games: From strategic to dynamic robustness - https://arxiv.org/abs/2512.08138 - arXiv:2512.08138v1 Announce Type: cross -Abstract: In this paper, we examine the robustness of Nash equilibria in continuous games, under both strategic and dynamic uncertainty. Starting with the former, we introduce the notion of a robust equilibrium as those equilibria that remain invariant to small -- but otherwise arbitrary -- perturbations to the game's payoff structure, and we provide a crisp geometric characterization thereof. Subsequently, we turn to the question of dynamic robustness, and we examine which equilibria may arise as stable limit points of the dynamics of "follow the regularized leader" (FTRL) in the presence of randomness and uncertainty. Despite their very distinct origins, we establish a structural correspondence between these two notions of robustness: strategic robustness implies dynamic robustness, and, conversely, the requirement of strategic robustness cannot be relaxed if dynamic robustness is to be maintained. Finally, we examine the rate of convergence to robust equilibria as a function of the underlying regularizer, and we show that entropically regularized learning converges at a geometric rate in games with affinely constrained action spaces. - oai:arXiv.org:2512.08138v1 - cs.GT - cs.LG - math.OC - Wed, 10 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Kyriakos Lotidis, Panayotis Mertikopoulos, Nicholas Bambos, Jose Blanchet - - - The strength of weak coupling - https://arxiv.org/abs/2512.08141 - arXiv:2512.08141v1 Announce Type: cross -Abstract: A paradoxical idea in quantum transport is that attaching weakly-coupled edges to a large base graph creates high-fidelity quantum state transfer. We provide a mathematical treatment that rigorously prove this folklore idea. Our proofs are elementary and build upon the Feshbach-Schur method from perturbation theory. We also show the idea is effective in circumventing Anderson localization in spin chains and finding speedups in hitting times useful for quantum search. - oai:arXiv.org:2512.08141v1 - quant-ph - math.CO - Wed, 10 Dec 2025 00:00:00 -0500 + Massless Majorana spinors in the Kerr spacetime + https://arxiv.org/abs/2512.09253 + arXiv:2512.09253v1 Announce Type: cross +Abstract: In this paper, we show that massive Majorana spinors \eqref{1.2} do not exist if they are $t$-dependent or $\phi$-dependent in Kerr, or Kerr-(A)dS spacetimes. For massless Majorana spinors in the non-extreme Kerr spacetime, the Dirac equation can be separated into radial and angular equations, parameterized by two complex constants $\epsilon_1$, $\epsilon_2$. If at least one of $\epsilon_1$, $\epsilon_2$ is zero, massless Majorana spinors can be solved explicitly. If $\epsilon_1$, $\epsilon_2$ are nonzero, we prove the nonexistence of massless time-periodic Majorana spinors in the non-extreme Kerr spacetime which are $L^p$ outside the event horizon for $ 0<p\le\frac{6}{|\epsilon_1|+|\epsilon_2| +2}$. We then provide the Hamiltonian formulation for massless Majorana spinors and prove that the self-adjointness of the Hamiltonian leads to the angular momentum $a=0$ and spacetime reduces to the Schwarzschild spacetime, moreover, the massless Majorana spinor must be $\phi$-independent. Finally, we show that, in the Schwarzschild spacetime, for initial data with $L^2$ decay at infinity, the probability of the massless Majorana spinors to be in any compact region of space tends to zero as time tends to infinity. + oai:arXiv.org:2512.09253v1 + gr-qc + hep-th + math.DG + Thu, 11 Dec 2025 00:00:00 -0500 cross - http://creativecommons.org/licenses/by/4.0/ - Alastair Kay, Christino Tamon + http://creativecommons.org/publicdomain/zero/1.0/ + Tianyuan Cai, Xiao Zhang - Uncertainty quantification for mixed membership in multilayer networks with degree heterogeneity using Gaussian variational inference - https://arxiv.org/abs/2512.08146 - arXiv:2512.08146v1 Announce Type: cross -Abstract: Analyzing multilayer networks is central to understanding complex relational measurements collected across multiple conditions or over time. A pivotal task in this setting is to quantify uncertainty in community structure while appropriately pooling information across layers and accommodating layer-specific heterogeneity. Building on the multilayer degree-corrected mixed-membership (ML-DCMM) model, which captures both stable community membership profiles and layer-specific vertex activity levels, we propose a Bayesian inference framework based on a spectral-assisted likelihood. We then develop a computationally efficient Gaussian variational inference algorithm implemented via stochastic gradient descent. Our theoretical analysis establishes a variational Bernstein--von Mises theorem, which provides a frequentist guarantee for using the variational posterior to construct confidence sets for mixed memberships. We demonstrate the utility of the method on a U.S. airport longitudinal network, where the procedure yields robust estimates, natural uncertainty quantification, and competitive performance relative to state-of-the-art methods. - oai:arXiv.org:2512.08146v1 - stat.ME + Debiased Bayesian Inference for High-dimensional Regression Models + https://arxiv.org/abs/2512.09257 + arXiv:2512.09257v1 Announce Type: cross +Abstract: There has been significant progress in Bayesian inference based on sparsity-inducing (e.g., spike-and-slab and horseshoe-type) priors for high-dimensional regression models. The resulting posteriors, however, in general do not possess desirable frequentist properties, and the credible sets thus cannot serve as valid confidence sets even asymptotically. We introduce a novel debiasing approach that corrects the bias for the entire Bayesian posterior distribution. We establish a new Bernstein-von Mises theorem that guarantees the frequentist validity of the debiased posterior. We demonstrate the practical performance of our proposal through Monte Carlo simulations and two empirical applications in economics. + oai:arXiv.org:2512.09257v1 + econ.EM math.ST stat.CO + stat.ME + stat.ML stat.TH - Wed, 10 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Fangzheng Xie, Hsin-Hsiung Huang - - - Reeb Graph of Sample Thickenings - https://arxiv.org/abs/2512.08159 - arXiv:2512.08159v1 Announce Type: cross -Abstract: We consider the Reeb graph of a thickening of points sampled from an unknown space. Our main contribution is a framework to transfer reconstruction results similar to the well-known work of Niyogi, Smale, and Weinberger to the setting of Reeb graphs. To this end, we first generalize and study the interleaving distances for Reeb graphs. We find that many of the results previously established for constructible spaces also hold for general topological spaces. We use this to show that under certain conditions for topological spaces with real-valued Lipschitz maps, the Reeb graph of a sample thickening approximates the Reeb graph of the underlying space. Finally, we provide an algorithm for computing the Reeb graph of a sample thickening. - oai:arXiv.org:2512.08159v1 - cs.CG - math.AT - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - H{\aa}vard Bakke Bjerkevik, Nello Blaser, Lars M. Salbu + Qihui Chen, Zheng Fang, Ruixuan Liu - Security Analysis of Integer Learning with Errors with Rejection Sampling - https://arxiv.org/abs/2512.08172 - arXiv:2512.08172v1 Announce Type: cross -Abstract: At ASIACRYPT 2018, a digital attack based on linear least squares was introduced for a variant of the learning with errors (LWE) problem which omits modular reduction known as the integer learning with errors problem (ILWE). In this paper, we present a theoretical and experimental study of the effectiveness of the attack when applied directly to small parameter ILWE instances found in popular digital signature schemes such as CRYSTALS-Dilithium which utilize rejection sampling. Unlike other studies which form ILWE instances based on additional information obtained from side-channel attacks, we take a more direct approach to the problem by constructing our ILWE instance from only the obtained signatures. We outline and introduce novel techniques in our simulation designs such as modular polynomial arithmetic via matrices in $\mathbb{R}$, as well as algorithms for handling large sample sizes efficiently. Our experimental results reinforce the proclaimed security of signature schemes based on ILWE. We additionally discuss the implications of our work and digital signatures as a whole in regards to real-world applications such as in Intelligent Transportation Systems (ITS). - oai:arXiv.org:2512.08172v1 - cs.CR - cs.IT - math.IT - Wed, 10 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Kyle Yates, Antsa Pierrottet, Abdullah Al Mamun, Ryann Cartor, Mashrur Chowdhury, Shuhong Gao - - - Bayesian Semiparametric Mixture Cure (Frailty) Models - https://arxiv.org/abs/2512.08173 - arXiv:2512.08173v1 Announce Type: cross -Abstract: In recent years, mixture cure models have gained increasing popularity in survival analysis as an alternative to the Cox proportional hazards model, particularly in settings where a subset of patients is considered cured. The proportional hazards mixture cure model is especially advantageous when the presence of a cured fraction can be reasonably assumed, providing a more accurate representation of long-term survival dynamics. In this study, we propose a novel hierarchical Bayesian framework for the semiparametric mixture cure model, which accommodates both the inclusion and exclusion of a frailty component, allowing for greater flexibility in capturing unobserved heterogeneity among patients. Samples from the posterior distribution are obtained using a Markov chain Monte Carlo method, leveraging a hierarchical structure inspired by Bayesian Lasso. Comprehensive simulation studies are conducted across diverse scenarios to evaluate the performance and robustness of the proposed models. Bayesian model comparison and assessment are performed using various criteria. Finally, the proposed approaches are applied to two well-known datasets in the cure model literature: the E1690 melanoma trial and a colon cancer clinical trial. - oai:arXiv.org:2512.08173v1 + MoDaH achieves rate optimal batch correction + https://arxiv.org/abs/2512.09259 + arXiv:2512.09259v1 Announce Type: cross +Abstract: Batch effects pose a significant challenge in the analysis of single-cell omics data, introducing technical artifacts that confound biological signals. While various computational methods have achieved empirical success in correcting these effects, they lack the formal theoretical guarantees required to assess their reliability and generalization. To bridge this gap, we introduce Mixture-Model-based Data Harmonization (MoDaH), a principled batch correction algorithm grounded in a rigorous statistical framework. + Under a new Gaussian-mixture-model with explicit parametrization of batch effects, we establish the minimax optimal error rates for batch correction and prove that MoDaH achieves this rate by leveraging the recent theoretical advances in clustering data from anisotropic Gaussian mixtures. This constitutes, to the best of our knowledge, the first theoretical guarantee for batch correction. Extensive experiments on diverse single-cell RNA-seq and spatial proteomics datasets demonstrate that MoDaH not only attains theoretical optimality but also achieves empirical performance comparable to or even surpassing those of state-of-the-art heuristics (e.g., Harmony, Seurat-V5, and LIGER), effectively balancing the removal of technical noise with the conservation of biological signal. + oai:arXiv.org:2512.09259v1 stat.ME math.ST - stat.CO - stat.ML + q-bio.GN stat.TH - Wed, 10 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Fatih K{\i}z{\i}laslan, Valeria Vitelli - - - Worst-case generation via minimax optimization in Wasserstein space - https://arxiv.org/abs/2512.08176 - arXiv:2512.08176v1 Announce Type: cross -Abstract: Worst-case generation plays a critical role in evaluating robustness and stress-testing systems under distribution shifts, in applications ranging from machine learning models to power grids and medical prediction systems. We develop a generative modeling framework for worst-case generation for a pre-specified risk, based on min-max optimization over continuous probability distributions, namely the Wasserstein space. Unlike traditional discrete distributionally robust optimization approaches, which often suffer from scalability issues, limited generalization, and costly worst-case inference, our framework exploits the Brenier theorem to characterize the least favorable (worst-case) distribution as the pushforward of a transport map from a continuous reference measure, enabling a continuous and expressive notion of risk-induced generation beyond classical discrete DRO formulations. Based on the min-max formulation, we propose a Gradient Descent Ascent (GDA)-type scheme that updates the decision model and the transport map in a single loop, establishing global convergence guarantees under mild regularity assumptions and possibly without convexity-concavity. We also propose to parameterize the transport map using a neural network that can be trained simultaneously with the GDA iterations by matching the transported training samples, thereby achieving a simulation-free approach. The efficiency of the proposed method as a risk-induced worst-case generator is validated by numerical experiments on synthetic and image data. - oai:arXiv.org:2512.08176v1 - stat.ML - cs.LG - math.OC - Wed, 10 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Xiuyuan Cheng, Yao Xie, Linglingzhi Zhu, Yunqin Zhu - - - Bounding the Minimal Current Harmonic Distortion in Optimal Modulation of Single-Phase Power Converters - https://arxiv.org/abs/2512.08201 - arXiv:2512.08201v1 Announce Type: cross -Abstract: Optimal pulse patterns (OPPs) are a modulation technique in which a switching signal is computed offline through an optimization process that accounts for selected performance criteria, such as current harmonic distortion. The optimization determines both the switching angles (i.e., switching times) and the pattern structure (i.e., the sequence of voltage levels). This optimization task is a challenging mixed-integer nonconvex problem, involving integer-valued voltage levels and trigono metric nonlinearities in both the objective and the constraints. We address this challenge by reinterpreting OPP design as a periodic mode-selecting optimal control problem of a hybrid system, where selecting angles and levels corresponds to choosing jump times in a transition graph. This time-domain formulation enables the direct use of convex-relaxation techniques from optimal control, producing a hierarchy of semidefinite programs that lower-bound the minimal achievable harmonic distortion and scale subquadratically with the number of converter levels and switching angles. Numerical results demonstrate the effectiveness of the proposed approachs - oai:arXiv.org:2512.08201v1 - eess.SY - cs.SY - math.OC - Wed, 10 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jared Miller, Petros Karamanakos, Tobias Geyer - - - Haagerup Symmetry in $(E_8)_1$? - https://arxiv.org/abs/2512.08225 - arXiv:2512.08225v1 Announce Type: cross -Abstract: We suggest that the chiral $(\mathfrak{e}_8)_1$ theory -- in many senses the simplest VOA -- may have Haagerup symmetry $\mathcal{H}_i$ for $i=1,2,3$. Likewise, we suggest that the non-chiral $(E_8)_1$ WZW model may have $\mathcal{H}_i \times \mathcal{H}_i^\textrm{op}$ symmetry, and that gauging the diagonal symmetry gives a $c=8$ theory with $\mathcal{Z}(\mathcal{H}_3)$ symmetry, which is the theory predicted in \cite{Evans:2010yr}. Along the way, we show that $(E_8)_1$ also has a $\mathrm{Fib} \times \mathrm{Fib}^\text{op}$ symmetry, and that gauging the diagonal symmetry gives the $(G_2)_1 \times (F_4)_1$ WZW model, explaining the well-known conformal embedding $(G_2)_1 \times (F_4)_1 \subset (E_8)_1$. Finally, we suggest a relation to theories with $\mathcal{H}_3$ symmetry at $c=2,6$, complimenting the discussion with new modular bootstrap results. - oai:arXiv.org:2512.08225v1 - hep-th - math-ph - math.CT - math.MP - math.QA - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jan Albert, Yamato Honda, Justin Kaidi, Yunqin Zheng + Yang Cao, Zongming Ma - Wishart kernel density estimation for strongly mixing time series on the cone of positive definite matrices - https://arxiv.org/abs/2512.08232 - arXiv:2512.08232v1 Announce Type: cross -Abstract: A Wishart kernel density estimator (KDE) is introduced for density estimation in the cone of positive definite matrices. The estimator is boundary-aware and mitigates the boundary bias suffered by conventional KDEs, while remaining simple to implement. Its mean squared error, uniform strong consistency on expanding compact sets, and asymptotic normality are established under the Lebesgue measure and suitable mixing conditions. This work represents the first study of density estimation on this space under any metric. For independent observations, an asymptotic upper bound on the mean absolute error is also derived. A simulation study compares the performance of the Wishart KDE to another boundary-aware KDE that relies on the matrix-variate lognormal distribution proposed by Schwartzman [Int. Stat. Rev., 2016, 84(3), 456-486]. Results suggest that the Wishart KDE is superior for a selection of autoregressive coefficient matrices and innovation covariance matrices when estimating the stationary marginal density of a Wishart autoregressive process. To illustrate the practical utility of the Wishart KDE, an application to finance is made by estimating the marginal density function of a time series of realized covariance matrices, calculated from 5-minute intra-day returns, between the share prices of Amazon Corp. and the Standard & Poor's 500 exchange-traded fund over a one-year period. All code is publicly available via the R package ksm to facilitate implementation of the method and reproducibility of the findings. - oai:arXiv.org:2512.08232v1 + On the inverse of covariance matrices for unbalanced crossed designs + https://arxiv.org/abs/2512.09273 + arXiv:2512.09273v1 Announce Type: cross +Abstract: This paper addresses a long-standing open problem in the analysis of linear mixed models with crossed random effects under unbalanced designs: how to find an analytic expression for the inverse of $\mathbf{V}$, the covariance matrix of the observed response. The inverse matrix $\mathbf{V}^{-1}$ is required for likelihood-based estimation and inference. However, for unbalanced crossed designs, $\mathbf{V}$ is dense and the lack of a closed-form representation for $\mathbf{V}^{-1}$, until now, has made using likelihood-based methods computationally challenging and difficult to analyse mathematically. We use the Khatri--Rao product to represent $\mathbf{V}$ and then to construct a modified covariance matrix whose inverse admits an exact spectral decomposition. Building on this construction, we obtain an elegant and simple approximation to $\mathbf{V}^{-1}$ for asymptotic unbalanced designs. For non-asymptotic settings, we derive an accurate and interpretable approximation under mildly unbalanced data and establish an exact inverse representation as a low-rank correction to this approximation, applicable to arbitrary degrees of unbalance. Simulation studies demonstrate the accuracy, stability, and computational tractability of the proposed framework. + oai:arXiv.org:2512.09273v1 stat.ME - math.PR math.ST - stat.AP stat.TH - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - L\'eo R. Belzile, Christian Genest, Fr\'ed\'eric Ouimet, Donald Richards + Ziyang Lyu, S. A. Sisson, A. H. Welsh - Wavelet-Accelerated Physics-Informed Quantum Neural Network for Multiscale Partial Differential Equations - https://arxiv.org/abs/2512.08256 - arXiv:2512.08256v1 Announce Type: cross -Abstract: This work proposes a wavelet-based physics-informed quantum neural network framework to efficiently address multiscale partial differential equations that involve sharp gradients, stiffness, rapid local variations, and highly oscillatory behavior. Traditional physics-informed neural networks (PINNs) have demonstrated substantial potential in solving differential equations, and their quantum counterparts, quantum-PINNs, exhibit enhanced representational capacity with fewer trainable parameters. However, both approaches face notable challenges in accurately solving multiscale features. Furthermore, their reliance on automatic differentiation for constructing loss functions introduces considerable computational overhead, resulting in longer training times. To overcome these challenges, we developed a wavelet-accelerated physics-informed quantum neural network that eliminates the need for automatic differentiation, significantly reducing computational complexity. The proposed framework incorporates the multiresolution property of wavelets within the quantum neural network architecture, thereby enhancing the network's ability to effectively capture both local and global features of multiscale problems. Numerical experiments demonstrate that our proposed method achieves superior accuracy while requiring less than five percent of the trainable parameters compared to classical wavelet-based PINNs, resulting in faster convergence. Moreover, it offers a speedup of three to five times compared to existing quantum PINNs, highlighting the potential of the proposed approach for efficiently solving challenging multiscale and oscillatory problems. - oai:arXiv.org:2512.08256v1 - cs.LG - math.AP - math.QA - Wed, 10 Dec 2025 00:00:00 -0500 + A Propagator-based Multi-level Monte Carlo Method for Kinetic Neutral Species in Edge Plasmas + https://arxiv.org/abs/2512.09334 + arXiv:2512.09334v1 Announce Type: cross +Abstract: We propose and investigate a new multi-level Monte Carlo scheme for numerical solutions of the kinetic Boltzmann equation for neutral species in edge plasmas. In particular, this method explicitly exploits a key structural property of neutral particle dynamics: the prevalence of frequent collisions for which the outgoing velocity is determined by local plasma parameters. Using this property, we derive a multi-level algorithm based on collision event propagator and show, both analytically and through numerical experiments, that it reproduces the results of standard Monte Carlo methods. We further demonstrate that, in the context of coupled plasma-neutral edge simulations employing correlated Monte Carlo, the proposed scheme retains trajectory correlation to machine precision as the system evolves, whereas conventional methods exhibit rapid decorrelation. These results indicate that the propagator-based multi-level Monte Carlo scheme is a promising candidate for use in fully implicit Jacobian-free Newton-Krylov (JFNK) solvers for coupled plasma-neutral systems. + oai:arXiv.org:2512.09334v1 + physics.plasm-ph + cs.NA + math.NA + physics.comp-ph + Thu, 11 Dec 2025 00:00:00 -0500 cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Deepak Gupta, Himanshu Pandey, Ratikanta Behera + Gregory J. Parker, Maxim V. Umansky, Benjamin D. Dudson - Photon Phase-Space Dynamics in a Plasma Wakefield Accelerator - https://arxiv.org/abs/2512.08295 - arXiv:2512.08295v1 Announce Type: cross -Abstract: Frequency up-shifting of laser light in a beam-driven plasma wakefield has the potential to provide high-intensity sources of short wavelength radiation. Simulations have demonstrated that a laser pulse can undergo large frequency shifts, limited only by the drive beam energy, when the plasma density is tailored to match the accelerating phase of the wake to the group velocity of the pulse. Here, we study the dynamical evolution of photons in the phase-space vicinity of the plasma wake- phase matching condition. Numerical calculations using a photon kinetic model are validated by direct comparison with full electromagnetic particle-in-cell simulations. These calculations form the basis of a linear theory of the photon dynamics which reveals several important results, including scalings for the properties of the witness pulse and a self-similar solution for the photon phase-space dynamics. One prediction of the theory is that the pulse can be compressed indefinitely with no lower bound on the duration. This predication suggests that photon acceleration can provide a novel source of sub-femtosecond, short wavelength radiation. - oai:arXiv.org:2512.08295v1 - physics.plasm-ph - math-ph - math.MP - physics.optics - Wed, 10 Dec 2025 00:00:00 -0500 + Branching Strategies Based on Subgraph GNNs: A Study on Theoretical Promise versus Practical Reality + https://arxiv.org/abs/2512.09355 + arXiv:2512.09355v1 Announce Type: cross +Abstract: Graph Neural Networks (GNNs) have emerged as a promising approach for ``learning to branch'' in Mixed-Integer Linear Programming (MILP). While standard Message-Passing GNNs (MPNNs) are efficient, they theoretically lack the expressive power to fully represent MILP structures. Conversely, higher-order GNNs (like 2-FGNNs) are expressive but computationally prohibitive. In this work, we investigate Subgraph GNNs as a theoretical middle ground. Crucially, while previous work [Chen et al., 2025] demonstrated that GNNs with 3-WL expressive power can approximate Strong Branching, we prove a sharper result: node-anchored Subgraph GNNs whose expressive power is strictly lower than 3-WL [Zhang et al., 2023] are sufficient to approximate Strong Branching scores. However, our extensive empirical evaluation on four benchmark datasets reveals a stark contrast between theory and practice. While node-anchored Subgraph GNNs theoretically offer superior branching decisions, their $O(n)$ complexity overhead results in significant memory bottlenecks and slower solving times than MPNNs and heuristics. Our results indicate that for MILP branching, the computational cost of expressive GNNs currently outweighs their gains in decision quality, suggesting that future research must focus on efficiency-preserving expressivity. + oai:arXiv.org:2512.09355v1 + cs.LG + cs.AI + cs.NA + math.NA + Thu, 11 Dec 2025 00:00:00 -0500 cross http://creativecommons.org/licenses/by/4.0/ - Neil Beri, John Palastro, Qian Qian, Kyle Miller, Brandon Russell, Alexander Thomas + Junru Zhou, Yicheng Wang, Pan Li - Low Rank Support Quaternion Matrix Machine - https://arxiv.org/abs/2512.08327 - arXiv:2512.08327v1 Announce Type: cross -Abstract: Input features are conventionally represented as vectors, matrices, or third order tensors in the real field, for color image classification. Inspired by the success of quaternion data modeling for color images in image recovery and denoising tasks, we propose a novel classification method for color image classification, named as the Low-rank Support Quaternion Matrix Machine (LSQMM), in which the RGB channels are treated as pure quaternions to effectively preserve the intrinsic coupling relationships among channels via the quaternion algebra. For the purpose of promoting low-rank structures resulting from strongly correlated color channels, a quaternion nuclear norm regularization term, serving as a natural extension of the conventional matrix nuclear norm to the quaternion domain, is added to the hinge loss in our LSQMM model. An Alternating Direction Method of Multipliers (ADMM)-based iterative algorithm is designed to effectively resolve the proposed quaternion optimization model. Experimental results on multiple color image classification datasets demonstrate that our proposed classification approach exhibits advantages in classification accuracy, robustness and computational efficiency, compared to several state-of-the-art methods using support vector machines, support matrix machines, and support tensor machines. - oai:arXiv.org:2512.08327v1 - cs.CV + Rates and architectures for learning geometrically non-trivial operators + https://arxiv.org/abs/2512.09376 + arXiv:2512.09376v1 Announce Type: cross +Abstract: Deep learning methods have proven capable of recovering operators between high-dimensional spaces, such as solution maps of PDEs and similar objects in mathematical physics, from very few training samples. This phenomenon of data-efficiency has been proven for certain classes of elliptic operators with simple geometry, i.e., operators that do not change the domain of the function or propagate singularities. However, scientific machine learning is commonly used for problems that do involve the propagation of singularities in a priori unknown ways, such as waves, advection, and fluid dynamics. In light of this, we expand the learning theory to include double fibration transforms--geometric integral operators that include generalized Radon and geodesic ray transforms. We prove that this class of operators does not suffer from the curse of dimensionality: the error decays superalgebraically, that is, faster than any fixed power of the reciprocal of the number of training samples. Furthermore, we investigate architectures that explicitly encode the geometry of these transforms, demonstrating that an architecture reminiscent of cross-attention based on levelset methods yields a parameterization that is universal, stable, and learns double fibration transforms from very few training examples. Our results contribute to a rapidly-growing line of theoretical work on learning operators for scientific machine learning. + oai:arXiv.org:2512.09376v1 cs.LG - math.OC - stat.ML - Wed, 10 Dec 2025 00:00:00 -0500 + cs.CV + eess.IV + math.DG + Thu, 11 Dec 2025 00:00:00 -0500 cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Wang Chen, Ziyan Luo, Shuangyue Wang - - - Enhancing Explainability of Graph Neural Networks Through Conceptual and Structural Analyses and Their Extensions - https://arxiv.org/abs/2512.08344 - arXiv:2512.08344v1 Announce Type: cross -Abstract: Graph Neural Networks (GNNs) have become a powerful tool for modeling and analyzing data with graph structures. The wide adoption in numerous applications underscores the value of these models. However, the complexity of these methods often impedes understanding their decision-making processes. Current Explainable AI (XAI) methods struggle to untangle the intricate relationships and interactions within graphs. Several methods have tried to bridge this gap via a post-hoc approach or self-interpretable design. Most of them focus on graph structure analysis to determine essential patterns that correlate with prediction outcomes. While post-hoc explanation methods are adaptable, they require extra computational resources and may be less reliable due to limited access to the model's internal workings. Conversely, Interpretable models can provide immediate explanations, but their generalizability to different scenarios remains a major concern. To address these shortcomings, this thesis seeks to develop a novel XAI framework tailored for graph-based machine learning. The proposed framework aims to offer adaptable, computationally efficient explanations for GNNs, moving beyond individual feature analysis to capture how graph structure influences predictions. - oai:arXiv.org:2512.08344v1 - cs.AI - cs.IT - cs.LG - math.IT - Wed, 10 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Tien Cuong Bui - - - On the existence of personal equilibria - https://arxiv.org/abs/2512.08348 - arXiv:2512.08348v1 Announce Type: cross -Abstract: We consider an investor who, while maximizing his/her expected utility, also compares the outcome to a reference entity. We recall the notion of personal equilibrium and show that, in a multistep, generically incomplete financial market model such an equilibrium indeed exists, under appropriate technical assumptions. - oai:arXiv.org:2512.08348v1 - q-fin.PM - math.PR - Wed, 10 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Laurence Carassus, Mikl\'os R\'asonyi + T. Mitchell Roddenberry, Leo Tzou, Ivan Dokmani\'c, Maarten V. de Hoop, Richard G. Baraniuk - A Distribution Testing Approach to Clustering Distributions - https://arxiv.org/abs/2512.08376 - arXiv:2512.08376v1 Announce Type: cross -Abstract: We study the following distribution clustering problem: Given a hidden partition of $k$ distributions into two groups, such that the distributions within each group are the same, and the two distributions associated with the two clusters are $\varepsilon$-far in total variation, the goal is to recover the partition. We establish upper and lower bounds on the sample complexity for two fundamental cases: (1) when one of the cluster's distributions is known, and (2) when both are unknown. Our upper and lower bounds characterize the sample complexity's dependence on the domain size $n$, number of distributions $k$, size $r$ of one of the clusters, and distance $\varepsilon$. In particular, we achieve tightness with respect to $(n,k,r,\varepsilon)$ (up to an $O(\log k)$ factor) for all regimes. - oai:arXiv.org:2512.08376v1 - cs.DS - cs.IT - math.IT - math.ST - stat.ML - stat.TH - Wed, 10 Dec 2025 00:00:00 -0500 + Time-Discretized Simulation of Vehicle Platoons for Safety Analysis with Guaranteed Error Bounds + https://arxiv.org/abs/2512.09416 + arXiv:2512.09416v1 Announce Type: cross +Abstract: Wireless communication is essential to achieve coordinated control in vehicle platoons. However, packet losses in wireless communication can cause critical safety issues when they occur in conjunction with sudden brakes. In this paper, we propose simulation-based methods that allow the study of such safety issues by determining the absolute minimum distance between vehicles over time for various control parameters that guarantee string stability. For our proposed time-discretized simulations, we provide two methods for selecting different time-step intervals to ensure that the error in distance approximation remains within specified bounds at all times. Through numerical examples we demonstrate that among control parameters that guarantee string stability some perform better than others under simultaneously occurring packet losses and sudden brakes. + oai:arXiv.org:2512.09416v1 + eess.SY + cs.SY + math.OC + Thu, 11 Dec 2025 00:00:00 -0500 cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Gunjan Kumar, Yash Pote, Jonathan Scarlett + Yuhao Chen, Ahmet Cetinkaya - Many interacting particles in solution. I. Screening-ranged expansions of electrostatic potential and energy - https://arxiv.org/abs/2512.08407 - arXiv:2512.08407v1 Announce Type: cross -Abstract: We present an analytical many-body formalism for systems of spherical particles carrying arbitrary free charge distributions and interacting in a polarizable electrolyte solution, that we model within the linearized Poisson--Boltzmann framework. Building on the detailed spectral analysis of the associated nonstandard Neumann--Poincar\'e-type operators developed in our companion study~\cite{supplem_pre_math}, we construct exact explicit expansions of the electrostatic potential and energy in ascending orders of Debye screening thereby obtaining systematic "screening-ranged" series for potentials and energies. These screening-ranged expansions provide a unified and tractable description of many-body electrostatics. We demonstrate the versatility of the approach by showing how it generalizes and improves upon both classical and modern methods, enabling rigorous treatment of heterogeneously charged systems (such as Janus particles) and accurate modeling of higher-order phenomena (such as asymmetric dielectric screening, opposite-charge repulsion, like-charge attraction) as well as yielding many-body generalizations to analytical explicit results previously known only in the two-body setting. - oai:arXiv.org:2512.08407v1 + Exact Screening-Ranged Expansions for Many-Body Electrostatics + https://arxiv.org/abs/2512.09421 + arXiv:2512.09421v1 Announce Type: cross +Abstract: We present an exact many-body framework for electrostatic interactions among $N$ arbitrarily charged spheres in an electrolyte, modeled by the linearized Poisson--Boltzmann equation. Building on a spectral analysis of nonstandard Neumann--Poincar\'e-type operators introduced in a companion mathematical work~\cite{supplem_pre_math}, we construct convergent screening-ranged series for the potential, interaction energy, and forces, where each term is associated with a well-defined Debye--H\"uckel screening order and can be obtained evaluating an analytical expression rather than numerically solving an infinitely dimensional linear system. This formulation unifies and extends classical and recent approaches, providing a rigorous basis for electrostatic interactions among heterogeneously charged particles (including Janus colloids) and yielding many-body generalizations of analytical closed-form results previously available only for two-body systems. The framework captures and clarifies complex effects such as asymmetric dielectric screening, opposite-charge repulsion, and like-charge attraction, which remain largely analytically elusive in existing treatments. Beyond its fundamental significance, the method leads to numerically efficient schemes, offering a versatile tool for modeling colloids and soft/biological matter in electrolytic solution. + oai:arXiv.org:2512.09421v1 cond-mat.soft math-ph math.MP physics.bio-ph physics.chem-ph physics.comp-ph - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Sergii V. Siryk, Walter Rocchia - Universal recoverability of quantum states in tracial von-Neumann algebras - https://arxiv.org/abs/2512.08418 - arXiv:2512.08418v1 Announce Type: cross -Abstract: In this paper, we discuss a refinement of quantum data processing inequality for the sandwiched quasi-relative entropy $\mathcal{S}_2$ on a tracial von-Neumann algebra. The main result is a universal recoverability bound with the Petz recovery map, which was previously obtained in the finite dimensional setup. - oai:arXiv.org:2512.08418v1 - quant-ph - math.OA - Wed, 10 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Saptak Bhattacharya - - - A Grover-compatible manifold optimization algorithm for quantum search - https://arxiv.org/abs/2512.08432 - arXiv:2512.08432v1 Announce Type: cross -Abstract: Grover's algorithm is a fundamental quantum algorithm that offers a quadratic speedup for the unstructured search problem by alternately applying physically implementable oracle and diffusion operators. In this paper, we reformulate the unstructured search as a maximization problem on the unitary manifold and solve it via the Riemannian gradient ascent (RGA) method. To overcome the difficulty that generic RGA updates do not, in general, correspond to physically implementable quantum operators, we introduce Grover-compatible retractions to restrict RGA updates to valid oracle and diffusion operators. Theoretically, we establish a local Riemannian $\mu$-Polyak-{\L}ojasiewicz (PL) inequality with $\mu = \tfrac{1}{2}$, which yields a linear convergence rate of $1 - \kappa^{-1}$ toward the global solution. Here, the condition number $\kappa = L_{\mathrm{Rie}} / \mu$, where $L_{\mathrm{Rie}}$ denotes the Riemannian Lipschitz constant of the gradient. Taking into account both the geometry of the unitary manifold and the special structure of the cost function, we show that $L_{\mathrm{Rie}} = O(\sqrt{N})$ for problem size $N = 2^n$. Consequently, the resulting iteration complexity is $O(\sqrt{N} \log(1/\varepsilon))$ for attaining an $\varepsilon$-accurate solution, which matches the quadratic speedup of $O(\sqrt{N})$ achieved by Grover's algorithm. These results demonstrate that an optimization-based viewpoint can offer fresh conceptual insights and lead to new advances in the design of quantum algorithms. - oai:arXiv.org:2512.08432v1 - quant-ph + Advancing Research via Human-AI Interactive Theorem Proving + https://arxiv.org/abs/2512.09443 + arXiv:2512.09443v1 Announce Type: cross +Abstract: We investigate how large language models can be used as research tools in scientific computing while preserving mathematical rigor. We propose a human-in-the-loop workflow for interactive theorem proving and discovery with LLMs. Human experts retain control over problem formulation and admissible assumptions, while the model searches for proofs or contradictions, proposes candidate properties and theorems, and helps construct structures and parameters that satisfy explicit constraints, supported by numerical experiments and simple verification checks. Experts treat these outputs as raw material, further refine them, and organize the results into precise statements and rigorous proofs. We instantiate this workflow in a case study on the connection between manifold optimization and Grover's quantum search algorithm, where the pipeline helps identify invariant subspaces, explore Grover-compatible retractions, and obtain convergence guarantees for the retraction-based gradient method. The framework provides a practical template for integrating large language models into frontier mathematical research, enabling faster exploration of proof space and algorithm design while maintaining transparent reasoning responsibilities. Although illustrated on manifold optimization problems in quantum computing, the principles extend to other core areas of scientific computing. + oai:arXiv.org:2512.09443v1 + cs.HC + cs.AI math.OC - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Zhijian Lai, Dong An, Jiang Hu, Zaiwen Wen + http://creativecommons.org/licenses/by/4.0/ + Chenyi Li, Zhijian Lai, Dong An, Jiang Hu, Zaiwen Wen - Learned iterative networks: An operator learning perspective - https://arxiv.org/abs/2512.08444 - arXiv:2512.08444v1 Announce Type: cross -Abstract: Learned image reconstruction has become a pillar in computational imaging and inverse problems. Among the most successful approaches are learned iterative networks, which are formulated by unrolling classical iterative optimisation algorithms for solving variational problems. While the underlying algorithm is usually formulated in the functional analytic setting, learned approaches are often viewed as purely discrete. In this chapter we present a unified operator view for learned iterative networks. Specifically, we formulate a learned reconstruction operator, defining how to compute, and separately the learning problem, which defines what to compute. In this setting we present common approaches and show that many approaches are closely related in their core. We review linear as well as nonlinear inverse problems in this framework and present a short numerical study to conclude. - oai:arXiv.org:2512.08444v1 - eess.IV - cs.LG + Modeling Complex Multiphysics Systems with Discrete Element Method Enriched with the Kernel-Independent Fast Multipole Method + https://arxiv.org/abs/2512.09478 + arXiv:2512.09478v1 Announce Type: cross +Abstract: The paper describes the coupling of the MercuryDPM discrete element method (DEM) code and the implementation of the kernel-independent fast multipole method (KIFMM). The combined simulation framework allows addressing the large class of multiscale problems, including both the mechanical interactions of particulates at the fine scale and the long-range interactions of various natures at the coarse scale. Among these are electrostatic interactions in powders, clays, and particulates, magnetic interactions in ferromagnetic granulates, and gravitational interactions in asteroid clouds. The formalism of rigid clumps is successfully combined with KIFMM, enabling addressing problems involving complex long-large interactions between non-spherical particles with arbitrary charge distributions. The capabilities of our technique are demonstrated in several application examples. + oai:arXiv.org:2512.09478v1 + cond-mat.soft cs.NA - math.FA math.NA - math.OC - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Andreas Hauptmann, Ozan \"Oktem - - - Minimax and Bayes Optimal Adaptive Experimental Design for Treatment Choice - https://arxiv.org/abs/2512.08513 - arXiv:2512.08513v1 Announce Type: cross -Abstract: We consider an adaptive experiment for treatment choice and design a minimax and Bayes optimal adaptive experiment with respect to regret. Given binary treatments, the experimenter's goal is to choose the treatment with the highest expected outcome through an adaptive experiment, in order to maximize welfare. We consider adaptive experiments that consist of two phases, the treatment allocation phase and the treatment choice phase. The experiment starts with the treatment allocation phase, where the experimenter allocates treatments to experimental subjects to gather observations. During this phase, the experimenter can adaptively update the allocation probabilities using the observations obtained in the experiment. After the allocation phase, the experimenter proceeds to the treatment choice phase, where one of the treatments is selected as the best. For this adaptive experimental procedure, we propose an adaptive experiment that splits the treatment allocation phase into two stages, where we first estimate the standard deviations and then allocate each treatment proportionally to its standard deviation. We show that this experiment, often referred to as Neyman allocation, is minimax and Bayes optimal in the sense that its regret upper bounds exactly match the lower bounds that we derive. To show this optimality, we derive minimax and Bayes lower bounds for the regret using change-of-measure arguments. Then, we evaluate the corresponding upper bounds using the central limit theorem and large deviation bounds. - oai:arXiv.org:2512.08513v1 - econ.EM - cs.LG - math.ST - stat.ME - stat.ML - stat.TH - Wed, 10 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Masahiro Kato + http://creativecommons.org/licenses/by/4.0/ + Igor A. Ostanin - A Novel Wasserstein Quaternion Generative Adversarial Network for Color Image Generation - https://arxiv.org/abs/2512.08542 - arXiv:2512.08542v1 Announce Type: cross -Abstract: Color image generation has a wide range of applications, but the existing generation models ignore the correlation among color channels, which may lead to chromatic aberration problems. In addition, the data distribution problem of color images has not been systematically elaborated and explained, so that there is still the lack of the theory about measuring different color images datasets. In this paper, we define a new quaternion Wasserstein distance and develop its dual theory. To deal with the quaternion linear programming problem, we derive the strong duality form with helps of quaternion convex set separation theorem and quaternion Farkas lemma. With using quaternion Wasserstein distance, we propose a novel Wasserstein quaternion generative adversarial network. Experiments demonstrate that this novel model surpasses both the (quaternion) generative adversarial networks and the Wasserstein generative adversarial network in terms of generation efficiency and image quality. - oai:arXiv.org:2512.08542v1 - cs.CV - cs.AI - cs.NA - math.NA - Wed, 10 Dec 2025 00:00:00 -0500 + Spontaneous symmetry breaking on graphs and lattices + https://arxiv.org/abs/2512.09480 + arXiv:2512.09480v1 Announce Type: cross +Abstract: Spontaneous symmetry breaking is a cornerstone modern physics, defining a wealth of phenomena in condensed-matter and high-energy physics, and beyond. It requires an infinite number of degrees of freedom, and even then, for continuous symmetries, it only works if the spatial dimension is not too low, following the classic results of Coleman, Hohenberg, Mermin and Wagner. While usually discussed in the context of quantum and statistical field theories, and in particular, effective field theories, there are advantages in addressing the same kind of phenomena on discrete geometric structures rather than conventional manifolds. When the space is discretized into a lattice, a lucid picture of conventional spontaneous symmetry breaking springs up, with the ultraviolet issues of continuum quantum field theory out-of-sight, and the key effect, which is infrared in nature, revealed through elementary harmonic oscillator networks. From there, it is natural to generalize lattices to other graphs/networks. In this setting, the presence of spontaneous symmetry breaking is controlled by fractional generalizations of resistance distance and the Kirchhoff index, and most broadly by the spectral dimension. Predictably, because of richness of discrete geometric structures in comparison with continuous manifolds, a broader array of geometries emerge where spontaneous breaking of continuous symmetries is blocked by large fluctuations. + oai:arXiv.org:2512.09480v1 + cond-mat.dis-nn + hep-th + math-ph + math.MP + Thu, 11 Dec 2025 00:00:00 -0500 cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Zhigang Jia, Duan Wang, Hengkai Wang, Yajun Xie, Meixiang Zhao, Xiaoyu Zhao + Oleg Evnin - Heuristics for Combinatorial Optimization via Value-based Reinforcement Learning: A Unified Framework and Analysis - https://arxiv.org/abs/2512.08601 - arXiv:2512.08601v1 Announce Type: cross -Abstract: Since the 1990s, considerable empirical work has been carried out to train statistical models, such as neural networks (NNs), as learned heuristics for combinatorial optimization (CO) problems. When successful, such an approach eliminates the need for experts to design heuristics per problem type. Due to their structure, many hard CO problems are amenable to treatment through reinforcement learning (RL). Indeed, we find a wealth of literature training NNs using value-based, policy gradient, or actor-critic approaches, with promising results, both in terms of empirical optimality gaps and inference runtimes. Nevertheless, there has been a paucity of theoretical work undergirding the use of RL for CO problems. To this end, we introduce a unified framework to model CO problems through Markov decision processes (MDPs) and solve them using RL techniques. We provide easy-to-test assumptions under which CO problems can be formulated as equivalent undiscounted MDPs that provide optimal solutions to the original CO problems. Moreover, we establish conditions under which value-based RL techniques converge to approximate solutions of the CO problem with a guarantee on the associated optimality gap. Our convergence analysis provides: (1) a sufficient rate of increase in batch size and projected gradient descent steps at each RL iteration; (2) the resulting optimality gap in terms of problem parameters and targeted RL accuracy; and (3) the importance of a choice of state-space embedding. Together, our analysis illuminates the success (and limitations) of the celebrated deep Q-learning algorithm in this problem context. - oai:arXiv.org:2512.08601v1 + Estimation of Stochastic Optimal Transport Maps + https://arxiv.org/abs/2512.09499 + arXiv:2512.09499v1 Announce Type: cross +Abstract: The optimal transport (OT) map is a geometry-driven transformation between high-dimensional probability distributions which underpins a wide range of tasks in statistics, applied probability, and machine learning. However, existing statistical theory for OT map estimation is quite restricted, hinging on Brenier's theorem (quadratic cost, absolutely continuous source) to guarantee existence and uniqueness of a deterministic OT map, on which various additional regularity assumptions are imposed to obtain quantitative error bounds. In many real-world problems these conditions fail or cannot be certified, in which case optimal transportation is possible only via stochastic maps that can split mass. To broaden the scope of map estimation theory to such settings, this work introduces a novel metric for evaluating the transportation quality of stochastic maps. Under this metric, we develop computationally efficient map estimators with near-optimal finite-sample risk bounds, subject to easy-to-verify minimal assumptions. Our analysis further accommodates common forms of adversarial sample contamination, yielding estimators with robust estimation guarantees. Empirical experiments are provided which validate our theory and demonstrate the utility of the proposed framework in settings where existing theory fails. These contributions constitute the first general-purpose theory for map estimation, compatible with a wide spectrum of real-world applications where optimal transport may be intrinsically stochastic. + oai:arXiv.org:2512.09499v1 stat.ML cs.LG - math.OC - Wed, 10 Dec 2025 00:00:00 -0500 + math.ST + stat.TH + Thu, 11 Dec 2025 00:00:00 -0500 cross - http://creativecommons.org/licenses/by/4.0/ - Orit Davidovich, Shimrit Shtern, Segev Wasserkrug, Nimrod Megiddo + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Sloan Nietert, Ziv Goldfeld - $\mathcal{PT}$-symmetric cavity magnomechanics with gain-assisted transparency and amplification - https://arxiv.org/abs/2512.08612 - arXiv:2512.08612v1 Announce Type: cross -Abstract: We investigate magnomechanically induced transparency in a parity-time-symmetric cavity magnomechanical system with traveling-field-induced non-Hermiticity. The setup consists of a microwave cavity mode coupled to magnons in a single-crystal yttrium iron garnet sphere, which in turn are hybridized with a vibrational mechanical mode through magnetostrictive interaction. In the Hermitian regime, strong photon-magnon coupling generates a single transparency window in the cavity transmission, which splits into a doublet when the magnon is coherently hybridized with the mechanical mode via magnomechanical coupling. This establishes a versatile platform in which the transparency spectrum can be engineered from single- to multi-window response using experimentally accessible, scaled magnomechanical interactions. When a non-Hermitian coupling is introduced, the system enters a parity-time-broken regime in which the transparency ceases to be purely passive and becomes gain assisted, leading to asymmetric transmission with amplification on one side of the resonance and enhanced absorption on the other. By tuning the cavity detuning, we convert magnomechanical transparency into Fano-type line shapes with strongly non-Lorentzian phase dispersion and map their deformation into asymmetric, gain-assisted Fano ridges in the joint space of probe and magnon detunings. Finally, we analyze the associated group delay and show that both slow- and fast-light behavior can be widely tuned by varying the photon-magnon and magnomechanical couplings together with the non-Hermitian strength, highlighting parity-time-symmetric cavity magnomechanics as a promising platform for reconfigurable quantum signal processing and enhanced sensing. - oai:arXiv.org:2512.08612v1 - quant-ph - math-ph - math.MP - physics.optics - Wed, 10 Dec 2025 00:00:00 -0500 + Explainable Verification of Hierarchical Workflows Mined from Event Logs with Shapley Values + https://arxiv.org/abs/2512.09562 + arXiv:2512.09562v1 Announce Type: cross +Abstract: Workflow mining discovers hierarchical process trees from event logs, but it remains unclear why such models satisfy or violate logical properties, or how individual elements contribute to overall behavior. We propose to translate mined workflows into logical specifications and analyze properties such as satisfiability, liveness, and safety with automated theorem provers. On this basis, we adapt Shapley values from cooperative game theory to attribute outcomes to workflow elements and quantify their contributions. Experiments on benchmark datasets show that this combination identifies critical nodes, reveals redundancies, and exposes harmful structures. This outlines a novel direction for explainable workflow analysis with direct relevance to software engineering practice, supporting compliance checks, process optimization, redundancy reduction, and the design of next-generation process mining tools. + oai:arXiv.org:2512.09562v1 + cs.SE + cs.IT + math.IT + Thu, 11 Dec 2025 00:00:00 -0500 cross http://creativecommons.org/licenses/by/4.0/ - Cham Oumie, Wu-Ming Liu, Kashif Ammar Yasir + Radoslaw Klimek, Jakub Blazowski - Flow-Based Modelling of Population Dynamics with Consecutive Continuous Mutations - https://arxiv.org/abs/2512.08660 - arXiv:2512.08660v1 Announce Type: cross -Abstract: We develop a continuous mathematical model of population dynamics that describes the sequential emergence of new genotypes under limited resources. The framework models genotype density as a nonlinear flow in mutation space, combining transport driven by a time-dependent mutation rate with logistic growth and nonlocal competition. For the advection-reaction regime without reverse mutations, we derive analytical solutions using the method of characteristics and obtain explicit expressions for time-varying carrying capacities and mutation velocities. We analyze how decaying and accelerating mutation rates shape the saturation and propagation of population fronts through level-set geometry. When reverse mutations are included, the system becomes a quasilinear parabolic equation with diffusion in genotype space; numerical experiments show that backward mutation flows stabilize the dynamics and smooth the evolving fronts. The proposed model generalizes classical quasispecies and Crow-Kimura formulations by incorporating logistic regulation, variable mutation rates, and reversible transitions, offering a unified approach to evolutionary processes relevant to virology, bacterial adaptation, and tumor progression. - oai:arXiv.org:2512.08660v1 - q-bio.PE + Lazy Diffusion: Mitigating spectral collapse in generative diffusion-based stable autoregressive emulation of turbulent flows + https://arxiv.org/abs/2512.09572 + arXiv:2512.09572v1 Announce Type: cross +Abstract: Turbulent flows posses broadband, power-law spectra in which multiscale interactions couple high-wavenumber fluctuations to large-scale dynamics. Although diffusion-based generative models offer a principled probabilistic forecasting framework, we show that standard DDPMs induce a fundamental \emph{spectral collapse}: a Fourier-space analysis of the forward SDE reveals a closed-form, mode-wise signal-to-noise ratio (SNR) that decays monotonically in wavenumber, $|k|$ for spectra $S(k)\!\propto\!|k|^{-\lambda}$, rendering high-wavenumber modes indistinguishable from noise and producing an intrinsic spectral bias. We reinterpret the noise schedule as a spectral regularizer and introduce power-law schedules $\beta(\tau)\!\propto\!\tau^\gamma$ that preserve fine-scale structure deeper into diffusion time, along with \emph{Lazy Diffusion}, a one-step distillation method that leverages the learned score geometry to bypass long reverse-time trajectories and prevent high-$k$ degradation. Applied to high-Reynolds-number 2D Kolmogorov turbulence and $1/12^\circ$ Gulf of Mexico ocean reanalysis, these methods resolve spectral collapse, stabilize long-horizon autoregression, and restore physically realistic inertial-range scaling. Together, they show that na\"ive Gaussian scheduling is structurally incompatible with power-law physics and that physics-aware diffusion processes can yield accurate, efficient, and fully probabilistic surrogates for multiscale dynamical systems. + oai:arXiv.org:2512.09572v1 + physics.flu-dyn + cs.AI math.DS - Wed, 10 Dec 2025 00:00:00 -0500 + nlin.CD + physics.ao-ph + Thu, 11 Dec 2025 00:00:00 -0500 cross http://creativecommons.org/licenses/by/4.0/ - Alexander Bratus, Tatiana Yakushkina, Vladimir Posvyanski + Anish Sambamurthy, Ashesh Chattopadhyay - Many interacting particles in solution. II. Screening-ranged expansion of electrostatic forces - https://arxiv.org/abs/2512.08682 - arXiv:2512.08682v1 Announce Type: cross -Abstract: We present a fully analytical integration of the Maxwell stress tensor and derive exact relations for interparticle forces in systems of multiple dielectric spheres immersed in a polarizable ionic solvent, within the framework of the linearized Poisson--Boltzmann theory. Building upon the screening-ranged (in ascending orders of Debye screening) expansions of the potentials developed and rigorously analyzed in the accompanying works \cite{supplem_pre,supplem_pre_math,supplem_prl}, we construct exact screening-ranged many-body expansions for electrostatic forces in explicit analytical form. These results establish a rigorous foundation for evaluating screened electrostatic interactions in complex particle systems and provide direct analytical connections to, and systematic improvements upon, various earlier approximate or limited-case formulations available in the literature, both at zero and finite ionic strength. - oai:arXiv.org:2512.08682v1 - cond-mat.soft - math-ph - math.MP - physics.bio-ph - physics.chem-ph - physics.comp-ph - Wed, 10 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Sergii V. Siryk, Walter Rocchia - - - Many interacting particles in solution. III. Spectral analysis of the associated Neumann--Poincar\'e-type operators - https://arxiv.org/abs/2512.08684 - arXiv:2512.08684v1 Announce Type: cross -Abstract: The interaction of particles in an electrolytic medium can be calculated by solving the Poisson equation inside the solutes and the linearized Poisson--Boltzmann equation in the solvent, with suitable boundary conditions at the interfaces. Analytical approaches often expand the potentials in spherical harmonics, relating interior and exterior coefficients and eliminating some coefficients in favor of others, but a rigorous spectral analysis of the corresponding formulations is still lacking. Here, we introduce composite many-body Neumann--Poincar\'e-type operators and prove that they are compact with spectral radii strictly less than one. These results provide the foundation for systematic screening-ranged expansions, in powers of the Debye screening parameters, of electrostatic potentials, interaction energies, and forces, and establish the analytical framework for the accompanying works~\cite{supplem_prl,supplem_pre,supplem_pre_force}. - oai:arXiv.org:2512.08684v1 - cond-mat.soft + Unified theory of local integrals of motion + https://arxiv.org/abs/2512.09595 + arXiv:2512.09595v1 Announce Type: cross +Abstract: Many-body localization (MBL) is understood theoretically through the existence of an extensive number of local integrals of motion (LIOMs). These conserved quantities are related to the microscopic quantum degrees of freedom that are spatially localized. Here, we present a general framework for constructing exact LIOMs with the desired locality and quantum numbers supplied as input rather than arising as emergent properties. We show that one can express the task of finding LIOMs as an optimization problem. In simple cases, solving this problem amounts to matrix diagonalization, while in more complex settings, it connects to the question of finding classical ground states of spin-glass models. We illustrate our theory using paradigmatic examples of single-particle Anderson localization and MBL in interacting spin chains. These developments unify previous results and reveal intriguing connections among many-body localization, spin-glass physics and constrained optimization problems. + oai:arXiv.org:2512.09595v1 + cond-mat.dis-nn math-ph math.MP - physics.bio-ph - physics.chem-ph - physics.comp-ph - Wed, 10 Dec 2025 00:00:00 -0500 + quant-ph + Thu, 11 Dec 2025 00:00:00 -0500 cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Sergii V. Siryk, Walter Rocchia + Ben Craps, Oleg Evnin, Dmitry Kovrizhin, Gabriele Pascuzzi - Calibration of a DEM contact model for wet industrial granular materials - https://arxiv.org/abs/2512.08685 - arXiv:2512.08685v1 Announce Type: cross -Abstract: This study presents and calibrates a Discrete Element Method (DEM) contact model for wet granular materials in the pendular regime. The model extends a previously calibrated dry contact formulation by incorporating liquid bridges that generate capillary adhesion between particles, while liquid migration is represented through evolving bridge volumes. Two reactor-grade polypropylene powders with different particle size distributions, bulk densities, and surface morphologies are investigated, resulting in distinct wetting behavior. A schematic framework is introduced to relate increasing liquid content to the transition from dry to wet contacts using two key parameters: the minimum liquid film volume and the maximum liquid bridge volume. These parameters are calibrated using dynamic angle of repose measurements from rotating drum experiments. The calibrated model reproduces the experimental flow behavior of both powders: full agreement is obtained for the coarser, more porous powder across all liquid contents, while for the finer, denser powder, agreement is achieved at low to moderate liquid contents. At higher liquid contents, discrepancies arise due to agglomeration effects amplified by particle scaling. These results demonstrate the effectiveness of the dynamic angle of repose as a calibration target and highlight the limitations of particle scaling for strongly cohesive wet granular systems. The proposed framework provides a practical basis for DEM-based modeling of wet powder flow in industrial processes. - oai:arXiv.org:2512.08685v1 - cond-mat.soft - cs.NA - math-ph - math.MP - math.NA - Wed, 10 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Sahar Pourandi, P. Christian van der Sande, Igor A. Ostanin, Thomas Weinhart - - - Gradient-Informed Monte Carlo Fine-Tuning of Diffusion Models for Low-Thrust Trajectory Design - https://arxiv.org/abs/2512.08705 - arXiv:2512.08705v1 Announce Type: cross -Abstract: Preliminary mission design of low-thrust spacecraft trajectories in the Circular Restricted Three-Body Problem is a global search characterized by a complex objective landscape and numerous local minima. Formulating the problem as sampling from an unnormalized distribution supported on neighborhoods of locally optimal solutions, provides the opportunity to deploy Markov chain Monte Carlo methods and generative machine learning. In this work, we extend our previous self-supervised diffusion model fine-tuning framework to employ gradient-informed Markov chain Monte Carlo. We compare two algorithms - the Metropolis-Adjusted Langevin Algorithm and Hamiltonian Monte Carlo - both initialized from a distribution learned by a diffusion model. Derivatives of an objective function that balances fuel consumption, time of flight and constraint violations are computed analytically using state transition matrices. We show that incorporating the gradient drift term accelerates mixing and improves convergence of the Markov chain for a multi-revolution transfer in the Saturn-Titan system. Among the evaluated methods, MALA provides the best trade-off between performance and computational cost. Starting from samples generated by a baseline diffusion model trained on a related transfer, MALA explicitly targets Pareto-optimal solutions. Compared to a random walk Metropolis algorithm, it increases the feasibility rate from 17.34% to 63.01% and produces a denser, more diverse coverage of the Pareto front. By fine-tuning a diffusion model on the generated samples and associated reward values with reward-weighted likelihood maximization, we learn the global solution structure of the problem and eliminate the need for a tedious separate data generation phase. - oai:arXiv.org:2512.08705v1 + Adaptive Optimal Control for Avatar-Guided Motor Rehabilitation in Virtual Reality + https://arxiv.org/abs/2512.09667 + arXiv:2512.09667v1 Announce Type: cross +Abstract: A control-theoretic framework for autonomous avatar-guided rehabilitation in virtual reality, based on interpretable, adaptive motor guidance through optimal control, is presented. The framework faces critical challenges in motor rehabilitation due to accessibility, cost, and continuity of care, with over 50% of patients inability to attend regular clinic sessions. The system enables post-stroke patients to undergo personalized therapy in immersive virtual reality at home, while being monitored by clinicians. The core is a nonlinear, human-in-the-loop control strategy, where the avatar adapts in real time to the patient's performance. Balance between following the patient's movements and guiding them to ideal kinematic profiles based on the Hogan minimum-jerk model is achieved through multi-objective optimal control. A data-driven "ability index" uses smoothness metrics to dynamically adjust control gains according to the patient's progress. The system was validated through simulations and preliminary trials, and shows potential for delivering adaptive, engaging and scalable remote physiotherapy guided by interpretable control-theoretic principles. + oai:arXiv.org:2512.09667v1 eess.SY - cs.LG + cs.HC cs.SY math.OC - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jannik Graebner, Ryne Beeson + http://creativecommons.org/licenses/by-nc-nd/4.0/ + Francesco De Lellis, Maria Lombardi, Egidio De Benedetto, Pasquale Arpaia, Mario di Bernardo - Applications of Singular Entropy to Signals and Singular Smoothness to Images - https://arxiv.org/abs/2512.08717 - arXiv:2512.08717v1 Announce Type: cross -Abstract: This paper explores signal and image analysis by using the Singular Value Decomposition (SVD) and its extension, the Generalized Singular Value Decomposition (GSVD). A key strength of SVD lies in its ability to separate information into orthogonal subspaces. While SVD is a well-established tool in ECG analysis, particularly for source separation, this work proposes a refined method for selecting a threshold to distinguish between maternal and fetal components more effectively. In the first part of the paper, the focus is onmedical signal analysis,where the concepts of Energy Gap Variation (EGV) and Singular Energy are introduced to isolate fetal and maternal ECG signals, improving the known ones. Furthermore, the approach is significantly enhanced by the application of GSVD, which provides additional discriminative power for more accurate signal separation. The second part introduces a novel technique called Singular Smoothness, developed for image analysis. This method incorporates Singular Entropy and the Frobenius normto evaluate information density, and is applied to the detection of natural anomalies such asmountain fractures and burned forest regions. Numerical experiments are presented to demonstrate the effectiveness of the proposed approaches. - oai:arXiv.org:2512.08717v1 + Flexible Reconfigurable Intelligent Surface-Aided Covert Communications in UAV Networks + https://arxiv.org/abs/2512.09714 + arXiv:2512.09714v1 Announce Type: cross +Abstract: In recent years, unmanned aerial vehicles (UAVs) have become a key role in wireless communication networks due to their flexibility and dynamic adaptability. However, the openness of UAV-based communications leads to security and privacy concerns in wireless transmissions. This paper investigates a framework of UAV covert communications which introduces flexible reconfigurable intelligent surfaces (F-RIS) in UAV networks. Unlike traditional RIS, F-RIS provides advanced deployment flexibility by conforming to curved surfaces and dynamically reconfiguring its electromagnetic properties to enhance the covert communication performance. We establish an electromagnetic model for F-RIS and further develop a fitted model that describes the relationship between F-RIS reflection amplitude, reflection phase, and incident angle. To maximize the covert transmission rate among UAVs while meeting the covert constraint and public transmission constraint, we introduce a strategy of jointly optimizing UAV trajectories, F-RIS reflection vectors, F-RIS incident angles, and non-orthogonal multiple access (NOMA) power allocation. Considering this is a complicated non-convex optimization problem, we propose a deep reinforcement learning (DRL) algorithm-based optimization solution. Simulation results demonstrate that our proposed framework and optimization method significantly outperform traditional benchmarks, and highlight the advantages of F-RIS in enhancing covert communication performance within UAV networks. + oai:arXiv.org:2512.09714v1 eess.SP - cs.NA - math.NA - Wed, 10 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Oscar Romero, N\'estor Thome - - - Vacuum Energy and Topological Mass in Interacting Elko and Scalar Field Theories - https://arxiv.org/abs/2512.08750 - arXiv:2512.08750v1 Announce Type: cross -Abstract: In this paper, we consider a four-dimensional system composed of a mass-dimension-one fermionic field, also known as Elko, interacting with a real scalar field. Our main objective is to analyze the Casimir effects associated with this system, assuming that both the Elko and scalar fields satisfy Dirichlet boundary conditions on two large parallel plates separated by a distance $L$. In this scenario, we calculate the vacuum energy density and its first-order correction in the coupling constants of the theory. Additionally, we consider the mass correction for each field separately, namely the topological mass that arises from the boundary conditions imposed on the fields and which also depends on the coupling constants. To develop this analysis, we use the mathematical formalism known as the effective potential, expressed as a path integral in quantum field theory. - oai:arXiv.org:2512.08750v1 - hep-th - math-ph - math.MP - quant-ph - Wed, 10 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - A. J. D. Farias Junior, A. Smirnov, Herondy F. Santana Mota, E. R. Bezerra de Mello - - - Brachistochrone-ruled timelike surfaces in Newtonian and relativistic spacetimes - https://arxiv.org/abs/2512.08776 - arXiv:2512.08776v1 Announce Type: cross -Abstract: We introduce and study \emph{brachistochrone-ruled timelike surfaces} in Newtonian and relativistic spacetimes. Starting from the classical cycloidal brachistochrone in a constant gravitational field, we construct a Newtonian ``brachistochrone-ruled worldsheet'' whose rulings are time-minimizing trajectories between pairs of endpoints. We then generalize this construction to stationary Lorentzian spacetimes by exploiting the reduction of arrival-time functionals to Finsler- or Jacobi-type length functionals on a spatial manifold. In this framework, relativistic brachistochrones arise as geodesics of an associated Finsler structure, and brachistochrone-ruled timelike surfaces are timelike surfaces ruled by these time-minimizing worldlines. We work out explicit examples in Minkowski spacetime and in the Schwarzschild exterior: in the flat case, for a bounded-speed time functional, the brachistochrones are straight timelike lines and a simple family of brachistochrone-ruled surfaces turns out to be totally geodesic; in the Schwarzschild case, we show how coordinate-time minimization at fixed energy reduces to geodesics of a Jacobi metric on the spatial slice, and outline a numerical scheme for constructing brachistochrone-ruled timelike surfaces. Finally, we discuss basic geometric properties of such surfaces and identify natural Jacobi fields along the rulings. - oai:arXiv.org:2512.08776v1 - gr-qc - math-ph - math.DG - math.MP - Wed, 10 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by-sa/4.0/ - Ferhat Ta\c{s} - - - Axial Symmetric Navier Stokes Equations and the Beltrami /anti Beltrami spectrum in view of Physics Informed Neural Networks - https://arxiv.org/abs/2512.08846 - arXiv:2512.08846v1 Announce Type: cross -Abstract: In this paper, I further continue an investigation on Beltrami Flows began in 2015 with A. Sorin and amply reprised and developed in 2022 with M. Trigiante. Instead of a compact $3$-torus $T^3=\mathbb{R}^3/\Lambda$ where $\Lambda$ is a crystallographic lattice, as done in previous work, here I considered flows confined in a cylinder with identified opposite bases. In this topology I considered axial symmetric flows and found a complete basis of axial symmetric harmonic $1$-forms that, for each energy level, decomposes into six components: two Beltrami, two anti-Beltrami and two closed forms. These objects, that are written in terms of trigonometric and Bessel functions, constitute a function basis for an $L^2$ space of axial symmetric flows. I have presented a general scheme for the search of axial symmetric solutions of Navier Stokes equation by reducing the latter to an hierachy of quadratic relations on the development coefficients of the flow in the above described functional basis. It is proposed that the coefficients can be determined by means of a Physics Informed like Neural Network optimization recursive algorithm. Indeed the present paper provides the theoretical foundations for such a algorithmic construction that is planned for a future publication. - oai:arXiv.org:2512.08846v1 - physics.flu-dyn cs.IT - math-ph math.IT - math.MP - math.OC - Wed, 10 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Pietro Fr\'e - - - A New Application of Hoeffding's Inequality Can Give Traders Early Warning of Financial Regime Change - https://arxiv.org/abs/2512.08851 - arXiv:2512.08851v1 Announce Type: cross -Abstract: Hoeffding's Inequality provides the maximum probability that a series of n draws from a bounded random variable differ from the variable's true expectation u by more than given tolerance t. The random variable is typically the error rate of a classifier in machine learning applications. Here, a trading strategy is premised on the assumption of an underlying distribution of causal factors, in other words, a market regime, and the random variable is the performance of that trading strategy. A larger deviation of observed performance from the trader's expectation u can be characterized as a lower probability that the financial regime supporting that strategy remains in force, and a higher probability of financial regime change. The changing Hoeffding probabilities can be used as an early warning indicator of this change. - oai:arXiv.org:2512.08851v1 - q-fin.RM - math.PR - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 cross - http://creativecommons.org/licenses/by/4.0/ - Daniel Egger, Jacob Vestal - - - On Twists of A Family of Elliptic Curves and Their $ L-$Function - https://arxiv.org/abs/1511.07581 - arXiv:1511.07581v3 Announce Type: replace -Abstract: Let $ E $ be an elliptic curve defined over a number field, the conjecture of Birch and Swinnerton-Dyer (BSD, for short) asserts a deep relation between the group $ E(K) $ of rational points and the $ L-$function $ L(E/K, s)$ of $ E $ at $ s = 1. $ Very few explicit results about $ E(K) $ and $ L(1) $ are known, even no general method is known to determine $ L(1) $ vanishing or not for a given elliptic curve. In this paper, we study some quantities related to BSD of a special class of elliptic curves, more precisely, we study the arithmetic of quadratic twists of elliptic curves $ y^{2} = x(x + \varepsilon p )(x + \varepsilon q) $ and their $L-$function. Based on some classical works, especially those of Greenberg, Kramer-Tunnell, Kato-Rohrlich, Manin and Mazur, under some conditions, we obtain results about the vanishing of the value at $ s = 1 $ of the $ L$-function, and explicitly determine the following quantities: the norm index $ \delta (E, \Q, K), $ the root numbers, the set of anomalous prime numbers, a few prime numbers at which the image of Galois representation are surjective. We also study the relation between the ranks of the Mordell-Weil groups, Selmer groups and Shafarevich-Tate groups, and the structure about the $ l^{\infty }-$Selmer groups and the Mordell-Weil groups over $ \Z_{l}-$extension via Iwasawa theory. These results provide some useful evidence toward verifying the BSD for a family of elliptic curves. - oai:arXiv.org:1511.07581v3 - math.NT - math.AG - Wed, 10 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Derong Qiu - - - Generalized weight properties of resultants and discriminants, and applications to projective enumerative geometry - https://arxiv.org/abs/1811.10692 - arXiv:1811.10692v3 Announce Type: replace -Abstract: The goal of this text is to understand and prove a formula stated by Salmon, which gives the first terms of some Taylor expansion of the discriminant of a plane algebraic curve. Salmon uses his formula to derive various enumerative quantities for surfaces in $\mathbf{P}^3$. We provide complete proofs of this formula and its enumerative applications, and extend Salmon's considerations to hypersurfaces in a projective space of arbitrary dimension. To this end, we introduce the concept of reduced discriminant, and provide a thorough study of its weight properties; the latter are deeply linked to projective enumerative geometric properties. - oai:arXiv.org:1811.10692v3 - math.AG - math.AC - Wed, 10 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Laurent Bus\'e, Thomas Dedieu - - - Paschke duality and assembly maps - https://arxiv.org/abs/2107.02843 - arXiv:2107.02843v4 Announce Type: replace -Abstract: We construct a natural transformation between two versions of $G$-equivariant $K$-homology with coefficients in a $G$-$C^{*}$-category for a countable discrete group $G$. Its domain is a coarse geometric $K$-homology and its target is the usual analytic $K$-homology. Following classical terminology, we call this transformation the Paschke transformation. We show that under certain finiteness assumptions on a $G$-space $X$, the Paschke transformation is an equivalence on $X$. As an application, we provide a direct comparison of the homotopy theoretic Davis-L\"uck assembly map with Kasparov's analytic assembly map appearing in the Baum-Connes conjecture. - oai:arXiv.org:2107.02843v4 - math.AT - math.KT - math.OA - Wed, 10 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Ulrich Bunke, Alexander Engel, Markus Land + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Chong Huang, Gaojie Chen, Zhuoao Xu, Jing Zhu, Taisong Pan, Rahim Tafazolli, Wei Huang - The Sierpinski Carpet as a Final Coalgebra - https://arxiv.org/abs/2110.06404 - arXiv:2110.06404v3 Announce Type: replace -Abstract: We advance the program of connections between final coalgebras as sources of circularity in mathematics and fractal sets of real numbers. In particular, we are interested in the Sierpinski carpet, taking it as a fractal subset of the unit square. We construct a category of square sets and an endofunctor on it which corresponds to the operation of gluing copies of a square set along segments. We show that the initial algebra and final coalgebra exist for our functor, and that the final coalgebra is bi-Lipschitz equivalent to the Sierpinski carpet. Along the way, we make connections to topics such as the iterative construction of initial algebras as colimits, corecursive algebras, and the classic treatment of fractal sets due to Hutchinson. - oai:arXiv.org:2110.06404v3 - math.CT - Wed, 10 Dec 2025 00:00:00 -0500 - replace + Origins of Instability in Dynamical Systems on Undirected Networks + https://arxiv.org/abs/2512.09765 + arXiv:2512.09765v1 Announce Type: cross +Abstract: Robustness to perturbation is a key topic in the study of complex systems occurring across a wide variety of applications from epidemiology to biochemistry. Here we analyze the eigenspectrum of the Jacobian matrices associated to a general class of networked dynamical systems, which contains information on how perturbations to a stationary state develop over time. We find that stability is always determined by a spectral outlier, but with pronounced differences to the corresponding eigenvector in different regimes. We show that, depending on model details, instability may originate in nodes of anomalously low or high degree, or may occur everywhere in the network at once. Importantly, the dependence on extremal degrees results in considerable finite-size effects with different scaling depending on the ensemble degree distribution. Our results have potentially useful applications in network monitoring to predict or prevent catastrophic failures, and we validate our analytical findings through applications to epidemic dynamics and gene regulatory systems. + oai:arXiv.org:2512.09765v1 + nlin.AO + math-ph + math.MP + physics.bio-ph + Thu, 11 Dec 2025 00:00:00 -0500 + cross http://creativecommons.org/licenses/by/4.0/ - 10.4204/EPTCS.372.18 - EPTCS 372, 2022, pp. 249-261 - Victoria Noquez (Saint Mary's College of California), Lawrence S. Moss (Indiana University Bloomington) + Shraosi Dawn, Subrata Ghosh, Chandrakala Meena, Tim Rogers, Chittaranjan Hens - Astral Space: Convex Analysis at Infinity - https://arxiv.org/abs/2205.03260 - arXiv:2205.03260v4 Announce Type: replace -Abstract: Not all convex functions on $\mathbb{R}^n$ have finite minimizers; some can only be minimized by a sequence as it heads to infinity. In this work, we aim to develop a theory for understanding such minimizers at infinity. We study astral space, a compact extension of $\mathbb{R}^n$ to which such points at infinity have been added. Astral space is constructed to be as small as possible while still ensuring that all linear functions can be continuously extended to the new space. Although astral space includes all of $\mathbb{R}^n$, it is not a vector space, nor even a metric space. However, it is sufficiently well-structured to allow useful and meaningful extensions of concepts of convexity, conjugacy, and subdifferentials. We develop these concepts and analyze various properties of convex functions on astral space, including the detailed structure of their minimizers, exact characterizations of continuity, and convergence of descent algorithms. - oai:arXiv.org:2205.03260v4 - math.OC + Optimal certification of constant-local Hamiltonians + https://arxiv.org/abs/2512.09778 + arXiv:2512.09778v1 Announce Type: cross +Abstract: We study the problem of certifying local Hamiltonians from real-time access to their dynamics. Given oracle access to $e^{-itH}$ for an unknown $k$-local Hamiltonian $H$ and a fully specified target Hamiltonian $H_0$, the goal is to decide whether $H$ is exactly equal to $H_0$ or differs from $H_0$ by at least $\varepsilon$ in normalized Frobenius norm, while minimizing the total evolution time. We introduce the first intolerant Hamiltonian certification protocol that achieves optimal performance for all constant-locality Hamiltonians. For general $n$-qubit, $k$-local, traceless Hamiltonians, our procedure uses $O(c^k/\varepsilon)$ total evolution time for a universal constant $c$, and succeeds with high probability. In particular, for $O(1)$-local Hamiltonians, the total evolution time becomes $\Theta(1/\varepsilon)$, matching the known $\Omega(1/\varepsilon)$ lower bounds and achieving the gold-standard Heisenberg-limit scaling. Prior certification methods either relied on implementing inverse evolution of $H$, required controlled access to $e^{-itH}$, or achieved near-optimal guarantees only in restricted settings such as the Ising case ($k=2$). In contrast, our algorithm requires neither inverse evolution nor controlled operations: it uses only forward real-time dynamics and achieves optimal intolerant certification for all constant-locality Hamiltonians. + oai:arXiv.org:2512.09778v1 + quant-ph + cs.CC + cs.DS + cs.IT cs.LG - Wed, 10 Dec 2025 00:00:00 -0500 - replace + math.IT + Thu, 11 Dec 2025 00:00:00 -0500 + cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Miroslav Dud\'ik, Robert E. Schapire, Matus Telgarsky + Junseo Lee, Myeongjin Shin - Limit results for distributed estimation of invariant subspaces in multiple networks inference and PCA - https://arxiv.org/abs/2206.04306 - arXiv:2206.04306v5 Announce Type: replace -Abstract: Several statistical problems, such as multiple heterogeneous graph analysis, distributed PCA, integrative data analysis, and simultaneous dimension reduction of images, can involve a collection of $m$ matrices whose leading subspaces $U^{(i)}$ consist of a shared subspace $U_c$ and individual subspaces $U_s^{(i)}$. We consider a distributed estimation procedure that first obtains $\hat U^{(i)}$ as the leading singular vectors for each observed noisy matrix, then computes the leading left singular vectors of the concatenated matrix $[\hat U^{(1)}|\hat U^{(2)}|\dots|\hat U^{(m)}]$ as $\hat U_c$, and finally computes the leading singular vectors of the projection of each $\hat U^{(i)}$ onto the orthogonal complement of $\hat U_c$ as $\hat U_s^{(i)}$. In this paper, we provide a framework for deriving limit results for such distributed estimation procedures, including expansions of estimation errors in both common and individual subspaces and their asymptotically normal approximations. We apply this framework specifically to (1) parameter estimation for multiple heterogeneous random graphs with shared subspaces, and (2) distributed PCA for independent sub-Gaussian random vectors with spiked covariance structures. Leveraging these results, we also consider a two-sample test for the null hypothesis that a pair of random graphs have the same edge probabilities, and present a test statistic whose limiting distribution converges to a central (resp., non-central) $\chi^2$ distribution under the null (resp., local alternative) hypothesis. - oai:arXiv.org:2206.04306v5 - math.ST - stat.TH - Wed, 10 Dec 2025 00:00:00 -0500 - replace + Certificates for nonnegativity of multivariate integer polynomials under perturbations + https://arxiv.org/abs/2512.09808 + arXiv:2512.09808v1 Announce Type: cross +Abstract: We develop a general and unconditional framework for certifying the global nonnegativity of multivariate integer polynomials; based on rewriting them as sum of squares modulo their gradient ideals. We remove the two structural assumptions typically required by other approaches, namely that the polynomial attains its infimum and zero-dimensionality of the gradient ideal. Our approach combines a denominator-free stereographic transformation with a refined variant of the Hanzon--Jibetean perturbation scheme. The stereographic transformation preserves nonnegativity while making the polynomial coercive, with explicit bounds on the radius of positivity and on the nonzero critical values. Subsequently, we apply carefully constructed explicit perturbations that enforce zero-dimensionality of the gradient ideal without altering nonnegativity, allowing us to invoke recent algorithms to derive algebraic certificates or rational witness points. We present three algorithms implementing our framework and analyze their bit complexity in detail, which is single exponential with respect to the number of variables. A second contribution is a new explicit SOS perturbation scheme, which allows us to perturb any nonnegative polynomial in such a way that it can be written as a sum of squares (SOS). In contrast to Lasserre's classical SOS approximation, which guaranties density but currently does not provide an effective control over the perturbation size, we only derive concrete perturbation bounds ensuring that a nonnegative polynomial enters the SOS cone. + oai:arXiv.org:2512.09808v1 + cs.SC + math.OC + Thu, 11 Dec 2025 00:00:00 -0500 + cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Runbing Zheng, Minh Tang + Mat\'ias R Bender (TROPICAL), Kozhasov Khazhgali (UniCA), Tsigaridas Elias (OURAGAN), Zhu Chaoping (OURAGAN) - Saturation Properties of Ultrafilters in Canonical Inner Models - https://arxiv.org/abs/2212.14096 - arXiv:2212.14096v2 Announce Type: replace -Abstract: We improve Galvin's Theorem for ultrafilters which are p-point limits of p-points. This implies that in all the canonical inner models up to a superstrong cardinal, every $\kappa$-complete ultrafilter over a measurable cardinal $\kappa$ satisfies the Galvin property. On the other hand, we prove that supercompact cardinals always carry non-Galvin $\kappa$-complete ultrafilters. Finally, we prove that $\diamondsuit(\kappa)$ implies the existence of a $\kappa$-complete filter which extends the club filter and fails to satisfy the Galvin property. This answers questions \cite[Question 5.22]{TomMotiII},\cite[Question 3.4]{Non-GalvinFil} and questions ,\cite[Question 4.5]{BenGarShe},\cite[Question 2.26]{bgp}. - oai:arXiv.org:2212.14096v2 - math.LO - Wed, 10 Dec 2025 00:00:00 -0500 - replace + Bayesian Networks, Markov Networks, Moralisation, Triangulation: a Categorical Perspective + https://arxiv.org/abs/2512.09908 + arXiv:2512.09908v1 Announce Type: cross +Abstract: Moralisation and Triangulation are transformations allowing to switch between different ways of factoring a probability distribution into a graphical model. Moralisation allows to view a Bayesian network (a directed model) as a Markov network (an undirected model), whereas triangulation addresses the opposite direction. We present a categorical framework where these transformations are modelled as functors between a category of Bayesian networks and one of Markov networks. The two kinds of network (the objects of these categories) are themselves represented as functors from a `syntax' domain to a `semantics' codomain. Notably, moralisation and triangulation can be defined inductively on such syntax via functor pre-composition. Moreover, while moralisation is fully syntactic, triangulation relies on semantics. This leads to a discussion of the variable elimination algorithm, reinterpreted here as a functor in its own right, that splits the triangulation procedure in two: one purely syntactic, the other purely semantic. This approach introduces a functorial perspective into the theory of probabilistic graphical models, which highlights the distinctions between syntactic and semantic modifications. + oai:arXiv.org:2512.09908v1 + cs.AI + cs.LO + math.CT + Thu, 11 Dec 2025 00:00:00 -0500 + cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Tom Benhamou + Antonio Lorenzin, Fabio Zanasi - Detecting ideals in reduced crossed product C*-algebras of topological dynamical systems - https://arxiv.org/abs/2301.01027 - arXiv:2301.01027v3 Announce Type: replace -Abstract: We introduce the $\ell^1$-ideal intersection property for crossed product C*-algebras. It is implied by C*-simplicity as well as C*-uniqueness. We show that topological dynamical systems of arbitrary lattices in connected Lie groups, arbitrary linear groups over the integers in a number field and arbitrary virtually polycyclic groups have the $\ell^1$-ideal intersection property. On the way, we extend previous results on C*-uniqueness of $\mathrm{L}^1$-groupoid algebras to the general twisted setting. - oai:arXiv.org:2301.01027v3 - math.OA - math.DS - math.GR - Wed, 10 Dec 2025 00:00:00 -0500 + A chronology of continued square roots and other continued compositions, through the year 2016 + https://arxiv.org/abs/1707.06139 + arXiv:1707.06139v5 Announce Type: replace +Abstract: An infinite continued composition is an expression of the form \begin{equation*} \lim_{n\to\infty}t_0\circ t_1 \circ t_2 \circ \cdots \circ t_n(c)\;, \end{equation*} where the $t_i$ are maps from a set $D$ to itself, the initial value $c$ is a point in $D$, and the order of operations proceeds from right to left. + This document is a bibliography, in chronological order through the year 2016, of selected continued compositions whose primary sources have typically been obscure. In particular, we include continued square roots: \begin{equation*} a_0+\sqrt{a_1+\sqrt{a_2+\sqrt{\ldots}}}\;, \end{equation*} as well as continued powers, continued cotangents, continued logarithms, and $f$-expansions. However, we do not include continued fractions, continued exponentials, or forms such as infinite sums and products in which the $t_i$ are linear functions, because the literature on these forms is extensive. + oai:arXiv.org:1707.06139v5 + math.HO + math.CA + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Are Austad, Sven Raum + Dixon J. Jones - A Small Ultrafilter Number at Every Singular Cardinal - https://arxiv.org/abs/2302.07311 - arXiv:2302.07311v2 Announce Type: replace -Abstract: We obtain a small ultrafilter number at $\aleph_{\omega_1}$. Moreover, we develop a version of the overlapping strong extender forcing with collapses which can keep the top cardinal $\kappa$ inaccessible. We apply this forcing to construct a model where $\kappa$ is the least inaccessible and $V_\kappa$ is a model of GCH at regulars, failures of SCH at singulars, and the ultrafilter numbers at all singulars are small. - oai:arXiv.org:2302.07311v2 - math.LO - Wed, 10 Dec 2025 00:00:00 -0500 + High Codimension Mean Curvature Flow with Surgery + https://arxiv.org/abs/2004.07163 + arXiv:2004.07163v3 Announce Type: replace +Abstract: We construct a mean curvature flow with surgery for submanifolds of arbitrary codimension. The theory applies to closed submanifolds satisfying a natural quadratic pinching condition, which serves as the high-codimension analogue of 2-convexity and is preserved under the flow in dimensions $n \geq 8$. Our results therefore are in line with the current state-of-the-art in codimension one (where at present 2-convexity is required for surgery). Central to our analysis is a collection of new a priori estimates for the second fundamental form, uniform across surgeries, which yield a precise description of high-curvature regions and permit controlled surgeries. This provides the first notion of mean curvature flow through singularities with topological control in higher codimensions. As a consequence we obtain a sharp classification: Every closed quadratically 2-convexity submanifold is diffeomorphic either to $\mathbb{S}^n$ or to a finite connected sum of $\mathbb{S}^{n-1}$-bundles over $\mathbb{S}^1$. + oai:arXiv.org:2004.07163v3 + math.DG + Thu, 11 Dec 2025 00:00:00 -0500 replace - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Tom Benhamou, Sittinon Jirattikansakul + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Stephen Lynch, Huy The Nguyen - On $ p-$Rationality of Cubic and Quartic Number Fields - https://arxiv.org/abs/2304.10157 - arXiv:2304.10157v3 Announce Type: replace -Abstract: In this paper, a new criterion is given to determine the $p-$rationality of some complex cubic number fields in terms of $ p-$divisibility of certain terms of a third-order recurrence sequence, several illustrated examples are constructed,the relations between generalized $ abc-$conjecture and the $p-$rationality are discussed, from which some explicit fields satisfying Greenberg's Generalized Conjecture (GGC, for short) are obtained. - oai:arXiv.org:2304.10157v3 - math.NT - Wed, 10 Dec 2025 00:00:00 -0500 + Additive C*-categories and K-theory + https://arxiv.org/abs/2010.14830 + arXiv:2010.14830v3 Announce Type: replace +Abstract: We review the notions of a multiplier category and the $W^{*}$-envelope of a $C^{*}$-category. We then consider the notion of an orthogonal sum of a (possibly infinite) family of objects in a $C^{*}$-category. Furthermore, we construct reduced crossed products of $C^{*}$-categories with groups. We axiomatize the basic properties of the $K$-theory for $C^{*}$-categories in the notion of a homological functor. We then study various rigidity properties of homological functors in general, and special additional features of the $K$-theory of $C^{*}$-categories. As an application we construct and study interesting functors on the orbit category of a group from $C^{*}$-categorical data. + oai:arXiv.org:2010.14830v3 + math.KT + math.AT + math.OA + Thu, 11 Dec 2025 00:00:00 -0500 replace - http://creativecommons.org/licenses/by/4.0/ - Hang Li, Derong Qiu + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Ulrich Bunke, Alexander Engel - Lorentzian polynomials on cones - https://arxiv.org/abs/2304.13203 - arXiv:2304.13203v2 Announce Type: replace -Abstract: Inspired by the theory of hyperbolic polynomials and Hodge theory, we develop the theory of Lorentzian polynomials on cones. This notion captures the Hodge-Riemann relations of degree zero and one. Motivated by fundamental properties of volume polynomials of Chow rings of simplicial fans, we define a class of multivariate polynomials which we call hereditary polynomials. We give a complete and easily checkable characterization of hereditary Lorentzian polynomials. This characterization is used to give elementary and simple proofs of the Heron-Rota-Welsh conjecture for the characteristic polynomial of a matroid, and the Alexandrov-Fenchel inequalities for convex bodies. - We then characterize Chow rings of simplicial fans which satisfy the Hodge-Riemann relations of degree zero and one, and we prove that this property only depends on the support of the fan. - Several different characterizations of Lorentzian polynomials on cones are provided. - oai:arXiv.org:2304.13203v2 - math.CO - Wed, 10 Dec 2025 00:00:00 -0500 + The multiple points of maps from sphere to Euclidean space + https://arxiv.org/abs/2109.11575 + arXiv:2109.11575v4 Announce Type: replace +Abstract: In this paper, we obtain some sufficient conditions to guarantee the existence of multiple points of maps from $S^m$ to $\mathbb{R}^d$. Our main tool is the ideal-valued index of $G$-space defined by E. Fadell and S. Husseini. We obtain more detailed relative positional relationship of multiple points. It is proved that for a continuous real value function $f: S^m\rightarrow \mathbb{R}$ such that $f(-p)=-f(p)$, if $m+1$ is a power of $2$, then there are $m+1$ points $p_1, \ldots, p_{m+1}$ in $S^m$ such that $f(p_1)=\cdots=f(p_{m+1})$, where $p_1, \ldots, p_{m+1}$ are linearly dependent and any $m$ points of $p_1, \ldots, p_{m+1}$ are linearly independent. As a generalization of Hopf's theorem, we also prove that for any continuous map $f: S^m\rightarrow \mathbb{R}^d$, if $m> d$, then there exists a pair of mutually orthogonal points having the same image in addition to the antipodal points. + oai:arXiv.org:2109.11575v4 + math.AT + math.GT + Thu, 11 Dec 2025 00:00:00 -0500 replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Petter Br\"and\'en, Jonathan Leake + http://creativecommons.org/licenses/by-nc-nd/4.0/ + Jun Wang, Xuezhi Zhao - The Galvin property under the Ultrapower Axiom - https://arxiv.org/abs/2306.15078 - arXiv:2306.15078v4 Announce Type: replace -Abstract: We continue the study of the Galvin property from \cite{bgs} and \cite{Benhamou2}. In particular, we deepen the connection between certain diamond-like principles and non-Galvin ultrafilters. We also show that any Dodd sound non p-point ultrafilter is non-Galvin. We use these ideas to formulate what appears to be the optimal large cardinal hypothesis implying the existence of a non-Galvin ultrafilter, improving on a result from \cite{Benhamou_Dobrinen}. Finally, we use a strengthening of the Ultrapower Axiom to prove that in all the known canonical inner models, a $\kappa$-complete ultrafilter has the Galvin property if and only if it is an iterated sum of $p$-points. - oai:arXiv.org:2306.15078v4 - math.LO - Wed, 10 Dec 2025 00:00:00 -0500 + Equiangular lines via matrix projection + https://arxiv.org/abs/2110.15842 + arXiv:2110.15842v5 Announce Type: replace +Abstract: In 1973, Lemmens and Seidel posed the problem of determining the maximum number of equiangular lines in $\mathbb{R}^r$ with angle $\arccos(\alpha)$ and gave a partial answer in the regime $r \leq 1/\alpha^2 - 2$. At the other extreme where $r$ is at least exponential in $1/\alpha$, recent breakthroughs have led to an almost complete resolution of this problem. In this paper, we introduce a new method for obtaining upper bounds which unifies and improves upon previous approaches, thereby yielding bounds which bridge the gap between the aforementioned regimes and are best possible either exactly or up to a small multiplicative constant. Our approach relies on orthogonal projection of matrices with respect to the Frobenius inner product and as a byproduct, it yields the first extension of the Alon-Boppana theorem to dense graphs, with equality for strongly regular graphs corresponding to $\binom{r+1}{2}$ equiangular lines in $\mathbb{R}^r$. Applications of our method in the complex setting will be discussed as well. + oai:arXiv.org:2110.15842v5 + math.CO + cs.IT + math.IT + math.MG + quant-ph + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - 10.4153/S0008414X2400052X - Can. J. Math.-J. Can. Math. 77 (2025) 1686-1717 - Tom Benhamou, Gabriel Goldberg + Igor Balla - Sliced Wasserstein distance between probability measures on Hilbert spaces - https://arxiv.org/abs/2307.05802 - arXiv:2307.05802v3 Announce Type: replace -Abstract: The sliced Wasserstein distance as well as its variants have been widely considered in comparing probability measures defined on $\mathbb R^d$. Here we derive the notion of sliced Wasserstein distance for measures on an infinite dimensional separable Hilbert spaces, depict the relation between sliced Wasserstein distance and narrow convergence of measures and quantize the approximation via empirical measures. - oai:arXiv.org:2307.05802v3 - math.MG - math.OC - math.PR - Wed, 10 Dec 2025 00:00:00 -0500 + Pants complex, TQFT and hyperbolic geometry + https://arxiv.org/abs/2111.14415 + arXiv:2111.14415v4 Announce Type: replace +Abstract: We introduce a coarse perspective on relations of the $SU(2)$-Witten-Reshetikhin-Turaev TQFT, the Weil-Petersson geometry of the Teichm\"uller space, and volumes of hyperbolic 3-manifolds. Using data from the asymptotic expansions of the curve operators in the skein theoretic version of the $SU(2)$-TQFT, we define the quantum intersection number between pants decompositions of a closed surface. We show that the quantum intersection number admits two sided bounds in terms of the geometric intersection number and we use it to obtain a metric on the pants graph of surfaces. Using work of Brock we show that the pants graph equipped with this metric is quasi-isometric to the Teichm\"uller space with the Weil-Petersson metric and that the translation length of our metric provides two sided linear bounds on the volume of hyperbolic fibered manifolds. We briefly discuss how these relations are interpeted from the view point of $SU(2)$-character varieties of 3-manifolds. + We also obtain a characterization of pseudo-Anosov mapping classes in terms of asymptotics of the quantum intersection number under iteration in the mapping class group and relate these asymptotics with stretch factors. We also discuss how these results fit with a conjecture of Andersen, Masbaum and Ueno about quantum representations of mapping class groups. + oai:arXiv.org:2111.14415v4 + math.GT + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Ruiyu Han + Renaud Detcherry, Efstratia Kalfagianni - On the descendent Gromov-Witten theory of a K3 surface - https://arxiv.org/abs/2308.09074 - arXiv:2308.09074v2 Announce Type: replace -Abstract: We study the reduced descendent Gromov-Witten theory of K3 surfaces in primitive curve classes. We present a conjectural closed formula for the stationary theory, which generalizes the Bryan-Leung formula. We also prove a new recursion that allows to remove descendent insertions of $1$ in many instances. Together this yields an efficient way to compute a large class of invariants (modulo the conjecture on the stationary part). As a corollary we conjecture a surprising polynomial structure which underlies the Gromov-Witten invariants of the K3 surface. - oai:arXiv.org:2308.09074v2 - math.AG - Wed, 10 Dec 2025 00:00:00 -0500 + Existential characterizations of monadic NIP + https://arxiv.org/abs/2209.05120 + arXiv:2209.05120v3 Announce Type: replace +Abstract: We show that if a universal theory is not monadically NIP, then this is witnessed by a canonical configuration defined by an existential formula. As a consequence, we show that a hereditary class of relational structures is NIP (resp. stable) if and only if it is monadically NIP (resp. monadically stable). As another consequence, we show that if such a class is not monadically NIP, then it has superexponential growth rate. + oai:arXiv.org:2209.05120v3 + math.LO + math.CO + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Georg Oberdieck + Samuel Braunfeld, Michael C. Laskowski - Beyond the Hodge Theorem: curl and asymmetric pseudodifferential projections - https://arxiv.org/abs/2309.02015 - arXiv:2309.02015v4 Announce Type: replace -Abstract: We develop a new approach to the study of spectral asymmetry. Working with the operator $\operatorname{curl}:=*\mathrm{d}$ on a connected oriented closed Riemannian 3-manifold, we construct, by means of microlocal analysis, the asymmetry operator -- a scalar pseudodifferential operator of order $-3$. The latter is completely determined by the Riemannian manifold and its orientation, and encodes information about spectral asymmetry. The asymmetry operator generalises and contains the classical eta invariant traditionally associated with the asymmetry of the spectrum, which can be recovered by computing its regularised operator trace. Remarkably, the whole construction is direct and explicit. - oai:arXiv.org:2309.02015v4 - math.DG + Brownian windings, Stochastic Green's formula and inhomogeneous magnetic impurities + https://arxiv.org/abs/2301.00551 + arXiv:2301.00551v2 Announce Type: replace +Abstract: We give a general Green formula for the planar Brownian motion, which we apply to study the Aharonov--Bohm effect induced by Poisson distributed magnetic impurities on a Brownian electron in the presence of an inhomogeneous magnetic field. + oai:arXiv.org:2301.00551v2 + math.PR math-ph - math.AP math.MP - math.SP - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - Matteo Capoferri, Dmitri Vassiliev + Isao Sauzedde - Crystalline representations and Wach modules in the relative case II - https://arxiv.org/abs/2309.16446 - arXiv:2309.16446v2 Announce Type: replace -Abstract: We study relative Wach modules generalising our previous works on this subject. Our main result shows a categorical equivalence between relative Wach modules and lattices inside relative crystalline representations. Using this result, we deduce a purity statement for relative crystalline representations and provide a criteria for checking crystallinity of relative $p$-adic representations. Furthermore, we interpret relative Wach modules as modules with $q$-connections, and show that for a crystalline representation, its associated Wach module together with the Nygaard filtration is the canonical $q$-deformation (after inverting $p$) of the filtered $(\varphi,\partial)$-module associated to the representation. - oai:arXiv.org:2309.16446v2 - math.NT + Filtrations on quantum cohomology from the Floer theory of $\mathbb{C}^*$-actions + https://arxiv.org/abs/2304.13026 + arXiv:2304.13026v5 Announce Type: replace +Abstract: We construct a filtration by ideals on quantum cohomology for symplectic manifolds with a Hamiltonian $S^1$-action that extends to a pseudoholomorphic $\mathbb{C}^*$-action. These spaces include all Conical Symplectic Resolutions, in particular all Quiver Varieties. In particular, we obtain a family of filtrations on singular cohomology for any Conical Symplectic Resolution, that is sensitive to the choice of $\mathbb{C}^*$-action. The symplectic form is rarely exact at infinity for these spaces, so substantial foundational work is carried out to rigorously define Floer theory, in particular symplectic cohomology. Using Floer theory, we construct a periodic persistence module, giving rise to a graded periodic barcode associated to the $\mathbb{C}^*$-action. This encodes birth-death phenomena of Floer invariants. Our filtrations can be viewed as a Floer-theoretic analogue of Atiyah-Bott filtrations, arising from stratifying a manifold by gradient flowlines of a Morse-Bott function, but they are distinct from those and they can detect non-topological properties of the quantum product. + oai:arXiv.org:2304.13026v5 + math.SG math.AG - Wed, 10 Dec 2025 00:00:00 -0500 + math.DG + math.RT + Thu, 11 Dec 2025 00:00:00 -0500 replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Abhinandan + http://creativecommons.org/licenses/by/4.0/ + Alexander F. Ritter, Filip \v{Z}ivanovi\'c - The refined class number formula for Drinfeld modules - https://arxiv.org/abs/2309.17256 - arXiv:2309.17256v2 Announce Type: replace -Abstract: Let $K/k$ be a finite Galois extension of global function fields. Let $E$ be a Drinfeld module over $k$. We state and prove an equivariant refinement of Taelman's analogue of the analytic class number formula for $(E,K/k)$, and derive explicit consequences for the Galois structure of the Taelman class group of $E$ over $K$. - oai:arXiv.org:2309.17256v2 - math.NT - Wed, 10 Dec 2025 00:00:00 -0500 + Filtrations on quantum cohomology via Morse-Bott-Floer Spectral Sequences + https://arxiv.org/abs/2304.14384 + arXiv:2304.14384v4 Announce Type: replace +Abstract: Using Morse-Bott-Floer spectral sequences, we describe a filtration by ideals on quantum cohomology for symplectic manifolds with a Hamiltonian $S^1$-action that extends to a pseudoholomorphic $\mathbb{C}^*$-action. These spaces include all Conical Symplectic Resolutions, in particular all Quiver Varieties. Our spectral sequences give explicit descriptions of birth-death phenomena of the barcode of the persistence module associated to the $\mathbb{C}^*$-action. This paper contains the foundational work to rigorously construct a filtration on Floer complexes from the $\mathbb{C}^*$-action, announced in our earlier paper. A substantial appendix on Morse-Bott-Floer theory deals with several of the technical difficulties of the paper. We compute a plethora of explicit examples, each highlighting various features, for Springer resolutions, ADE resolutions, and several Slodowy varieties of type A. We also consider certain Higgs moduli spaces, for which we compare our filtration with the famous P=W filtration. + oai:arXiv.org:2304.14384v4 + math.SG + math.RT + Thu, 11 Dec 2025 00:00:00 -0500 replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Mar\'ia In\'es de Frutos-Fern\'andez, Daniel Macias Castillo, Daniel Mart\'inez Marqu\'es + http://creativecommons.org/licenses/by/4.0/ + Alexander F. Ritter, Filip \v{Z}ivanovi\'c - Diffusion Models for Wireless Communications - https://arxiv.org/abs/2310.07312 - arXiv:2310.07312v4 Announce Type: replace -Abstract: A comprehensive study on the applications of denoising diffusion models for wireless systems is provided. The article highlights the capabilities of diffusion models in learning complicated signal distributions, modeling wireless channels, and denoising and reconstructing distorted signals. First, fundamental working mechanism of diffusion models is introduced. Then the recent advances in applying diffusion models to wireless systems are reviewed. Next, two case studies are provided, where conditional diffusion models (CDiff) are proposed for data reconstruction enhancement, covering both the conventional digital communication systems, as well as the semantic communication (SemCom) setups. The first case study highlights about 10 dB improvement in data reconstruction under low-SNR regimes, while mitigating the need to transmit redundant bits for error correction codes in digital systems. The second study further extends the case to a SemCom setup, where diffusion autoencoders showcase superior performance compared to legacy autoencoders and variational autoencoder (VAE) architectures. Finally, future directions and existing challenges are discussed. - oai:arXiv.org:2310.07312v4 + Entropy Functions on Two-Dimensional Faces of Polymatroidal Region of Degree Four: Part I: Problem Formulation and More + https://arxiv.org/abs/2305.06250 + arXiv:2305.06250v4 Announce Type: replace +Abstract: Characterization of entropy functions is of fundamental importance in information theory. By imposing constraints on their Shannon outer bound, i.e., the polymatroidal region, one obtains the faces of the region and entropy functions on them with special structures. In this series of two papers, we characterize entropy functions on the 2-dimensional faces of the polymatroidal region of degree 4. In Part I, we formulate the problem, enumerate all 59 types of 2-dimensional faces of the region by an algorithm, and fully characterize entropy functions on 49 types of them. Among them, those non-trivial cases are mainly characterized by the graph-coloring technique. The entropy functions on the remaining 10 types of faces will be characterized in Part II, among which 8 types are fully characterized, and 2 types are partially characterized. + oai:arXiv.org:2305.06250v4 cs.IT - cs.AI - cs.LG + math.CO math.IT - Wed, 10 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Mehdi Letafati, Samad Ali, Matti Latva-aho - - - A kernel-based method for Schr\"odinger bridges - https://arxiv.org/abs/2310.14522 - arXiv:2310.14522v5 Announce Type: replace -Abstract: We characterize the Schr\"odinger bridge problems by a family of Mckean-Vlasov stochastic control problems with no terminal time distribution constraint. In doing so, we use the theory of Hilbert space embeddings of probability measures and then describe the constraint as penalty terms defined by the maximum mean discrepancy in the control problems. A sequence of the probability laws of the state processes resulting from $\epsilon$-optimal controls converges to a unique solution of the Schr\"odinger's problem under mild conditions on given initial and terminal time distributions and an underlying diffusion process. We propose a neural SDE based deep learning algorithm for the Mckean-Vlasov stochastic control problems. Several numerical experiments validate our methods. - oai:arXiv.org:2310.14522v5 - math.OC - cs.NA - math.NA - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Yumiharu Nakano + Shaocheng Liu, Qi Chen - Behrend's function is not constant on $\mathrm{Hilb}^n(\mathbb{A}^3)$ - https://arxiv.org/abs/2311.05408 - arXiv:2311.05408v2 Announce Type: replace -Abstract: We prove the statement in the title for $n\geq 24$. - oai:arXiv.org:2311.05408v2 - math.AG - Wed, 10 Dec 2025 00:00:00 -0500 + Towards a theory of natural directed paths + https://arxiv.org/abs/2306.02792 + arXiv:2306.02792v4 Announce Type: replace +Abstract: We introduce the abstract setting of presheaf category on a thick category of cubes. Precubical sets, symmetric transverse sets, symmetric precubical sets and the new category of (non-symmetric) transverse sets are examples of this structure. All these presheaf categories share the same metric and homotopical properties from a directed homotopy point of view. This enables us to extend Raussen's notion of natural $d$-path for each of them. Finally, we adapt Ziemia\'{n}ski's notion of cube chain to this abstract setting and we prove that it has the expected behavior on precubical sets. As an application, we verify that the formalization of the parallel composition with synchronization of process algebra using the coskeleton functor of the category of symmetric transverse sets has a category of cube chains with the correct homotopy type. + oai:arXiv.org:2306.02792v4 + math.CT + cs.LO + math.AT + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - 10.2140/gt.2025.29.4469 - Geom. Topol. 29 (2025) 4469-4476 - J. Jelisiejew, M. Kool, R. F. Schmiermann + Philippe Gaucher - On the convergence of adaptive approximations for stochastic differential equations - https://arxiv.org/abs/2311.14201 - arXiv:2311.14201v5 Announce Type: replace -Abstract: In this paper, we study numerical approximations for stochastic differential equations (SDEs) that use adaptive step sizes. In particular, we consider a general setting where decisions to reduce step sizes are allowed to depend on the future trajectory of the underlying Brownian motion. Since these adaptive step sizes may not be previsible, the standard mean squared error analysis cannot be directly applied to show that the numerical method converges to the solution of the SDE. Building upon the pioneering work of Gaines and Lyons, we instead use rough path theory to establish pathwise convergence for a wide class of adaptive numerical methods on general Stratonovich SDEs (with sufficiently smooth vector fields). To our knowledge, this is the first convergence guarantee that applies to standard solvers, such as the Milstein and Heun methods, with non-previsible step sizes. In our analysis, we require adaptive step sizes to have a "no skip" property and to take values at only dyadic times. Secondly, in contrast to the Euler-Maruyama method, we require the SDE solver to have unbiased "L\'evy area" terms in its Taylor expansion. We conjecture that for adaptive SDE solvers more generally, convergence is still possible provided the method does not introduce "L\'evy area bias". We present a simple example where the step size control can skip over previously considered times, resulting in the numerical method converging to an incorrect limit (i.e. not the Stratonovich SDE). Finally, we conclude with an experiment demonstrating the accuracy of Heun's method and a newly introduced Splitting Path-based Runge-Kutta scheme (SPaRK) when used with adaptive step sizes. - oai:arXiv.org:2311.14201v5 - math.NA - cs.NA + Characterization of the threshold for multi-range percolation on oriented trees + https://arxiv.org/abs/2307.01554 + arXiv:2307.01554v2 Announce Type: replace +Abstract: We give a characterization of the percolation threshold for a multirange model on oriented trees, as the first positive root of a polynomial, with the use of a multi-type Galton-Watson process. This gives in particular the exact value of the critical point for the model studied in [2] and [3] for k = 2. + oai:arXiv.org:2307.01554v2 math.PR - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 replace - http://creativecommons.org/licenses/by/4.0/ - James Foster, Andra\v{z} Jelin\v{c}i\v{c} + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Olivier Couronn\'e (MODAL'X, FP2M) - Duality of Hoffman constants - https://arxiv.org/abs/2312.09858 - arXiv:2312.09858v3 Announce Type: replace -Abstract: Suppose $A\in \mathbb{R}^{m\times n}$, and $R\subseteq \mathbb{R}^n$ and $S\subseteq \mathbb{R}^m$ are {\em reference} polyhedral cones with dual cones $R^*\subseteq \mathbb{R}^n, \; S^*\subseteq \mathbb{R}^m$. We show that a suitable Slater condition implies a {\em duality inequality} between the Hoffman constants of the feasibility problems $$ \begin{array}{r} Ax-b \in S\\ x \in R \end{array} \qquad\text{ and }\qquad \begin{array}{r} c-A^T y \in R^*\\ y \in S^*. \end{array} $$ As an interesting application, we show a striking identity between the Hoffman constants of {\em box-constrained} feasibility problems with a similar primal-dual format, but where one of the reference sets is a box and the other is a linear subspace. We also establish a surprising identity between Hoffman constants of box-constrained feasibility problems and the chi condition measures for weighted least-squares problems. - oai:arXiv.org:2312.09858v3 - math.OC - Wed, 10 Dec 2025 00:00:00 -0500 + Nonparametric estimation of the job-size distribution for an M/G/1 queue with Poisson sampling + https://arxiv.org/abs/2307.10116 + arXiv:2307.10116v4 Announce Type: replace +Abstract: This work presents a non-parametric estimator for the cumulative distribution function (CDF) of the job-size distribution for a queue with compound Poisson input. The workload process is observed according to an independent Poisson sampling process. The nonparametric estimator is constructed by first estimating the characteristic function (CF) and then applying an inversion formula. The convergence rate of the CF estimator at $s$ is shown to be of the order of $s^2/n$, where $n$ is the sample size. This convergence rate is leveraged to explore the bias-variance tradeoff of the inversion estimator. It is demonstrated that within a certain class of continuous distributions, the risk, in terms of MSE, is uniformly bounded by $C n^{-\frac{\eta}{1+\eta}}$, where $C$ is a positive constant and the parameter $\eta>0$ depends on the smoothness of the underlying class of distributions. A heuristic method is further developed to address the case of an unknown rate of the compound Poisson input process. + oai:arXiv.org:2307.10116v4 + math.ST + math.PR + stat.TH + Thu, 11 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - Javier F. Pena, Juan C. Vera, Luis F. Zuluaga - - - Commutativity of Cofinal Types - https://arxiv.org/abs/2312.15261 - arXiv:2312.15261v2 Announce Type: replace -Abstract: We continue the study of the pseudo-intersection property with respect to an ideal introduced in \cite{TomNatasha2}. Our theory applies to the study of the Tukey types of general sums of ultrafilters, which, as evidenced by the results of this paper, can be quite complex. It also applies to construct a large class of ultrafilter $\mathcal{C}$ over $\omega$ such that any two ultrafilters $U,V\in \mathcal{C}$ commute; that is, $U\cdot V\equiv_T V\cdot U$. The class $\mathcal{C}$ class contains most known cofinal types of ultrafilters on $\omega$. This is in sharp contrast to the Rudin-Keisler ordering. In the third part of this paper, we apply our results to study the class of ultrafilters Tukey above $\omega^\omega$. Specifically, we prove that ultrafilters without the $I$-p.i.p are always above $I^\omega$ and in particular non-$p$-points are Tukey above $\omega^\omega$. Finally, we introduce the hierarchy of $\alpha$-almost rapid ultrafilters. We prove that it is consistent for them to form a strictly wider class than the rapid ultrafilters, and give an example of a non-rapid $p$-point ultrafilter which is Tukey above $\omega^\omega$. This addresses and answers several questions from \cite{TomNatasha,TomNatasha2,Dobrinen/Todorcevic11,Milovich08}. - oai:arXiv.org:2312.15261v2 - math.LO - Wed, 10 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Tom Benhamou + Liron Ravner - Geometric approach for the identification of Hamiltonian systems of quasi-Painlev\'e type - https://arxiv.org/abs/2402.19053 - arXiv:2402.19053v4 Announce Type: replace -Abstract: Some new Hamiltonian systems of quasi-Painlev\'e type are presented and the analogue of Okamoto's space of initial conditions computed. Using the geometric approach that was introduced originally for the identification problem of Painlev\'e equations, comparing the irreducible components of the inaccessible divisors arising in the blow-up process, we find bi-rational coordinate changes between some of these systems that give rise to the same global Hamiltonian structure. This scheme thus gives a method for identifying Hamiltonian systems up to bi-rational maps, which is performed in this article for systems of quasi-Painlev\'e type having singularities that are either square-root type algebraic poles or ordinary poles. - oai:arXiv.org:2402.19053v4 - math.CA - math-ph - math.AG + Finiteness of hyperbolic entropy for holomorphic foliations with non-degenerate singularities + https://arxiv.org/abs/2311.17236 + arXiv:2311.17236v2 Announce Type: replace +Abstract: Consider $\mathscr{F}=(M,\mathscr{L},E)$ a Brody-hyperbolic foliation on a compact complex surface $M$. Suppose that the singularities of $\mathscr{F}$ are all non-degenerate. We show that the hyperbolic entropy of $\mathscr{F}$ is finite. + oai:arXiv.org:2311.17236v2 + math.DS math.CV - math.MP - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - 10.1088/1751-8121/adb819 10.1088/1751-8121/adb819 10.1088/1751-8121/adb819 - J. Phys. A: Math. Theor. 58, 095202, 2025 - Marta Dell'Atti, Thomas Kecker + Fran\c{c}ois Bacher - Weak solutions to Kolmogorov-Fokker-Planck equations: regularity, existence and uniqueness - https://arxiv.org/abs/2403.17464 - arXiv:2403.17464v3 Announce Type: replace -Abstract: We prove existence, uniqueness and regularity of weak solutions of Kolmogorov--Fokker--Planck equations with either local or non-local diffusion in the velocity variable and rough diffusion coefficients or kernels. Our results cover the Cauchy problem and allow a broad class of source terms under minimal assumptions. The core of the analysis is a set of sharp kinetic embeddings \`a la Lions and transfer-of-regularity results \`a la Bouchut--H\''ormander. We formulate these tools in a homogeneous, scale-invariant form, available for a large range of regularity parameters. - oai:arXiv.org:2403.17464v3 - math.AP - Wed, 10 Dec 2025 00:00:00 -0500 + The Brauer Group of $\mathscr{Y}_0(2)$ + https://arxiv.org/abs/2311.18132 + arXiv:2311.18132v4 Announce Type: replace +Abstract: We determine the Brauer group of the Deligne-Mumford stack $\mathscr{Y}_0(2)$, the moduli space of elliptic curves with a marked $2$-torsion subgroup over bases of arithmetic interest. Antieau and Meier determine the Brauer group for $\mathscr{M}_{1,1}$, the moduli stack of elliptic curves by exploiting the fact it is covered by the Legendre family and using the Hochschild-Serre spectral sequence. Over an algebraically closed field, Shin uses the coarse space map to determine the Brauer group of $\mathscr{M}_{1,1}$. We combine techniques from both papers to determine the Brauer group of $\mathscr{Y}_0(2)$. + oai:arXiv.org:2311.18132v4 + math.AG + math.NT + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Pascal Auscher (LMO, FAMSI), Cyril Imbert (DMA), Lukas Niebel + Niven Achenjang, Deewang Bhamidipati, Aashraya Jha, Caleb Ji, Rose Lopez - On the linearization of analytic diffeomorphisms of the torus - https://arxiv.org/abs/2404.04410 - arXiv:2404.04410v2 Announce Type: replace -Abstract: We provide an arithmetic condition weaker then the Bryuno condition for which it is possible to apply a KAM scheme in dimension greater then one. The KAM scheme will be provided in the setting of linearization of analytic diffeomorphisms of the torus that are close to a rotation. - oai:arXiv.org:2404.04410v2 - math.DS - Wed, 10 Dec 2025 00:00:00 -0500 + A new bound for the Fourier-Entropy-Influence conjecture + https://arxiv.org/abs/2312.08271 + arXiv:2312.08271v2 Announce Type: replace +Abstract: In this paper, we prove that the Fourier entropy of an $n$-dimensional boolean function $f$ can be upper-bounded by $O(I(f)+ \sum\limits_{k\in[n]}I_k(f)\log \frac{1}{I_k(f)})$, where $I(f)$ is its total influence and $I_k(f)$ is the influence of the $k$-th coordinate. The proof is elementary and uses iterative bounds on moments of Fourier coefficients over different levels. + oai:arXiv.org:2312.08271v2 + math.CO + math.FA + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Fernando Argentieri, Livia Corsi - - - Numerical integrators for confined Langevin dynamics - https://arxiv.org/abs/2404.16584 - arXiv:2404.16584v2 Announce Type: replace -Abstract: We derive and analyze numerical methods for underdamped (kinetic) Langevin dynamics in a domain with elastic reflection at the boundary. First-order approximations are based on an Euler-type scheme incorporating collision-handling at the boundary. To achieve second order, composition schemes are derived based on decomposition of the generator into collisional drift, impulse, and stochastic momentum evolution. In a deterministic setting, this approach would typically lead to first-order approximation, even in symmetric compositions, but we find that the stochastic method can provide second-order weak approximation with a single gradient evaluation, both at finite times and in the ergodic limit. We provide analysis of this observation, as well as numerical demonstration, and we compare and contrast the performance of different variants of the integration method using model problems. - oai:arXiv.org:2404.16584v2 - math.NA - cs.NA - math.PR - Wed, 10 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - B. Leimkuhler, A. Sharma, M. V. Tretyakov + Xiao Han - Rockafellian Relaxation for PDE-Constrained Optimization with Distributional Uncertainty - https://arxiv.org/abs/2405.00176 - arXiv:2405.00176v2 Announce Type: replace -Abstract: Stochastic optimization problems are generally known to be ill-conditioned to the form of the underlying uncertainty. A framework is introduced for optimal control problems with partial differential equations as constraints that is robust to inaccuracies in the precise form of the problem uncertainty. The framework is based on problem relaxation and involves optimizing a bivariate, "Rockafellian" objective functional that features both a standard control variable and an additional perturbation variable that handles the distributional ambiguity. In the presence of distributional corruption, the Rockafellian objective functionals are shown in the appropriate settings to $\Gamma$-converge to uncorrupted objective functionals in the limit of vanishing corruption. Numerical examples illustrate the framework's utility for outlier detection and removal and for variance reduction. - oai:arXiv.org:2405.00176v2 - math.OC - Wed, 10 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Harbir Antil, Sean P. Carney, Hugo D\'iaz, Johannes O. Royset - - - Minimax optimal seriation in polynomial time - https://arxiv.org/abs/2405.08747 - arXiv:2405.08747v3 Announce Type: replace -Abstract: We consider the seriation problem, whose goal is to recover a hidden ordering from a noisy observation of a permuted Robinson matrix. We establish sharp minimax rates under average-Lipschitz conditions that strictly extend the bi-Lipschitz framework of [Giraud et al., 2023]. We further design a polynomial-time algorithm that attains these optimal rates, thereby resolving two open questions raised in [Giraud et al., 2023]. Finally, our analysis extends to a broader class of matrices beyond those generated by exact permutations. - oai:arXiv.org:2405.08747v3 - math.ST - stat.TH - Wed, 10 Dec 2025 00:00:00 -0500 + Symmetric noncrossing partitions of an annulus with double points + https://arxiv.org/abs/2312.17331 + arXiv:2312.17331v3 Announce Type: replace +Abstract: For affine Coxeter groups of affine types $\tilde D$ and $\tilde B$, we model the interval $[1,c]_T$ in the absolute order by symmetric noncrossing partitions of an annulus with one or two double points. In type $\tilde B$ (and \emph{almost} in type $\tilde D$), the diagrams also model the larger lattice defined by McCammond and Sulway. + oai:arXiv.org:2312.17331v3 + math.CO + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Yann Issartel, Christophe Giraud, Nicolas Verzelen + Nathan Reading - Resolvent estimates in Schatten spaces for Laplace-Beltrami operators on compact manifolds - https://arxiv.org/abs/2405.09957 - arXiv:2405.09957v2 Announce Type: replace -Abstract: We prove resolvent estimates in Schatten spaces for Laplace-Beltrami operators on compact manifolds at the critical exponent. Our proof only uses known bounds for the Hadamard parametrix. - oai:arXiv.org:2405.09957v2 - math.AP - math.SP - Wed, 10 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Jean-Claude Cuenin - - - Toward a generalization of Lehmer's problem to adelic curves - https://arxiv.org/abs/2405.15572 - arXiv:2405.15572v2 Announce Type: replace -Abstract: In this short note, we investigate the generalization of Lehmer's problem to finitely generated fields over $\mathbb{Q}$. - oai:arXiv.org:2405.15572v2 + Signed $p$-adic $L$-functions of Bianchi modular forms + https://arxiv.org/abs/2401.15881 + arXiv:2401.15881v4 Announce Type: replace +Abstract: Let $p\geq 3$ be a prime number and $K$ be a quadratic imaginary field in which $p$ splits as $\mathfrak{p}\overline{\mathfrak{p}}$. Let $\mathcal{F}$ be a cuspidal Bianchi eigenform over $K$ of weight $(k,k)$, where $k\geq 0$ is an integer, level $\mathfrak{m}$ coprime to $p$, and non-ordinary at both of the primes above $p$. We assume $\mathcal{F}$ has trivial nebentypus. For $\mathfrak{q}\in\{\mathfrak{p}, \overline{\mathfrak{p}}\}$, let $a_{\mathfrak{q}}$ be the $T_{\mathfrak{q}}$ Hecke eigenvalue of $\mathcal{F}$ and let $\alpha_{\mathfrak{q}},\beta_{\mathfrak{q}}$ be the roots of polynomial $X^{2} -a_{\mathfrak{q}}X+ p^{k+1}$. Then we have four $p$-stabilizations of $\mathcal{F}$: $\mathcal{F}^{\alpha_{\mathfrak{p}},\alpha_{\overline{\mathfrak{p}}}}, \mathcal{F}^{\alpha_{\mathfrak{p}},\beta_{\overline{\mathfrak{p}}}}, \mathcal{F}^{\beta_{\mathfrak{p}},\alpha_{\overline{\mathfrak{p}}}},$ and $ \mathcal{F}^{\beta_{\mathfrak{p}},\beta_{\overline{\mathfrak{p}}}}$ which are Bianchi cuspforms of level $p\mathfrak{m}$. By the works of Williams, to each $p$-stabilization $\mathcal{F}^{*,\dagger}$, we can attach a locally analytic distribution $L_{p}(\mathcal{F}^{*,\dagger})$ over the ray class group $\text{Cl}(K,p^{\infty})$. On viewing $L_{p}(\mathcal{F}^{*,\dagger})$ as a two-variable power series with coefficients in some $p$-adic field having unbounded denominators satisfying certain growth conditions, we decompose this power series into a linear combination of power series with bounded coefficients in the spirit of Pollack, Sprung, and Lei--Loeffler--Zerbes. + oai:arXiv.org:2401.15881v4 math.NT - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 replace - http://creativecommons.org/licenses/by/4.0/ - Mounir Hajli + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Mihir Deo - Self-similar blowup for the cubic Schr\"odinger equation - https://arxiv.org/abs/2406.16597 - arXiv:2406.16597v3 Announce Type: replace -Abstract: We give a rigorous proof for the existence of a finite-energy, self-similar solution to the focusing cubic Schr\"odinger equation in three spatial dimensions. The proof is computer-assisted and relies on a fixed point argument that shows the existence of a solution in the vicinity of a numerically constructed approximation. The latter is obtained by a standard pseudo-spectral method. The computer-assisted part of the rigorous proof uses nothing but fraction arithmetic in order to obtain quantitative bounds for the fixed point argument. - oai:arXiv.org:2406.16597v3 + An explicit Euler method for Sobolev vector fields with applications to the continuity equation on non cartesian grids + https://arxiv.org/abs/2402.04118 + arXiv:2402.04118v4 Announce Type: replace +Abstract: We prove a novel stability estimate in $L^\infty _t (L^p _x)$ between the regular Lagrangian flow of a Sobolev vector field and a piecewise affine approximation of such flow. This approximation of the flow is obtained by a (sort of) explicit Euler method, and it is the crucial tool to prove approximation results for the solution of the continuity equation by using the representation of the solution as the push-forward via the regular Lagrangian flow of the initial datum. We approximate the solution in two ways, one probabilistic and one deterministic, using different approximations for both the flow and the initial datum. Such estimates for the solution of the continuity equation are derived on non Cartesian grids and without the need to assume a CFL condition. + oai:arXiv.org:2402.04118v4 math.AP - math-ph - math.MP - Wed, 10 Dec 2025 00:00:00 -0500 + cs.NA + math.NA + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Roland Donninger, Birgit Sch\"orkhuber + Tommaso Cortopassi - A connection between Lipschitz and Kazhdan constants for groups of homeomorphisms of the real line - https://arxiv.org/abs/2407.03579 - arXiv:2407.03579v3 Announce Type: replace -Abstract: We exhibit an obstruction for groups with Relative Property (T) to act on the real line by bi-Lipschitz homeomorphisms. This condition is expressed in terms of the Lipschitz and Kazhdan constants associated to finite generating subsets. As an application, we obtain an explicit lower bound for the Lipschitz constants associated to actions of the semidirect product $\mathbb{F}_2\ltimes\mathbb{Z}^2$. We also obtain an upper bound for the Kazhdan constants of pairs of orderable groups, depending only on the cardinal of the generating subset. - oai:arXiv.org:2407.03579v3 - math.GR - math.DS + H\"ormander type Fourier multiplier theorem and Nikolskii inequality on quantum tori, and applications + https://arxiv.org/abs/2402.17353 + arXiv:2402.17353v5 Announce Type: replace +Abstract: In this paper, we study H\"ormander type Fourier multiplier theorem and the Nikolskii inequality on quantum tori. On the way to obtain these results, we also prove some classical inequalities such as Paley type, Hausdorff-Young-Paley, Hardy-Littlewood, and Logarithmic Sobolev inequalities on quantum tori. As applications we establish embedding theorems between Sobolev, Besov spaces as well as embeddings between Besov and Wiener and Beurling spaces on quantum tori. We also analyse $\beta$-versions of Wiener and Beurling spaces and their embeddings, and interpolation properties of all these spaces on quantum tori. As an applications of the analysis, we also derive a version of the Nash inequality, and the time decay for solutions of a heat type equation. + oai:arXiv.org:2402.17353v5 math.FA - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Ignacio Vergara + 10.1007/s00041-025-10217-z + Michael Ruzhansky, Serikbol Shaimardan, Kanat Tulenov - Sequences with Inequalities - https://arxiv.org/abs/2408.00319 - arXiv:2408.00319v2 Announce Type: replace -Abstract: We consider infinite sequences of positive numbers. The connection between log-concavity and the Bessenrodt--Ono inequality had been in the focus of several papers. This has applications in the white noise distribution theory and combinatorics. We improve a recent result of Benfield and Roy and show that for the sequence of partition numbers $\{p(n)\}$ Nicolas' log-concavity result implies the result of Bessenrodt and Ono towards $p(n) \, p(m) > p(n+m)$. We provide several examples. Benfield and Roy gave a conjecture related to $\ell $-ary partition numbers. We prove part of this conjecture. - oai:arXiv.org:2408.00319v2 - math.CO - math.NT - Wed, 10 Dec 2025 00:00:00 -0500 + IDLA with sources in a hyperplane of $\mathbb{Z}^d$ + https://arxiv.org/abs/2403.12590 + arXiv:2403.12590v3 Announce Type: replace +Abstract: We consider a random growth model based on the IDLA protocol with sources in a hyperplane of $Z^d$ . We provide a stabilization result and a shape theorem generalizing [7] in any dimension by introducing new techniques leading to a rough global upper bound. + oai:arXiv.org:2403.12590v3 + math.PR + Thu, 11 Dec 2025 00:00:00 -0500 replace - http://creativecommons.org/licenses/by/4.0/ - Bernhard Heim und Markus Neuhauser + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Electronic Journal of Probability, 2025, 30 (136) + Nicolas Chenavier (LMPA), David Coupier (LMPA), Keenan Penner (LMPA), Arnaud Rousselle (IMB) - On $m$-point homogeneous polyhedra in $3$-dimensional Euclidean space - https://arxiv.org/abs/2408.09911 - arXiv:2408.09911v3 Announce Type: replace -Abstract: This paper is devoted to the study of the $m$-point homogeneity property for the vertex sets of polytopes in Euclidean spaces. In particular, we present the classifications of $2$-point and $3$-point homogeneous polyhedra in $\mathbb{R}^3$. - oai:arXiv.org:2408.09911v3 - math.MG - Wed, 10 Dec 2025 00:00:00 -0500 + Two-dimensional fluids via matrix hydrodynamics + https://arxiv.org/abs/2405.14282 + arXiv:2405.14282v4 Announce Type: replace +Abstract: Two-dimensional (2-D) incompressible, inviscid fluids produce fascinating patterns of swirling motion. How and why the patterns emerge are long-standing questions, first addressed in the 19th century by Helmholtz, Kirchhoff, and Kelvin. Countless researchers have since contributed to innovative techniques and results. Yet, the overarching problem of swirling 2-D motion and its long-time behavior remains largely open. Here we shed light on this problem via a link to isospectral matrix flows. The link is established through V. Zeitlin's beautiful model for the numerical discretization of Euler's equations in 2-D. When considered on the sphere, Zeitlin's model offers deep connections between 2-D hydrodynamics and unitary representations of the rotation group. Consequently, it provides a dictionary that maps hydrodynamical concepts to matrix Lie theory, which in turn gives connections to matrix factorizations, random matrices, and integrability theory, for example. Results about finite-dimensional matrices can then be transferred to infinite-dimensional fluids via quantization theory, which is here used as an analysis tool (albeit traditionally describing the limit between quantum and classical physics). We demonstrate how the dictionary is constructed and how it unveils techniques for 2-D hydrodynamics. We also give accompanying convergence results for Zeitlin's model on the sphere. + oai:arXiv.org:2405.14282v4 + math.AP + math-ph + math.DG + math.MP + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - V. N. Berestovskii, Yu. G. Nikonorov + 10.1007/s00205-025-02154-4 + Klas Modin, Milo Viviani - Near coincidences and nilpotent division fields - https://arxiv.org/abs/2409.00881 - arXiv:2409.00881v2 Announce Type: replace -Abstract: Let $E/\mathbb{Q}$ be an elliptic curve. We say that $E$ has a near coincidence of level $(n,m)$ if $m \mid n$ and $\mathbb{Q}(E[n]) = \mathbb{Q}(E[m],\zeta_{n})$. We classify near coincidences of prime power level and use this result to give a classification of values of $n$ for which ${\rm Gal}(\mathbb{Q}(E[n])/\mathbb{Q})$ is a nilpotent group. Along the way we prove a Gauss-Wantzel analog for the elliptic curve $E\colon y^2 = x^3-x$, showing that $\mathbb{Q}(E[n])/\mathbb{Q}$ is constructible if and only if $\varphi(n)$ is a power of 2. Assuming that there are no non-CM rational points on the modular curves $X_{ns}^{+}(p)$ for primes $p > 11$, we show that ${\rm Gal}(\mathbb{Q}(E[n])/\mathbb{Q})$ nilpotent implies that $n$ is a power of $2$ or $n \in \{ 3, 5, 6, 7, 15, 21 \}$. - oai:arXiv.org:2409.00881v2 - math.NT - Wed, 10 Dec 2025 00:00:00 -0500 + Tree independence number III. Thetas, prisms and stars + https://arxiv.org/abs/2406.13053 + arXiv:2406.13053v5 Announce Type: replace +Abstract: We prove that for every $t\in \mathbb{N}$, there exists $\tau=\tau(t)\in \mathbb{N}$ such that every (theta, prism, $K_{1,t}$)-free graph has tree independence number at most $\tau$ (where we allow "prisms" to have one path of length zero). + oai:arXiv.org:2406.13053v5 + math.CO + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Harris Daniels, Jeremy Rouse + Maria Chudnovsky, Sepehr Hajebi, Nicolas Trotignon - Siegel-Veech Constants for Cyclic Covers of Generic Translation Surfaces - https://arxiv.org/abs/2409.06600 - arXiv:2409.06600v2 Announce Type: replace -Abstract: We compute the asymptotic number of cylinders, weighted by their area to any non-negative power, on any cyclic branched cover of any generic translation surface in any stratum. Our formulas depend only on topological invariants of the cover and number-theoretic properties of the degree: in particular, the ratio of the related Siegel-Veech constants for the locus of covers and for the base stratum component is independent of the number of branch values. One surprising corollary is that this ratio for $area^3$ Siegel-Veech constants is always equal to the reciprocal of the degree of the cover. A key ingredient is a classification of the connected components of certain loci of cyclic branched covers. - oai:arXiv.org:2409.06600v2 + Determining Modes, State Reconstruction, and Intertwinement: A Synchronization Framework + https://arxiv.org/abs/2408.01064 + arXiv:2408.01064v2 Announce Type: replace +Abstract: This article studies the interrelation between the determining modes property in the two-dimensional (2D) Navier-Stokes equations (NSE) of incompressible fluids and the reconstruction property of two filtering algorithms for continuous data assimilation applied to the 2D NSE. These two properties are realized as manifestations of a more general phenomenon of "self-synchronous intertwinement." It is shown that this concept is a logically stronger form of asymptotic enslavement, as characterized by the existence of finitely many determining modes in the 2D NSE. In particular, this stronger form is shown to imply convergence of the direct-replacement filter and the nudging filter from continuous data assimilation (CDA), and then subsequently invoked to show that convergence in these filters implies that the 2D NSE possesses finitely many determining modes. The main achievement of this article is to therefore to develop a new conceptual framework, that of self-synchronous intertwinement, through which the precise inter-relationship between the determining modes property and synchronization phenomenon in these CDA filters is rigorously established and made decisively clear. The theoretical results are then complemented by numerical experiments that confirm the conclusions of the theorems. + oai:arXiv.org:2408.01064v2 + math.AP math.DS - math.GT - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - David Aulicino, Aaron Calderon, Carlos Matheus, Nick Salter, Martin Schmoll - - - The class of the Prym-Brill-Noether divisor - https://arxiv.org/abs/2409.13034 - arXiv:2409.13034v2 Announce Type: replace -Abstract: For $r\geq 3$ and $g= \frac{r(r+1)}{2}$, we study the Prym-Brill-Noether variety $V^r(C,\eta)$ associated to Prym curves $[C,\eta]$. The locus $\mathcal{R}_g^r$ in $\mathcal{R}_g$ parametrizing Prym curves $(C, \eta)$ with nonempty $V^r(C,\eta)$ is a divisor. We compute some key coefficients of the class $[\overline{\mathcal{R}}_g^r]$ in $\mathrm{Pic}_\mathbb{Q}(\overline{\mathcal{R}}_g)$. Furthermore, we examine a strongly Brill-Noether divisor in $\overline{\mathcal{M}}_{g-1,2}$: we show its irreducibility and compute some of its coefficients in $\mathrm{Pic}_\mathbb{Q}(\overline{\mathcal{M}}_{g-1,2})$. As a consequence of our results, the moduli space $\mathcal{R}_{14,2}$ is of general type. - oai:arXiv.org:2409.13034v2 - math.AG - Wed, 10 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Andrei Bud + Elizabeth Carlson, Aseel Farhat, Vincent R. Martinez, Collin Victor - A lower bound theorem for $d$-polytopes with $2d+2$ vertices - https://arxiv.org/abs/2409.14294 - arXiv:2409.14294v2 Announce Type: replace -Abstract: We establish a lower bound theorem for the number of $k$-faces ($1\le k\le d-2$) in a $d$-dimensional polytope $P$ (abbreviated as a $d$-polytope) with $2d+2$ vertices, extending the previously known case for $k=1$. We identify all minimisers for $d\le 5$. Two distinct lower bounds emerge, depending on the number of facets of $P$. When $P$ has precisely $d+2$ facets, the lower bound is tight when $d$ is odd. If $P$ has at least $d+3$ facets, the lower bound is always tight, and equality holds for some $1\le k\le d-2$ only when $P$ has precisely $d+3$ facets. - Moreover, for $1\le k\le \ceil{d/3}-2$, the minimisers among $d$-polytopes with $2d+2$ vertices have precisely $d+3$ facets, while for $\floor{0.4d}\le k\le d-1$, the lower bound arises from $d$-polytopes with $d+2$ facets. - oai:arXiv.org:2409.14294v2 - math.CO - Wed, 10 Dec 2025 00:00:00 -0500 + Proximality, stability, and central limit theorem for random maps on an interval + https://arxiv.org/abs/2408.07398 + arXiv:2408.07398v2 Announce Type: replace +Abstract: Stochastic dynamical systems consisting of non-invertible continuous maps on an interval are studied. It is proved that if they satisfy the recently introduced so-called $\mu$-injectivity and some mild assumptions, then proximality, asymptotic stability and a central limit theorem hold. + oai:arXiv.org:2408.07398v2 + math.DS + math.FA + math.PR + Thu, 11 Dec 2025 00:00:00 -0500 replace - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Guillermo Pineda-Villavicencio, Aholiab Tritama, Jie Wang, David Yost + http://creativecommons.org/licenses/by-sa/4.0/ + Sander C. Hille, Katarzyna Horbacz, Hanna Oppelmayer, Tomasz Szarek - Rigid $G$-connections and nilpotency of $p$-curvatures - https://arxiv.org/abs/2410.09929 - arXiv:2410.09929v2 Announce Type: replace -Abstract: Motivated by Simpson's conjecture on the motivicity of rigid irreducible connections, Esnault and Groechenig demonstrated that the mod-$p$ reductions of such connections on smooth projective varieties have nilpotent $p$-curvatures. In this paper, we extend their result to integrable $G$-connections. - oai:arXiv.org:2410.09929v2 - math.AG - Wed, 10 Dec 2025 00:00:00 -0500 + Generic bases of skew-symmetrizable affine type cluster algebras + https://arxiv.org/abs/2409.03954 + arXiv:2409.03954v2 Announce Type: replace +Abstract: Geiss, Leclerc and Schr\"oer introduced a class of 1-Iwanaga-Gorenstein algebras $H$ associated to symmetrizable Cartan matrices with acyclic orientations, generalizing the path algebras of acyclic quivers. They also proved that indecomposable rigid $H$-modules of finite projective dimension are in bijection with non-initial cluster variables of the corresponding Fomin-Zelevinsky cluster algebra. In this article, we prove in all affine types that their conjectural Caldero-Chapoton type formula on these modules coincide with the Laurent expression of cluster variables. By taking generic Caldero-Chapoton functions on varieties of modules of finite projective dimension, we obtain bases for affine type cluster algebras with full-rank coefficients containing all cluster monomials. + oai:arXiv.org:2409.03954v2 + math.RT + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Pengfei Huang, Yichen Qin, Hao Sun + Lang Mou, Xiuping Su - Seminorm estimates and joint ergodicity for pairwise independent Hardy sequences - https://arxiv.org/abs/2410.15130 - arXiv:2410.15130v3 Announce Type: replace -Abstract: We develop a robust structure theory for multiple ergodic averages of commuting transformations along Hardy sequences of polynomial growth. We then apply it to derive a number of novel results on joint ergodicity, recurrence and convergence. In particular, we prove joint ergodicity for (a) pairwise independent Hardy sequences and weakly mixing transformations, (b) strongly independent Hardy sequences and ergodic transformations, (c) strongly irrationally independent Hardy sequences and totally ergodic transformations. We use these joint ergodicity results to provide new recurrence results for multidimensional patterns along strongly independent Hardy sequences, showing for instance that all subsets of $\mathbb{Z}^2$ of positive upper density contain patterns of the form - $$ (m_1, m_2),\; (m_1 + \lfloor n^{\sqrt{2}}\rfloor, m_2),\; (m_1, m_2 + \lfloor n^{\sqrt{2}} + n^{1/2}\rfloor).$$ - Last but not least, we positively resolve the joint ergodicity classification problem for pairwise independent Hardy sequences, of which the aforementioned families are special cases. - While building on recent technical advances (e.g. PET coefficient tracking schemes and joint ergodicity criteria), our work introduces a number of technical developments of its own. We construct a suitable generalization of Host-Kra and box seminorms that quantitatively control ergodic averages along Hardy sequences. - We subsequently use them to obtain Host-Kra seminorm estimates for averages along all pairwise independent Hardy sequences. Furthermore, we develop an ergodic version of the quantitative concatenation argument that has recently found extensive use in combinatorics, number theory and harmonic analysis. Lastly, we obtain new simultaneous Taylor approximations for Hardy sequences, a crucial ingredient to deal with the aforementioned classes of Hardy sequences. - oai:arXiv.org:2410.15130v3 - math.DS - math.CO - math.NT - Wed, 10 Dec 2025 00:00:00 -0500 + Ill-posedness of the Dirichlet problem for 2D Lagrangian mean curvature equation + https://arxiv.org/abs/2409.04816 + arXiv:2409.04816v2 Announce Type: replace +Abstract: We investigate the Dirichlet problem of the two dimensional Lagrangian mean curvature equation in a bounded domain. Infinitely many $C^{1, \alpha} (\alpha\in (0,\frac{1}{5}))$ very weak solutions are built through Nash-Kuiper construction. Moreover, we note there are infinitely many $C^{1, \alpha}$ very weak solutions that can not be improved to be $C^{2, \alpha}$. + oai:arXiv.org:2409.04816v2 + math.AP + Thu, 11 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - Sebasti\'an Donoso, Andreas Koutsogiannis, Borys Kuca, Wenbo Sun, Konstantinos Tsinas + Wentao Cao, Zhehui Wang - Transitivity of real Anosov diffeomorphisms - https://arxiv.org/abs/2410.15740 - arXiv:2410.15740v3 Announce Type: replace -Abstract: We prove the transitivity of real Anosov diffeomorphisms, which are Anosov diffeomorphisms where stable and unstable spaces decompose into a continuous sum of invariant one-dimensional sub-spaces with uniform contraction/expansion over the ambient manifold. We prove that if a stable/unstable curve has a well-defined length in a conformal hyperbolic distance, then it has a globally defined holonomy. We exhibit a conformal hyperbolic distance with well-defined length of stable/unstable curves for each real Anosov diffeomorphism. - oai:arXiv.org:2410.15740v3 - math.DS - math.DG - Wed, 10 Dec 2025 00:00:00 -0500 + Ornstein-Uhlenbeck fluctuations for the line counting process of the ancestral selection graph + https://arxiv.org/abs/2409.10360 + arXiv:2409.10360v3 Announce Type: replace +Abstract: For the Moran model with strong or moderately strong selection we prove that the fluctuations around the deterministic limit of the line counting process of the ancestral selection graph converge to an Ornstein-Uhlenbeck process. To this purpose we provide an extension of a functional limit theorem by Ethier and Kurtz 1986. This result and a small adaptation of our arguments can also be used to obtain the scaling limit for the fluctuations of certain logistic branching processes. + oai:arXiv.org:2409.10360v3 + math.PR + Thu, 11 Dec 2025 00:00:00 -0500 replace - http://creativecommons.org/licenses/by/4.0/ - Bernardo Carvalho + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Florin Boenkost, Anna-Lena Weinel - The Kodaira dimension of even spin strata of Abelian differentials - https://arxiv.org/abs/2410.18719 - arXiv:2410.18719v2 Announce Type: replace -Abstract: The even spin components of the strata of Abelian differentials are difficult to handle from a birational geometry perspective due to the fact that their spin line bundles have more sections than expected. Nevertheless, in this paper, we prove that for large genus, the minimal even spin components are of general type. This result complements the previous work by the second and third authors, together with Costantini, on the Kodaira dimension of general strata and the minimal odd spin components of Abelian differentials. Our main technical tool is the computation and estimation of a series of effective divisor classes on the even spin components. - oai:arXiv.org:2410.18719v2 - math.AG - Wed, 10 Dec 2025 00:00:00 -0500 + On approximately orthogonality preserving and reversing operators + https://arxiv.org/abs/2409.12546 + arXiv:2409.12546v4 Announce Type: replace +Abstract: We study approximately orthogonality (in the sense of Dragomir) preserving and reversing operators. We show that for some orthogonality notations, an operator defined from a finite-dimensional Banach space to a normed linear space is approximately orthogonality preserving/reversing if and only if it is an injective operator. This result implies that for some orthogonality notations, any operator defined from an $n$-dimensional Banach space to another $n$-dimensional Banach space is approximately orthogonality preserving/reversing if and only if it is a scalar multiple of an $\varepsilon$-isometry. We show that any $\varepsilon$-isometry and maps close to $\varepsilon$-isometries defined from a normed linear space to another normed linear space are approximately orthogonality preserving/reversing for some orthogonality notations. We also study the locally approximate orthogonality preserving and reversing operators defined on some finite-dimensional Banach spaces. + oai:arXiv.org:2409.12546v4 + math.FA + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Andrei Bud, Dawei Chen, Martin M\"oller + Divya Khurana - Boundary trace theorems for symmetric reflected diffusions - https://arxiv.org/abs/2410.19201 - arXiv:2410.19201v2 Announce Type: replace -Abstract: Starting with a transient irreducible diffusion process $X^0$ on a locally compact separable metric space $(D, d)$, one can construct a canonical symmetric reflected diffusion process $\bar X$ on a completion $D^*$ of $(D, d)$ through the theory of reflected Dirichlet spaces. The boundary trace process $\check X$ of $X$ on the boundary $\partial D:=D^*\setminus D$ is the reflected diffusion process $\bar X$ time-changed by a smooth measure $\nu$ having full quasi-support on $\partial D$. The Dirichlet form of the trace process $\check X$ is called the trace Dirichlet form. In the first part of the paper, we give a Besov space type characterization of the domain of the trace Dirichlet form for any good smooth measure $\nu$ on the boundary $\partial D$. In the second part of this paper, we study properties of the harmonic measure of $\bar X$ on the boundary $\partial D$. In particular, we provide a condition equivalent to the doubling property of the harmonic measure. Finally, we characterize and provide estimates of the jump kernel of the trace Dirichlet form under the doubling condition of the harmonic measure on $\partial D$. - oai:arXiv.org:2410.19201v2 + Disordered Gibbs measures and Gaussian conditioning + https://arxiv.org/abs/2409.19453 + arXiv:2409.19453v2 Announce Type: replace +Abstract: We study the law of a random field $f_N(\boldsymbol{\sigma})$ evaluated at a random sample from the Gibbs measure associated to a Gaussian field $H_N(\boldsymbol{\sigma})$. In the high-temperature regime, we show that bounds on the probability that $f_N(\boldsymbol{\sigma})\in A$ for $\boldsymbol{\sigma}$ randomly sampled from the Gibbs measure can be deduced from similar bounds for deterministic $\boldsymbol{\sigma}$ under the conditional Gaussian law given that $H_N(\boldsymbol{\sigma})/N=E$ for $E$ close to the derivative $F'(\beta)$ of the free energy (which is the typical value of $H_N(\boldsymbol{\sigma})/N$ under the Gibbs measure). In the more challenging low-temperature regime we restrict to $k$-RSB spherical spin glasses, proving a similar result, now with a more elaborate conditioning. Namely, with $q_i$ denoting the locations of the non-zero atoms of the Parisi measure, in addition to specifying that $H_N(\boldsymbol{\sigma})/N=E$, here one needs to also condition on the energy and its gradient at points $\mathbf{x}_1,\ldots,\mathbf{x}_k$ such that $\langle \mathbf{x}_i,\mathbf{x}_j\rangle/N=q_{i\wedge j}$ and $\langle \mathbf{x}_i,\boldsymbol{\sigma}\rangle/N\approx q_{i}$. Like in the high-temperature phase, the energy and gradient values on which one conditions are also specified by the model's Parisi measure. We apply our general results to two important problems from statistical physics. That is, computing the Franz-Parisi potential at any temperature and, reducing certain asymptotics of Langevin dynamics with initial conditions distributed according to the Gibbs measure, to the more manageable problem of studying dynamics with non-random initial conditions and conditional disorder. + oai:arXiv.org:2409.19453v2 math.PR - Wed, 10 Dec 2025 00:00:00 -0500 + math-ph + math.MP + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Shiping Cao, Zhen-Qing Chen + Amir Dembo, Eliran Subag - Approaches to critical point theory via sequential and parametrized topological complexity - https://arxiv.org/abs/2411.01980 - arXiv:2411.01980v3 Announce Type: replace -Abstract: The Lusternik-Schnirelmann category of a space was introduced to obtain a lower bound on the number of critical points of a $C^1$-function on a given manifold. Related to Lusternik-Schnirelmann category and motivated by topological robotics, the topological complexity (TC) of a space is a numerical homotopy invariant whose topological properties are an active field of research. The notions of sequential and parametrized topological complexity extend the ideas of topological complexity. While the definition of TC is closely related to Lusternik-Schnirelmann category, the connections of sequential and parametrized TC to critical point theory have not been fully explored yet. In this article we apply methods from Lusternik-Schnirelmann theory to establish various lower bounds on numbers of critical points of functions in terms of sequential and parametrized TCs. We carry out several consequences and applications of these bounds, among them a computation of the parametrized TC of the unit tangent bundles of $(4m-1)$-spheres. - oai:arXiv.org:2411.01980v3 - math.GT - math.AT - math.DS - Wed, 10 Dec 2025 00:00:00 -0500 + Weinstein exactness of nearby Lagrangians and related questions + https://arxiv.org/abs/2410.04158 + arXiv:2410.04158v4 Announce Type: replace +Abstract: We address the following problem: if a Hamiltonian diffeomorphism maps a Lagrangian submanifold $L$ to a small Weinstein neighborhood of $L$, is the image necessarily Hamiltonian isotopic to $L$ inside that neighborhood? On the one hand, we show that the question can have a negative answer in any symplectic manifold of dimension at least six. On the other hand, we answer an a priori weaker form of the question in the positive in various cases when $L$ satisfies a rationality condition: we prove that the image of $L$ is often exact inside the Weinstein neighborhood. We provide applications to the Lagrangian counterpart of the $C^0$ flux conjecture, to $C^0$-rigidity phenomena of Hamiltonian diffeomorphisms, and to topological properties of spaces of Lagrangians with the same rationality constraint. Moreover, we state and prove cases of an analogue of Viterbo's spectral norm conjecture for non-exact Lagrangians; in the process, we make progress on an old question of Viterbo regarding integer difference vectors between points of Lagrangians. + oai:arXiv.org:2410.04158v4 + math.SG + Thu, 11 Dec 2025 00:00:00 -0500 replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Stephan Mescher, Maximilian Stegemeyer + http://creativecommons.org/licenses/by/4.0/ + Marcelo S. Atallah, Jean-Philippe Chass\'e, R\'emi Leclercq, Egor Shelukhin - Asymptotic stability equals exponential stability -- while you twist your eyes - https://arxiv.org/abs/2411.03277 - arXiv:2411.03277v3 Announce Type: replace -Abstract: Suppose that two vector fields on a smooth manifold render some equilibrium point globally asymptotically stable (GAS). We show that there exists a homotopy between the corresponding semiflows such that this point remains GAS along this homotopy. - oai:arXiv.org:2411.03277v3 - math.DS - cs.SY - eess.SY + Optimal Transportation by Orthogonal Coupling Dynamics + https://arxiv.org/abs/2410.08060 + arXiv:2410.08060v2 Announce Type: replace +Abstract: Many numerical and learning algorithms rely on the solution of the Monge-Kantorovich problem and Wasserstein distances, which provide appropriate distributional metrics. While the natural approach is to treat the problem as an infinite-dimensional linear programming, such a methodology limits the computational performance due to the polynomial scaling with respect to the sample size along with intensive memory requirements. We propose a novel alternative framework to address the Monge-Kantorovich problem based on a projection type gradient descent scheme. The dynamics builds on the notion of the conditional expectation, where the connection with the opinion dynamics is leveraged to devise efficient numerical schemes. We demonstrate that the resulting dynamics recovers random maps with favourable computational performance. Along with the theoretical insight, the proposed dynamics paves the way for innovative approaches to construct numerical schemes for computing optimal transport maps as well as Wasserstein distances. + oai:arXiv.org:2410.08060v2 math.OC - Wed, 10 Dec 2025 00:00:00 -0500 + cs.AI + Thu, 11 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - Wouter Jongeneel + Mohsen Sadr, Peyman Mohajerin Esfahani, Hossein Gorji - Geometrically constrained walls in three dimensions - https://arxiv.org/abs/2412.04161 - arXiv:2412.04161v4 Announce Type: replace -Abstract: We study geometrically constrained magnetic walls in a three dimensional geometry where two bulks are connected by a thin neck. Without imposing any symmetry assumption on the domain, we investigate the scaling of the energy as the size of the neck vanishes. We identify five significant scaling regimes, for all of which we characterise the energy scaling and identify the asymptotic behaviour of the domain wall. Finally, we notice the emergence of sub-regimes that are not present in the previous works due to restrictive symmetry assumptions. - oai:arXiv.org:2412.04161v4 - math.AP - Wed, 10 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Riccardo Cristoferi, Gabriele Fissore, Marco Morandotti - - - Applications of the Magidor Iteration to Ultrafilter Theory - https://arxiv.org/abs/2412.09683 - arXiv:2412.09683v2 Announce Type: replace -Abstract: We characterize sums of normal ultrafilters after the Magidor iteration (product) of Prikry forcings over a discrete set of measurable cardinals. We apply this to show that the weak Ultrapower Axiom is not equivalent to the Ultrapower Axiom. We also construct a non-rigid ultrapower and two uniform ultrafilters on different cardinals that have the same ultrapower. - oai:arXiv.org:2412.09683v2 - math.LO - Wed, 10 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Tom Benhamou, Gabriel Goldberg - - - Structure fault diameter of hypercubes - https://arxiv.org/abs/2412.09885 - arXiv:2412.09885v2 Announce Type: replace -Abstract: Structure connectivity and substructure connectivity are innovative indicators for assessing network reliability and fault tolerance. Similarly, fault diameter evaluates fault tolerance and transmission delays in networks. This paper extends the concept of fault diameter by introducing two new variants: structure fault diameter and substructure fault diameter, derived from structure connectivity and substructure connectivity respectively. For a connected graph $G$ with $W$-structure connectivity $\kappa(G;W)$ or $W$-substructure connectivity $\kappa^s(G;W)$, the $W$-structure fault diameter $D_f(G;W)$ and $W$-substructure fault diameter $D_f^s(G;W)$ are defined as the maximum diameter of any subgraph of $G$ resulting from removing up to $\kappa(G;W)-1$ $W$-structures or $\kappa^s(G;W)-1$ $W$-substructures. For the $n$-dimensional hypercube $Q_n$ with $n \geq 3$ and $1 \leq m \leq n - 2$, we determine both $D_f(Q_n;Q_m)$ and $D_f^s(Q_n;Q_1)$. These findings generalize existing results for the diameter and fault diameter of $Q_n$, providing a broader understanding of the hypercube's structural properties under fault conditions. - oai:arXiv.org:2412.09885v2 + Principal minors of tree distance matrices + https://arxiv.org/abs/2411.11488 + arXiv:2411.11488v2 Announce Type: replace +Abstract: We prove that the principal minors of the distance matrix of a tree satisfy a combinatorial expression involving counts of rooted spanning forests of the underlying tree. This generalizes a result of Graham and Pollak, and refines a result of Graham and Lov\'asz on the coefficients of the characteristic polynomial of the distance matrix. We also give such an expression for the case of trees with edge lengths. We use arguments motivated by potential theory on graphs. Our formulas can be expressed in terms of evaluations of Symanzik polynomials. + oai:arXiv.org:2411.11488v2 math.CO - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Honggang Zhao, Eminjan Sabir, Cheng-Kuan Lin + Harry Richman, Farbod Shokrieh, Chenxi Wu - Rainbow Arborescence Conjecture - https://arxiv.org/abs/2412.15457 - arXiv:2412.15457v2 Announce Type: replace -Abstract: The famous Ryser--Brualdi--Stein conjecture asserts that every $k \times k$ Latin square contains a partial transversal of size $k-1$. Since its appearance, the conjecture has attracted significant interest, leading to several proposed generalizations. One of the most notable of these, by Aharoni, Kotlar, and Ziv, conjectures that $k$ disjoint common bases of two matroids of rank $k$ have a common independent partial transversal of size $k-1$. Although simple counterexamples show that the size $k-1$ above cannot be improved to $k$ (i.e., a transversal instead of a partial transversal), it is remarkable that no such counterexample is known for the special case of spanning arborescences. This motivated the formulation of the Rainbow Arborescence Conjecture: any graph on $n$ vertices formed by the union of $n-1$ spanning arborescences contains an arborescence using exactly one arc from each. - We prove several partial results on this conjecture. We show that the computational problem of testing the existence of such an arborescence with a fixed root is NP-complete, verify the conjecture in several special cases, and study relaxations of the problem. In particular, we establish the validity of the conjecture when the underlying undirected graph is a cycle; this also yields a new result on systems of distinct representatives for intervals on a cycle. - oai:arXiv.org:2412.15457v2 - math.CO - cs.DM - cs.DS - Wed, 10 Dec 2025 00:00:00 -0500 + Refining Concentration for Gaussian Quadratic Chaos + https://arxiv.org/abs/2412.03774 + arXiv:2412.03774v3 Announce Type: replace +Abstract: We slightly modify the proof of Hanson-Wright inequality (HWI) for concentration of Gaussian quadratic chaos where we tighten the bound by increasing the absolute constant in its formulation from the largest known value of 0.125 to at least 0.145 in the symmetric case. We also present a sharper version of an inequality due to Laurent and Massart (LMI) through which we increase the absolute constant in HWI from the largest available value of approximately $0.134$ due to LMI itself to at least $0.152$ in the positive-semidefinite case. A new sequence of concentration bounds indexed by $m=1,2,3,\cdots, \infty$ is developed that involves Schatten norms of the underlying matrix. The case $m=1$ recovers HWI. These bounds undergo a phase transition in the sense that if the tail parameter is smaller than a critical threshold $\tau_c$, then $m=1$ is the tightest and if it is larger than $\tau_c$, then $m=\infty$ is the tightest. This leads to a novel bound called the~$m_\infty$-bound. A separate concentration bound named twin to HWI is also developed that is tighter than HWI for both sufficiently small and large tail parameter. Finally, we explore concentration bounds when the underlying matrix is positive-semidefinite and only the dimension~$n$ and its largest eigenvalue are known. Five candidates are examined, namely, the $m_\infty$-bound, relaxed versions of HWI and LMI, the $\chi^2$-bound and the large deviations bound. The sharpest among these is always either the $m_\infty$-bound or the $\chi^2$-bound. The case of even dimension is given special attention. If $n=2,4,6$, the $\chi^2$-bound is tighter than the $m_\infty$-bound. If $n$ is an even integer greater than or equal to 8, the $m_\infty$-bound is sharper than the $\chi^2$-bound if and only if the ratio of the tail parameter over the largest eigenvalue lies inside a finite open interval which expands indefinitely as $n$ grows. + oai:arXiv.org:2412.03774v3 + math.PR + cs.IT + math.IT + Thu, 11 Dec 2025 00:00:00 -0500 replace - http://creativecommons.org/licenses/by/4.0/ - Krist\'of B\'erczi, Tam\'as Kir\'aly, Yutaro Yamaguchi, Yu Yokoi + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Kamyar Moshksar - Simple proof of robustness for Bayesian heavy-tailed linear regression models - https://arxiv.org/abs/2501.06349 - arXiv:2501.06349v3 Announce Type: replace -Abstract: In the Bayesian literature, a line of research called resolution of conflict is about the characterization of robustness against outliers of statistical models. The robustness characterization of a model is achieved by establishing the limiting behaviour of the posterior distribution under an asymptotic framework in which the outliers move away from the bulk of the data. The proofs of the robustness characterization results, especially the recent ones for regression models, are technical and not intuitive, limiting the accessibility and preventing the development of theory in that line of research. In this paper, we highlight that the proof complexity is due to the generality of the assumptions on the prior distribution. To address the issue of accessibility, we present a significantly simpler proof for a linear regression model with a specific class of prior distributions, among which we find typically used prior distributions. The class of prior distributions is such that each regression coefficient has a sub-exponential distribution, which allows to exploit a tail bound, contrarily to previous approaches. The proof is intuitive and uses classical results of probability theory. The generality of the assumption on the error distribution is also appealing; essentially, it can be any distribution with regularly varying or log-regularly varying tails. So far, there does not exist a result in such generality for models with regularly varying distributions. We also investigate the necessity of the assumptions. To promote the development of theory in resolution of conflict, we highlight how the key steps of the proof can be adapted for other models and present an application of the proof technique in the context of generalized linear models. - oai:arXiv.org:2501.06349v3 - math.ST - stat.TH - Wed, 10 Dec 2025 00:00:00 -0500 + Irregular Hodge numbers of Frenkel--Gross connections + https://arxiv.org/abs/2412.05849 + arXiv:2412.05849v3 Announce Type: replace +Abstract: Frenkel and Gross constructed a family of connections on $\mathbb{P}^1\backslash\{0,\infty\}$, for almost simple groups $\check{G}$ and their representations. In this article, we calculate the irregular Hodge numbers of these Frenkel--Gross connections, and, as an application, we prove a conjecture of Katzarkov--Kontsevich--Pantev for mirror Landau-Ginzburg models of minuscule homogeneous spaces. + oai:arXiv.org:2412.05849v3 + math.AG + Thu, 11 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - Philippe Gagnon + Yichen Qin, Christian Sevenheck, Peter Spacek - Total preprojective algebras - https://arxiv.org/abs/2502.04683 - arXiv:2502.04683v3 Announce Type: replace -Abstract: We introduce total preprojective algebras $\Psi$ of path algebras of Dynkin quivers $kQ$, and prove that they are isomorphic to $2$-Auslander algebras of preprojective algebras $\Pi$ of $kQ$. In particular, $\Psi$ has global dimension $3$ and dominant dimension $3$. We also describe $\Psi$ as a tensor algebra of a certain explicit bimodule over the Auslander algebra of $kQ$. As an application, we give a presentation of $\Psi$ by explicit quivers with relations. More generally, we introduce total $(d+1)$-preprojective algebras of $d$-representation finite algebras, and give all the corresponding results. - oai:arXiv.org:2502.04683v3 - math.RT - Wed, 10 Dec 2025 00:00:00 -0500 + A stability condition on weighted manifolds + https://arxiv.org/abs/2412.09396 + arXiv:2412.09396v2 Announce Type: replace +Abstract: We will present an estimate for the first eigenvalue of the Dirichlet and Neumann problems in terms of the Bakry-\'Emery Ricci curvature for a compact weighted manifold. As an application we will establish a stability condition for a h-minimal hypersurface. + oai:arXiv.org:2412.09396v2 + math.DG + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Aaron Chan, Osamu Iyama, Rene Marczinzik + A. C. Bezerra, T. Castro Silva, F. Manfio - Reconstruction of frequency-localized functions from pointwise samples via least squares and deep learning - https://arxiv.org/abs/2502.09794 - arXiv:2502.09794v2 Announce Type: replace -Abstract: Recovering frequency-localized functions from pointwise data is a fundamental task in signal processing. We examine this problem from an approximation-theoretic perspective, focusing on least squares and deep learning-based methods. First, we establish a novel recovery theorem for least squares approximations using the Slepian basis from uniform random samples in low dimensions, explicitly tracking the dependence of the bandwidth on the sampling complexity. Building on these results, we then present a recovery guarantee for approximating bandlimited functions via deep learning from pointwise data. This result, framed as a practical existence theorem, provides conditions on the network architecture, training procedure, and data acquisition sufficient for accurate approximation. To complement our theoretical findings, we perform numerical comparisons between least squares and deep learning for approximating one- and two-dimensional functions. We conclude with a discussion of the theoretical limitations and the practical gaps between theory and implementation. - oai:arXiv.org:2502.09794v2 - math.CA - cs.LG - cs.NA - math.NA - Wed, 10 Dec 2025 00:00:00 -0500 + Derivation of the Chern-Simons-Schr\"odinger equation from the dynamics of an almost-bosonic-anyon gas + https://arxiv.org/abs/2412.13080 + arXiv:2412.13080v3 Announce Type: replace +Abstract: We study the time evolution of an initial product state in a system of almost-bosonic-extended-anyons in the large-particle limit. We show that the dynamics of this system can be well approximated, in finite time, by a product state evolving under the effective Chern--Simons--Schr\"odinger equation. Furthermore, we provide a convergence rate for the approximation in terms of the radius $R = (\log N)^{\frac{1}{2}+\varepsilon}$ of the extended anyons. These results establish a rigorous connection between the microscopic dynamics of almost-bosonic-anyon gases and the emergent macroscopic behavior described by the Chern--Simons--Schr\"odinger equation. + oai:arXiv.org:2412.13080v3 + math-ph + math.AP + math.MP + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - A. Martina Neuman, Andres Felipe Lerma Pineda, Jason J. Bramburger, Simone Brugiapaglia + Th\'eotime Girardot, Jinyeop Lee - The plus construction with respect to subrings of the rationals - https://arxiv.org/abs/2502.11839 - arXiv:2502.11839v4 Announce Type: replace -Abstract: We construct explicit models of universal $H \mathbb{Z}[J^{-1}]$-acyclic spaces $\mathcal M$, for any subset $J$ of the prime numbers. The corresponding nullification functors provide thus plus construction functors for ordinary homology with $\mathbb{Z}[J^{-1}]$ coefficients. Motivated by classical results about Quillen's plus construction for integral homology, we prove that the $H \mathbb{Z}[J^{-1}]$-acyclization functor and the $\mathcal M$-cellularization functor coincide. We show that the acyclization-plus construction fiber sequence is always a cofiber sequence for simply connected spaces, but almost never so when the plus construction is not simply connected, unlike in the classical case. - oai:arXiv.org:2502.11839v4 - math.AT - math.GR - math.KT - Wed, 10 Dec 2025 00:00:00 -0500 + Partial Semigroupoid Actions on Sets + https://arxiv.org/abs/2412.14068 + arXiv:2412.14068v2 Announce Type: replace +Abstract: We introduce partial semigroupoid actions on sets and demonstrate that each such action admits universal globalization. Our construction extends the universal globalization for partial category actions given by P. Nystedt (Lundstr\"om) and the tensor product globalization for strong partial semigroup actions given by G. Kudryavtseva and V. Laan, thereby unifying the theory of partial actions for both categories and semigroups. + oai:arXiv.org:2412.14068v2 + math.RA + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Guille Carri\'on Santiago, Ram\'on Flores, J\'er\^ome Scherer + 10.1007/s00233-025-10605-3 + Rafael Haag Petasny, Tha\'isa Tamusiunas - BGG Sequences -- A Riemannian perspective - https://arxiv.org/abs/2502.17016 - arXiv:2502.17016v2 Announce Type: replace -Abstract: BGG resolutions and generalized BGG resolutions from representation theory of semisimple Lie algebras have been generalized to sequences of invariant differential operators on manifolds endowed with a geometric structure belonging to the family of parabolic geometries. Two of these structures, conformal structures and projective structures, occur as weakenings of a Riemannian metric respectively of a specified torsion-free connection on the tangent bundle. In particular, one obtains BGG sequences on open subsets of $\mathbb R^n$ as very special cases of the construction. It turned out that several examples of the latter sequences are of interest in applied mathematics, since they can be used to construct numerical methods to study operators relevant for elasticity theory, numerical relativity and related fields. - This article is intended to provide an intermediate level between BGG sequences for parabolic geometries and the case of domains in $\mathbb R^n$. We provide a construction of conformal BGG sequences on Riemannian manifolds and of projective BGG sequences on manifolds endowed with a volume preserving linear connection on their tangent bundle. These constructions do not need any input from parabolic geometries. Except from standard differential geometry methods the only deeper input comes from representation theory. So one can either view the results as a simplified version of the constructions for parabolic geometries in an explicit form. Alternatively, one can view them as providing an extension of the simplified constructions for domains in $\Bbb R^n$ to general Riemannian manifolds or to manifolds endowed with an appropriate connection on the tangent bundle. - oai:arXiv.org:2502.17016v2 - math.DG - cs.NA - math.NA - Wed, 10 Dec 2025 00:00:00 -0500 + Random additive perturbation of a $k$ term recurrence relation + https://arxiv.org/abs/2412.14781 + arXiv:2412.14781v2 Announce Type: replace +Abstract: We are interested in stochastic processes satisfying a nonlinear recurrence relation of the form $$X_{n + k} = \Phi_0 (X_n, ..., X_{n + k - 1}) + \Theta_n$$ where $\Theta$ is a noise term. We establish the existence of an invariant measure for this process under given sufficient conditions on $\Phi_0.$ + oai:arXiv.org:2412.14781v2 + math.DS + math.PR + Thu, 11 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - Andreas Cap + Lisette Jager, Killian Verdure - Optimal Trickle-Down Theorems for Path Complexes via C-Lorentzian Polynomials with Applications to Sampling and Log-Concave Sequences - https://arxiv.org/abs/2503.01005 - arXiv:2503.01005v3 Announce Type: replace -Abstract: Let $X$ be a $d$-partite $d$-dimensional simplicial complex with parts $T_1,\dots,T_d$ and let $\mu$ be a distribution on the facets of $X$. Informally, we say $(X,\mu)$ is a path complex if for any $i<j<k$ and $F \in T_i,G \in T_j, K\in T_k$, we have $\mathbb{P}_\mu[F,K | G]=\mathbb{P}_\mu[F|G]\cdot\mathbb{P}_\mu[K|G].$ We develop a new machinery with $\mathcal{C}$-Lorentzian polynomials to show that if all links of $X$ of co-dimension 2 have spectral expansion at most $1/2$, then $X$ is a $1/2$-local spectral expander. We then prove that one can derive fast-mixing results and log-concavity statements for top-link spectral expanders. - We use our machinery to prove fast mixing results for sampling maximal flags of flats of distributive lattices (a.k.a. linear extensions of posets) subject to external fields, and to sample maximal flags of flats of "typical" modular lattices. We also use it to re-prove the Heron-Rota-Welsh conjecture and to prove a conjecture of Chan and Pak which gives a generalization of Stanley's log-concavity theorem. Lastly, we use it to prove near optimal trickle-down theorems for "sparse complexes" such as constructions by Lubotzky-Samuels-Vishne, Kaufman-Oppenheim, and O'Donnell-Pratt. - oai:arXiv.org:2503.01005v3 - math.CO - cs.CC - cs.DS - Wed, 10 Dec 2025 00:00:00 -0500 + Numerical analysis of a stabilized scheme for an optimal control problem governed by a parabolic convection--diffusion equation + https://arxiv.org/abs/2412.21070 + arXiv:2412.21070v3 Announce Type: replace +Abstract: We consider an optimal control problem on a bounded domain $\Omega\subset\mathbb{R}^2,$ governed by a parabolic convection--diffusion--reaction equation with pointwise control constraints. We follow the optimize--then--discretize approach, in which the state and co-state variables are discretized using the piecewise linear finite element method. For stabilization, we apply the algebraic flux correction method. Temporal discretization is performed using the backward Euler method. The discrete control variable is obtained by projecting the discretized adjoint state onto the set of admissible controls. The resulting stabilized fully--discrete scheme is nonlinear and a fixed point argument is used to prove its existence and uniqueness under a mild condition between the time step $k$ and the mesh size $h,$ e.g., $k = \mathcal{O}(h).$ Furthermore, assuming sufficient regularity of the exact solution, we derive error estimates in the $L^{2}$ and energy norms with respect to the spatial variable, and in the $\ell^\infty$ norm with respect to time for the state and co-state variables. For the control variable, we also derive an $L^{2}$-norm error estimate with respect to space and an $\ell^\infty$-norm estimate in time. Finally, we present numerical experiments that validate the the order of convergence of the stabilized fully--discrete scheme based on the algebraic flux correction method. We also test the stabilized fully--discrete scheme in optimal control problems that governed by a convection--dominant equation where the solution possesses interior layers. + oai:arXiv.org:2412.21070v3 + math.NA + cs.NA + Thu, 11 Dec 2025 00:00:00 -0500 replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jonathan Leake, Kasper Lindberg, Shayan Oveis Gharan + http://creativecommons.org/licenses/by-nc-nd/4.0/ + Christos Pervolianakis - On Solving Minimization and Min-Max Problems by First-Order Methods with Relative Error in Gradients - https://arxiv.org/abs/2503.06628 - arXiv:2503.06628v3 Announce Type: replace -Abstract: First-order methods for minimization and saddle point (min-max) problems are widely used for solving large-scale problems, in particular arising in machine learning. The majority of works obtain favorable complexity guarantees of such methods, assuming that exact gradient information is available. At the same time, even the use of floating-point representation of real numbers already leads to relative error in all the computations. Relative errors also arise in such applications as bilevel optimization, inverse problems, derivative-free optimization, and inexact proximal methods. This paper answers several theoretical open questions on first-order optimization methods under relative errors in the first-order oracle. We propose an explicit single-loop accelerated gradient method that preserves optimal linear convergence rate under maximal possible relative error in the gradient, and explore the tradeoff between the relative error and deterioration in the linear convergence rate. We further explore similar questions for saddle point problems and nonlinear equations, showing, for the first time in the literature, that a variant of gradient descent-ascent and the extragradient method are robust to such errors and providing estimates for the maximum level of noise that does not break linear convergence. - oai:arXiv.org:2503.06628v3 - math.OC - Wed, 10 Dec 2025 00:00:00 -0500 + King's Conjecture and the Cox category + https://arxiv.org/abs/2501.00130 + arXiv:2501.00130v2 Announce Type: replace +Abstract: We state and prove a realization of King's Conjecture for a category glued from the derived categories of all of the toric varieties arising from a given Cox ring. Our perspective extends ideas of Beilinson and Bondal to all semiprojective toric varieties. + oai:arXiv.org:2501.00130v2 + math.AG + math.AC + Thu, 11 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - Artem Vasin, Valery Krivchenko, Dmitry Kovalev, Fedyor Stonyakin, Nazarii Tupitsa, Pavel Dvurechensky, Mohammad Alkousa, Nikita Kornilov, Alexander Gasnikov + Matthew R. Ballard, Christine Berkesch, Michael K. Brown, Lauren Cranton Heller, Daniel Erman, David Favero, Sheel Ganatra, Andrew Hanlon, Jesse Huang - Recovering Parameters from Edge Fluctuations: Beta-Ensembles and Critically-Spiked Models - https://arxiv.org/abs/2503.14414 - arXiv:2503.14414v2 Announce Type: replace -Abstract: Let $\Lambda=\{\Lambda_0,\Lambda_1,\Lambda_2,\ldots\}$ be the point process that describes the edge scaling limit of either (i) "regular" beta-ensembles with inverse temperature $\beta>0$, or (ii) the top eigenvalues of Wishart or Gaussian invariant random matrices perturbed by $r_0\geq1$ critical spikes. In other words, $\Lambda$ is the eigenvalue point process of one of the scalar or multivariate stochastic Airy operators. We prove that a single observation of $\Lambda$ suffices to recover (almost surely) either (i) $\beta$ in the case of beta-ensembles, or (ii) $r_0$ in the case of critically-spiked models. Our proof relies on the recently-developed semigroup theory for the multivariate stochastic Airy operators. - Going beyond these parameter-recovery applications, our results also (iii) refine our understanding of the rigidity properties of $\Lambda$, and (iv) shed new light on the equality (in distribution) of stochastic Airy spectra with different dimensions and the same Robin boundary conditions. - oai:arXiv.org:2503.14414v2 - math.PR - math-ph - math.MP - Wed, 10 Dec 2025 00:00:00 -0500 + Cubic fourfolds with a symplectic automorphism of prime order + https://arxiv.org/abs/2501.03869 + arXiv:2501.03869v4 Announce Type: replace +Abstract: We determine the algebraic and transcendental lattices of a general cubic fourfold with a symplectic automorphism of prime order. We prove that cubic fourfolds admitting a symplectic automorphism of order at least three are rational, and we exihibit two families of rational cubic fourfolds that are not equivariantly rational with respect to their group of automorphisms. As an application, we determine the cohomological action of symplectic birational transformations of manifolds of OG10 type that are induced by prime order sympletic automorphisms of cubic fourfolds. + oai:arXiv.org:2501.03869v4 + math.AG + Thu, 11 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - Pierre Yves Gaudreau Lamarre + Simone Billi, Annalisa Grossi, Lisa Marquand - Dual-Source SPIR over a noiseless MAC without Data Replication or Shared Randomness - https://arxiv.org/abs/2503.14682 - arXiv:2503.14682v2 Announce Type: replace -Abstract: Information-theoretically secure Symmetric Private Information Retrieval (SPIR) is known to be infeasible over noiseless channels with a single server. Known solutions to overcome this infeasibility involve additional resources such as database replication, shared randomness, or noisy channels. In this paper, we propose an alternative approach for achieving SPIR with information-theoretic security guarantees, without relying on shared randomness, noisy channels, or data replication. Specifically, we demonstrate that it is sufficient to use a noiseless binary adder multiple-access channel, where inputs are controlled by two non-colluding servers and the output is observed by the client, alongside a public noiseless communication channel between the client and the servers. Furthermore, in this setting, we characterize the optimal file rates, i.e., the file lengths normalized by the number of channel uses, that can be transferred. - oai:arXiv.org:2503.14682v2 - cs.IT - cs.CR - math.IT - Wed, 10 Dec 2025 00:00:00 -0500 + On $p$-adic Asai $L$-functions of Bianchi modular forms at non-ordinary primes and their decomposition into bounded $p$-adic $L$-functions + https://arxiv.org/abs/2501.10581 + arXiv:2501.10581v2 Announce Type: replace +Abstract: Let $p$ be an odd prime integer, $F/\mathbb{Q}$ be an imaginary quadratic field, and $\Psi$ be a small slope cuspidal Bianchi modular form over $F$ which is non-ordinary at $p$. In this article, we first construct a $p$-adic distribution $L^{\mathrm{As}}_{p}(\Psi)$ that interpolates the twisted critical $L$-values of Asai (or twisted tensor) $L$-function of $\Psi$, generalizing the works of Loeffler--Williams from the ordinary case to the non-ordinary case. To obtain this distribution, we construct some polynomials using Asai--Eisenstein elements: the Betti analogue of the Euler system machinery, developed by Loeffler--Williams. We use some techniques analogous to those of Loeffler--Zerbes for interpolating the twists of Beilinson--Flach elements arising in the Euler system associated with Rankin--Selberg convolutions of elliptic modular forms. We also use the interpolation method developed by Amice--V\'elu, Perrin-Riou, and B\"uy\"ukboduk--Lei in the construction. Furthermore, under some assumptions, we decompose these unbounded $p$-adic distributions into the linear combination of bounded measures as done by Pollack, Sprung, and Lei--Loeffler--Zerbes in the elliptic modular forms case. + oai:arXiv.org:2501.10581v2 + math.NT + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Remi A. Chou - - - Hausdorff Stability of the Cut Locus Under $C^2$-Perturbations of the Metric - https://arxiv.org/abs/2503.19413 - arXiv:2503.19413v2 Announce Type: replace -Abstract: In this article, we prove the stability with respect to the Hausdorff metric $d_H$ of the cut locus $\mathrm{Cut}(p, \mathfrak{g})$ of a point $p$ in a compact Riemannian manifold $(M, \mathfrak{g})$ under $C^2$ perturbation of the metric. Specifically, given a sequence of metrics $\mathfrak{g}_i$ on $M$, converging to $\mathfrak{g}$ in the $C^2$ topology, and a sequence of points $p_i$ in $M$, converging to $p$, we show that $\lim_i d_{H}\left( \mathrm{Cut}(p_i, \mathfrak{g}_i), \mathrm{Cut}(p, \mathfrak{g}) \right) = 0$. Along the way, we also prove the continuous dependence of the cut time map on the metric. - oai:arXiv.org:2503.19413v2 - math.DG - Wed, 10 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - 10.1016/j.jmaa.2025.130324 - J. Math. Anal. Appl., Vol 557 (2), 2026 - Aritra Bhowmick, Jin-ichi Itoh, Sachchidanand Prasad + Mihir Deo - Measures that violate the Generalized Continuum Hypothesis - https://arxiv.org/abs/2503.20094 - arXiv:2503.20094v2 Announce Type: replace -Abstract: A simple \(P_\lambda\)-point on a regular cardinal \(\kappa\) is a uniform ultrafilter on \(\kappa\) with a mod-bounded decreasing generating sequence of length \(\lambda\). - We prove that if there is a simple $P_\lambda$-point ultrafilter over $\kappa>\omega$, then $\lambda=\mathfrak{d}_\kappa=\mathfrak{b}_\kappa=\mathfrak{u}_\kappa=\mathfrak{r}_\kappa=\mathfrak{s}_\kappa$. We show that such ultrafilters appear in the models of \cite{SimonOmer,BROOKETAYLOR201737}. We improve the lower bound for the consistency strength of the existence of a $P_{\kappa^{++}}$-point to a $2$-strong cardinal. Finally, we apply our arguments to obtain non-trivial lower bounds for (1) the statement that the generalized tower number $\mathfrak{t}_\kappa$ is greater than $\kappa^+$ and $\kappa$ is measurable, (2) the preservation of measurability after the generalized Mathias forcing, and (3) variations of filter games of \cite{NIELSEN_WELCH_2019,HolySchlicht:HierarchyRamseyLikeCardinals,MagForZem} in the case $2^\kappa>\kappa^+$. - oai:arXiv.org:2503.20094v2 - math.LO - Wed, 10 Dec 2025 00:00:00 -0500 + Non relativistic limit of the nonlinear Klein-Gordon equation: Uniform in time approximation of KAM solutions + https://arxiv.org/abs/2501.17691 + arXiv:2501.17691v2 Announce Type: replace +Abstract: We study the non relativistic limit of the solutions of the cubic nonlinear Klein--Gordon (KG) equation with periodic boundary conditions on an interval and we construct a family of time quasi periodic solutions which, after a Gauge transformation, converge globally uniformly in time to quasi periodic solutions of the cubic NLS. The proof is based on KAM theory. We emphasize that, regardless of the spatial domain, all the previous results concern approximations valid over compact time intervals. + oai:arXiv.org:2501.17691v2 + math-ph + math.AP + math.MP + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Tom Benhamou, Gabriel Goldberg + Dario Bambusi, Andrea Belloni, Filippo Giuliani - Fast formulas for the Hurwitz values $\zeta(2,a)$ and $\zeta(3,a)$ - https://arxiv.org/abs/2504.01975 - arXiv:2504.01975v5 Announce Type: replace -Abstract: We prove two fast formulas for the Hurwitz values $\zeta(2,a)$ and $\zeta(3,a)$ respectively with the help of the WZ method. In them $(a)_n$ denotes the rising factorial or Pochhammer's symbol defined by $(a)_0=1$ and $(a)_n=a(a+1)\cdots(a+n-1)$ for positive integers $n$. The Huwitz $\zeta$ function is defined by $\zeta(s,a)=\zeta(0,s,a)=\sum_{k=0}^{\infty} (k+a)^{-s}$. In addition, we can use these fast evaluations to compute also in a rapid way Dirichlet values of the kinds $L_{\chi}(2)$ and $L_{\chi}(3)$. - oai:arXiv.org:2504.01975v5 - math.NT - Wed, 10 Dec 2025 00:00:00 -0500 + Interpolation and random interpolation in de Branges-Rovnyak spaces + https://arxiv.org/abs/2502.09094 + arXiv:2502.09094v2 Announce Type: replace +Abstract: The aim of this paper is to characterize universal and multiplier interpolating sequences for de Branges-Rovnyak spaces H (b) where the defining function b is a general non-extreme rational function. Our results carry over to recently introduced higher order local Dirichlet spaces and thus generalize previously known results in classical local Dirichlet spaces. In this setting, we also investigate random interpolating sequences with prescribed radii, providing a 0 -1 law. This condition is automatic when b is rational non inner so that we can assume H (b) = M(a). By standard results in functional analysis, the corresponding norms are equivalent. In [18], the authors demonstrated that the decomposition (1) is orthogonal in the metric of M(a). + oai:arXiv.org:2502.09094v2 + math.CV + math.FA + math.PR + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jes\'us Guillera + Andreas Hartmann (IMB), Giuseppe Lamberti (IMB) - Sparse Tensor CCA via Manifold Optimization for Multi-View Learning - https://arxiv.org/abs/2504.02339 - arXiv:2504.02339v5 Announce Type: replace -Abstract: Tensor canonical correlation analysis (TCCA) has garnered significant attention due to its effectiveness in capturing high-order correlations in multi-view learning. However, existing TCCA methods often underemphasize the characterization of individual structures and lack algorithmic convergence guarantees. In order to deal with these challenges, we propose a novel sparse TCCA model called STCCA-L, which integrates sparse regularization of canonical matrices and Laplacian regularization of multi-order graphs into the TCCA framework, thereby effectively exploiting the geometric structure of individual views. To solve this non-convex model, we develop an efficient alternating manifold proximal gradient algorithm based on manifold optimization, which avoids computationally expensive full tensor decomposition and leverages a semi-smooth Newton method for resolving the subproblem. Furthermore, we rigorously prove the convergence of the algorithm and analyze its complexity. Experimental results on eight benchmark datasets demonstrate the superior classification performance of the proposed method. Notably, on the 3Sources dataset, it achieves improvements of at least 4.50\% in accuracy and 6.77\% in F1 score over competitors. Our code is available at https://github.com/zhudafa/STCCA-L. - oai:arXiv.org:2504.02339v5 - math.OC - Wed, 10 Dec 2025 00:00:00 -0500 + Generalizing Reduced Rank Extrapolation to Low-Rank Matrix Sequences + https://arxiv.org/abs/2502.09165 + arXiv:2502.09165v3 Announce Type: replace +Abstract: Reduced rank extrapolation (RRE) is an acceleration method typically used to accelerate the iterative solution of nonlinear systems of equations using a fixed-point process. In this context, the iterates are vectors generated from a fixed-point mapping function. However, when considering the iterative solution of large-scale matrix equations, the iterates are low-rank matrices generated from a fixed-point process for which, generally, the mapping function changes in each iteration. To enable acceleration of the iterative solution for these problems, we propose two novel generalizations of RRE. First, we show how to effectively compute RRE for sequences of low-rank matrices. Second, we derive a formulation of RRE that is suitable for fixed-point processes for which the mapping function changes each iteration. We demonstrate the potential of the methods on several numerical examples involving the iterative solution of large-scale Lyapunov and Riccati matrix equations. + oai:arXiv.org:2502.09165v3 + math.NA + cs.NA + Thu, 11 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - Yanjiao Zhu, Wanquan Liu, Xianchao Xiu, Jianqin Sun + Pascal den Boef, Patrick K\"urschner, Xiaobo Liu, Jos Maubach, Jens Saak, Wil Schilders, Jonas Schulze, Nathan van de Wouw - Order polytopes of crown posets - https://arxiv.org/abs/2504.05123 - arXiv:2504.05123v3 Announce Type: replace -Abstract: In the last decade, the order polytope of the zigzag poset has been thoroughly studied. A related poset, called \emph{crown poset}, obtained by adding an extra relation between the endpoints of an even zigzag poset, is not so well understood. In this paper, we study the order polytopes of crown posets. We provide explicit formulas for their $f$-vectors. We provide recursive formulas for their Ehrhart polynomial, giving a counterpart to formulas found in the zigzag case by Petersen--Zhuang (2025). We use these formulas to simplify a computation by Ferroni--Morales--Panova (2025) of the linear term of the order polynomial of these posets. Furthermore, we provide a combinatorial interpretation for the coefficients of the $h^*$-polynomial in terms of the cyclic swap statistic on cyclically alternating permutations, which provides a circular version of a result by Coons--Sullivant (2023). - oai:arXiv.org:2504.05123v3 - math.CO - Wed, 10 Dec 2025 00:00:00 -0500 + Primitive immersions of constant curvature of surfaces into flag manifolds + https://arxiv.org/abs/2502.15502 + arXiv:2502.15502v2 Announce Type: replace +Abstract: We investigate certain immersions of constant curvature from Riemann surfaces into flag manifolds equipped with invariant metrics, namely primitive lifts associated to pseudoholomorphic maps of surfaces into complex Grassmannians. We prove that a primitive immersion from the two-sphere into the full flag manifold which has constant curvature with respect to \emph{at least one} invariant metric is unitarily equivalent to the primitive lift of a Veronese map, hence it has constant curvature with respect to \emph{all} invariant metrics. We prove a partial generalization of this result to the case where the domain is a general simply connected Riemann surface. On the way, we consider the problem of finding the invariant metric on the flag manifold, under a certain normalization condition, that maximizes the induced area of the two-sphere by a given primitive immersion. + oai:arXiv.org:2502.15502v2 + math.DG + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - 10.1016/j.ejc.2025.104304 - European Journal of Combinatorics, Vol. 133, Mar. 2026, P. 104304 - Teemu Lundstr\"om, Leonardo Saud Maia Leite + Rui Pacheco, Mehmood Ur Rehman - Lorentzian Gromov-Hausdorff convergence and pre-compactness - https://arxiv.org/abs/2504.10380 - arXiv:2504.10380v4 Announce Type: replace -Abstract: The goal of the paper is to introduce a convergence \`a la Gromov-Hausdorff for Lorentzian spaces, building on $\epsilon$-nets consisting of causal diamonds and relying only on the time separation function. This yields a geometric notion of convergence, which can be applied to synthetic Lorentzian spaces (Lorentzian pre-length spaces) or smooth spacetimes. Among the main results, we prove a Lorentzian counterpart of the celebrated Gromov's pre-compactness theorem for metric spaces, where controlled covers by balls are replaced by controlled covers by diamonds. This yields a geometric pre-compactness result for classes of globally hyperbolic spacetimes, satisfying a uniform doubling property on Cauchy hypersurfaces and a suitable control on the causality, and a curvature-driven pre-compactness result. The final part of the paper establishes several applications: we show that Chru\'sciel-Grant approximations are an instance of the Lorentzian Gromov-Hausdorff convergence here introduced, we prove that timelike sectional curvature bounds are stable under such a convergence, we introduce timelike blow-up tangents and discuss connections with the main conjecture of causal set theory. - oai:arXiv.org:2504.10380v4 - math.DG - gr-qc + A microlocal pathway to spectral asymmetry: curl and the eta invariant + https://arxiv.org/abs/2502.18307 + arXiv:2502.18307v2 Announce Type: replace +Abstract: The notion of eta invariant is traditionally defined by means of analytic continuation. We prove, by examining the particular case of the operator curl, that the eta invariant can equivalently be obtained as the trace of the difference of positive and negative spectral projections, appropriately regularised. Our construction is direct, in the sense that it does not involve analytic continuation, and is based on the use of pseudodifferential techniques. This provides a novel approach to the study of spectral asymmetry of non-semibounded (pseudo)differential systems on manifolds which encompasses and extends previous results. + oai:arXiv.org:2502.18307v2 + math.SP math-ph - math.MG + math.AP + math.DG math.MP - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - Andrea Mondino, Clemens S\"amann + Matteo Capoferri, Dmitri Vassiliev - Improvements on exponential sums related to Piatetski-Shapiro primes - https://arxiv.org/abs/2504.11464 - arXiv:2504.11464v2 Announce Type: replace -Abstract: We prove a new bound to the exponential sum of the form $$ \sum_{h \sim H}\delta_h \mathop{\sum_{m\sim M}\sum_{n\sim N}}_{mn\sim x}a_{m}b_{n}\e\big(\alpha mn + h(mn + u)^{\gamma}\big), $$ by a new approach to the Type I sum. The sum can be applied to many problems related to Piatetski-Shapiro primes, which are primes of the form $\lfloor n^c \rfloor$. In this paper, we improve the admissible range of the Balog-Friedlander condition, which leads to an improvement to the ternary Goldbach problem with Piatetski-Shapiro primes. We also investigate the distribution of Piatetski-Shapiro primes in arithmetic progressions, Piatetski-Shapiro primes in the intersection of multiple Beatty sequences and so on. - oai:arXiv.org:2504.11464v2 - math.NT - Wed, 10 Dec 2025 00:00:00 -0500 + Biasing with an independent increment: Gaussian approximations and proximity of Poisson mixtures + https://arxiv.org/abs/2503.05586 + arXiv:2503.05586v3 Announce Type: replace +Abstract: By exploiting the well-known observation that size-biasing or zero-biasing an infinitely divisible random variable may be achieved by adding an independent increment, combined with tools from Stein's method for compound Poisson and Gaussian approximations, we establish three sets of approximation results: (a) bounds on the proximity of Poisson mixtures with infinitely divisible mixing distributions, (b) central limit theorems with explicit error bounds for sums of associated or negatively associated random variables which do not require boundedness of the underlying distributions, and (c) a Gaussian approximation theorem under a vanishing third moment condition. These exploit biasing by an independent increment directly, via an intermediate compound Poisson approximation, and through a convex ordering argument, respectively. Applications include a Dickman-type limit theorem, simple random sampling and urn models with overflow. + oai:arXiv.org:2503.05586v3 + math.PR + Thu, 11 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - Li Lu, Lingyu Guo, Victor Z. Guo + Fraser Daly - Computing the Tropical Abel--Jacobi Transform and Tropical Distances for Metric Graphs - https://arxiv.org/abs/2504.11619 - arXiv:2504.11619v3 Announce Type: replace -Abstract: Metric graphs are important models for capturing the structure of complex data across various domains. While much effort has been devoted to extracting geometric and topological features from graph data, computational aspects of metric graphs as abstract tropical curves remains unexplored. In this paper, we present the first computational and machine learning-driven study of metric graphs from the perspective of tropical algebraic geometry. Specifically, we study the tropical Abel--Jacobi transform, a vectorization of points on a metric graph via the tropical Abel--Jacobi map into its associated flat torus, the tropical Jacobian. We develop algorithms to compute this transform and investigate how the resulting embeddings depend on different combinatorial models of the same metric graph. - Once embedded, we compute pairwise distances between points in the tropical Jacobian under two natural metrics: the tropical polarization distance and the Foster--Zhang distance. Computing these distances are generally NP-hard as they turn out to be linked to classical lattice problems in computational complexity, however, we identify a class of metric graphs where fast and explicit computations are feasible. For the general case, we propose practical algorithms for both exact and approximate distance matrix computations using lattice basis reduction and mixed-integer programming solvers. Our work lays the groundwork for future applications of tropical geometry and the tropical Abel--Jacobi transform in machine learning and data analysis. - oai:arXiv.org:2504.11619v3 - math.AG - cs.NA + Hyperbolic Banach spaces + https://arxiv.org/abs/2503.10467 + arXiv:2503.10467v2 Announce Type: replace +Abstract: The standard theory of Banach spaces is built upon the notions of vector space, triangle inequality and Cauchy completeness. Here we propose a `hyperbolic' variant of this `elliptic' framework where general linear combinations are replaced by linear combinations with non-negative coefficients, triangle inequality is replaced by reverse triangle inequality and Cauchy completeness is replaced by the order-theoretic notion of directed completeness. + The motivation for our investigation is in non-smooth Lorentzian geometry: we believe that to unlock the full potential of the field, and ultimately extract more informations about the smooth world, some version of `Lorentzian functional analysis' is needed, especially in relation to timelike lower Ricci curvature bounds. + An example of structure we investigate is obtained by starting with a Banach space, multiplying it by $\mathbb R$ and considering the `future cone' in there. Because of this, some of the results in this manuscript might be read through the lenses of standard Banach spaces theory. From this perspective, the classical Hahn-Banach and Baire category theorems can be seen as consequences of statements obtained here. + A different kind of example is that of $L^p$ spaces for $p\leq1$. Their structure and natural duality relations fit particularly well in our framework, to the extent that they have been an important source of inspiration for the axiomatization chosen in this paper. + We also investigate the notion of directed completeness regardless of any algebraic structure, as we believe it is central even in the finite-dimensional non-smooth Lorentzian framework, for instance to achieve a compactness theorem \`a la Gromov. This study unveils connections between Geroch-Kronheimer-Penrose's concept of ideal point in a spacetime, Beppo Levi's monotone convergence theorem and certain aspects of domain theory. + oai:arXiv.org:2503.10467v2 + math.FA math.MG - math.NA - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Yueqi Cao, Anthea Monod + Nicola Gigli - A 2-distance set with 277 points in the Euclidean space of dimension 23 - https://arxiv.org/abs/2504.18110 - arXiv:2504.18110v2 Announce Type: replace -Abstract: We construct a $2$-distance set with $277$ points in the $23$-dimensional Euclidean space having distances $2$ and $\sqrt{6}$. - oai:arXiv.org:2504.18110v2 - math.CO - Wed, 10 Dec 2025 00:00:00 -0500 + Local controllability of a free-boundary problem for a class of one-dimensional degenerate parabolic equations + https://arxiv.org/abs/2503.11929 + arXiv:2503.11929v3 Announce Type: replace +Abstract: This paper is devoted to a study of the controllability of a free-boundary problem for a class of one-dimensional degenerate parabolic equations with distributed controls, locally supported in space. We prove that for any $T>0$, if the initial state is sufficiently small, there exists a control that drives the state exactly to rest at time $t = T$. The proof is based on Schauder's fixed point theorem, combined with appropriate estimates for solutions to degenerate parabolic equations and for control functions. + oai:arXiv.org:2503.11929v3 + math.OC + math.AP + Thu, 11 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - Hong-Jun Ge, Jack Koolen, Akihiro Munemasa + Lingyang Liu - Differentially Private Secure Multiplication with Erasures and Adversaries - https://arxiv.org/abs/2504.21178 - arXiv:2504.21178v2 Announce Type: replace -Abstract: We consider a private distributed multiplication problem involving N computation nodes and T colluding nodes. Shamir's secret sharing algorithm provides perfect information-theoretic privacy, while requiring an honest majority, i.e., N \ge 2T + 1. Recent work has investigated approximate computation and characterized privacy-accuracy trade-offs for the honest minority setting N \le 2T for real-valued data, quantifying privacy leakage via the differential privacy (DP) framework and accuracy via the mean squared error. However, it does not incorporate the error correction capabilities of Shamir's secret-sharing algorithm. This paper develops a new polynomial-based coding scheme for secure multiplication with an honest minority, and characterizes its achievable privacy-utility tradeoff, showing that the tradeoff can approach the converse bound as closely as desired. Unlike previous schemes, the proposed scheme inherits the capability of the Reed-Solomon (RS) code to tolerate erasures and adversaries. We utilize a modified Berlekamp-Welch algorithm over the real number field to detect adversarial nodes. - oai:arXiv.org:2504.21178v2 - cs.IT - math.IT - Wed, 10 Dec 2025 00:00:00 -0500 + Geometric Properties of Periodic Lattices in Function Fields + https://arxiv.org/abs/2503.11987 + arXiv:2503.11987v3 Announce Type: replace +Abstract: Periodic lattices are natural generalizations of lattices, which arise naturally in diophantine approximations with rationals of bounded denominators. In this paper, we prove analogues of classical theorems in geometry of numbers for periodic lattices in function fields. Moreover, we use special matrices to compute the covering and packing radii of special periodic lattices. + oai:arXiv.org:2503.11987v3 + math.NT + math.MG + Thu, 11 Dec 2025 00:00:00 -0500 replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Haoyang Hu, Viveck R. Cadambe + http://creativecommons.org/licenses/by-nc-nd/4.0/ + Noy Soffer Aranov - On strong Euler-homogeneity and Saito-holonomicity for complex hypersurfaces. Applications to a conjecture on free divisors - https://arxiv.org/abs/2504.21829 - arXiv:2504.21829v3 Announce Type: replace -Abstract: We first develop some criteria for a general divisor to be strongly Euler-homogeneous in terms of the Fitting ideals of certain modules. We also study new variants of Saito-holonomicity, generalizing Koszul-free type properties and characterizing them in terms of the same Fitting ideals. Thanks to these advances, we are able to make progress in the understanding of a conjecture from 2002: a free divisor satisfying the Logarithmic Comparison Theorem (LCT) must be strongly Euler-homogeneous. Previously, it was known to be true only for ambient dimension $n \leq 3$ or assuming Koszul-freeness. We prove it in the following new cases: assuming strong Euler-homogeneity on a punctured neighbourhood of a point; assuming the divisor is weakly Koszul-free; for $n=4$; for linear free divisors in $n=5$. Finally, we refute a conjecture stating that all linear free divisors satisfy LCT and are strongly Euler-homogeneous. - oai:arXiv.org:2504.21829v3 - math.AG - math.CV - Wed, 10 Dec 2025 00:00:00 -0500 + A Parametric Family of Polynomial Wavelets for Signal and Image Processing + https://arxiv.org/abs/2503.12403 + arXiv:2503.12403v2 Announce Type: replace +Abstract: This paper investigates the potential applications of a parametric family of polynomial wavelets that has been recently introduced starting from de la Vall\'ee Poussin (VP) interpolation at Chebyshev nodes. Unlike classical wavelets, which are constructed on the real line, these VP wavelets are defined on a bounded interval, offering the advantage of handling boundaries naturally while maintaining computational efficiency. In addition, the structure of these wavelets enables the use of fast algorithms for decomposition and reconstruction. Furthermore, the flexibility offered by a free parameter allows a better control of localized singularities, such as edges in images. On the basis of previous theoretical foundations, we show the effectiveness of the VP wavelets for basic signal denoising and image compression, emphasizing their potential for more advanced signal and image processing tasks. + oai:arXiv.org:2503.12403v2 + math.NA + cs.NA + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Abraham del Valle Rodr\'iguez + Mariantonia Cotronei, Woula Themistoclakis, Marc Van Barel - Advances on a conjecture about free divisors - https://arxiv.org/abs/2504.21834 - arXiv:2504.21834v3 Announce Type: replace -Abstract: In 2002, it was conjectured that a free divisor satisfying the so-called Logarithmic Comparison Theorem (LCT) must be strongly Euler-homogeneous. Today, it is known to be true only in ambient dimension less or equal than three or assuming Koszul-freeness. Thanks to our advances in the comprehension of strong Euler-homogeneity, we are able to prove the conjecture in the following new cases: assuming strong Euler-homogeneity on a punctured neighbourhood of a point; assuming the divisor is weakly Koszul-free; for ambient dimension $n=4$; for linear free divisors in ambient dimension $n=5$. We also refute a conjecture that states that all linear free divisors satisfy LCT and are strongly Euler-homogeneous. - oai:arXiv.org:2504.21834v3 - math.AG - math.CV - Wed, 10 Dec 2025 00:00:00 -0500 + On the numerical stability of sketched GMRES + https://arxiv.org/abs/2503.19086 + arXiv:2503.19086v2 Announce Type: replace +Abstract: We perform a backward stability analysis of preconditioned sketched GMRES [Nakatsukasa and Tropp, SIAM J. Matrix Anal. Appl, 2024] for solving linear systems $Ax=b$, and show that the backward stability at iteration $i$ depends on the conditioning of the Krylov basis $B_{1:i}$ as long as the condition number of $A B_{1:i}$ can be bounded by $1/O(u)$, where $u$ is the unit roundoff. Under this condition, we show that sketched GMRES is backward stable as long as the condition number of $B_{1:i}$ is not too large. Under additional assumptions, we then show that the stability of a restarted implementation of sketched GMRES can be independent of the condition number of $B_{1:i}$, and restarted sketched GMRES is backward stable. We also derive sharper bounds that explain why the backward error can be small even in cases when the basis $B_{1:i}$ is very ill-conditioned, which has been observed in the literature but not yet explained theoretically. We present numerical experiments to demonstrate the conclusions of our analysis, and also show that adaptively restarting where appropriate allows us to recover backward stability in sketched GMRES. + oai:arXiv.org:2503.19086v2 + math.NA + cs.NA + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Abraham del Valle Rodr\'iguez + Liam Burke, Erin Carson, Yuxin Ma - Quantitative lower bound for solutions to the Boltzmann equation in non-convex domains - https://arxiv.org/abs/2505.03396 - arXiv:2505.03396v4 Announce Type: replace -Abstract: In this article, we study the continuous mild solutions to the Boltzmann equation in a bounded spatial domain, under either angular cutoff assumption or non-cutoff assumption. Without assuming convexity of the spatial domain, we establish a Maxwellian lower bound in the cutoff case, and a weaker-than-Maxwellian lower bound for the non-cutoff case. This extends the results of \cite{Bri1,Bri2}, where the convexity of the domain was required. - oai:arXiv.org:2505.03396v4 + The incompressible limit of an inhomogeneous model of tissue growth + https://arxiv.org/abs/2503.19849 + arXiv:2503.19849v2 Announce Type: replace +Abstract: We study a porous medium equation that models tissue growth in a heterogeneous environment. We show that, in the incompressible limit, solutions converge to those of a weak form of a Hele-Shaw type free boundary problem. To obtain enough compactness to take the limit, we establish an $L^4$ bound on the gradient of the pressure and an estimate of Aronson-B\'{e}nilan type. + oai:arXiv.org:2503.19849v2 math.AP - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - Jhe-Kuan Su + Anthony Sulak, Olga Turanova - Trichotomy and $tK_m$-goodness of sparse graphs - https://arxiv.org/abs/2505.04142 - arXiv:2505.04142v2 Announce Type: replace -Abstract: Let $G$ be a connected graph with $n$ vertices and $n+k-2$ edges and $tK_m$ denote the disjoint union of $t$ complete graphs $K_m$. In this paper, by developing a trichotomy for sparse graphs, we show that for given integers $m\ge 2$ and $t\ge 1$, there exists a positive constant $c$ such that if $1\le k\le cn^{\frac{2}{m-1}}$ and $n$ is large, then $G$ is $tK_m$-good, that is, the Ramsey number is \[ r(G, tK_m)=(n-1)(m-1)+t\,. \] In particular, the above equality holds for any positive integers $k$, $m$, and $t$, provided $n$ is large. The case $t=1$ was obtained by Burr, Erd\H{o}s, Faudree, Rousseau, and Schelp (1980), and the case $k=1$ was established by Luo and Peng (2023). - oai:arXiv.org:2505.04142v2 - math.CO - Wed, 10 Dec 2025 00:00:00 -0500 + Higher-order asymptotic expansion with error estimate for the multidimensional Laplace-type integral under perturbations + https://arxiv.org/abs/2504.01310 + arXiv:2504.01310v3 Announce Type: replace +Abstract: We consider the asymptotic behavior of the multidimensional Laplace-type integral with a perturbed phase function. Under suitable assumptions, we derive a higher-order asymptotic expansion with an error estimate, generalizing some previous results including Laplace's method. The key points of the proof are a precise asymptotic analysis based on a lot of detailed Taylor expansions, and a careful consideration of the effects of the perturbations on the Hessian matrix of the phase function. + oai:arXiv.org:2504.01310v3 + math.CA + math.PR + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Yanbo Zhang, Yaojun Chen + Ikki Fukuda, Yoshiki Kagaya, Yuki Ueda - Auslander regularity of completed rings of $p$-adic differential operators - https://arxiv.org/abs/2505.08001 - arXiv:2505.08001v2 Announce Type: replace -Abstract: We prove that any smooth rigid analytic variety $X$ admits an affinoid covering $\{U_i\}$ such that the Banach algebras involved in the Fr\'echet--Stein presentation of the completed ring of differential operators D-cap$(U_i)$ are Auslander regular for each $i$. We use this result to prove projection formulae and adjunction results for coadmissible D-cap-modules. - oai:arXiv.org:2505.08001v2 - math.NT - math.RA - math.RT - Wed, 10 Dec 2025 00:00:00 -0500 + Sobolev-Poincar\'e inequalities for piecewise $W^{1,p}$ functions over general polytopic meshes + https://arxiv.org/abs/2504.03449 + arXiv:2504.03449v2 Announce Type: replace +Abstract: We establish Sobolev-Poincar\'e inequalities for piecewise $W^{1,p}$ functions over families of fairly general polytopic (thence also shape-regular simplicial and Cartesian) meshes in any dimension; amongst others, they cover the case of standard Poincar\'e inequalities for piecewise $W^{1,p}$ functions and can be useful in the analysis of nonconforming finite element discretizations of nonlinear problems. Crucial tools in their derivation are novel Sobolev-trace inequalities and Babu\v{s}ka-Aziz inequalities with mixed boundary conditions. We provide estimates with constants having an explicit dependence on the geometric properties of the domain and the underlying family of polytopic meshes. + oai:arXiv.org:2504.03449v2 + math.NA + cs.NA + Thu, 11 Dec 2025 00:00:00 -0500 replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Andreas Bode + http://creativecommons.org/licenses/by/4.0/ + Michele Botti, Lorenzo Mascotto - A new bijective proof of the $q$-Pfaff--Saalsch\"utz identity with applications to quantum groups - https://arxiv.org/abs/2505.08422 - arXiv:2505.08422v2 Announce Type: replace -Abstract: We present a combinatorial proof of the $q$-Pfaff--Saalsch\"utz identity by a composition of explicit bijections, in which $q$-binomial coefficients are interpreted as counting subspaces of $\mathbb{F}_q$-vector spaces. As a corollary, we obtain a new multiplication rule for quantum binomial coefficients and hence a new presentation of Lusztig's integral form $\mathcal{U}_{\mathbb{Z}[q, q^{-1}]}(\mathfrak{sl}_2)$ of the Cartan subalgebra of the quantum group $\mathcal{U}_q(\mathfrak{sl}_2)$. - oai:arXiv.org:2505.08422v2 - math.CO - math.QA - Wed, 10 Dec 2025 00:00:00 -0500 + The Monge-Amp\`ere system in dimension two is fully flexible in codimension two + https://arxiv.org/abs/2504.03582 + arXiv:2504.03582v2 Announce Type: replace +Abstract: We prove that every $\mathcal{C}^1(\bar\omega)$-regular subsolution of the Monge-Amp\`ere system posed on a $2$-dimensional domain $\omega$ and with target codimension $2$, can be uniformly approximated by its exact solutions with regularity $\mathcal{C}^{1,\alpha}(\bar\omega)$ for any $\alpha<\min\{1, \frac{s+\beta}{2}\}$, where $\mathcal{C}^{s,\beta}$ is the assumed regularity of the system's right hand side. This result suggests the full flexibility of Poznyak's theorem for isometric immersions of $2$d Riemannian manifolds into $\mathbb{R}^4$, and asserts it in the parallel setting of the Monge-Amp\`ere system. + oai:arXiv.org:2504.03582v2 + math.AP + Thu, 11 Dec 2025 00:00:00 -0500 replace - http://creativecommons.org/licenses/by-nc-nd/4.0/ - \'Alvaro Guti\'errez, \'Alvaro L. Mart\'inez, Micha{\l} Szwej, Mark Wildon + http://creativecommons.org/licenses/by/4.0/ + Dominik Inauen, Marta Lewicka - Minimal dispersion on the sphere - https://arxiv.org/abs/2505.10929 - arXiv:2505.10929v2 Announce Type: replace -Abstract: The minimal spherical cap dispersion ${\rm disp}_{\mathcal{C}}(n,d)$ is the largest number $\varepsilon\in (0,1]$ such that, for every $n$ points on the $d$-dimensional Euclidean unit sphere $\mathbb{S}^d$, there exists a spherical cap with normalized area $\varepsilon$ not containing any of these points. We study the behavior of ${\rm disp}_{\mathcal{C}}(n,d)$ as $n$ and $d$ grow to infinity. We develop connections to the problems of sphere covering and approximation of the Euclidean unit ball by inscribed polytopes. Existing and new results are presented in a unified way. Upper bounds on ${\rm disp}_{\mathcal{C}}(n,d)$ result from choosing the points independently and uniformly at random and possibly adding some well-separated points to close large gaps. Moreover, we study dispersion with respect to intersections of caps. - oai:arXiv.org:2505.10929v2 - math.MG - cs.NA - math.NA - Wed, 10 Dec 2025 00:00:00 -0500 + On the small boundary property and $\mathcal Z$-absorption + https://arxiv.org/abs/2504.03611 + arXiv:2504.03611v2 Announce Type: replace +Abstract: We introduce the Property (C) for a unital commutative sub-C*-algebra $D$ of a unital C*-algebra $A$, a version of the relative comparison property using almost normalizers. Under the assumption of this property, the $\mathcal Z$-absorption of $A$ is shown to imply the small boundary property of $(D, \mathrm{T}(A)|_D)$, where $A =\mathrm{C}(X) \rtimes \mathbb Z^d $ and $D = \mathrm{C}(X)$. + oai:arXiv.org:2504.03611v2 + math.OA + math.DS + Thu, 11 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - Alexander E. Litvak, Mathias Sonnleitner, Tomasz Szczepanski + George A. Elliott, Zhuang Niu - Cell structure of bipartite mediangle graphs - https://arxiv.org/abs/2505.23293 - arXiv:2505.23293v2 Announce Type: replace -Abstract: Genevois introduced and investigated mediangle graphs as a common generalization of median graphs (1-sekeleta of CAT(0) cube complexes) and Coxeter graphs (Cayley graphs of Coxeter systems) and studied groups acting on them. He asked if mediangle graphs can be endowed with the structure of a contractible cell complex. We answer this in the affirmative by proving that bipartite mediangle graphs are tope graphs of finitary Complexes of Oriented Matroids (COMs). We also show that the oriented matroids (OMs) constituting the cells of COMs arising from bipartite mediangle graphs are exactly the simplicial OMs. - oai:arXiv.org:2505.23293v2 + Paper BOAT + https://arxiv.org/abs/2504.04489 + arXiv:2504.04489v3 Announce Type: replace +Abstract: We derive a formula for computing the size of lower Bruhat intervals for elements in the dominant cone of an affine Weyl group of type $A$. This enumeration problem is reduced to counting lattice points in certain polyhedra. Our main tool is a decomposition -- or tiling -- of each interval into smaller, combinatorially tractable pieces, which we call paper boats. We also conjecture a generalization of this formula to all affine Weyl groups, restricted to elements in the lowest two-sided Kazhdan-Lusztig cell, which contains almost all of the elements. + oai:arXiv.org:2504.04489v3 math.CO math.GR - math.MG - Wed, 10 Dec 2025 00:00:00 -0500 + math.RT + Thu, 11 Dec 2025 00:00:00 -0500 replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Victor Chepoi, Kolja Knauer + http://creativecommons.org/licenses/by/4.0/ + Federico Castillo, Damian de la Fuente, Nicolas Libedinsky, David Plaza - Twisted Graded Categories - https://arxiv.org/abs/2506.11240 - arXiv:2506.11240v3 Announce Type: replace -Abstract: Given a presentably symmetric monoidal $\infty$-category $\mathcal{C}$ and an $\mathbb{E}_{\infty}$-monoid $M$, we introduce and classify twisted graded categories, which generalize the Day convolution structure on $\mathrm{Fun}(M, \mathcal{C})$. These are characterized by a braiding encoded in symmetric group actions on tensor powers, whose character we show depends only on the $\mathbb{T}$-equivariant monoidal dimension. We analyze the $\mathbb{T}$-action on the dimension of invertible objects and identify it with the $\mathbb{T}$-transfer map. Finally, we compute braiding characters in examples arising from higher cyclotomic extensions, such as the $(\mathbb{S}, n+1)$-oriented extension of $\mathrm{Mod}_{En}^{\wedge}$ at all primes and heights, and of the cyclotomic closure of $\mathrm{Vect}^n$ at low heights. - oai:arXiv.org:2506.11240v3 - math.AT + Day algebras + https://arxiv.org/abs/2504.06200 + arXiv:2504.06200v2 Announce Type: replace +Abstract: In this paper we show that the Day monoidal product generalises in a straightforward way to other algebraic constructions and partial algebraic constructions on categories. This generalisation was motivated by its applications in logic, for example in hybrid and separation logic. We use the description of the Day monoidal product using profunctors to show that the definition generalises to an extension of an arbitrary algebraic structure on a category to a pseudo-algebraic structure on a functor category. We provide two further extensions. First we consider the case where some of the operations on the category are partial, and second we show that the resulting operations on the functor category have adjoints (they are residuated). + oai:arXiv.org:2504.06200v2 math.CT - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 + replace + http://creativecommons.org/licenses/by/4.0/ + Edmund Robinson, Joshua Wrigley + + + Local Convergence Behavior of Extended LOBPCG for Computing Eigenvalues of Hermitian Matrices + https://arxiv.org/abs/2505.08218 + arXiv:2505.08218v3 Announce Type: replace +Abstract: This paper provides a comprehensive and detailed analysis of the local convergence behavior of an extended variation of the locally optimal preconditioned conjugate gradient method (LOBPCG) for computing the extreme eigenvalue of a Hermitian matrix. The convergence rates derived in this work are either obtained for the first time or sharper than those previously established, including those in Ovtchinnikov's work ({\em SIAM J. Numer. Anal.}, 46(5):2567--2592, 2008). The study also extends to generalized problems, including Hermitian matrix polynomials that admit an extended form of the Rayleigh quotient. The new approach used to obtain these rates may also serve as a valuable tool for the convergence analysis of other gradient-type optimization methods. + oai:arXiv.org:2505.08218v3 + math.NA + cs.NA + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Shai Keidar, Shaul Ragimov + Zhechen Shen, Xin Liang - Conley-Zehnder Indices of Spatial Rotating Kepler Problem - https://arxiv.org/abs/2506.14325 - arXiv:2506.14325v2 Announce Type: replace -Abstract: We study periodic orbits in the spatial rotating Kepler problem from a symplectic-topological perspective. Our first main result provides a complete classification of these orbits via a natural parametrization of the space of Kepler orbits, using angular momentum and the Laplace-Runge-Lenz vector. We then compute the Conley-Zehnder indices of non-degenerate orbits and the Robbin-Salamon indices of degenerate families, establishing their contributions to symplectic homology via the Morse-Bott spectral sequence. To address coordinate degeneracies in the spatial setting, we introduce a new coordinate system based on the Laplace-Runge-Lenz vector. These results offer a full symplectic-topological profile of the three-dimensional rotating Kepler problem and connect it to generators of symplectic homology. - oai:arXiv.org:2506.14325v2 - math.SG - math.DS - Wed, 10 Dec 2025 00:00:00 -0500 + Brackets in multicontact geometry and multisymplectization + https://arxiv.org/abs/2505.13224 + arXiv:2505.13224v2 Announce Type: replace +Abstract: In this paper we introduce a graded bracket of forms on multicontact manifolds. This bracket satisfies a graded Jacobi identity as well as two different versions of the Leibniz rule, one of them being a weak Leibniz rule, extending the well-known notions in contact geometry. In addition, we develop the multisymplectization of multicontact structures to relate these brackets to the ones present in multisymplectic geometry and obtain the field equations in an abstract context. The Jacobi bracket also permits to study the evolution of observables and study the dissipation phenomena, which we also address. Finally, we apply the results to classical dissipative field theories. + oai:arXiv.org:2505.13224v2 + math.DG + math-ph + math.MP + Thu, 11 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - Dongho Lee + Manuel de Le\'on, Rub\'en Izquierdo-L\'opez, Xavier Rivas - Disentangling tensor product structures - https://arxiv.org/abs/2506.21173 - arXiv:2506.21173v2 Announce Type: replace -Abstract: As a contribution to the field of quantum mereology, we study how a change of tensor product structure in a finite-dimensional Hilbert space affects its entanglement properties. In particular, we ask whether, given a time-evolving state, there exists a tensor product structure in which no entanglement is generated. We give a concrete, constructive example of disentangling tensor product structure in the case of a C-NOT gate evolution between two qbits, before showing that this cannot be achieved for most time-evolving quantum states. - oai:arXiv.org:2506.21173v2 + Asymptotics of the spectral data of perturbed Stark operators in the half-line with mixed boundary conditions + https://arxiv.org/abs/2505.15943 + arXiv:2505.15943v4 Announce Type: replace +Abstract: We obtain sharp asymptotic formulas for the eigenvalues and norming constants of Sturm-Liouville operators associated with the differential expression \[ -\frac{d^2}{dx^2} + x + q(x), \quad x\in [0,\infty), \] together with the boundary condition $\varphi'(0) - b\varphi(0) =0$, $b\in\mathbb{R}$, where \[ q\in \left\{ p\in L^2_{\mathbb{R}}(\mathbb{R}_+,(1+x)^r dx) : p'\in L^2_{\mathbb{R}}(\mathbb{R}_+,(1+x)^r dx)\right\} \] with $r>1$. + oai:arXiv.org:2505.15943v4 + math.SP math-ph math.MP - quant-ph - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 replace - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Antoine Soulas + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Julio H. Toloza, Alfredo Uribe - Generating systems, generalized Thomsen collections and derived categories of toric varieties - https://arxiv.org/abs/2506.23531 - arXiv:2506.23531v3 Announce Type: replace -Abstract: Bondal claims that for a smooth toric variety $X$, its bounded derived category of coherent sheaves $D_{c}^{b}(X)$ is generated by the Thomsen collection $T(X)$ of line bundles obtained as direct summands of the pushforward of $\mathcal{O}_{X}$ along a Frobenius map with sufficiently divisible degree. The claim is confirmed recently. In this article, we consider a generalized Thomsen collection of line bundles $T(X,D)$ with a $\mathbb{Q}$-divisor $D$ as an auxiliary input, which recovers Thomsen's oringinal collection by setting $D=0$. We introduce the notion of a generating system and prove a theorem on the generation of $\mathcal{O}_{X}$ using many line bundles arising from the generating system. As an application, we verify Bondal's claim for some toric varieties, using a different argument from existing works. - oai:arXiv.org:2506.23531v3 - math.AG - Wed, 10 Dec 2025 00:00:00 -0500 + Open interacting particle systems and Ising measures + https://arxiv.org/abs/2505.16701 + arXiv:2505.16701v2 Announce Type: replace +Abstract: We first survey some open questions concerning stochastic interacting particle systems with open boundaries. Then an asymmetric exclusion process with open boundaries that generalizes the lattice gas model of Katz, Lebowitz, and Spohn (KLS) is introduced and invariance of the one-dimensional Ising measure is proved. The stationary current is computed in explicit form and is shown to exhibit current reversal at some density. Based on the extremal-current principle for one-dimensional driven diffusive systems with one conservation law, the phase diagram for boundary-induced phase transitions is conjectured for this case. There are two extremal-current phases, unlike in the conventional open asymmetric simple exclusion process, which exhibits only one extremal-current phase or the previously considered conventional open KLS model with one or three extremal-current phases. + oai:arXiv.org:2505.16701v2 + math.PR + cond-mat.stat-mech + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Xiaodong Yi + Ngo P. N. Ngoc, Gunter M. Sch\"utz - Resnikoff silver numbers and tilings of the half-line (Dedicated to the memory of H.L.Resnikoff) - https://arxiv.org/abs/2507.03053 - arXiv:2507.03053v2 Announce Type: replace -Abstract: Building on work by H.L.Resnikoff we consider (Resnikoff) silver numbers, which generalize the familiar golden number. By definition, a silver number is the largest positive root of a certain polynomial called silver polynomial. In turn, a corresponding companion matrix of a silver polynomial gives rise to a well known construction of inflationary tilings of the (non-negative) real half-line, via an iteration of inflation and substitution. Resnikoff noted for the golden number $\phi$ that this tiling corresponds to the set of what he called $\phi$-integers. We generalize this result for a special class of silver numbers, the distinguished silver numbers, by showing that the integers for a distinguished silver number give rise to a tiling, of which we provide a precise description. For the general problem, whether the integers for an arbitrary silver number give rise to a tiling, we cannot give a general answer, but we show that tilings are obtained if and only if the differences of silver integers satisfy a (rather weak looking) non-accumulation condition. If tilings of this type exist for certain (necessarily non-distinguished) silver numbers, they would seem to form a class of inflationary tilings that differs from those obtained by inflation and substitution. In an Appendix we recall necessary notions and -- mostly known -- results, including the inflation-substitution construction principle for (one dimensional) inflationary tilings, in an elementary manner. For the readers' convenience we also collect the pertinent facts about non-negative matrices, thus the construction is accessible with only basic prerequisites from linear algebra and analysis. Finally, in our setting we give a detailed proof of a non-periodicity result that goes back to Penrose. - oai:arXiv.org:2507.03053v2 + Boundedness criteria for real quivers of rank 3 + https://arxiv.org/abs/2505.16955 + arXiv:2505.16955v2 Announce Type: replace +Abstract: We study the boundedness of a mutation class for quivers with real weights. The main result is a characterization of bounded mutation classes for real quivers of rank 3. + oai:arXiv.org:2505.16955v2 math.CO - Wed, 10 Dec 2025 00:00:00 -0500 + math.DS + math.RT + Thu, 11 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - Josef F. Dorfmeister, Sebastian Walcher - - - Mathematical Analysis of Subwavelength Resonance in Elastic Metascreen - https://arxiv.org/abs/2507.07837 - arXiv:2507.07837v2 Announce Type: replace -Abstract: The aim of this paper is to provide a comprehensive and mathematically rigorous analysis on determining the existence of subwavelength resonance in elastic metascreen and resonance frequency calculation based on asymptotic analysis of quasi-periodic layer potential operators. An elastic metascreen is a thin sheet with subwavelength structures, which nevertheless has a significant effect on elastic wave propagation at specific frequencies. Periodic subwavelength elastic scatterers positioned on a reflective plane are considered in this paper. Firstly an explicit formula of quasi-periodic Green's function of Lam\'{e} system with Dirichlet boundary condition is derived for the first time. The subsequent discussion is twofold. In the first part where the shear modulus of scatterers is assumed to tend to infinity, the subwavelength resonance frequencies are given and approximated field inside inclusions and far-away from metascreen are calculated to demonstrate the dramatic change of scattered field due to subwavelength resonance. In the second part where the shear modulus of background is assumed to go to infinity, the absence of subwavelength resonance is proved. Without imposing conditions on the material parameters, the discussion in this paper provides the necessary condition for the occurrence of subwavelength resonance. - oai:arXiv.org:2507.07837v2 - math.AP - Wed, 10 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Wei Wu, Youzi He + Roger Casals, Kenton Ke - Generalized $\eta -$Ricci solitons on LP-Sasakian manifolds admitting the general connection - https://arxiv.org/abs/2507.09954 - arXiv:2507.09954v3 Announce Type: replace -Abstract: We study the properties of LP-Sasakian manifolds endowed with generalized $% \eta -$Ricci solitons associated to the general connection. Finally, the existence of such solitons on a 4-dimensional LP-Sasakian manifold is proved by constructing a non-trivial example. - oai:arXiv.org:2507.09954v3 - math.DG - Wed, 10 Dec 2025 00:00:00 -0500 + Generalized Eshelby's inclusion and inhomogeneity problems for transient heat transfer + https://arxiv.org/abs/2506.16498 + arXiv:2506.16498v3 Announce Type: replace +Abstract: Eshelby's inclusion problems have been generalized to arbitrary shape of polygonal, polyhedral, and ellipsoidal inclusions embedded in an infinite isotropic domain under transient heat transfer, and Eshelby's tensors have been analytically derived to evaluate disturbed thermal fields caused by inclusions with a polynomial-form eigen-field. Transformed coordinates are applied to arbitrarily shaped inclusions for domain integrals of transient fundamental solutions. This formulation is for general transient heat transfer, and it can recover classic Eshelby's tensor for the ellipsoidal subdomain with explicit expression for the spherical domain in the steady state, Michelitsch's solution in the harmonic state, and recent solution in the transient state. The formulae for a polyhedral inclusion is verified by comparison to closed-form solutions of a spherical inclusion when the sphere is divided into many polyhedrons. The discontinuity of domain integrals for Eshelby's tensor are investigated the temporal effects are elaborated. The generalized formulation for Eshelby's problems enables the simulation and modeling of particulate composites containing inhomogeneities of various shapes for steady-state, harmonic and transient heat transfer in both two- and three-dimensional space through the equivalent inclusion method. + oai:arXiv.org:2506.16498v3 + math-ph + math.MP + Thu, 11 Dec 2025 00:00:00 -0500 replace - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Murat Altunba\c{s}, Ay\c{s}e Karanl{\i}k Akp{\i}nar + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + 10.1016/j.ijsolstr.2025.113725 + International Journal of Solids and Structures, 2026, Volume 325, 15 January, 113725 + Chunlin Wu, Zhenhua Wei, Huiming Yin - Ramsey numbers for sparse graphs versus path or cycle - https://arxiv.org/abs/2507.11835 - arXiv:2507.11835v4 Announce Type: replace -Abstract: The Ramsey numbers $r(G, C_k)$ and $r(G, P_k)$ involving cycles and paths are fundamental objects in extremal combinatorics. We substantially improve the seminal 1982 result of Burr, Erd\H{o}s, Faudree, Rousseau, and Schelp by weakening the key conditions required on the graph $G$. Our improvements are mainly driven by a novel reconstruction of the end-edge matching and an enhancement of the dichotomy lemma of Burr et al. (1982). - For odd cycles $C_k$ ($k\ge3$), we prove that $r(G, C_k) = 2n-1$ holds for connected $n$-vertex graphs $G$ under two density regimes: either $n = \Omega(k^2)$ with $e(G) \le (1 + O(1/k^2)) n$, or $n = \Omega(k)$ with minimum degree $\delta(G)\ge2$ and $e(G) \le (1 + O(1/k^2)) n$. - For paths $P_k$ ($k\ge2$), we prove that $r(G, P_k) = \max\{ n + \lfloor k/2\rfloor - 1, n + k - 2 - \alpha' - \gamma \},$ under analogous relaxed conditions: either $n = \Omega(k^2)$ with $e(G) \le (1 + O(1/k^2)) n$, or $n = \Omega(k)$ with $\delta(G)\ge2$ and $e(G) \le (1 + O(1/k)) n$. Here $\alpha'$ is the independence number of an appropriate subgraph of $G$ and $\gamma=0$ if $k-1$ divides $n+k-3-\alpha'$, and $\gamma=1$ otherwise. - Consequently, our results unify and recover the classical exact results $r(C_n,C_k)=2n-1$ for odd $k\ge3$ and $n=\Omega(k)$, and $r(P_n,P_k)=r(C_n,P_k)=n+\left\lfloor\frac{k}{2}\right\rfloor-1$ for $k\ge2$ and $n=\Omega(k)$. In these corollaries, the requirement $n=\Omega(k)$ is tight up to a constant factor, and the quadratic condition $n=\Omega(k^2)$ for general sparse graphs highlights the significant effect of leaves. - oai:arXiv.org:2507.11835v4 - math.CO - Wed, 10 Dec 2025 00:00:00 -0500 + A parametric tensor ROM for the shallow water dam break problem + https://arxiv.org/abs/2506.20007 + arXiv:2506.20007v2 Announce Type: replace +Abstract: We develop a variant of a tensor reduced-order model (tROM) for the parameterized shallow-water dam-break problem. This hyperbolic system presents multiple challenges for model reduction, including a slow decay of the Kolmogorov $N$-width of the solution manifold, shock formation, and the loss of smooth solution dependence on parameters. These issues limit the performance of traditional Proper Orthogonal Decomposition based ROMs. Our tROM approach, based on a low-rank tensor decomposition, builds a parameter-to-solution map from high-fidelity snapshots and constructs localized reduced bases via a local POD procedure. We apply this method to 1D dry-bed and wet-bed problems and 2D wet-bed problem with topography and bottom friction, showing that the non-interpolatory variant of the tROM, combined with Chebyshev sampling near critical parameter values, effectively captures parameter-dependent behavior and significantly outperforms standard POD-ROMs. This is especially evident in the wet-bed case, where POD-ROMs exhibit poor resolution of shock waves and spurious oscillations. + oai:arXiv.org:2506.20007v2 + math.NA + cs.NA + physics.flu-dyn + Thu, 11 Dec 2025 00:00:00 -0500 replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Chunchao Fan, Qizhong Lin + http://creativecommons.org/licenses/by-sa/4.0/ + Md Rezwan Bin Mizan, Maxim Olshanskii, Ilya Timofeyev - Optimal boundary regularity for mixed local and nonlocal equations - https://arxiv.org/abs/2507.13711 - arXiv:2507.13711v2 Announce Type: replace -Abstract: We provide sharp boundary regularity estimates for solutions to elliptic equations driven by an integro-differential operator obtained as the sum of a Laplacian with a nonlocal operator generalizing a fractional Laplacian. - Our approach makes use of weighted H\"older spaces as well as regularity estimates for the Laplacian in this context and a fixed-point argument. - We show the optimality of the obtained estimates by means of a counterexample that we have striven to keep as explicit as possible. - oai:arXiv.org:2507.13711v2 - math.AP - Wed, 10 Dec 2025 00:00:00 -0500 + Semiadditive Alternating Powers and Twisted Power Operation + https://arxiv.org/abs/2507.04124 + arXiv:2507.04124v2 Announce Type: replace +Abstract: We study a class of representations of symmetric groups in higher semiadditive categories. For these representations in $\mathrm{Mod}^{\wedge}_{E_n}$, the transchromatic character of Hopkins--Kuhn--Ravenel and Stapleton is recovered as a sequence of monoidal characters on suitable categorifications, giving an explicit algorithm for its computation, and relating it to the iterated monoidal character in $(\infty,n)$-categories. These representations also give rise to notions of alternating powers and power operations in semiadditive categories, extending the classical alternating powers and $\lambda$-operations in $\mathrm{K}$-theory. We provide explicit computations in both the chromatic and higher categorical settings at low heights. + oai:arXiv.org:2507.04124v2 + math.AT + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Nicola Abatangelo, Elisa Affili, Matteo Cozzi + Shai Keidar, Shaul Ragimov - Towards the classification of maximum scattered linear sets of $\mathrm{PG}(1,q^5)$ - https://arxiv.org/abs/2507.23409 - arXiv:2507.23409v2 Announce Type: replace -Abstract: Every maximum scattered linear set in $\mathrm{PG}(1,q^5)$ is the projection of an $\mathbb{F}_q$-subgeometry $\Sigma$ of $\mathrm{PG}(4,q^5)$ from a plane $\Gamma$ external to the secant variety to $\Sigma$. The pair $(\Gamma,\Sigma)$ will be called a projecting configuration for the linear set. The projecting configurations for the only known maximum scattered linear sets in $\mathrm{PG}(1,q^5)$, namely those of pseudoregulus and LP type, have been characterized in the literature by B. Csajb\'{o}k, C. Zanella in 2016 and by C. Zanella, F. Zullo in 2020. Let $(\Gamma,\Sigma)$ be a projecting configuration for a maximum scattered linear set in $\mathrm{PG}(1,q^5)$, let $\sigma$ be a generator of $\mathbb{G}=\mathrm{P}\Gamma \mathrm{L}(5,q^5)_\Sigma$, and $A=\Gamma\cap\Gamma^{\sigma^4}$, $B=\Gamma\cap\Gamma^{\sigma^3}$. If $A$ and $B$ are not both points, then the projected linear set is of pseudoregulus type. Then, suppose that they are points. The rank of a point $X$ is the vectorial dimension of the span of the orbit of $X$ under the action of $\mathbb{G}$. In this paper, by investigating the geometric properties of projecting configurations, it is proved that if at least one of the points $A$ and $B$ has rank 5, the associated maximum scattered linear set must be of LP type. Then, if a maximum scattered linear set of a new type exists, it must be such that $\mathrm{rk} A=\mathrm{rk} B=4$. In this paper we derive two possible polynomial forms that such a linear set must have. An exhaustive analysis by computer shows that for $q\leq 25$, no new maximum scattered linear set exists. - oai:arXiv.org:2507.23409v2 + Finite approximation of free groups II: the Theorems of Ash, Herwig-Lascar and Ribes-Zalesskii -- revisited and strengthened + https://arxiv.org/abs/2507.11685 + arXiv:2507.11685v2 Announce Type: replace +Abstract: Relations and interactions between the theorems of Ash, Herwig-Lascar and Ribes-Zalesskii are discussed and it is shown that these three theorems are equivalent in the sense that each of them can be derived from each other one. Some strengthening of these theorems that can be obtained by use of the groups provided by the third author's construction are also considered. + oai:arXiv.org:2507.11685v2 + math.GR math.CO - Wed, 10 Dec 2025 00:00:00 -0500 + math.LO + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Stefano Lia, Giovanni Longobardi, Corrado Zanella + K. Auinger, J. Bitterlich, M. Otto - Rational complex Bezier curves - https://arxiv.org/abs/2507.23485 - arXiv:2507.23485v3 Announce Type: replace -Abstract: In this paper we develop the formalism of rational complex Bezier curves. This framework is a simple extension of the CAD paradigm, since it describes arc of curves in terms of control polygons and weights, which are extended to complex values. One of the major advantages of this extension is that we may make use of two different groups of projective transformations. Besides the group of projective transformations of the real plane, we have the group of complex projective transformations. This allows us to apply useful transformations like the geometric inversion to curves in design. In addition to this, the use of the complex formulation allows to lower the degree of the curves in some cases. This can be checked using the resultant of two polynomials and provides a simple formula for determining whether a rational cubic curve is a conic or not. Examples of application of the formalism to classical curves are included. - oai:arXiv.org:2507.23485v3 + Quantifying Ocular Surface Changes with Contact Lens Wear + https://arxiv.org/abs/2507.13589 + arXiv:2507.13589v2 Announce Type: replace +Abstract: Over 140 million people worldwide and over 45 million people in the United States wear contact lenses; it is estimated that 12%-27.4% contact lens users stop wearing them due to discomfort. Contact lens mechanical interactions with the ocular surface have been found to affect the ocular surface itself. These mechanical interactions are difficult to measure and calculate in a clinical setting, and the research in this field is limited. This paper presents the first mathematical model that captures the interactions between the contact lens and the open eye, where the contact lens configuration, the contact lens suction pressure, and the deformed ocular shape are all emergent properties of the model. The non-linear coupling between the contact lens and the eye is achieved by assuming that the suction pressure under the lens is applied directly to the ocular surface through the post-lens tear film layer. The contact lens mechanics are modeled using a previous published model. We consider homogeneous and heterogeneous linear elastic eye models, different ocular shapes, different lens shapes and thickness profiles, and extract lens deformations, suction pressure profiles, and ocular deformations and stresses for all the considered scenarios. The model predicts higher ocular deformations and stresses at the center of the eye and in the limbal/scleral regions. Accounting for heterogeneous material eye parameters increases the magnitude of such deformations and stresses. The ocular displacements and stresses non-linearly increase as we increase the stiffness of the contact lens. Inserting a steeper contact lens on the eye results in a reduction of the ocular displacement at the center of the eye and a larger displacement at the edge of the contact lens. The model predictions are compared with experimental data and previously developed mathematical models. + oai:arXiv.org:2507.13589v2 math.NA - cs.GR cs.NA - Wed, 10 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by-nc-nd/4.0/ - A. Canton, L. Fernandez-Jambrina, M. J. Vazquez-Gallo - - - Branched Covers of Open Manifolds - https://arxiv.org/abs/2508.09842 - arXiv:2508.09842v2 Announce Type: replace -Abstract: For $m=2$ and $m=3$ we prove that any connected, oriented, open manifold $M^m$ admits a simple branched covering map over $\mathbb{R}^m$. When $M$ has $k$ ends and $k$ is finite, the degree of the cover can be taken to be $mk$. Regardless of the number of ends, $M$ admits a branched covering map of countably infinite degree over $\mathbb{R}^m$. We also investigate which compact manifolds are universal bases, that is, are branch covered by all compact manifolds in the same dimension. - oai:arXiv.org:2508.09842v2 - math.GT - Wed, 10 Dec 2025 00:00:00 -0500 + physics.bio-ph + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Mark Hughes, Alexandra Kjuchukova, Maggie Miller + 10.3934/mbe.2026008 + Mathematical Biosciences and Engineering (2026), Volume 23, Issue 1: 172-209 + Lucia Carichino, Kara L. Maki, David S. Ross, Riley K. Supple, Evan Rysdam - Line bundles and exact sequences for the ideal class group and the Picard group - https://arxiv.org/abs/2508.19889 - arXiv:2508.19889v2 Announce Type: replace -Abstract: For any extension of commutative rings $A\subseteq B$ we first naturally define a group $\Cl(A,B)$, that we call the ideal class group of this extension (we will see that both the classical ideal class group and, surprisingly, the Picard group are special cases of this structure), then, as a first main result, we obtain the following exact sequence of Abelian groups: ... - oai:arXiv.org:2508.19889v2 - math.AC - math.AG - Wed, 10 Dec 2025 00:00:00 -0500 + Adjoint path-kernel method for backpropagation and data assimilation in unstable diffusions + https://arxiv.org/abs/2507.21497 + arXiv:2507.21497v2 Announce Type: replace +Abstract: We derive the adjoint path-kernel method for computing parameter-gradients (linear responses) of SDEs. Its cost is almost independent of the number of parameters, and it works for non-hyperbolic systems with parameter-controlled multiplicative noise. With this new formula, we extend the conventional backpropagation method to settings with gradient explosion, and demonstrate it on the 40-dimensional Lorenz 96 system. + Moreover, we consider a difficult version of the 4D-Var data assimilation problem where (1) the deterministic part of the model is chaotic, (2) the loss is a single long-time functional accounting for discrepancies in both the observations and the dynamics, (3) some parameters in the dynamics are unknown, and (4) some coordinates of the states cannot be observed, and cannot be reasonably inferred from other coordinates within a short time. We model the correction term at each time-step separately as a parameterized function of the random state. With our new tool, we can run stochastic gradient descent to find the path and parameters that best match the low-dimensional observation data. We demonstrate this on the 10D Lorenz-96 system with 8D observations. + oai:arXiv.org:2507.21497v2 + math.PR + math.DS + physics.comp-ph + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Abolfazl Tarizadeh + Angxiu Ni - Universal Representation of Generalized Convex Functions and their Gradients - https://arxiv.org/abs/2509.04477 - arXiv:2509.04477v2 Announce Type: replace -Abstract: A wide range of optimization problems can often be written in terms of generalized convex functions (GCFs). When this structure is present, it can convert certain nested bilevel objectives into single-level problems amenable to standard first-order optimization methods. We provide a new differentiable layer with a convex parameter space and show (Theorems 5.1 and 5.2) that it and its gradient are universal approximators for GCFs and their gradients. We demonstrate how this parameterization can be leveraged in practice by (i) learning optimal transport maps with general cost functions and (ii) learning optimal auctions of multiple goods. In both these cases, we show how our layer can be used to convert the existing bilevel or min-max formulations into single-level problems that can be solved efficiently with first-order methods. - oai:arXiv.org:2509.04477v2 - math.OC - cs.LG - Wed, 10 Dec 2025 00:00:00 -0500 + Transient thermal analysis of a bi-layered composites with the dual-reciprocity inclusion-based boundary element method + https://arxiv.org/abs/2508.02683 + arXiv:2508.02683v2 Announce Type: replace +Abstract: This paper proposes a single-domain dual-reciprocity inclusion-based boundary element method (DR-iBEM) for a three-dimensional fully bonded bi-layered composite embedded with ellipsoidal inhomogeneities under transient/harmonic thermal loads. The heat equation is interpreted as a static one containing time- and frequency-dependent nonhomogeneous source terms, which is similar to eigen-fields but is transformed into a boundary integral by the dual-reciprocity method. Using the steady-state bimaterial Green's function, boundary integral equations are proposed to take into account continuity conditions of temperature and heat flux, which avoids setting up any continuity equations at the bimaterial interface. Eigen-temperature-gradients and eigen-heat-source are introduced to simulate the material mismatch in thermal conductivity and heat capacity, respectively. The DR-iBEM algorithm is particularly suitable for investigating the transient and harmonic thermal behaviors of bi-layered composites and is verified by the finite element method (FEM). Numerical comparison with the FEM demonstrates its robustness and accuracy. The method has been applied to a functionally graded material as a bimaterial with graded particle distributions, where particle size and gradation effects are evaluated. + oai:arXiv.org:2508.02683v2 + math.NA + cs.NA + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Moeen Nehzati + 10.1016/j.ijheatmasstransfer.2025.128116 + International Journal of Heat and Mass Transfer, 2026, volume 256, part 3, 128116 + Chunlin Wu, Liangliang Zhang, Tengxiang Wang, Huiming Yin - Knowledge Distillation Driven Semantic NOMA for Image Transmission with Diffusion Model - https://arxiv.org/abs/2509.07363 - arXiv:2509.07363v2 Announce Type: replace -Abstract: As a promising 6G enabler beyond conventional bit-level transmission, semantic communication can considerably reduce required bandwidth resources, while its combination with multiple access requires further exploration. This paper proposes a knowledge distillation-driven and diffusion-enhanced (KDD) semantic non-orthogonal multiple access (NOMA), named KDD-SemNOMA, for multi-user uplink wireless image transmission. Specifically, to ensure robust feature transmission across diverse transmission conditions, we firstly develop a ConvNeXt-based deep joint source and channel coding architecture with enhanced adaptive feature module. This module incorporates signal-to-noise ratio and channel state information to dynamically adapt to additive white Gaussian noise and Rayleigh fading channels. Furthermore, to improve image restoration quality without inference overhead, we introduce a two-stage knowledge distillation strategy, i.e., a teacher model, trained on interference-free orthogonal transmission, guides a student model via feature affinity distillation and cross-head prediction distillation. Moreover, a diffusion model-based refinement stage leverages generative priors to transform initial SemNOMA outputs into high-fidelity images with enhanced perceptual quality. Extensive experiments on CIFAR-10 and FFHQ-256 datasets demonstrate superior performance over state-of-the-art methods, delivering satisfactory reconstruction performance even at extremely poor channel conditions. These results highlight the advantages in both pixel-level accuracy and perceptual metrics, effectively mitigating interference and enabling high-quality image recovery. - oai:arXiv.org:2509.07363v2 + Riemann-Roch bases for arbitrary elliptic curve divisors and their application in cryptography + https://arxiv.org/abs/2508.04340 + arXiv:2508.04340v2 Announce Type: replace +Abstract: This paper presents explicit constructions of bases for Riemann-Roch spaces associated with arbitrary divisors on elliptic curves. In the context of algebraic geometry codes, the knowledge of an explicit basis for arbitrary divisors is especially valuable, as it enables efficient code construction. From a cryptographic point of view, codes associated with arbitrary divisors with many points are closer to Goppa codes, making them attractive for embedding in the McEliece cryptosystem. Using the results obtained in this work, it is also possible to efficiently construct quasi-cyclic subfield subcodes of elliptic codes. These codes enable a significant reduction in public key size for the McEliece cryptosystem and, consequently, represent promising candidates for integration into post-quantum code-based schemes. + oai:arXiv.org:2508.04340v2 cs.IT + cs.CR + math.AG math.IT - Wed, 10 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Qifei Wang, Zhen Gao, Shuo Sun, Zhijin Qin, Xiaodong Xu, Meixia Tao - - - Contractive kinetic Langevin samplers beyond global Lipschitz continuity - https://arxiv.org/abs/2509.12031 - arXiv:2509.12031v2 Announce Type: replace -Abstract: In this paper, we examine the problem of sampling from log-concave distributions with (possibly) superlinear gradient growth under kinetic (underdamped) Langevin algorithms. Using a carefully tailored taming scheme, we propose two novel discretizations of the kinetic Langevin SDE, and we show that they are both contractive and satisfy a log-Sobolev inequality. Building on this, we establish a series of non-asymptotic bounds in $2$-Wasserstein distance between the law reached by each algorithm and the underlying target measure. - oai:arXiv.org:2509.12031v2 - math.PR - cs.NA - math.NA - stat.ML - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 replace - http://creativecommons.org/licenses/by/4.0/ - Iosif Lytras, Panayotis Mertikopoulos + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Artyom Kuninets, Ekaterina Malygina - The integral Hasse principle for stacky curves associated to a family of generalized Fermat equations - https://arxiv.org/abs/2509.13248 - arXiv:2509.13248v2 Announce Type: replace -Abstract: We characterize the integral Hasse principle for an infinite family of spherical stacky curves with genus $g\in [2/3,1)$ that are defined using generalized Fermat equations, extending a result of Darmon and Granville. We then apply our methods to find that a positive proportion of curves in our family satisfy the integral Hasse principle. - oai:arXiv.org:2509.13248v2 - math.NT + Lie algebroids, quantum Poisson algebroids, and Lie algebroid connections + https://arxiv.org/abs/2508.05542 + arXiv:2508.05542v2 Announce Type: replace +Abstract: In this paper, we consider Lie algebroids over commutative ringed spaces. Lie algebroids over ringed spaces unify the existing notion of Lie algebroids over smooth manifolds, complex manifolds, analytic spaces, algebraic varieties, and schemes. We show that the universal enveloping algebroid of a Lie algebroid possesses a natural filtration that yields a structure of a sheaf of quantum Poisson algebras. We establish a bijective correspondence between sheaves of quantum Poisson algebras and Lie algebroids. We show that this correspondence leads to an adjunction between the two categories. We discuss this bijective correspondence in particular cases of Lie algebroids over ringed spaces and highlight the subsequent results. To characterize non-flat Lie algebroid connections, we construct a sheaf of twisted universal enveloping algebras for a Lie algebroid using Lie algebroid (hyper) cohomology. We show that our construction yields some of the existing constructions for Lie-Rinehart algebras and holomorphic Lie algebroids. As another application, we study the deformation groupoid of a Lie algebroid using the second hypercohomology of the Lie algebroid. + oai:arXiv.org:2508.05542v2 math.AG - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 replace - http://creativecommons.org/licenses/by/4.0/ - Juanita Duque-Rosero, Christopher Keyes, Andrew Kobin, Manami Roy, Soumya Sankar, Yidi Wang - - - Indoor Fluid Antenna Systems Enabled by Layout-Specific Modeling and Group Relative Policy Optimization - https://arxiv.org/abs/2509.15006 - arXiv:2509.15006v4 Announce Type: replace -Abstract: Fluid antenna system (FAS) revolutionizes wireless communications via utilizing position-flexible antennas that dynamically optimize channel conditions and mitigate multipath fading. This innovation is particularly valuable in indoor environments, in which signal propagation is severely degraded due to structural obstructions and complex multipath reflections. In this paper, we investigate the channel modeling and the joint optimization of antenna positioning, beamforming, and power allocation for indoor FAS. In particular, we propose a layout-specific channel model, and employ the novel group relative policy optimization (GRPO) algorithm for tackling the optimization problem. Compared to the state-of-the-art Sionna model, our model achieves an 83.3% reduction in computation time with an approximately 3 dB increase in root-mean-square error (RMSE). When simplified to a two-ray model, our model allows for a closed-form antenna position solution with near-optimal performance. For the joint optimization problem, our GRPO algorithm outperforms proximal policy optimization (PPO) and other baselines in sum-rate, while requiring only 50.8% computational resources of PPO, thanks to its group advantage estimation. Simulation results show that increasing either the group size or trajectory length in GRPO does not yield significant improvements in sum-rate, suggesting that these parameters can be selected conservatively without sacrificing performance. - oai:arXiv.org:2509.15006v4 - cs.IT - math.IT - Wed, 10 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Tong Zhang, Qianren Li, Shuai Wang, Wanli Ni, Jiliang Zhang, Rui Wang, Kai-Kit Wong, Chan-Byoung Chae + http://creativecommons.org/licenses/by-nc-nd/4.0/ + Satyendra Kumar Mishra, Abhishek Sarkar - On the Semicontinuity of Functionals on Function Spaces - https://arxiv.org/abs/2509.17426 - arXiv:2509.17426v2 Announce Type: replace -Abstract: Results on the upper and lower semicontinuity of functionals defined on spaces of convex and more general functions are established. In particular, the following result is obtained. Let $\phi(v; \cdot)$ be the density of the absolutely continuous part of a Radon measure $\Phi(v; \cdot)$ associated to a function $v\colon X\rightarrow \mathbb{R}$ defined on the topological measure space $(X,\lambda)$. For concave $\zeta\colon [0, \infty)\rightarrow[0,\infty)$ with $\lim_{t\to 0} \zeta(t)=0$ and $\lim_{t\to\infty}\zeta(t)/t= 0$, it is shown that the functional $v \mapsto \int_{X} \zeta(\phi(v;x))d\lambda(x)$ depends upper semicontinuously on $v$. Examples include functional affine surface areas for convex functions. - oai:arXiv.org:2509.17426v2 + The pure $Y=X^{d}$ truncated moment problem + https://arxiv.org/abs/2508.10375 + arXiv:2508.10375v2 Announce Type: replace +Abstract: Let $\beta \equiv\beta^{(2n)}$ be a real bivariate sequence of degree $2n$. We study the existence of representing measures for $\beta$ supported in the curve $y=x^{d}$ ($d\ge 1$) in the case when all column dependence relations in the moment matrix $M_n(\beta)$ are generated by the relation $Y=X^{d}$. We prove that the core variety of $\beta$, $\mathcal{CV}(L_{\beta})$, is nonempty (equivalently, representing measures exist) if and only if $C$, the partially defined core matrix of $\beta$, admits a positive, recursively generated completion $C[A]$. Moreover, $\mathcal{CV}(L_{\beta})$ is the entire curve $y=x^{d}$ if and only if there is a positive definite completion $C[A]$. In the remaining case, if there is a measure, it is unique and finitely atomic. For $d = 3$, we use these results to compute the core variety of $\beta$ and give new characterizations of the existence of representing measures, which complement a result of the first-named author. + oai:arXiv.org:2508.10375v2 math.FA - Wed, 10 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Fernanda M. Ba\^eta, Monika Ludwig - - - Almost disjoint families and some automorphic and injective properties of $\ell_\infty/c_0$ - https://arxiv.org/abs/2509.22376 - arXiv:2509.22376v2 Announce Type: replace -Abstract: Answering questions of A. Avil\'es, F. Cabello S\'anchez, J. Castillo, M. Gonz\'alez and Y. Moreno we show that the following statements are independent of the usual axioms ZFC with arbitrarily large continuum: for every (some) $\omega<\kappa<2^\omega$ - (1) any linear bounded operator $T: c_0(\kappa)\rightarrow\ell_\infty/c_0$ extends to any superspace of $c_0(\kappa)$. - (2) any isomorphism between any two copies of $c_0(\kappa)$ inside $\ell_\infty/c_0$ extends to an automorphism of $\ell_\infty/c_0$. - This contrasts with Boolean, Banach algebraic or isometric levels, where the objects known as Hausdorff gap and Luzin gap witness the failure in ZFC of the corresponding properties for the corresponding structures already at the first uncountable cardinal $\kappa=\omega_1$. In particular, consistently, any two pairwise disjoint families in $\wp(\mathbb N)/Fin$ of the same cardinality $\omega<\kappa<2^\omega$ can be mapped onto each other by a linear automorphism of $\ell_\infty/c_0$ regardless of their different combinatorial, algebraic or topological positions in $\wp(\mathbb N)/Fin$. - Our positive consistency results use a restricted version of Martin's axiom for a partial order that adds an infinite block diagonal matrix of an operator on $\ell_\infty$ which induces an operator on $\ell_\infty/c_0$. The construction of its finite blocks relies on a lemma of Bourgain and Tzafriri on finite dimensional Banach spaces. - Our negative consistency results rely on an analysis of almost disjoint families of $\mathbb N$, the embeddings of $c_0(\kappa)$ into $\ell_\infty/c_0$ they induce and their extensions to $\ell_\infty^c(\kappa)$. - oai:arXiv.org:2509.22376v2 - math.FA - math.LO - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Piotr Koszmider, Ma{\l}gorzata Rojek + Lawrence Fialkow, Alja\v{z} Zalar - Numerical approximations to invariant measures of hybrid stochastic differential equations with superlinear coefficients via the backward Euler-Maruyama method - https://arxiv.org/abs/2509.25799 - arXiv:2509.25799v2 Announce Type: replace -Abstract: For stochastic differential equations (SDEs) with Markovian switching, whose drift and diffusion coefficients are allowed to contain superlinear terms, the backward Euler-Maruyama (BEM) method is proposed to approximate the invariant measure. The existence and uniqueness of the invariant measure of the numerical solution generated by the BEM method is proved. Then the convergence of the numerical invariant measure to its underlying counterpart is shown. Those results obtained in this work release the requirement of the global Lipschitz condition on the diffusion coefficient in [X. Li et al. SIAM J. Numer. Anal. 56(3)(2018), pp. 1435-1455] and can also be regarded as a non-trivial extension of [W. Liu et al. Appl. Numer. Math. 184(2023), pp. 137-150] to the case of hybrid SDEs. - oai:arXiv.org:2509.25799v2 - math.NA - cs.NA - math.PR - Wed, 10 Dec 2025 00:00:00 -0500 + Inexact Zeroth-Order Nonsmooth and Nonconvex Stochastic Composite Optimization and Applications + https://arxiv.org/abs/2508.11519 + arXiv:2508.11519v2 Announce Type: replace +Abstract: In this paper we present an inexact zeroth-order method suitable for the solution nonsmooth and nonconvex stochastic composite optimization problems, in which the objective is split into a real-valued Lipschitz continuous stochastic function and an extended-valued (deterministic) proper, closed, and convex one. The algorithm operates under inexact oracles providing noisy (and biased) stochastic evaluations of the underlying finite-valued part of the objective function. We show that the proposed method converges (non-asymptotically), under very mild assumptions, close to a stationary point of an appropriate surrogate problem which is related (in a precise mathematical sense) to the original one. This, in turn, provides a new notion of approximate stationarity suitable nonsmooth and nonconvex stochastic composite optimization, generalizing conditions used in the available literature. + In light of the generic oracle properties under which the algorithm operates, we showcase the applicability of the approach in a wide range of problems including large classes of two-stage nonconvex stochastic optimization and nonconvex-nonconcave minimax stochastic optimization instances, without requiring convexity of the lower level problems, or even uniqueness of the associated lower level solution maps. We showcase how the developed theory can be applied in each of these cases under general assumptions, providing algorithmic methodologies that go beyond the current state-of-the-art appearing in each respective literature, enabling the solution of problems that are out of reach of currently available methodologies. + oai:arXiv.org:2508.11519v2 + math.OC + Thu, 11 Dec 2025 00:00:00 -0500 replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Wei Liu, Jie Xu + http://creativecommons.org/licenses/by/4.0/ + Spyridon Pougkakiotis, Dionysis Kalogerias - Cohomology of Small Cartesian Closed Categories - https://arxiv.org/abs/2510.00488 - arXiv:2510.00488v2 Announce Type: replace -Abstract: We show the isomorphism between the Quillen cohomology and the Baues-Wirsching cohomology of a cartesian closed category (CCC). This is an extension of the results of Dwyer-Kan for small categories and Jibladze-Pirashvili for small categories with finite products. These results implies that The Quillen cohomology of a CCC C coincides with that of C as a category with finite products, and also that of C as a small category - oai:arXiv.org:2510.00488v2 - math.CT - Wed, 10 Dec 2025 00:00:00 -0500 + Divisibility and Sequence Properties of $\sigma^+$ and $\varphi^+$ + https://arxiv.org/abs/2508.11660 + arXiv:2508.11660v2 Announce Type: replace +Abstract: Inspired by Lehmer's and Deaconescu's conjectures, as well as various analogue problems concerning Euler's totient function $\varphi(n)$, Schemmel's totient function $S_{2}(n)$, Jordan totient function $J_k$, and the unitary totient function $\varphi^{*}(n)$, we investigate analogous divisibility problems involving the functions $\sigma(n)$, $\sigma^{+}(n)$, and $\varphi^{+}(n)$. Further, we establish some interesting properties of the sequences $\left\{\sigma^+(n)\right\}_{n=1}^\infty$ and $\left\{\varphi^+(n)\right\}_{n=1}^\infty$, in particular, we prove that each of these sequences contains infinitely many arithmetic progressions of length $3$. + oai:arXiv.org:2508.11660v2 + math.GM + Thu, 11 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - Mirai Ikebuchi + 10.7546/nntdm.2025.31.4.899-907 + Notes on Number Theory and Discrete Mathematics, 31(4), 2025, 899-907 + Sagar Mandal - Trickle-down Theorems via C-Lorentzian Polynomials II: Pairwise Spectral Influence and Improved Dobrushin's Condition - https://arxiv.org/abs/2510.06549 - arXiv:2510.06549v2 Announce Type: replace -Abstract: Let $\mu$ be a probability distribution on a multi-state spin system on a set $V$ of sites. Equivalently, we can think of this as a $d$-partite simplical complex with distribution $\mu$ on maximal faces. For any pair of vertices $u,v\in V$, define the pairwise spectral influence $\mathcal{I}_{u,v}$ as follows. Let $\sigma$ be a choice of spins $s_w\in S_w$ for every $w\in V \setminus \{u,v\}$, and construct a matrix in $\mathbb{R}^{(S_u\cup S_v)\times (S_u\cup S_v)}$ where for any $s_u\in S_u, s_v\in S_v$, the $(us_u,vs_v)$-entry is the probability that $s_v$ is the spin of $v$ conditioned on $s_u$ being the spin of $u$ and on $\sigma$. Then $\mathcal{I}_{u,v}$ is the maximal second eigenvalue of this matrix, over all choices of spins for all $w \in V \setminus \{u,v\}$. Equivalently, $\mathcal{I}_{u,v}$ is the maximum local spectral expansion of links of codimension $2$ that include a spin for every $w \in V \setminus \{u,v\}$. - We show that if the largest eigenvalue of the pairwise spectral influence matrix with entries $\mathcal{I}_{u,v}$ is bounded away from 1, i.e. $\lambda_{\max}(\mathcal{I})\leq 1-\epsilon$ (and $X$ is connected), then the Glauber dynamics mixes rapidly and generate samples from $\mu$. This improves/generalizes the classical Dobrushin's influence matrix as the $\mathcal{I}_{u,v}$ lower-bounds the classical influence of $u\to v$. As a by-product, we also prove improved/almost optimal trickle-down theorems for partite simplicial complexes. The proof builds on the trickle-down theorems via $\mathcal{C}$-Lorentzian polynomials machinery recently developed by the authors and Lindberg. - oai:arXiv.org:2510.06549v2 - math.CO - cs.CC - cs.DS - Wed, 10 Dec 2025 00:00:00 -0500 + On a construction of stable maps from 3-manifolds into surfaces + https://arxiv.org/abs/2508.21337 + arXiv:2508.21337v2 Announce Type: replace +Abstract: For any link in the $3$-sphere, we give a visual construction of a stable map $f$ from the $3$-sphere into the real plane enjoying the following properties; $f$ has no cusp point, the set of definite fold points of $f$ coincides with the given link and $f$ only has certain type of fibers containing two indefinite fold points. As a corollary, we obtain a similar stable map from every closed orientable $3$-manifold into the $2$-sphere. + oai:arXiv.org:2508.21337v2 + math.GT + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jonathan Leake, Shayan Oveis Gharan + Gakuto Kato - On positive solutions of Lane-Emden equations on the integer lattice graphs - https://arxiv.org/abs/2510.08947 - arXiv:2510.08947v3 Announce Type: replace -Abstract: In this paper, we investigate the existence and nonexistence of positive solutions to the Lane-Emden equations $$ -\Delta u = Q |u|^{p-2}u $$ on the $d$-dimensional integer lattice graph $\mathbb{Z}^d$, as well as in the half-space and quadrant domains, under the zero Dirichlet boundary condition in the latter two cases. Here, $d \geq 2$, $p > 0$, and $Q$ denotes a Hardy-type positive potential satisfying $Q(x) \sim (1+|x|)^{-\alpha}$ with $\alpha \in [0, +\infty]$. \smallskip - We identify the Sobolev super-critical regions of the parameter pair $(\alpha, p)$ for which the existence of positive solutions is established via variational methods. In contrast, within the Serrin sub-critical regions of $(\alpha, p)$, we demonstrate nonexistence by iteratively analyzing the decay behavior at infinity, ultimately leading to a contradiction. Notably, in the full-space and half-space domains, there exists an intermediate regions between the Sobolev critical line and the Serrin critical line where the existence of positive solutions remains an open question. Such an intermediate region does not exist in the quadrant domain. - oai:arXiv.org:2510.08947v3 - math.AP - Wed, 10 Dec 2025 00:00:00 -0500 + Frobenius induced morphisms on moduli of sheaves on curves + https://arxiv.org/abs/2509.00444 + arXiv:2509.00444v2 Announce Type: replace +Abstract: We show the Frobenius pullback of a general semi-stable vector bundle in the moduli space of vector bundles with fixed rank and degree is still semi-stable by deformation trick. We then present several applications of the main theorem. + oai:arXiv.org:2509.00444v2 + math.AG + Thu, 11 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by-sa/4.0/ - Huyuan Chen, Bobo Hua, Feng Zhou - - - Intermittent solutions of the stationary 2D surface quasi-geostrophic equation in sharp $L^p$ spaces - https://arxiv.org/abs/2510.16583 - arXiv:2510.16583v4 Announce Type: replace -Abstract: In this paper we construct non-trivial solutions to the stationary dissipative surface quasi-geostrophic equation on the two dimensional torus which lie strictly below the critical regularity threshold of $\dot{H}^{-1/2}(\mathbb{T}^2)$. Specifically, for any $\alpha < 1/2$ and any dissipation exponent $0 < \gamma \leq 2$ we construct non-trivial solutions such that - $$ - u,\theta \in \dot{B}^{\alpha-1}_{\infty,\infty}(\mathbb{T}^2) \cap \dot{B}^{\alpha-1}_{2,2}(\mathbb{T}^2). - $$ - Due to the fact our solutions do not lie in $\dot{H}^{-1/2}(\mathbb{T}^2)$, this requires reinterpreting the notion of a solution. This leads us to formulate the notion of a weak paraproduct solution for the stationary SQG equation. The main new ingredient is the incorporation of intermittency into the construction of the solutions. This allows us to demonstrate non-trivial integrability results for certain fractional derivatives of our solutions. In particular, for highly intermittent solutions, we are able to conclude for every $1 \leq p < 4/3$ we can construct $u$ and $\theta$ lying in $L^p(\mathbb{T}^2)$. This result is sharp with respect to $L^p(\mathbb{T}^2)$ integrability. - oai:arXiv.org:2510.16583v4 - math.AP - Wed, 10 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Nicholas Gismondi, Alexandru F. Radu - - - Stability of torsion subgroups of elliptic curves over non-Galois extensions of odd prime degree - https://arxiv.org/abs/2510.18194 - arXiv:2510.18194v3 Announce Type: replace -Abstract: Let $K$ be a field of characteristic $0$ and $E/K$ an elliptic curve over $K$. For a finite extension $L/K$ and a prime~$\ell$, we provide Galois-theoretic sufficient conditions on $L/K$ under which $E\left(L\right)\left[\ell^{\infty}\right] = E\left(K\right)\left[\ell^{\infty}\right]$. For a non-Galois extension $L/K$ of prime degree, we relate the growth of the $\ell^{\infty}$-torsion subgroup of $E$ under the base change $L/K$ to the image of the mod-$\ell$ cyclotomic character. In particular, In particular, we refine Gonz{\'a}lez-Jim{\'e}nez's result by ruling out certain torsion structures for quintic non-Galois extensions $L/\mathbb{Q}$. - oai:arXiv.org:2510.18194v3 - math.NT - Wed, 10 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/publicdomain/zero/1.0/ - Bo-Hae Im, Hansol Kim + Jin Cao, Xiaoyu Su - Intersection theory and Siegel-Veech constants for Prym eigenform loci in $\Omega\mathcal{M}_3(2,2)^{\rm odd}$ - https://arxiv.org/abs/2510.23333 - arXiv:2510.23333v2 Announce Type: replace -Abstract: We compute the Siegel-Veech constants associated to saddle connections with distinct endpoints on Prym eigenforms for real quadratic orders with non-square discriminant in $\Omega \mathcal{M}_3(2,2)^{\rm odd}$. - oai:arXiv.org:2510.23333v2 - math.GT - math.AG - math.DS - Wed, 10 Dec 2025 00:00:00 -0500 + Explicit lower bounds for opaque sets of unit square and unit disc + https://arxiv.org/abs/2509.08842 + arXiv:2509.08842v2 Announce Type: replace +Abstract: Explicit lower bounds for the length of the shortest opaque set for the unit disc and the unit square in the Euclidean plane are derived. The results are based on an explicit application of the general method of Kawamura, Moriyama, Otachi and Pach. Employing a recent observation by Steinerberger on the possible orientations of straight barriers with length close to Jones' bound, we improve the bound for the unit square by more than a factor $3$. The bound for barriers of the unit disc is new and based on the idea that the free parameters in the general method from can be optimized due to the strong symmetry properties of the disc. Our approach illustrates both the power and the limitations of the method. + oai:arXiv.org:2509.08842v2 + math.MG + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Duc-Manh Nguyen + Markus Kiderlen, Florian Pausinger - Modulation groups - https://arxiv.org/abs/2510.23932 - arXiv:2510.23932v3 Announce Type: replace -Abstract: Conjectures of Braverman and Kazhdan, Ng\^o and Sakellaridis have motivated the development of Schwartz spaces for certain spherical varieties. We prove that under suitable assumptions these Schwartz spaces are naturally a representation of a group that we christen the modulation group. This provides a broad generalization of the defining representation of the metaplectic group. The example of a vector space and the zero locus of a quadric cone in an even number of variables are discussed in detail. In both of these cases the modulation group is closely related to algebraic groups, and we propose a conjectural method of linking modulation groups to ind-algebraic groups in general. At the end of the paper we discuss adelization and the relationship between representations of modulation groups and the Poisson summation conjecture. - oai:arXiv.org:2510.23932v3 - math.NT + On the diagonal of quartic hypersurfaces and $(2,3)$-complete intersection $n$-folds + https://arxiv.org/abs/2510.07111 + arXiv:2510.07111v2 Announce Type: replace +Abstract: We study the question of the existence of a decomposition of the diagonal for very general quartic and $(2,3)$-complete intersection $n$-folds. Using cycle-theoretic techniques of Lange, Pavic and Schreieder we reduce the question via a degeneration argument to the existence of such a decomposition for $n-1$-dimensional cubic hypersurfaces and their essential dimension. A result of Voisin on the essential dimension of complex cubic hypersurfaces of odd dimension (and of dimension four) then yields conditional statements that extend results of Nicaise and Ottem from stable rationality to the existence of a decomposition of the diagonal. As an application, we use a recent result of Engel, de Gaay Fortman and Schreieder on the decomposition of the diagonal for cubic threefolds to give a new proof of the non-retract rationality of a very general complex quartic $4$-fold, originally due to Totaro, and of a very general complex $(2,3)$-complete intersection $4$-fold, originally due to Skauli. + oai:arXiv.org:2510.07111v2 math.AG - math.RT - Wed, 10 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Jayce R. Getz, Armando Guti\'errez Terradillos, Farid Hosseinijafari, Bryan Hu, Seewoo Lee, Aaron Slipper, Marie-H\'el\`ene Tom\'e, HaoYun Yao, Alan Zhao - - - Formalization of Auslander--Buchsbaum--Serre criterion in Lean4 - https://arxiv.org/abs/2510.24818 - arXiv:2510.24818v3 Announce Type: replace -Abstract: We present a comprehensive formalization in the Lean4 theorem prover of the Auslander--Buchsbaum--Serre criterion, which characterizes regular local rings as those Noetherian local rings with finite global dimension. Rather than following the well-known proof that computes the projective dimension of the residue field via quotient by regular sequences and uses the Koszul complex to bound the cotangent space dimension by the global dimension, our approach is built systematically on the formalization of depth defined via the vanishing of Ext functors. We establish key homological results including Rees' theorem, the Auslander--Buchsbaum formula, and Ischebeck's theorem, and further develop the theories of Cohen--Macaulay modules and rings, including a complete formalization of the unmixedness theorem for Cohen--Macaulay rings. To prove the Auslander--Buchsbaum--Serre criterion, we show that maximal Cohen--Macaulay modules over regular local rings are free and establish a weakened form of the Ferrand--Vasconcelos theorem specific for the unique maximal ideal. As corollaries, we deduce that regularity can be checked at maximal ideals and formalize Hilbert's Syzygy Theorem. This work demonstrates how homological algebra can be effectively employed in the formalization of commutative algebra, providing extensive infrastructure for future developments in the field. - oai:arXiv.org:2510.24818v3 - math.AC - cs.FL - cs.LO - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Naillin Guan, Yongle Hu + Elia Fiammengo, Morten L\"uders - Fixed and periodic points of the intersection body operators of lower orders - https://arxiv.org/abs/2510.26381 - arXiv:2510.26381v3 Announce Type: replace -Abstract: For the intersection body operator of lower order $I_iK$ of a star body $K$ in $\mathbb{R}^n$, $i\in\{1, 2,\ldots, n-2\}$, we prove that $I_i^2K = cK$ iff $K$ is an origin-symmetric ball, and hence $I_iK = cK$ iff $K$ is an origin-symmetric ball. Combining the recent breakthrough (case $i = n-1$) of Milman, Shabelman and Yehudayoff (Invent. Math., 241 (2025), 509-558), slight modifications of two long-standing questions 8.6 and 8.7 posed by R. Gardner (Page 302, Geometric Tomography, Cambridge University Press, 1995) are completely solved. As applications, we show that for the spherical Radon transform $\mathcal{R}$, a non-negative $\rho\in L^{\infty}(\mathcal{S}^{n-1})$ satisfies $\mathcal{R}(\rho^i) = c\rho$ for some $c>0$ iff $\rho$ is constant. Also, the sharp Busemann intersection type inequalities are established. - oai:arXiv.org:2510.26381v3 - math.MG - Wed, 10 Dec 2025 00:00:00 -0500 + On Riemann wave superpositions obtained from the Euler system + https://arxiv.org/abs/2510.09576 + arXiv:2510.09576v5 Announce Type: replace +Abstract: The paper contains an analysis of the conditions for the existence of elastic versus non-elastic wave superpositions governed by the Euler system in (1+1)-dimensions. A review of recently obtained results is presented, including the introduction of the notion of quasi-rectifiability of vector fields and its application to both elastic and non- elastic wave superpositions. It is shown that the smallest real Lie algebra containing vector fields associated with the waves admitted by the Euler system is isomorphic to an infinite-dimensional Lie algebra which is the semi-direct sum of an Abelian ideal and the three-dimensional real Lie algebra. The maximal Lie module corresponding to the Euler system can be transformed, by an angle preserving transformation, to this algebra which is quasi-rectifiable and describes the behavior of wave superpositions. Based on these facts, we are able to find a parametrization of the region of non-elastic wave superpositions which allows for the construction of the reduced form of the Euler system. + oai:arXiv.org:2510.09576v5 + math-ph + math.AP + math.MP + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Cheng Lin, Ge Xiong + {\L}ukasz Chomienia, Alfred Michel Grundland - A Unified Computational Approach for Zero-Sum Linear-Quadratic Stochastic Differential Games in Infinite Horizons - https://arxiv.org/abs/2511.01538 - arXiv:2511.01538v2 Announce Type: replace -Abstract: This paper proposes a new method for finding closed-loop saddle points in zero-sum linear-quadratic stochastic differential games by decoupling their inherent structure. Specifically, we develop a nested iterative scheme that constructs a monotonically increasing sequence of matrices, thereby decomposing the original problem into interconnected subproblems. By sequentially computing the stabilizing solutions to the algebraic Riccati equations within each subproblem, we obtain the stabilizing solution to the original problem and rigorously establish the convergence of the iterative sequence. A numerical example further validates the effectiveness of the proposed method. To the best of our knowledge, this work extends the classical setting and provides the first general-purpose computational approach for this class of problems. - oai:arXiv.org:2511.01538v2 - math.OC - Wed, 10 Dec 2025 00:00:00 -0500 + Kernels of Brauer characters and Isaacs' partial characters + https://arxiv.org/abs/2510.11655 + arXiv:2510.11655v2 Announce Type: replace +Abstract: In this paper, we prove a property of kernels of Brauer characters. We propose a candidate for the kernels of Isaacs' partial characters, and we show that this candidate has the same property. + oai:arXiv.org:2510.11655v2 + math.GR + Thu, 11 Dec 2025 00:00:00 -0500 replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Yiyuan Wang + http://creativecommons.org/licenses/by/4.0/ + Mark L. Lewis - Tensor rank and dimension expanders - https://arxiv.org/abs/2511.02670 - arXiv:2511.02670v2 Announce Type: replace -Abstract: We prove a lower bound on the rank of tensors constructed from families of linear maps that `expand' the dimension of every subspace. Such families, called {\em dimension expanders} have been studied for many years with several known explicit constructions. Using these constructions we show that one can construct an explicit $[D]\times [n] \times [n]$-tensor with rank at least $(2 - \epsilon)n$, with $D$ a constant depending on $\epsilon$. Our results extend to border rank over the real or complex numbers. - oai:arXiv.org:2511.02670v2 - math.CO - cs.CC - Wed, 10 Dec 2025 00:00:00 -0500 + On Complexity of Model-Based Derivative-Free Methods + https://arxiv.org/abs/2510.14935 + arXiv:2510.14935v2 Announce Type: replace +Abstract: In many applications of mathematical optimization, one may wish to optimize an objective function without access to its derivatives. These situations call for derivative-free optimization (DFO) methods. Among the most successful approaches in practice are model-based trust-region methods, such as those pioneered by M.J.D Powell. While relatively complex to implement, these methods are now available in standard scientific computing platforms, including MATLAB and SciPy. However, theoretical analysis of their computational complexity lags behind practice. In particular, it is important to bound the number of function evaluations required to achieve a desired level of accuracy. In this paper we systematically derive complexity bounds for classical model-based trust-region methods and their modern variations. We establish, for the first time, that these methods can have the same worst case complexity than any other known DFO method. + oai:arXiv.org:2510.14935v2 + math.OC + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Zeev Dvir + Abraar Chaudhry, Katya Scheinberg - Dynamics generated by spatially growing derivations on quasi-local algebras - https://arxiv.org/abs/2511.02941 - arXiv:2511.02941v2 Announce Type: replace -Abstract: We prove global existence and uniqueness of dynamics on the quasi-local algebra $\mathcal{A}$ of a quantum lattice system for spatially growing derivations $\mathcal{L}_\Phi = \sum_x [ \Phi_x , \cdot ]$. Existing results assume that the local terms $\Phi_x\in\mathcal{A}$ of the generator are uniformly bounded in space with respect to appropriate weighted norms $\lVert \Phi_x \rVert_{G,x}$. Analogous to the global existence result for first order ODEs, we show that global existence and uniqueness persist if the size of the local terms $\lVert \Phi_x \rVert_{G,x}$ grows at most linearly in space. This considerably enlarges the class of derivations known to have well-defined dynamics. Moreover, we obtain Lieb-Robinson bounds with exponential light cones for such dynamics. - For the proof, we assume Lieb-Robinson bounds with linear light cones for dynamics, whose generators have uniformly bounded local terms. Such bounds are known to hold, for example, if the local terms are of finite range or exponentially localized. - oai:arXiv.org:2511.02941v2 + Laurent sequences, extended Rota Algebras and Categorical Discretization of Dynamical Systems + https://arxiv.org/abs/2510.15489 + arXiv:2510.15489v2 Announce Type: replace +Abstract: We introduce a novel integrability-preserving discretization for a broad class of differential equations with variable coefficients, encompassing both linear and nonlinear cases. The construction is achieved via a categorical approach that enables a unified treatment of continuous and discrete dynamical systems. + Our theoretical framework is grounded on a novel generalization of G. C. Rota's finite operator calculus, which enables us to extend the theory of basic sequence of polynomials to the setting of Laurent polynomials. Accordingly, we introduce the notion of an \textit{extended Rota algebra}, defined as a Galois differential algebra in which all difference operators act as derivations on the space of Laurent power series with respect to a suitably defined functional product. + The core of our theory relies on the existence of covariant functors between the newly proposed Rota category of Galois differential algebras and suitable categories of abstract dynamical systems. + In this setting, under certain regularity assumptions, a differential equation and its discrete analogues are naturally interpreted as objects of the same category. This perspective enables the construction of a vast class of integrable maps that share with their continuous analogues a wide set of exact solutions, \textit{regular} or \textit{singular} and, in the linear case, the Picard-Vessiot group. + oai:arXiv.org:2510.15489v2 math-ph math.MP - quant-ph - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - Stefan Teufel, Marius Wesle, Tom Wessel + Miguel A. Rodriguez, Piergiulio Tempesta - The Rainbow Arborescence Problem on Cycles - https://arxiv.org/abs/2511.04953 - arXiv:2511.04953v2 Announce Type: replace -Abstract: The rainbow arborescence conjecture posits that if the arcs of a directed graph with $n$ vertices are colored by $n-1$ colors such that each color class forms a spanning arborescence, then there is a spanning arborescence that contains exactly one arc of every color. We prove that the conjecture is true if the underlying undirected graph is a cycle. - oai:arXiv.org:2511.04953v2 - math.CO - cs.DM - Wed, 10 Dec 2025 00:00:00 -0500 + Anderson-type acceleration method for Deep Neural Network optimization + https://arxiv.org/abs/2510.20254 + arXiv:2510.20254v2 Announce Type: replace +Abstract: In this paper we consider the neural network optimization. We develop Anderson-type acceleration method for the stochastic gradient decent method and it improves the network permanence very much. We demonstrate the applicability of the method for Deep Neural Network (DNN) and Convolution Neural Network (CNN). + oai:arXiv.org:2510.20254v2 + math.NA + cs.NA + math.OC + Thu, 11 Dec 2025 00:00:00 -0500 replace - http://creativecommons.org/licenses/by/4.0/ - Krist\'of B\'erczi, Tam\'as Kir\'aly, Yutaro Yamaguchi, Yu Yokoi + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Kazufumi Ito, Tiancheng Xue - Nilpotence of $\eta$ in \'etale motivic spectra - https://arxiv.org/abs/2511.09476 - arXiv:2511.09476v2 Announce Type: replace -Abstract: We show that every object of the stable \'etale motivic homotopy category over any scheme is $\eta$-complete. In some cases we show that in fact the fourth power of $\eta$ is null, whereas the third power of $\eta$ is always nonvanishing, similar to the situation in topology. Moreover, we prove an \'etale version of May's nilpotence conjecture, that states that $H\mathbb{Z} \in \mathrm{Sp}$ detects the vanishing of $\mathbf{E}_\infty$-rings. We use this to show a version of Nishida's nilpotence theorem in $\mathrm{SH}_{\operatorname{\acute{e}t}}(S)$, i.e. that any positive degree self map of the unit is nilpotent. - oai:arXiv.org:2511.09476v2 + Rationality of cycles modulo 2 on products of generically smooth quadrics in characteristic 2 + https://arxiv.org/abs/2510.22502 + arXiv:2510.22502v2 Announce Type: replace +Abstract: A 2022 result of Karpenko establishes a conjecture of Hoffmann-Totaro on the possible values of the first higher isotropy index of an arbitrary anisotropic quadratic form of given dimension over an arbitrary field. For nondegenerate forms, this essentially goes back to a 2003 article of the same author on quadratic forms over fields of characteristic not $2$. To handle the more involved case of degenerate forms in characteristic $2$, Karpenko showed that certain aspects of the algebraic-geometric approach to nondegenerate quadratic forms developed by Karpenko, Merkurjev, Rost, Vishik and others can be adapted to a study of rational cycles modulo $2$ on powers of a given generically smooth quadric. In this paper, we extend this to a broader study of rational cycles modulo $2$ on arbitrary products of generically smooth quadrics in characteristic $2$. A basic objective is to have tools available to study correspondences between general quadrics, in particular, between smooth and non-smooth quadrics. Applications of the theory to the study of degenerate quadratic forms in characteristic $2$ are provided, and a number of open problems on forms of this type are also formulated and discussed. + oai:arXiv.org:2510.22502v2 math.AG - math.AT - Wed, 10 Dec 2025 00:00:00 -0500 + math.KT + Thu, 11 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - Klaus Mattis, Swann Tubach + Stephen Scully, Guangzhao Zhu - A new generalization of the Narayana numbers inspired by linear operators on associative $d$-ary algebras - https://arxiv.org/abs/2511.13671 - arXiv:2511.13671v2 Announce Type: replace -Abstract: We introduce and study a generalization of the Narayana numbers $N_d(n,k) = \frac{1}{n+1} \binom{n+1}{k+1} \binom{ n + (n-k)(d-2)+1}{k}$ for integers $d \geq 2$ and $n,k \geq 0$. This two-parameter array extends the classical Narayana numbers ($d=2$) and yields a $d$-ary analogue of the Catalan numbers $C_d(n) = \sum_{k=0}^n N_d(n,k)$. We give nine combinatorial interpretations of $N_d(n,k)$ that unify and generalize known combinatorial interpretations of the Narayana numbers and $C_3(n)$ in the literature. In particular, we show that $N_d(n,k)$ counts a natural class of operator monomials over a $d$-ary associative algebra, thereby extending a result of Bremner and Elgendy for the binary case. We also construct explicit bijections between these monomials and several families of classic combinatorial objects, including Schr\"{o}der paths, Dyck paths, rooted ordered trees, and $231$-avoiding permutations. - oai:arXiv.org:2511.13671v2 - math.CO - math.RA - Wed, 10 Dec 2025 00:00:00 -0500 + Diffusion operators on $p$-adic analytic manifolds + https://arxiv.org/abs/2510.22563 + arXiv:2510.22563v4 Announce Type: replace +Abstract: Kernel functions for Laplacian integral operators are constructed on $p$-adic analytic manifolds using charts and transition maps from an atlas with connected nerve complex. In the compact case, an operator of Vladimirov-Taibleson type parametrised by a real parameter $s$ is defined. Its kernel function uses a geodetic-like distance function on the nerve complex of its atlas. The $L^2$-spectrum of this operator is established, and it is shown that it gives rise to a Feller semigroup. In this way, the Cauchy problem for the corresponding heat equation is solved in the positive by a transition function of a Markov process. The existence of a heat kernel function and a Green function in the case $s > 1$ is proven. As an application, it is shown how to express the number of points on the reduction curve defined over the residue field of an elliptic curve with good reduction in terms of the eigenvalues of a Vladimirov-Taibleson-like operator. This provides for an alternative way of counting points on elliptic curves defined over finite fields. + oai:arXiv.org:2510.22563v4 + math.AP + Thu, 11 Dec 2025 00:00:00 -0500 replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Yu Hin Au, Murray R. Bremner + http://creativecommons.org/licenses/by/4.0/ + Patrick Erik Bradley - Tracially lyriform $\mathrm{C}^*$-algebras - https://arxiv.org/abs/2511.15596 - arXiv:2511.15596v2 Announce Type: replace -Abstract: Quantum metric Choquet simplices are special kinds of compact quantum metric spaces designed for distance measurement in and around the category of stably finite Elliott-classifiable $\mathrm{C}^*$-algebras. The primary objective of this article is to introduce versions of these structures for which the associated tracial metrics need not be induced by Lipschitz seminorms and may induce strictly stronger topologies than the weak$^*$-topology. The resulting category of 'tracially lyriform $\mathrm{C}^*$-algebras' behaves well with respect to sequential inductive limits and accommodates the full family of classical $p$-Wasserstein metrics on probability spaces, including $p=\infty$. Examples of projectionless, classifiable tracial Wasserstein spaces are built as noncommutative spaces of observables of certain compact length spaces, including: fractals like the Sierpi\'nski gasket, the Sierpi\'nski carpet and the Menger sponge; finite-dimensional Alexandrov spaces with two-sided curvature bounds; and metric spaces like simplicial spheres and balls that are Lipschitz equivalent to Riemannian. These simplicial structures are used as building blocks that furnish arbitrary simple inductive limits of prime dimension drop algebras with tracial lyriform structure. Appealing to optimal transport theory, we study the geometry and statistics of the spaces of embeddings of these building blocks and their limits into suitable classifiable $\mathrm{C}^*$-algebras like the Jiang-Su algebra $\mathcal{Z}$ or the universal UHF algebra $\mathcal{Q}$. - oai:arXiv.org:2511.15596v2 - math.OA - math.MG - Wed, 10 Dec 2025 00:00:00 -0500 + The $p$-th dual Minkowski problem for the $k$-torsional rigidity corresponding to a $k$-Hessian equation + https://arxiv.org/abs/2510.25435 + arXiv:2510.25435v2 Announce Type: replace +Abstract: The study of the dual curvature measures [Y. Huang, E. Lutwak, D. Yang \& G. Y. Zhang, Acta. Math. 216 (2016): 325-388], which connects the cone-volume measure and Aleksandrov's integral curvature, and has created a precedent for the theoretical research of the dual Brunn-Minkowski theory. + Motivated by the foregoing groundbreaking works, the present paper introduces the $p$-th dual $k$-torsional rigidity associated with a $k$-Hessian equation and establishes its Hadamard variational formula with $1\leq k\leq n-1$, which induces the $p$-th dual $k$-torsional measure. Further, based on the $p$-th dual $k$-torsional measure, this article, for the first time, proposes the $p$-th dual Minkowski problem of the $k$-torsional rigidity which can be equivalently converted to a nonlinear partial differential equation in smooth case: \begin{align}\label{eq01} f(x)=\tau(|\nabla h|^2+h^2)^{\frac{p-n}{2}}h_{\Omega}(x)|Du(\nu^{-1}_\Omega(x))|^{k+1}\sigma_{n-k}(h_{ij}(x)+h_\Omega(x)\delta_{ij}), \end{align} where $\tau>0$ is a constant, $f$ is a positive smooth function defined on $S^{n-1}$ and $\sigma_{n-k}$ is the $(n-k)$-th elementary symmetric function of the principal curvature radii. We confirm the existence of smooth non-even solution to the $p$-th dual Minkowski problem of the $k$-torsional rigidity for $p<n-2$ by the method of a curvature flow which converges smoothly to the solution of equation (\ref{eq01}). Specially, a novel approach for the uniform lower bound estimation in the $C^0$ estimation for the solution to the curvature flow is presented with the help of invariant functional $\Phi(\Omega_t)$. + oai:arXiv.org:2510.25435v2 + math.DG + math.AP + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Bhishan Jacelon + Xia Zhao, Peibiao Zhao - Dynamics of Ideal Fluid Flows - https://arxiv.org/abs/2511.16254 - arXiv:2511.16254v2 Announce Type: replace -Abstract: We will discuss various aspects of the incompressible Euler equation. We will discuss, in particular, problems related to the least action principle, the existence of special solutions, the problem of solvability, singularity formation, and asymptotic behavior. - oai:arXiv.org:2511.16254v2 - math.AP - physics.flu-dyn - Wed, 10 Dec 2025 00:00:00 -0500 + Sharp Fuss-Catalan thresholds in graph bootstrap percolation + https://arxiv.org/abs/2510.26724 + arXiv:2510.26724v2 Announce Type: replace +Abstract: We study graph bootstrap percolation on the Erd\H{o}s-R\'enyi random graph ${\mathcal G}_{n,p}$. For all $r \ge 5$, we locate the sharp $K_r$-percolation threshold $p_c \sim (\gamma n)^{-1/\lambda}$, solving a problem of Balogh, Bollob\'as and Morris. The case $r=3$ is the classical graph connectivity threshold, and the threshold for $r=4$ was found using strong connections with the well-studied $2$-neighbor dynamics from statistical physics. When $r \ge 5$, such connections break down, and the process exhibits much richer behavior. The constants $\lambda=\lambda(r)$ and $\gamma=\gamma(r)$ in $p_c$ are determined by a class of $\left({r\choose2}-1\right)$-ary tree-like graphs, which we call $K_r$-tree witness graphs. These graphs are associated with the most efficient ways of adding a new edge in the $K_r$-dynamics, and they can be counted using the Fuss-Catalan numbers. Also, in the subcritical setting, we determine the asymptotic number of edges added to ${\mathcal G}_{n,p}$, showing that the edge density increases only by a constant factor, whose value we identify. + oai:arXiv.org:2510.26724v2 + math.PR + math.CO + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Tarek M. Elgindi + Zsolt Bartha, Brett Kolesnik, Gal Kronenberg, Yuval Peled - Perfect Sets of Liouville Numbers with Controlled Self-Powers - https://arxiv.org/abs/2511.17414 - arXiv:2511.17414v2 Announce Type: replace -Abstract: We study the arithmetic behavior of self-powers $x^x$ when $x$ is a Liouville number. Using recent ideas on strengthened Liouville approximation, we develop flexible constructions that illuminate how transcendence, Liouville properties, and "large" topological size interact in this setting. As a concrete outcome, we build a perfect set of Liouville numbers of continuum cardinality whose finite sums, finite products, and self-powers all remain Liouville. These results show that rich algebraic and topological structures persist inside the Liouville universe for the map $x\mapsto x^x$. - oai:arXiv.org:2511.17414v2 - math.NT - Wed, 10 Dec 2025 00:00:00 -0500 + Statistical Properties of Rectified Flow + https://arxiv.org/abs/2511.03193 + arXiv:2511.03193v3 Announce Type: replace +Abstract: Rectified flow (Liu et al., 2022; Liu, 2022; Wu et al., 2023) is a method for defining a transport map between two distributions, and enjoys popularity in machine learning, although theoretical results supporting the validity of these methods are scant. The rectified flow can be regarded as an approximation to optimal transport, but in contrast to other transport methods that require optimization over a function space, computing the rectified flow only requires standard statistical tools such as regression or density estimation, which we leverage to develop empirical versions of transport maps. We study some structural properties of the rectified flow, including existence, uniqueness, and regularity, as well as the related statistical properties, such as rates of convergence and central limit theorems, for some selected estimators. To do so, we analyze the bounded and unbounded cases separately as each presents unique challenges. In both cases, we are able to establish convergence at faster rates than those for the usual nonparametric regression and density estimation. + oai:arXiv.org:2511.03193v3 + math.ST + cs.LG + stat.ME + stat.ML + stat.TH + Thu, 11 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - Sidney A. Morris, Marcelo O. Ribeiro, Diego Marques - - - Explicit Formulas and Combinatorial Interpretation of Triangular Arrays - https://arxiv.org/abs/2511.18351 - arXiv:2511.18351v2 Announce Type: replace -Abstract: In this work, the weighted paths to interpret any triangular array of the form - \[ - T(n,k)=(a_2 n + a_1 k + a_0)\,T(n-1,k) - + (b_2 n + b_1 k + b_0)\,T(n-1,k-1), - \] - allowing a structural analysis of the coefficients $\big(T(n,k)\big)_{n,k\in \mathbb{N}}$. - This leads to explicit expressions for general $T(n,k)$, with simpler formulas arising in the cases $a_2=0$ or $b_2=0$, as well as in the fully general case. - Applications include explicit formulas for the $r$-Eulerian numbers and the marked $r$-Eulerian numbers ones. We will write also the case where $b_{n,k}=1$, as a matrix of passage. - \textbf{Keywords:} triangular recurrence, weighted paths, $r$-Eulerian numbers, combinatorial interpretation. - oai:arXiv.org:2511.18351v2 + Gonzalo Mena, Arun Kumar Kuchibhotla, Larry Wasserman + + + Pieri Rule for GQs Computed via Strict Decomposition Tableaux + https://arxiv.org/abs/2511.05734 + arXiv:2511.05734v2 Announce Type: replace +Abstract: $GQ$ functions are symmetric functions indexed by strict partitions that represent $K$-theoretic Schubert classes in the Lagrangian Grassmannian. Buch and Ravikumar proved a Pieri rule for expanding $GQ_{\lambda}\cdot GQ_p$ in terms of $GQ$s via certain shifted skew tableaux. In this paper we identify an alternative family of shifted tableaux that enumerates this Pieri rule. This partially resolves a conjecture from previous work that these tableaux enumerate the expansion of $GQ_{\lambda} \cdot GQ_{\tau}$ in terms of $GQ$s where $\tau$ is a trapezoid shape. + oai:arXiv.org:2511.05734v2 math.CO - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - Voalaza Mahavily Romuald, Benjamin Randrianirina + Joshua Arroyo - L- and M-weakly compact multilinear operators and their linear adjoints - https://arxiv.org/abs/2511.21358 - arXiv:2511.21358v2 Announce Type: replace -Abstract: Let $X_1, \ldots, X_m$ be Banach spaces and let $E_1, \ldots, E_m,F$ be Banach lattices. Our main results read as follows: (i) The linear adjoint $A^*$ of a continuous multilinear operator $A \colon X_1 \times \cdots \times X_m \to F$ is $M$-weakly compact if and only if $A$ is $L$-weakly compact. (ii) The linear adjoint $A^*$ of a multilinear operator of order bounded variation $A \colon E_1 \times \cdots \times E_m \to F$ is $L$-weakly compact if and only if the linearization of $A$ on the positive projective tensor product is $M$-weakly compact. In our way to prove these results, we develop the basic theory of linear adjoints of multilinear operators between Riesz spaces, we prove that multilinear operators of order bounded variation between Banach lattices are continuous, and we explore different notions of multilinear operators of $M$-weakly compact-type. - oai:arXiv.org:2511.21358v2 - math.FA - Wed, 10 Dec 2025 00:00:00 -0500 + Finite Volume Analysis of the Poisson Problem via a Reduced Discontinuous Galerkin Space + https://arxiv.org/abs/2511.09099 + arXiv:2511.09099v2 Announce Type: replace +Abstract: In this paper, we propose and analyze a high-order finite volume method for the Poisson problem based on the reduced discontinuous Galerkin (RDG) space. The main idea is to employ the RDG space as the trial space and the piecewise constant space as the test space, thereby formulating the scheme in a Petrov-Galerkin framework. This approach inherits the local conservation property of finite volume methods while benefiting from the approximation capabilities of discontinuous Galerkin spaces with significantly fewer degrees of freedom. We establish a rigorous error analysis of the proposed scheme: in particular, we prove optimal-order convergence in the DG energy norm and suboptimal-order convergence in \(L^2\) norm. The theoretical analysis is supported by a set of one- and two-dimensional numerical experiments with Dirichlet and periodic boundary conditions, which confirm both the accuracy and efficiency of the method. The significance of this work lies in bridging finite volume and discontinuous Galerkin methodologies through the RDG space, thus enabling finite volume schemes with a mathematically rigorous convergence theory. + oai:arXiv.org:2511.09099v2 + math.NA + cs.NA + Thu, 11 Dec 2025 00:00:00 -0500 replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Geraldo Botelho, Ariel Mon\c{c}\~ao + http://creativecommons.org/licenses/by-nc-nd/4.0/ + Wenbo Hu, Yinhua Xia - On the $2$-torsion in class groups of number fields - https://arxiv.org/abs/2511.21899 - arXiv:2511.21899v2 Announce Type: replace -Abstract: In $2020$, Bhargava, Shankar, Taniguchi, Thorne, Tsimerman, and Zhao proved that for a finite extension $K/\mathbb{Q}$ of degree $n\geq 5$, the size of the $2$-torsion class group is bounded by $\# h_{2}(K)=O_{n,\varepsilon}(D_{K}^{\frac{1}{2}-\frac{1}{2n}+\varepsilon})$, where $D_{K}$ is the absolute discriminant of $K$. In the present paper, we improve their bound by proving that $\# h_{2}(K)=O_{n,\varepsilon}(D_{K}^{\frac{1}{2}-\frac{1}{2n}-\delta_{K}+\varepsilon})$, for a constant $\delta_{K}\geq\frac{1}{28n}-\frac{3}{28n(n-1)}$. - oai:arXiv.org:2511.21899v2 - math.NT - Wed, 10 Dec 2025 00:00:00 -0500 + A New Perspective on Double-S Curve Motions of Higher Order and Optimal Motion Planning + https://arxiv.org/abs/2511.12615 + arXiv:2511.12615v3 Announce Type: replace +Abstract: This paper presents and proves an equation for the time horizon of symmetric trajectories with zero boundary conditions and bounded derivatives of arbitrary order. This equation holds regardless of the number of phases comprising the associated motion. This avoids case distinctions in calculations. Application examples of motions with minimum time, minimum velocity, and minimum acceleration are discussed. Furthermore, an algorithm is derived that reduces the time minimization problem to solving a system of equations. This algorithm avoids nested case distinctions and complex optimizations. + oai:arXiv.org:2511.12615v3 + math.OC + Thu, 11 Dec 2025 00:00:00 -0500 replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Dante Bonolis + http://creativecommons.org/licenses/by-nc-nd/4.0/ + Rico Z\"ollner - Oriented Grassmannian Bundle, Normal Curvature Reduction, and Persistent Homology - https://arxiv.org/abs/2511.22603 - arXiv:2511.22603v2 Announce Type: replace -Abstract: We consider a smooth closed orientable submanifold $M \subset \mathbb{R}^D$ with narrow cycles. We embed $M$ into a scaled oriented Grassmannian bundle via the Gauss map in order to enlarge the scale of these cycles. Under mild assumptions, we show that this embedding reduces the normal curvature of the embedded submanifold in directions where the original normal curvature is large. For smooth closed hypersurfaces, we further show that this construction increases the distance between antipodal points of narrow cycles for fixed volume. - We then obtain an explicit range of radii for which the ambient \v{C}ech complex on this Grassmannian bundle is homotopy equivalent to the embedded manifold, yielding lower bounds on the scales at which the \v{C}ech filtration recovers the homology of $M$. Since the distance induced by the embedding depends on both positions and oriented tangent spaces, we work with Whitney $C^1$ convergence of embeddings and prove that the associated \v{C}ech persistent homology is stable with respect to the interleaving distance. Finally, we describe a procedure for computing a distance matrix for a finite subset with respect to this embedding and illustrate the construction on several examples, including an approximate quasi-halo orbit in the Saturn--Enceladus system. - oai:arXiv.org:2511.22603v2 - math.DG + String topology and graph cobordisms + https://arxiv.org/abs/2511.14978 + arXiv:2511.14978v2 Announce Type: replace +Abstract: We introduce a symmetric monoidal $\infty$-category $\mathrm{GrCob}$ of graph cobordisms between spaces, and use the homology of its morphism spaces to define string operations. Precisely, for an $E_\infty$-ring spectrum $R$ and an oriented $d$-dimensional $R$-Poincar\'e duality space $M$, we construct a "graph field theory" $\mathrm{GFT}_M$, i.e. a symmetric monoidal functor from a suitable $R$-linearisation of $\mathrm{GrCob}^\mathrm{op}$ to the category $\mathrm{Mod}_R$ of $R$-modules in spectra; the graph field theory takes an object $X\in\mathrm{GrCob}^\mathrm{op}$, i.e. a space, to the $R$-module $\Sigma_+^\infty\mathrm{map}(X,M)\otimes R$ of $R$-chains on the mapping space from $X$ to $M$; by selecting suitable graph cobordisms we recover the basic string operations given by restriction, cross product with the fundamental class, and the Chas-Sullivan operations. + The construction is natural with respect to oriented homotopy equivalences of $R$-Poincar\'e duality spaces; in particular, restricting to the endomorphisms of $\emptyset\in\mathrm{GrCob}^\mathrm{op}$, we obtain characteristic classes of $R$-oriented $M$-fibrations parametrised by the suitably twisted homology of $\mathbf{B}\mathrm{Out}(F_n)$, recovering results of Berglund and Barkan-Steinebrunner. + Finally, we describe explicitly the morphism spaces in $\mathrm{GrCob}$, answering along the way a question by Hatcher. This allows us to construct a symmetric monoidal functor from the open-closed cobordism $\infty$-category $\mathcal{OC}$ to $\mathrm{GrCob}$. Composing with $\mathrm{GFT}_M$, we obtain an open-closed field theory with values in $\mathrm{Mod}_R$, attaining values $\Sigma^\infty_+LM\otimes R$ and $\Sigma^\infty_+M\otimes R$ at the circle and at the interval, respectively. We expect this to recover and extend constructions of Cohen, Godin and others. + oai:arXiv.org:2511.14978v2 math.AT - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Dongwoo Gang + http://creativecommons.org/licenses/by/4.0/ + Andrea Bianchi - Exponentially Slow Mixing of the Low Temperature SK Model - https://arxiv.org/abs/2511.22621 - arXiv:2511.22621v2 Announce Type: replace -Abstract: We give a short proof that low-temperature dynamics for the Sherrington-Kirkpatrick model have mixing time exponential in the system size, based on the recently proved existence of gapped spin configurations by (Minzer-Sah-Sawhney 2023, Dandi-Gamarnik-Zdeborov\'a 2023). This result is in contrast with a well established physics prediction which posits a stretched exponential mixing time of order $e^{N^{1/3 \pm o(1)}}$. Our proof clarifies that this prediction cannot apply to mixing from worst case initial conditions, but should presumably be understood to concern dynamics from a suitably random initialization. - oai:arXiv.org:2511.22621v2 - math.PR - cond-mat.dis-nn + Gibbs polystability of Fano manifolds, stability thresholds and symmetry breaking + https://arxiv.org/abs/2511.16173 + arXiv:2511.16173v2 Announce Type: replace +Abstract: We extend the probabilistic approach for constructing Kahler-Einstein metrics on log Fano manifolds - involving random point processes - to the case of non-discrete automorphism groups, by explicitly breaking the symmetry. This yields a new algebraic notion of Gibbs polystability, conjecturally equivalent to K-polystability. The definition involves a limit of log canonical thresholds on the GIT semistable locus of the N-fold products of the Fano manifold that we conjecture coincides with an analytic reduced stability threshold encoding the coercivity of the K-energy functional modulo automorphisms. These conjectures follow from an overarching conjectural Large Deviation Principle for the limit when N tends to infinity. We prove several of our conjectures for log Fano curves. By imposing a moment constraint, we derive a strengthened form of the sharp logarithmic Hardy-Littlewood-Sobolev inequality on the two-sphere, that implies the sharp form of Aubin's refinement of the Moser-Trudinger inequality. In companion papers we will present applications to Onsager's point vortex model on the two-sphere and the AdS/CFT correspondence. + oai:arXiv.org:2511.16173v2 + math.DG math-ph + math.AG math.MP - Wed, 10 Dec 2025 00:00:00 -0500 + math.PR + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Mark Sellke + Rolf Andreasson, Robert J. Berman, Ludvig Svensson - Global dynamics in a reaction-diffusion competition model with edge behavior - https://arxiv.org/abs/2512.00339 - arXiv:2512.00339v2 Announce Type: replace -Abstract: In this paper, we investigate a two-species competition model in a landscape consisting of a finite number of adjacent patches. For the two-patch scenario, by treating edge behavior at the interface as a strategy, it has been shown that there exists an ideal free distribution (IFD) strategy, which is a globally evolutionarily stable strategy. Specifically, when the resident species follows the IFD strategy and the mutant species does not, the mutant species is unable to invade the resident population. Building on this foundation, our work focuses on exploring the dynamics of the system when neither species can adopt the IFD strategy. We demonstrate that if the strategies of both species either exceed or fall below the IFD strategy, the mutant species can outcompete and eliminate the resident species, provided that its strategy is closer to the IFD strategy and its diffusion rates are equal to or slower than those of the resident species. Furthermore, if the strategies of the two species lie on opposite sides of the IFD strategy, the two species can coexist. This result is further extended to the case of an arbitrary but finite number of patches. - oai:arXiv.org:2512.00339v2 - math.DS - Wed, 10 Dec 2025 00:00:00 -0500 + Data-driven Analysis of First-Order Methods via Distributionally Robust Optimization + https://arxiv.org/abs/2511.17834 + arXiv:2511.17834v2 Announce Type: replace +Abstract: We consider the problem of analyzing the probabilistic performance of first-order methods when solving convex optimization problems drawn from an unknown distribution only accessible through samples. By combining performance estimation (PEP) and Wasserstein distributionally robust optimization (DRO), we formulate the analysis as a tractable semidefinite program. Our approach unifies worst-case and average-case analyses by incorporating data-driven information from the observed convergence of first-order methods on a limited number of problem instances. This yields probabilistic, data-driven performance guarantees in terms of the expectation or conditional value-at-risk of the selected performance metric. Experiments on smooth convex minimization, logistics regression, and Lasso show that our method significantly reduces the conservatism of classical worst-case bounds and narrows the gap between theoretical and empirical performance. + oai:arXiv.org:2511.17834v2 + math.OC + Thu, 11 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - Kuiyue Liu, Shanshan Chen + Jisun Park, Vinit Ranjan, Bartolomeo Stellato - Time-periodic non-radial solutions near monotone vortices in linearized 2D Euler - https://arxiv.org/abs/2512.01730 - arXiv:2512.01730v2 Announce Type: replace -Abstract: We study the linearized 2D Euler equations around radial vortex profiles. Previous works have shown that the strict monotonicity of the vorticity profile leads to axisymmetrization and inviscid damping of non-radial perturbations. - Given any strictly decreasing radial vortex, we construct arbitrarily close (in low H\"{o}lder norms $C^\alpha$, with $0<\alpha < 1$) radial profiles that are merely non-increasing, for which non-radial, time-periodic solutions to the linearized equation exist. This shows that both axisymmetrization and inviscid damping are not robust under small, low-regularity perturbations of the background profile that violate strict monotonicity. - oai:arXiv.org:2512.01730v2 - math.AP - Wed, 10 Dec 2025 00:00:00 -0500 + Solving a Research Problem in Mathematical Statistics with AI Assistance + https://arxiv.org/abs/2511.18828 + arXiv:2511.18828v2 Announce Type: replace +Abstract: Over the last few months, AI models including large language models have improved greatly. There are now several documented examples where they have helped professional mathematical scientists prove new results, sometimes even helping resolve known open problems. In this short note, we add another example to the list, by documenting how we were able to solve a previously unsolved research problem in robust mathematical statistics with crucial help from GPT-5. Our problem concerns robust density estimation, where the observations are perturbed by Wasserstein-bounded contaminations. In a previous preprint (Chao and Dobriban, 2023, arxiv:2308.01853v2), we have obtained upper and lower bounds on the minimax optimal estimation error; which were, however, not sharp. + Starting in October 2025, making significant use of GPT-5 Pro, we were able to derive the minimax optimal error rate (reported in version 3 of the above arxiv preprint). GPT-5 provided crucial help along the way, including by suggesting calculations that we did not think of, and techniques that were not familiar to us, such as the dynamic Benamou-Brenier formulation, for key steps in the analysis. Working with GPT-5 took a few weeks of effort, and we estimate that it could have taken several months to get the same results otherwise. At the same time, there are still areas where working with GPT-5 was challenging: it sometimes provided incorrect references, and glossed over details that sometimes took days of work to fill in. We outline our workflow and steps taken to mitigate issues. Overall, our work can serve as additional documentation for a new age of human-AI collaborative work in mathematical science. + oai:arXiv.org:2511.18828v2 + math.ST + cs.AI + cs.LG + stat.TH + Thu, 11 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - \'Angel Castro, Daniel Lear + Edgar Dobriban - On Topology of Three-dimensional Continua with Singular Points - https://arxiv.org/abs/2512.02385 - arXiv:2512.02385v2 Announce Type: replace -Abstract: We propose to model the topology of three-dimensional (3D) continua by Yin sets, regular open semianalytic sets with bounded boundary. Our model differs from manifold-based models in that singular points of a 3D continuum, i.e., boundary points where the tangent plane is not uniquely defined, are treated not as anomalies but as a central subject of our theoretical investigation. We characterize the local and global topology of Yin sets. Then we give a unique boundary representation of Yin sets based on the notion of a glued surface, a quotient space of an orientable compact 2-manifold along a one-dimensional CW complex. Our results apply to 3D continua with arbitrarily complex topology and may be useful in a number of scientific and engineering applications such as solid modeling, computer-aided design, and numerical simulations of multiphase flows with topological changes. - oai:arXiv.org:2512.02385v2 + Complex structures of the Gibbons-Hawking ansatz with infinite topological type + https://arxiv.org/abs/2511.18836 + arXiv:2511.18836v3 Announce Type: replace +Abstract: In this paper, we study the complex structures of complete hyperk\"ahler four-manifolds of infinite topological type arising from the Gibbons-Hawking ansatz. We show that for almost all complex structures in the hyperk\"ahler family, the manifold is biholomorphic to a hypersurface in $\mathbb{C}^3$ defined by an explicit entire function. For the remaining complex structures, we further prove that the manifold is biholomorphic to the minimal resolution of a singular surface in $\mathbb{C}^3$ under certain conditions. Thus, we partially extend LeBrun's celebrated work to the context of countably many punctures. + oai:arXiv.org:2511.18836v3 + math.DG + Thu, 11 Dec 2025 00:00:00 -0500 + replace + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Wenxin He, Bin Xu + + + A note on TQFTs for orientable 2-dimensional cobordisms + https://arxiv.org/abs/2511.19373 + arXiv:2511.19373v2 Announce Type: replace +Abstract: Topological quantum field theories (TQFTs) are symmetric monoidal functors out of cobordism categories. In dimension two, oriented TQFTs are famously classified by commutative Frobenius algebras. In the unoriented setting, the classification requires additional data: an involution and a value assigned to the M\"obius strip. In this work, we describe an intermediate framework that classifies 2-dimensional TQFTs for orientable cobordisms, in an appropriate sense. Our motivation arises from skein-theoretic models of surfaces embedded in 3-manifolds and Khovanov homology, where surfaces are often treated as unoriented, even though the associated 2-dimensional TQFTs themselves need not be fully unoriented. + oai:arXiv.org:2511.19373v2 + math.QA math.GT - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Hao Liang, Yunhao Qiu, Yan Tan, Qinghai Zhang + Leon J. Goertz, Paul Wedrich - Strengthening Han's Fourier Entropy-Influence Inequality via an Information-Theoretic Proof - https://arxiv.org/abs/2512.03117 - arXiv:2512.03117v3 Announce Type: replace -Abstract: We strengthen Han's Fourier entropy-influence inequality $$ H[\widehat{f}] \leq C_{1}I(f) + C_{2}\sum_{i\in [n]}I_{i}(f)\ln\frac{1}{I_{i}(f)} $$ originally proved for $\{-1,1\}$-valued Boolean functions with $C_{1}=3+2\ln 2$ and $C_{2}=1$. We show, by a short information-theoretic proof, that it in fact holds with sharp constants $C_{1}=C_{2}=1$ for all real-valued Boolean functions of unit $L^{2}$-norm, thereby establishing the inequality as an elementary structural property of Shannon entropy and influence. - oai:arXiv.org:2512.03117v3 - cs.IT - math.IT - Wed, 10 Dec 2025 00:00:00 -0500 + Dense Matchings of Linear Size in Graphs with Independence Number 2 + https://arxiv.org/abs/2512.01401 + arXiv:2512.01401v2 Announce Type: replace +Abstract: For a real number $c > 4$, we prove that every graph $G$ with $\alpha(G) \leq 2$ and $|V(G)| \geq ct$ has a matching $M$ with $|M| = t$ such that the number of non-adjacent pairs of edges in $M$ is at most: \begin{equation*} + \left( \frac{1}{c\left(c-1\right)^2} + O_c\left(t^{-1/3} \right) \right) \binom{t}{2}. \end{equation*} This is related to an open problem of Seymour (2016) about Hadwiger's Conjecture, who asked if there is a constant $\varepsilon > 0$ such that every graph $G$ with $\alpha(G) \leq 2$ has $\text{had}(G) \geq (\frac{1}{3} + \varepsilon) |V(G)|$. + oai:arXiv.org:2512.01401v2 + math.CO + Thu, 11 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - Peijie Li, Guangyue Han + Jung Hon Yip - Sharp thresholds, hitting times and the power of choice for random geometric graphs - https://arxiv.org/abs/2512.04191 - arXiv:2512.04191v2 Announce Type: replace -Abstract: We consider a random geometric graph process where random points $(X_i)_{i \ge 1}$ are embedded consecutively in the $d$-dimensional unit torus $\mathbb{T}^d$, and every two points at distance at most $r$ form an edge. As $r\to 0$, we confirm that well-known hitting time results for $k$-connectivity (with $k\ge 1$ fixed) and Hamiltonicity in the Erd\H{o}s-R\'enyi graph process also hold for the considered geometric analogue. Moreover, we exhibit a sort of probabilistic monotonicity for each of these properties. - We also study a geometric analogue of the power of choice where, at each step, an agent is given two random points sampled independently and uniformly from $\mathbb{T}^d$ and must add exactly one of them to the already constructed point set. When the agent is allowed to make their choice with the knowledge of the entire sequence of random points (offline 2-choice), we show that they can construct a connected graph at the first time $t$ when none of the first $t$ pairs of proposed points contains two isolated vertices in the graph induced by $(X_i)_{i=1}^{2t}$, and maintain connectivity thereafter by following a simple algorithm. We also derive analogous results for $k$-connectivity and Hamiltonicity. This shows that each of the said properties can be attained two times faster (time-wise) and with four times fewer points in the offline 2-choice process compared to the 1-choice process. - In the online version where the agent only knows the process until the current time step, we show that $k$-connectivity and Hamiltonicity cannot be significantly accelerated (time-wise) but may be realised on two times fewer points compared to the 1-choice analogue. - oai:arXiv.org:2512.04191v2 + A dimer view on Fox's trapezoidal conjecture + https://arxiv.org/abs/2512.02314 + arXiv:2512.02314v2 Announce Type: replace +Abstract: Fox's conjecture (1962) states that the sequence of absolute values of the coefficients of the Alexander polynomial of alternating links is trapezoidal. While the conjecture remains open in general, a number of special cases have been settled, some quite recently: Fox's conjecture was shown to hold for special alternating links by Hafner, M\'esz\'aros, and Vidinas (2023) and for certain diagrammatic Murasugi sums of special alternating links by Azarpendar, Juh\'asz, and K\'alm\'an (2024). In this paper, we give an alternative proof of Azarpendar, Juh\'asz, and K\'alm\'an's aforementioned beautiful result via a dimer model for the Alexander polynomial. In doing so, we not only obtain a significantly shorter proof of Azarpendar, Juh\'asz, and K\'alm\'an's result than the original, but we also obtain several theorems of independent interest regarding the Alexander polynomial, which are readily visible from the dimer point of view. + oai:arXiv.org:2512.02314v2 math.CO - math.PR - Wed, 10 Dec 2025 00:00:00 -0500 + math.GT + Thu, 11 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - Dawid Ignasiak, Lyuben Lichev + Karola M\'esz\'aros, Melissa Sherman-Bennett, Alexander Vidinas - The Polynomial Freiman-Ruzsa (Marton) Conjecture in Integers and Finite Fields via Spectral Stability - https://arxiv.org/abs/2512.04433 - arXiv:2512.04433v3 Announce Type: replace -Abstract: We settle the Polynomial Freiman--Ruzsa (PFR/Marton) conjecture for the integers and for cyclic groups. More precisely, we show that if $A$ is a finite subset of $\mathbb{Z}$ or $\mathbb{Z}/N\mathbb{Z}$ with $|A+A| \le K|A|$, then there is a subgroup $H$ of index at most $K^{O(1)}$ such that $A$ is contained in at most $K^{O(1)}$ cosets of $H$. The proof is based on a new spectral stability dichotomy for the $L^4$ Fourier mass of $\mathbf{1}_A$: either this mass is concentrated on a span of size $K^{O(1)}$, or, after passing to a quotient of codimension $K^{O(1)}$, the doubling constant of the image of $A$ decreases by a definite power of $K$. Using Freiman modeling we transfer this dichotomy to cyclic groups, obtain polynomial Bogolyubov-type bounds, and deduce Marton's conjecture in $\mathbb{Z}$ and $\mathbb{Z}/N\mathbb{Z}$. As a corollary, we also recover and extend the finite-field formulation of Marton's conjecture: in odd characteristic we obtain a direct spectral proof, and together with the characteristic-2 result of Green, Gowers, Manners, and Tao this yields a complete resolution of the conjecture for all finite fields. For context beyond finite fields, we recall their theorem for abelian groups of bounded exponent. - oai:arXiv.org:2512.04433v3 - math.CO - math.NT - Wed, 10 Dec 2025 00:00:00 -0500 + On Topology of Three-dimensional Continua with Singular Points + https://arxiv.org/abs/2512.02385 + arXiv:2512.02385v3 Announce Type: replace +Abstract: We propose to model the topology of three-dimensional (3D) continua by Yin sets, regular open semianalytic sets with bounded boundary. Our model differs from manifold-based models in that singular points of a 3D continuum, i.e., boundary points where the tangent plane is not uniquely defined, are treated not as anomalies but as a central subject of our theoretical investigation. We characterize the local and global topology of Yin sets. Then we give a unique boundary representation of Yin sets based on the notion of a glued surface, a quotient space of an orientable compact 2-manifold along a one-dimensional CW complex. Our results apply to 3D continua with arbitrarily complex topology and may be useful in a number of scientific and engineering applications such as solid modeling, computer-aided design, and numerical simulations of multiphase flows with topological changes. + oai:arXiv.org:2512.02385v3 + math.GT + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Mohammad Taha Kazemi Moghadam + Hao Liang, Yunhao Qiu, Yan Tan, Qinghai Zhang - Seaweed algebras with restricted part sizes - https://arxiv.org/abs/2512.05890 - arXiv:2512.05890v2 Announce Type: replace -Abstract: Seaweed algebras are a class of Lie algebras that are naturally characterized by a pair of compositions, which in turn are represented visually as planar graphs called meanders. These meanders provide a straightforward method for computing the index of the associated algebra. The goal of this paper is to enumerate those seaweed algebras with a fixed index and whose associated compositions have restricted part sizes. In particular, we enumerate those with composition part sizes from so-called acyclic sets. We also establish a bijection between sets of indecomposable seaweed algebras with meanders with certain restricted part sizes and sets of permutations with restricted displacements. In certain cases, the index of the algebra can be determined by a simple statistic on the permutation. - oai:arXiv.org:2512.05890v2 - math.CO - Wed, 10 Dec 2025 00:00:00 -0500 + Numerical Analysis of the 2D Stochastic Navier-Stokes Equations: Convergence under Transport Noise and No-slip Boundary Conditions + https://arxiv.org/abs/2512.03483 + arXiv:2512.03483v2 Announce Type: replace +Abstract: This work is concerned with the numerical approximation of the two-dimensional stochastic Navier-Stokes equation with transport noise and no-slip boundary conditions on a convex polygonal domain. The analysis is challenged by the solution's low spatial regularity and the non-Lipschitz nonlinearity. We derive a convergence rate in the mean-square sense for a spatial semidiscretization. Furthermore, for the full discretization, we prove convergence in probability and establish an explicit rate with respect to the time step. + oai:arXiv.org:2512.03483v2 + math.NA + cs.NA + math.PR + Thu, 11 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - Kassie Archer, Aaron Geary, Robert P. Laudone + Binjie Li, Qin Zhou - A simplified formula for the matched projection of an idempotent - https://arxiv.org/abs/2512.05970 - arXiv:2512.05970v2 Announce Type: replace -Abstract: Let $\mathcal{L}(H)$ be the set of all adjointable operators on a Hilbert $C^*$-module $H$. For each $T\in\mathcal{L}(H)$, $T^*$ denotes its adjoint operator, and $|T^*|$ is the positive square root of $TT^*$. We establish a simplified formula for the matched projection $m(Q)$ of an idempotent $Q\in\mathcal{L}(H)$ as $$m(Q)=\frac{I+|Q^*|-|I-Q^*|}{2},$$ where $I$ is the identity operator on $H$. This explicit expression allows for the direct derivation of some basic properties of $m(Q)$. - oai:arXiv.org:2512.05970v2 - math.FA - Wed, 10 Dec 2025 00:00:00 -0500 + Multiparameter quantum general linear supergroup + https://arxiv.org/abs/2512.05777 + arXiv:2512.05777v2 Announce Type: replace +Abstract: We introduce uniparametric and multiparametric quantisations of the general linear supergroup, in the form of "quantised function algebras", both in a formal setting - yielding "quantum formal series Hopf superalgebras", a` la Drinfeld - and in a polynomial one - closer to Manin's point of view. In the uniparametric setting, we start from quantised universal enveloping superalgebras over gl(n) - endowed with a super-structure - as in [Ya1] and [Zha]: through a direct approach, we construct their linear dual, thus finding the quantum formal series Hopf superalgebras mentioned above, which are described in detail via an explicit presentation. Starting from the latter, then, we perform a deformation by a well-chosen 2-cocycle, thus getting a multiparametric quantisation, described again by an explicit presentation: this is, in turn, the dual to the multiparametric quantised universal enveloping algebra over gl(n) from [GGP]. We also provide some "polynomial versions" of these quantisations, both for the uniparametric and the multiparametric case. In particular, we compare the latter to Manin's quantum function algebras from [Ma]. Finally, both for the uniparametric and the multiparametric setting, we provide suitable PBW-like theorems, in "formal" and in "polynomial" versions alike. + oai:arXiv.org:2512.05777v2 + math.QA + Thu, 11 Dec 2025 00:00:00 -0500 replace - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Qingxiang Xu + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Fabio Gavarini, Margherita Paolini - Unifying Entropy Regularization in Optimal Control: From and Back to Classical Objectives via Iterated Soft Policies and Path Integral Solutions - https://arxiv.org/abs/2512.06109 - arXiv:2512.06109v2 Announce Type: replace -Abstract: This paper develops a unified perspective on several stochastic optimal control formulations through the lens of Kullback-Leibler regularization. We propose a central problem that separates the KL penalties on policies and transitions, assigning them independent weights, thereby generalizing the standard trajectory-level KL-regularization commonly used in probabilistic and KL-regularized control. This generalized formulation acts as a generative structure allowing to recover various control problems. These include the classical Stochastic Optimal Control (SOC), Risk-Sensitive Optimal Control (RSOC), and their policy-based KL-regularized counterparts. The latter we refer to as soft-policy SOC and RSOC, facilitating alternative problems with tractable solutions. Beyond serving as regularized variants, we show that these soft-policy formulations majorize the original SOC and RSOC problem. This means that the regularized solution can be iterated to retrieve the original solution. Furthermore, we identify a structurally synchronized case of the risk-seeking soft-policy RSOC formulation, wherein the policy and transition KL-regularization weights coincide. Remarkably, this specific setting gives rise to several powerful properties such as a linear Bellman equation, path integral solution, and, compositionality, thereby extending these computationally favourable properties to a broad class of control problems. - oai:arXiv.org:2512.06109v2 + New Results on the Polyak Stepsize: Tight Convergence Analysis and Universal Function Classes + https://arxiv.org/abs/2512.06231 + arXiv:2512.06231v2 Announce Type: replace +Abstract: In this paper, we revisit a classical adaptive stepsize strategy for gradient descent: the Polyak stepsize (PolyakGD), originally proposed in Polyak (1969). We study the convergence behavior of PolyakGD from two perspectives: tight worst-case analysis and universality across function classes. As our first main result, we establish the tightness of the known convergence rates of PolyakGD by explicitly constructing worst-case functions. In particular, we show that the $O((1-\frac{1}{\kappa})^K)$ rate for smooth strongly convex functions and the $O(1/K)$ rate for smooth convex functions are both tight. Moreover, we theoretically show that PolyakGD automatically exploits floating-point errors to escape the worst-case behavior. Our second main result provides new convergence guarantees for PolyakGD under both H\"older smoothness and H\"older growth conditions. These findings show that the Polyak stepsize is universal, automatically adapting to various function classes without requiring prior knowledge of problem parameters. + oai:arXiv.org:2512.06231v2 math.OC - cs.LG - cs.RO - cs.SY - eess.SY - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 replace - http://creativecommons.org/licenses/by/4.0/ - Ajinkya Bhole, Mohammad Mahmoudi Filabadi, Guillaume Crevecoeur, Tom Lefebvre + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Chang He, Wenzhi Gao, Bo Jiang, Madeleine Udell, Shuzhong Zhang - A note on Johnson's rule for minimizing makespan in the Two-Machine Flow Shop scheduling problem - https://arxiv.org/abs/2512.06119 - arXiv:2512.06119v2 Announce Type: replace -Abstract: We consider Johnson's rule for minimizing the makespan in the two-machine flow shop scheduling problem. We show that although the worst-case complexity of Johnson's rule is O(n log n), since it requires a complete sorting of the jobs, it is possible to detect in linear time whenever a full sort can be avoided and the optimal solution can be computed in linear time. Computational testing indicates that the linear time complexity always occurs in practice on standard benchmark instances with uniform distribution of the processing times. - oai:arXiv.org:2512.06119v2 - math.OC - Wed, 10 Dec 2025 00:00:00 -0500 + Generalizing quadratic $\mathbb{R}$-Algebraic sets in $\mathbb{CP}^{n}$ + https://arxiv.org/abs/2512.06472 + arXiv:2512.06472v2 Announce Type: replace +Abstract: Motivated by our study of the complex Banach conjecture, we characterize a complex ellipsoids $\mathcal E$ as compact subsets of $\mathbb C^n$, with the property that every complex line intersect $\mathcal E$ either in a single point or in the complex affine image of the unit disk. This characterization leads to the main interest of this paper. We study the topological behavior of compact subsets of $\mathbb{CP}^n$ with the property that any complex line that intersects them does either at a single point, at the boundary of a complex disk, or along the entire line. In particular, we are interested in quadratic $\R$-algebraic subsets of $\mathbb{CP}^n$. + oai:arXiv.org:2512.06472v2 + math.GT + math.CV + Thu, 11 Dec 2025 00:00:00 -0500 replace - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Federico Della Croce, Quentin Schau + http://creativecommons.org/publicdomain/zero/1.0/ + Javier Bracho, Luis Montejano - The Hurwitz existence problem and the prime-degree conjecture: A computational perspective - https://arxiv.org/abs/2512.06545 - arXiv:2512.06545v2 Announce Type: replace -Abstract: We investigate the Hurwitz existence problem from a computational viewpoint. Leveraging the symmetric-group algorithm by Zheng and building upon implementations originally developed by Baroni, we achieve a complete and non-redundant enumeration of all non-realizable partition triples for positive integers up to $31$. These results are further categorized into four types according to their underlying mathematical structure; it is observed that nearly nine-tenths of them can be explained by known theoretical results. As an application, we verify the prime-degree conjecture for all primes less than $32$. In light of the exponential memory growth inherent in existing computational approaches -- which limits their feasibility at higher degrees -- we propose a novel software architecture designed to stabilize memory usage, thereby facilitating further detection of exceptional cases in the Hurwitz existence problem. The complete dataset of non-realizable partition triples, along with our implementation, will been made public on GitHub. - oai:arXiv.org:2512.06545v2 - math.GR - Wed, 10 Dec 2025 00:00:00 -0500 + Metric Diophantine approximation on fractals + https://arxiv.org/abs/2512.07204 + arXiv:2512.07204v2 Announce Type: replace +Abstract: Inspired by a problem proposed by Mahler, we will address the following related question, 'How well can irrationals in a missing digit set be approximated by rationals with polynomial denominators?' and prove some related results. To achieve this, we will be closely looking at Khintchine's theorem, particularly the convergence case and aim to prove a Khintchine-like convergence theorem for missing digit sets with large bases and rationals with polynomial denominators. + oai:arXiv.org:2512.07204v2 + math.NT + Thu, 11 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Yiru Wang, Bingqian Li, Yi Zhou, Zhiqiang Wei, Yu Ye, Yiqian Shi, Bin Xu - - - A new generalization of the McKay conjecture for $p$-solvable groups - https://arxiv.org/abs/2512.07073 - arXiv:2512.07073v2 Announce Type: replace -Abstract: Let $P$ be a Sylow $p$-subgroup of a finite $p$-solvable group $G$, where $p$ is a prime. Using a normal $p$-series $\mathcal{N}$ of $G$, we introduce the notion of $(\mathcal{N},p)$-stable characters and prove that $G$ and ${\bf N}_G(P)$ have equal numbers of such characters, which gives a new generalization of the McKay conjecture for $p$-solvable groups. Also, we establish a canonical bijection between these characters in the case where $G$ has odd order. Our proofs depend heavily on the theory of self-stabilizing pairs founded by M. L. Lewis, as well as some results of $\pi$-special characters due to I. M. Isaacs. - oai:arXiv.org:2512.07073v2 - math.GR - Wed, 10 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/publicdomain/zero/1.0/ - Huimin Chang, Ping Jin + James Wyatt - Copositivity, discriminants and nonseparable signed supports - https://arxiv.org/abs/2512.07373 - arXiv:2512.07373v2 Announce Type: replace -Abstract: In this work we establish a connection between copositivity, that is, nonnegativity on the positive orthant, of sparse real Laurent polynomials and discriminants. Specifically, we consider Laurent polynomials in the positive orthant with fixed support and fixed coefficient signs. We provide a criterion to decide whether a given polynomial is copositive that is based in determining the intersection points of the signed discriminant and a path going through the coefficients of the polynomial. If the signed support satisfies a combinatorial condition termed nonseparability, we show additionally that this intersection consists of one point, and that tracking one path in homotopy continuation methods suffices to decide upon copositivity. - Building on these results, we show that any copositive polynomial with nonseparable signed support can be decomposed into a sum of nonnegative circuit polynomials, generalising thereby previously known supports having this property. - oai:arXiv.org:2512.07373v2 + An effective criterion for multiple positive zeros of vertically parametrized polynomial systems + https://arxiv.org/abs/2512.07560 + arXiv:2512.07560v2 Announce Type: replace +Abstract: We present an effective criterion for determining whether a (augmented) vertically parametrized polynomial system admits multiple positive zeros for some choice of parameter values. Our method builds on previous algorithms from chemical reaction network theory and reduces the question to checking the feasibility of a linear system of equalities and inequalities. Our criterion provides a sufficient condition for the absence of multiple positive zeros that applies to any augmented vertically parametrized polynomial system, and we show that when the kernel of the coefficient matrix of the system displays a certain sparsity structure, this condition becomes also necessary. We give thereby a full characterization of the existence of multiple zeros for this type of systems. + oai:arXiv.org:2512.07560v2 math.AG - math.CO - math.OC - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - Elisenda Feliu, Joan Ferrer, M\'at\'e L. Telek + Carles Checa, Elisenda Feliu - Intersection problems for linear codes and polynomials over finite fields - https://arxiv.org/abs/2512.07547 - arXiv:2512.07547v2 Announce Type: replace -Abstract: This paper proves a stability result for a variation of the Erd\H{o}s-Ko-Rado theorem in the context of polynomials over finite fields. Let $\mathcal F$ be a family of polynomials of degree at most $k \geq 3$ in $\mathbb F_q[X]$. Call $\mathcal F$ intersecting if for any two polynomials $f, g$ in $\mathcal F$, there exists a point $x \in \mathbb F_q$ for which $f(x) = g(x)$. An intersecting family is called a star if it consists of all polynomials $f$ with ${\rm deg } f \leq k$ such that $f(x) = y$ for some fixed points $x, y \in \mathbb F_q$. In this paper we prove that if $\mathcal F$ is an intersecting family with $|\mathcal F| \geq \frac 1{\sqrt 2} q^k + \mathcal O(q^{k-1})$, then $\mathcal F$ is contained in a star. In fact, we prove that this is still true if we also evaluate the polynomials "at infinity", which is equivalent to studying the problem for homogeneous bivariate polynomials. - The proof technique extends to a general framework for intersection problems of linear codes $C$. One has to investigate the geometry of the projective system $\mathcal S$ associated to $C$. If the hyperplanes that don't intersect $\mathcal S$ are well spread out with respect to the points not on $\mathcal S$, then one obtains stability results, showing that any intersecting family of reasonably large size is contained in a star. - oai:arXiv.org:2512.07547v2 - math.CO - Wed, 10 Dec 2025 00:00:00 -0500 + Symmetric weak multicategories + https://arxiv.org/abs/2512.07732 + arXiv:2512.07732v2 Announce Type: replace +Abstract: A multicategory is what remains of a monoidal category when monoidal product is not available. A weak multicategory means that hom-sets are in fact categories, and in place of usual equations, there are natural isomorphisms, which have to satisfy their own equations. A symmetric weak multicategory implies a weak multicategory with a weak (up to a cocycle) action of symmetric groups. + oai:arXiv.org:2512.07732v2 + math.CT + Thu, 11 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - Sam Adriaensen + Volodymyr Lyubashenko - Entropy-Smooth Structures on Topological Manifolds - https://arxiv.org/abs/2512.07660 - arXiv:2512.07660v2 Announce Type: replace -Abstract: We introduce an information-theoretic framework for smooth structures on topological manifolds, replacing coordinate charts with small-scale entropy data of local probability probes. A concise set of axioms identifies admissible coordinate functions and reconstructs a smooth atlas directly from the quadratic entropy response. We prove that this entropy-smooth structure is equivalent to the classical smooth structure, stable under perturbations, and compatible with products, submanifolds, immersions, and diffeomorphisms. This establishes smoothness as an information-theoretic phenomenon and forms the foundational layer of a broader program linking entropy, diffusion, and differential geometry. - oai:arXiv.org:2512.07660v2 - math.DG - math.GN - Wed, 10 Dec 2025 00:00:00 -0500 + Free Boundary Problem for inhomogeneous Navier-Stokes equations + https://arxiv.org/abs/2512.08039 + arXiv:2512.08039v2 Announce Type: replace +Abstract: We study free boundary problems for incompressible inhomogeneous flows governed by the Navier--Stokes equations, focusing on the regularity and global-in-time well-posedness of solutions in critical functional frameworks for small initial data. + We introduce a novel analytical framework for free boundary problems formulated as perturbations of the half-space. Our approach relies on the natural Lagrangian change of coordinates and a detailed analysis of the linearized problem (the Stokes system) in the maximal regularity regime, formulated in the Lebesgue spaces $L_p(0,T; L_q)$, including time-weighted variants. The main difficulty lies in the treatment of boundary terms, for which we apply a new technique based on complex interpolation to control nonlinear terms in fractional Sobolev spaces. This strategy also allows us to handle the case of variable density, which is not easily addressed by approaches based on Besov spaces. + Using this framework and real interpolation techniques, we construct also solutions in the Lorentz class $L_{p,1}(0,T; L_q)$ in time. The method further enables a rigorous study of the stability of equilibrium configurations. In particular, we resolve the problem in two spatial dimensions, where the interplay between geometry and regularity is especially subtle. Beyond these specific applications, the proposed approach provides a powerful tool for broader classes of nonlinear PDEs and further developments in maximal regularity theory. + oai:arXiv.org:2512.08039v2 + math.AP + Thu, 11 Dec 2025 00:00:00 -0500 replace - http://creativecommons.org/licenses/by/4.0/ - Amandip Sangha + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Piotr B. Mucha, Tomasz Piasecki, Yoshihiro Shibata - Exact supported co-degree bounds for Hamilton cycles - https://arxiv.org/abs/2512.07751 - arXiv:2512.07751v2 Announce Type: replace -Abstract: For any $k\ge 3$ and $\ell \in [k-1]$ such that $(k,\ell) \ne (3,1)$, we show that any sufficiently large $k$-graph $G$ must contain a Hamilton $\ell$-cycle provided that it has no isolated vertices and every set of $k-1$ vertices contained in an edge is contained in at least $\left(1 - \frac{1}{\lfloor{\frac{k}{k-\ell}\rfloor}(k-\ell)}\right)n - (k - 3)$ edges. We also show that this bound is tight for infinitely many values of $k$ and $\ell$ and is off by at most $1$ for all others, and is hence essentially optimal. This improves an asymptotic version of this result due to Mycroft and Z\'arate-Guer\'en, and the case $\ell = k-1$ completely resolves a conjecture of Illingworth, Lang, M\"uyesser, Parczyk and Sgueglia. - These results support the utility of $\textit{minimum}$ $\textit{supported}$ $\textit{co-degree}$ conditions in a $k$-graph, a recently introduced variant of the standard notion of minimum co-degree applicable to $k$-graphs with non-trivial strong independent sets. Our proof techniques involve a novel blow-up tiling framework introduced by Lang, avoiding traditional approaches using the regularity and blow-up lemmas. - oai:arXiv.org:2512.07751v2 - math.CO - Wed, 10 Dec 2025 00:00:00 -0500 + Adversarial Barrier in Uniform Class Separation + https://arxiv.org/abs/2512.08149 + arXiv:2512.08149v2 Announce Type: replace +Abstract: We identify a strong structural obstruction to Uniform Separation in constructive arithmetic. The mechanism is independent of semantic content; it emerges whenever two distinct evaluator predicates are sustained in parallel and inference remains uniformly representable in an extension of HA. Under these conditions, any putative Uniform Class Separation principle becomes a distinguished instance of a fixed point construction. The resulting limitation is stricter in scope than classical separation barriers (Baker; Rudich; Aaronson et al.) insofar as it constrains the logical form of uniform separation within HA, rather than limiting particular relativizing, naturalizing, or algebrizing techniques. + oai:arXiv.org:2512.08149v2 + math.LO + cs.CC + cs.LO + Thu, 11 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - Shoham Letzter, Arjun Ranganathan + Milan Rosko - Correlation length in random MPS and PEPS - https://arxiv.org/abs/1906.11682 - arXiv:1906.11682v4 Announce Type: replace-cross -Abstract: Tensor network states are used extensively as a mathematically convenient description of physically relevant states of many-body quantum systems. Those built on regular lattices, i.e. matrix product states (MPS) in dimension 1 and projected entangled pair states (PEPS) in dimension 2 or higher, are of particular interest in condensed matter physics. The general goal of this work is to characterize which features of MPS and PEPS are generic and which are, on the contrary, exceptional. This problem can be rephrased as follows: given an MPS or PEPS sampled at random, what are the features that it displays with either high or low probability? One property which we are particularly interested in is that of having either rapidly decaying or long-range correlations. In a nutshell, our main result is that translation-invariant MPS and PEPS typically exhibit exponential decay of correlations at a high rate. We have two distinct ways of getting to this conclusion, depending on the dimensional regime under consideration. Both yield intermediate results which are of independent interest, namely: the parent Hamiltonian and the transfer operator of such MPS and PEPS typically have a large spectral gap. In all these statements, our aim is to get a quantitative estimate of the considered quantity (generic correlation length or spectral gap), which has the best possible dependency on the physical and bond dimensions of the random MPS or PEPS. - oai:arXiv.org:1906.11682v4 - quant-ph - cond-mat.str-el - hep-th - math-ph - math.MP - math.PR - Wed, 10 Dec 2025 00:00:00 -0500 - replace-cross - http://creativecommons.org/licenses/by/4.0/ - 10.1007/s00023-021-01087-4 - Annales Henri Poincare, Vol. 23, pp. 141-222 (2022) - C\'ecilia Lancien, David P\'erez-Garc\'ia - - - Degenerate crossing number and signed reversal distance - https://arxiv.org/abs/2308.10666 - arXiv:2308.10666v3 Announce Type: replace-cross -Abstract: Given a graph drawn in the plane, the degenerate crossing number of the drawing is the number of points in the plane which are contained in the relative interior of at least two edges, where each edge is required to be drawn as a simple arc. The degenerate crossing number of a graph is the minimum degenerate crossing number among all its drawings. - Given a drawing, cutting a neighborhood of the surface around each crossing and pasting a M\"obius band gives a non-orientable surface, on which the drawing of the graph can be extended to an embedding. From this observation, Mohar derived that the degenerate crossing number of a graph is at most its non-orientable genus, and conjectured that these quantities are equal for every graph. He also made a stronger conjecture for loopless pseudo-triangulations with a fixed embedding scheme. - In this paper, we prove a structure theorem that allows to understand when the degenerate crossing number and non-orientable genus coincide in a large class of loopless bipartite embedding schemes. In particular, we provide a counterexample to Mohar's stronger conjecture, but show that in the vast majority of the 2-vertex cases, as well as for many bipartite graphs, Mohar's conjecture is satisfied. - The reversal distance between two signed permutations is the minimum number of reversals that transform one permutation to the other one. If we represent the trajectory of each element of a signed permutation under successive reversals by a simple arc, we obtain a drawing of a 2-vertex embedding scheme with degenerate crossings. Our main result is proved by leveraging this connection and a classical result in genome rearrangement (the Hannenhalli--Pevzner algorithm) and can also be understood as an extension of this algorithm when the reversals do not necessarily happen in a monotone order. - oai:arXiv.org:2308.10666v3 - cs.CG + Roth-type theorems in additive combinatroics + https://arxiv.org/abs/2512.08455 + arXiv:2512.08455v2 Announce Type: replace +Abstract: In this article we will introduce a central problem in additive combinatorics, which arised from the famous van der Waerden theorem and an early conjecture of Erd\H{o}s and Tur\'{a}n. The first important theorem was due to Roth in 1953. There were a number of generalized or improved results afterwards, which we call Roth-type theorems. We will list them and try to give concise expositions to the ideas in some of the proofs without much prior knowledge. + oai:arXiv.org:2512.08455v2 math.CO - Wed, 10 Dec 2025 00:00:00 -0500 - replace-cross - http://creativecommons.org/licenses/by/4.0/ - Niloufar Fuladi, Alfredo Hubard, Arnaud de Mesmay - - - Local Zeta Functions of Multiparameter Calabi-Yau Threefolds from the Picard-Fuchs Equations - https://arxiv.org/abs/2405.08067 - arXiv:2405.08067v4 Announce Type: replace-cross -Abstract: The deformation approach of arXiv:2104.07816 for computing zeta functions of one-parameter Calabi-Yau threefolds is generalised to cover also multiparameter manifolds. Consideration of the multiparameter case requires the development of an improved formalism. This allows us, among other things, to make progress on some issues left open in previous work, such as the treatment of apparent and conifold singularities and changes of coordinates. We also discuss the efficient numerical computation of the zeta functions. As examples, we compute the zeta functions of the two-parameter mirror octic, a non-symmetric split of the quintic threefold also with two parameters, and the $S_5$ symmetric five-parameter Hulek-Verrill manifolds. These examples allow us to exhibit the several new types of geometries for which our methods make practical computations possible. They also act as consistency checks, as our results reproduce and extend those of arXiv:hep-th/0409202 and arXiv:math/0304169. To make the methods developed here more approachable, a Mathematica package "CY3Zeta" for computing the zeta functions of Calabi-Yau threefolds, which is attached to this paper, is presented. - oai:arXiv.org:2405.08067v4 - hep-th math.NT - Wed, 10 Dec 2025 00:00:00 -0500 - replace-cross - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Philip Candelas, Xenia de la Ossa, Pyry Kuusela + Thu, 11 Dec 2025 00:00:00 -0500 + replace + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Weiwen Zhang - Explosive neural networks via higher-order interactions in curved statistical manifolds - https://arxiv.org/abs/2408.02326 - arXiv:2408.02326v3 Announce Type: replace-cross -Abstract: Higher-order interactions underlie complex phenomena in systems such as biological and artificial neural networks, but their study is challenging due to the scarcity of tractable models. By leveraging a generalisation of the maximum entropy principle, we introduce curved neural networks as a class of models with a limited number of parameters that are particularly well-suited for studying higher-order phenomena. Through exact mean-field descriptions, we show that these curved neural networks implement a self-regulating annealing process that can accelerate memory retrieval, leading to explosive order-disorder phase transitions with multi-stability and hysteresis effects. Moreover, by analytically exploring their memory-retrieval capacity using the replica trick, we demonstrate that these networks can enhance memory capacity and robustness of retrieval over classical associative-memory networks. Overall, the proposed framework provides parsimonious models amenable to analytical study, revealing higher-order phenomena in complex networks. - oai:arXiv.org:2408.02326v3 - cond-mat.dis-nn - cond-mat.stat-mech + Performance Analysis of Quantum CSS Error-Correcting Codes via MacWilliams Identities + https://arxiv.org/abs/2305.01301 + arXiv:2305.01301v3 Announce Type: replace-cross +Abstract: We analyze the performance of quantum stabilizer codes, one of the most important classes for practical implementations, on both symmetric and asymmetric quantum channels. To this aim, we first derive the weight enumerator (WE) for the undetectable errors based on the quantum MacWilliams identities. The WE is then used to evaluate tight upper bounds on the error rate of CSS quantum codes with \acl{MW} decoding. For surface codes we also derive a simple closed form expression of the bounds over the depolarizing channel. We introduce a novel approach that combines the knowledge of WE with a logical operator analysis, allowing the derivation of the exact asymptotic error rate for short codes. For example, on a depolarizing channel with physical error rate $\rho \to 0$, the logical error rate $\rho_\mathrm{L}$ is asymptotically $\rho_\mathrm{L} \approx 16 \rho^2$ for the $[[9,1,3]]$ Shor code, $\rho_\mathrm{L} \approx 16.3 \rho^2$ for the $[[7,1,3]]$ Steane code, $\rho_\mathrm{L} \approx 18.7 \rho^2$ for the $[[13,1,3]]$ surface code, and $\rho_\mathrm{L} \approx 149.3 \rho^3$ for the $[[41,1,5]]$ surface code. For larger codes our bound provides $\rho_\mathrm{L} \approx 1215 \rho^4$ and $\rho_\mathrm{L} \approx 663 \rho^5$ for the $[[85,1,7]]$ and the $[[181,1,10]]$ surface codes, respectively. Finally, we extend our analysis to include realistic, noisy syndrome extraction circuits by modeling error propagation throughout gadgets. This enables estimation of logical error rates under faulty measurements. The performance analysis serves as a design tool for developing fault-tolerant quantum systems by guiding the selection of quantum codes based on their error correction capability. Additionally, it offers a novel perspective on quantum degeneracy, showing it represents the fraction of non-correctable error patterns shared by multiple logical operators. + oai:arXiv.org:2305.01301v3 + quant-ph cs.IT math.IT - nlin.AO - stat.ML - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 replace-cross http://creativecommons.org/licenses/by/4.0/ - 10.1038/s41467-025-61475-w - Aguilera, M., Morales, P.A., Rosas, F.E. et al. Explosive neural networks via higher-order interactions in curved statistical manifolds. Nature Communications 16, 6511 (2025) - Miguel Aguilera, Pablo A. Morales, Fernando E. Rosas, Hideaki Shimazaki - - - Asynchronous Stochastic Approximation with Applications to Average-Reward Reinforcement Learning - https://arxiv.org/abs/2409.03915 - arXiv:2409.03915v3 Announce Type: replace-cross -Abstract: This paper investigates the stability and convergence properties of asynchronous stochastic approximation (SA) algorithms, with a focus on extensions relevant to average-reward reinforcement learning. We first extend a stability proof method of Borkar and Meyn to accommodate more general noise conditions than previously considered, thereby yielding broader convergence guarantees for asynchronous SA. To sharpen the convergence analysis, we further examine the shadowing properties of asynchronous SA, building on a dynamical systems approach of Hirsch and Bena\"{i}m. These results provide a theoretical foundation for a class of relative value iteration-based reinforcement learning algorithms -- developed and analyzed in a companion paper -- for solving average-reward Markov and semi-Markov decision processes. - oai:arXiv.org:2409.03915v3 - cs.LG - math.OC - Wed, 10 Dec 2025 00:00:00 -0500 - replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Huizhen Yu, Yi Wan, Richard S. Sutton - - - Fast Switching in Mixed-Integer Model Predictive Control - https://arxiv.org/abs/2411.19300 - arXiv:2411.19300v4 Announce Type: replace-cross -Abstract: We deduce stability results for finite control set and mixed-integer model predictive control with a downstream oversampling phase. The presentation rests upon the inherent robustness of model predictive control with stabilizing terminal conditions and techniques for solving mixed-integer optimal control problems by continuous optimization. Partial outer convexification and binary relaxation transform mixed-integer problems into common optimal control problems. We deduce nominal asymptotic stability for the resulting relaxed system formulation and implement sum-up rounding to restore efficiently integer feasibility on an oversampling time grid. If fast control switching is technically possible and inexpensive, we can approximate the relaxed system behavior in the state space arbitrarily close. We integrate input perturbed model predictive control with practical asymptotic stability. Numerical experiments illustrate practical relevance of fast control switching. - oai:arXiv.org:2411.19300v4 - eess.SY - cs.SY - math.OC - Wed, 10 Dec 2025 00:00:00 -0500 - replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Artemi Makarow, Christian Kirches + Diego Forlivesi, Lorenzo Valentini, Marco Chiani - Regge symmetry of 6j-symbols of the Lorentz group - https://arxiv.org/abs/2412.09425 - arXiv:2412.09425v3 Announce Type: replace-cross -Abstract: In this paper we derive new symmetry and new expression for $6j$-symbols of the unitary principal series representations of the $SL(2,\mathbb{C})$ group. This allowed us to derive for them the analogue of the Regge symmetry. - oai:arXiv.org:2412.09425v3 - hep-th + A new use of nonlocal symmetries for computing Liouvillian first integrals of rational second order ordinary differential equations + https://arxiv.org/abs/2310.04850 + arXiv:2310.04850v2 Announce Type: replace-cross +Abstract: Here we present an efficient method for finding and using a nonlocal symmetry admitted by a rational second order ordinary differential equation (rational 2ODE) in order to find a Liouvillian first integral (belonging to a vast class of Liouvillian functions). In a first stage, we construct an algorithm (improving the methodde veloped in [1]) that computes a nonlocal symmetry of a rational 2ODE. In ase cond stage, based on the knowledge of this symmetry, it is possible to construct three polynomial vector fields (in R2), which "share" the Liouvillian first integral with the rational 2ODE. These "plane" polynomial vector fields can be used to construct a procedure (based on an idea developed in [2]) to determine an integrating factor for the rational 2ODE with a fast probabilistic algorithm. The main advantages of the proposed method are: the obtaining of the nonlocal symmetry is algorithmic and very efficient and, furthermore, its use to find an integrating factor is a sequence of linear or quasilinear processes. + oai:arXiv.org:2310.04850v2 + nlin.CD math-ph math.MP - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 replace-cross - http://creativecommons.org/licenses/by/4.0/ - 10.1007/s13324-025-01113-2 - Anal.Math.Phys. 15, 113 (2025) - Elena Apresyan, Gor Sarkissian + http://creativecommons.org/licenses/by-nc-nd/4.0/ + I. Deme, L. G. S. Duarte, L. A. C. P. da Mota - Spaces of initial conditions for quartic Hamiltonian systems of Painlev\'e and quasi-Painlev\'e type - https://arxiv.org/abs/2412.17135 - arXiv:2412.17135v2 Announce Type: replace-cross -Abstract: The geometric approach for Painlev\'e and quasi-Painlev\'e differential equations in the complex plane is applied to non-autonomous Hamiltonian systems, quartic in the dependent variables. By computing their defining manifolds (analogue of the Okamoto's space of initial conditions in the quasi-Painlev\'e case), we provide a classification of such systems. We distinguish the various cases by the local behaviour at the movable singularities of the solutions, which are algebraic poles or ordinary poles. The principal cases are categorised by the initial base points of the system in the extended phase space $\mathbb{CP}^2$ and their multiplicities, arising from the coalescence of $4$ simple base points in the generic case. Through the mechanisms of coalescence of base points and degeneration (by setting certain coefficient functions in the Hamiltonian to $0$), all possible sub-cases of quartic Hamiltonian systems with the quasi-Painlev\'e property are obtained, and are characterised by their corresponding Newton polygons. As particular sub-cases we recover certain systems equivalent to known Painlev\'e equations, or variants thereof. The resulting picture is a multi-faceted description of each case: the local behaviour around singularities, the surface type, and the Newton polygon. - oai:arXiv.org:2412.17135v2 - nlin.SI - math.CA - Wed, 10 Dec 2025 00:00:00 -0500 + Flexible realizations existence: NP-completeness on sparse graphs and algorithms + https://arxiv.org/abs/2412.13721 + arXiv:2412.13721v2 Announce Type: replace-cross +Abstract: One of the questions in Rigidity Theory is whether a realization of the vertices of a graph in the plane is flexible, namely, if it allows a continuous deformation preserving the edge lengths. A flexible realization of a connected graph in the plane exists if and only if the graph has a NAC-coloring, which is a surjective edge coloring by two colors such that for each cycle, either all the edges have the same color, or there are at least two edges of each color. The question whether a graph has a NAC-coloring, and hence also the existence of a flexible realization, has been proven to be NP-complete. We show that this question is also NP-complete on graphs with maximum degree five and on graphs with the average degree at most $4+\varepsilon$ for every fixed $\varepsilon >0$. We also show that NAC-colorings can be counted in linear time for graphs with bounded treewidth. Since the only existing implementation of checking the existence of a NAC-coloring is rather naive, we propose new algorithms along with their implementation, which is significantly faster. We also focus on searching all NAC-colorings of a graph, since they provide useful information about its possible flexible realizations. + oai:arXiv.org:2412.13721v2 + cs.CG + math.CO + Thu, 11 Dec 2025 00:00:00 -0500 replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Marta Dell'Atti, Thomas Kecker + http://creativecommons.org/licenses/by/4.0/ + Petr La\v{s}tovi\v{c}ka, Jan Legersk\'y - Universal criterion for selective outcomes under stochastic resetting - https://arxiv.org/abs/2502.09127 - arXiv:2502.09127v2 Announce Type: replace-cross -Abstract: Resetting plays a pivotal role in optimizing the completion time of complex first passage processes with single or multiple outcomes/exit possibilities. While it is well established that the coefficient of variation -- a statistical dispersion defined as a ratio of the fluctuations over the mean of the first passage time -- must be larger than unity for resetting to be beneficial for any outcome averaged over all the possibilities, the same can not be said while conditioned on a particular outcome. The purpose of this letter is to derive a universal condition which reveals that two statistical metric -- the mean and coefficient of variation of the conditional times -- come together to determine when resetting can expedite the completion of a selective outcome, and furthermore can govern the biasing between preferential and non-preferential outcomes. The universality of this result is demonstrated for a one dimensional diffusion process subjected to resetting with two absorbing boundaries. - oai:arXiv.org:2502.09127v2 - cond-mat.stat-mech - cond-mat.soft + Revenue Maximization Under Sequential Price Competition Via The Estimation Of s-Concave Demand Functions + https://arxiv.org/abs/2503.16737 + arXiv:2503.16737v5 Announce Type: replace-cross +Abstract: We consider price competition among multiple sellers over a selling horizon of $T$ periods. In each period, sellers simultaneously offer their prices (which are made public) and subsequently observe their respective demand (not made public). The demand function of each seller depends on all sellers' prices through a private, unknown, and nonlinear relationship. We propose a dynamic pricing policy that uses semi-parametric least-squares estimation and show that when the sellers employ our policy, their prices converge at a rate of $O(T^{-1/7})$ to the Nash equilibrium prices that sellers would reach if they were fully informed. Each seller incurs a regret of $O(T^{5/7})$ relative to a dynamic benchmark policy. A theoretical contribution of our work is proving the existence of equilibrium under shape-constrained demand functions via the concept of $s$-concavity and establishing regret bounds of our proposed policy. Technically, we also establish new concentration results for the least squares estimator under shape constraints. Our findings offer significant insights into dynamic competition-aware pricing and contribute to the broader study of non-parametric learning in strategic decision-making. + oai:arXiv.org:2503.16737v5 + stat.ML + cs.LG math.PR - physics.chem-ph - Wed, 10 Dec 2025 00:00:00 -0500 + math.ST + stat.TH + Thu, 11 Dec 2025 00:00:00 -0500 replace-cross http://creativecommons.org/licenses/by/4.0/ - 10.1103/p3yc-kmt1 - Phys. Rev. E 112, 034116, 2025 - Suvam Pal, Leonardo Dagdug, Dibakar Ghosh, Denis Boyer, Arnab Pal + Daniele Bracale, Moulinath Banerjee, Cong Shi, Yuekai Sun - Residual-based Chebyshev filtered subspace iteration for sparse Hermitian eigenvalue problems tolerant to inexact matrix-vector products - https://arxiv.org/abs/2503.22652 - arXiv:2503.22652v4 Announce Type: replace-cross -Abstract: Chebyshev Filtered Subspace Iteration (ChFSI) has emerged as a robust alternative to Krylov eigensolvers for extracting a small subset of extremal eigenpairs from large sparse matrices, particularly in situations where these eigenpairs must be computed repeatedly as the system matrix evolves within an outer iteration. In this work, we propose R-ChFSI, a residual based reformulation of ChFSI designed to exhibit strong convergence properties even when the matrix-vector products are computed inexactly. We derive convergence guarantees under matrix-vector product approximations, providing a rigorous foundation for the method in large-scale eigenvalue computations. The tolerance of R-ChFSI to inexact matrix-vector products enables an efficient treatment of generalized Hermitian definite eigenproblems of the form $\textbf{A} \textbf{x} = \lambda \textbf{B} \textbf{x}$ where exact factorizations or high-accuracy iterative solves for evaluating $\textbf{B}^{-1}$ are often prohibitively expensive. Moreover, R-ChFSI naturally accommodates low-precision arithmetic for both standard and generalized eigenproblems, making it well-suited for modern hardware accelerators optimised for mixed-precision computation. To demonstrate the effectiveness of the approach, extensive numerical experiments are conducted on finite-element discretized eigenproblems with millions of degrees of freedom, solving for thousands of eigenpairs arising in \emph{ab initio} material modelling using Kohn-Sham density functional theory. For generalized eigenproblems employing approximate $\textbf{B}^{-1}$, R-ChFSI achieves desired residual norms orders of magnitude smaller than those obtained with standard ChFSI. In addition, R-ChFSI reliably reaches target residual tolerances (e.g., 10$^{-8}$) even with FP32 and TF32 arithmetic, significantly outperforming standard ChFSI in similar settings. - oai:arXiv.org:2503.22652v4 - physics.comp-ph - cs.NA - math.NA - Wed, 10 Dec 2025 00:00:00 -0500 + Inference on effect size after multiple hypothesis testing + https://arxiv.org/abs/2503.22369 + arXiv:2503.22369v3 Announce Type: replace-cross +Abstract: Significant treatment effects are often emphasized when interpreting and summarizing empirical findings in studies that estimate multiple, possibly many, treatment effects. Under this kind of selective reporting, conventional treatment effect estimates may be biased and their corresponding confidence intervals may undercover the true effect sizes. We propose new estimators and confidence intervals that provide valid inferences on the effect sizes of the significant effects after multiple hypothesis testing. Our methods are based on the principle of selective conditional inference and complement a wide range of tests, including step-up tests and bootstrap-based step-down tests. Our approach is scalable, allowing us to study an application with over 370 estimated effects. We justify our procedure for asymptotically normal treatment effect estimators. We provide two empirical examples that demonstrate bias correction and confidence interval adjustments for significant effects. The magnitude and direction of the bias correction depend on the correlation structure of the estimated effects and whether the interpretation of the significant effects depends on the (in)significance of other effects. + oai:arXiv.org:2503.22369v3 + econ.EM + math.ST + stat.TH + Thu, 11 Dec 2025 00:00:00 -0500 replace-cross - http://creativecommons.org/publicdomain/zero/1.0/ - Nikhil Kodali, Kartick Ramakrishnan, Phani Motamarri + http://creativecommons.org/licenses/by-sa/4.0/ + Andreas Dzemski, Ryo Okui, Wenjie Wang - Quantum Glassiness From Efficient Learning - https://arxiv.org/abs/2505.00087 - arXiv:2505.00087v3 Announce Type: replace-cross -Abstract: We show a relation between quantum learning theory and algorithmic hardness. We use the existence of efficient, local learning algorithms for energy estimation -- such as the classical shadows algorithm -- to prove that finding near-ground states of disordered quantum systems exhibiting a certain topological property is impossible in the average case for Lipschitz quantum algorithms. A corollary of our result is that many standard quantum algorithms fail to find near-ground states of these systems, including time-$T$ Lindbladian dynamics from an arbitrary initial state, time-$T$ quantum annealing, phase estimation to $T$ bits of precision, and depth-$T$ variational quantum algorithms, whenever $T$ is less than some universal constant times the logarithm of the system size. To achieve this, we introduce a generalization of the overlap gap property (OGP) for quantum systems that we call the quantum overlap gap property (QOGP). We prove that preparing low-energy states of systems which exhibit the QOGP is intractable for quantum algorithms whose outputs are stable under perturbations of their inputs. We then prove that the QOGP is satisfied for a sparsified variant of the quantum $p$-spin model, giving the first known algorithmic hardness-of-approximation result for quantum algorithms in finding the ground state of a non-stoquastic, noncommuting quantum system. Inversely, we show that the Sachdev--Ye--Kitaev (SYK) model does not exhibit the QOGP, consistent with previous evidence that the model is rapidly mixing at low temperatures. - oai:arXiv.org:2505.00087v3 + Entangled Subspaces through Algebraic Geometry + https://arxiv.org/abs/2504.11525 + arXiv:2504.11525v2 Announce Type: replace-cross +Abstract: We propose an algebraic geometry-inspired approach for constructing entangled subspaces within the Hilbert space of a multipartite quantum system. Specifically, our method employs a modified Veronese embedding, restricted to the conic, to define subspaces within the symmetric part of the Hilbert space. By utilizing this technique, we construct the minimal-dimensional, non-orthogonal yet Unextendible Product Basis (nUPB), enabling the decomposition of the multipartite Hilbert space into a two-dimensional subspace, complemented by a Genuinely Entangled Subspace (GES) and a maximal-dimensional Completely Entangled Subspace (CES). In multiqudit systems, we determine the maximum achievable dimension of a symmetric GES and demonstrate its realization through this construction. Furthermore, we systematically investigate the transition from the conventional Veronese embedding to the modified one by imposing various constraints on the affine coordinates, which, in turn, increases the CES dimension while reducing that of the GES. + oai:arXiv.org:2504.11525v2 quant-ph - cond-mat.dis-nn - cond-mat.stat-mech - math-ph - math.MP - Wed, 10 Dec 2025 00:00:00 -0500 - replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Eric R. Anschuetz - - - $f(R,\mathcal{G})$-cosmological dynamics in the FLRW background - https://arxiv.org/abs/2505.02663 - arXiv:2505.02663v2 Announce Type: replace-cross -Abstract: We examine the cosmological dynamics of Einstein-Gauss-Bonnet gravity models in a four-dimensional spatially flat FLRW metric. These models are described by $f\left( R,\mathcal{G}\right) =f\left( R+\mu \mathcal{G}\right) $ theory of gravity. They are equivalent to models linear in the Ricci scalar $R$ and in the Gauss-Bonnet scalar $\mathcal{G}$ with one nonminimally coupled scalar field without kinetic term. We analyze the stability of the de Sitter solutions and construct the phase space of the field equations to investigate the cosmological evolution. We show that $f\left( R+\mu \mathcal{G}\right) $-theory provides a double inflationary epoch, this can be used to unify the early-time and late-time acceleration phases of the universe. Moreover, we discuss the initial value problem for theory to be cosmologically viable. Finally, the effects of the cold dark matter in cosmic evolution are discussed. - oai:arXiv.org:2505.02663v2 - gr-qc - hep-th math-ph + math.AG math.MP - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 replace-cross http://creativecommons.org/licenses/by/4.0/ - 10.1007/s10714-025-03489-9 - Gen. Rel. Gravit. 57, 153 (2025) - Nikolaos Dimakis, Alex Giacomini, Genly Leon, Andronikos Paliathanasis, Ekaterina Pozdeeva, Sergey Vernov - - - Ergodic and synthetic Koopman analyses of cat maps onto classical 2-tori - https://arxiv.org/abs/2505.10293 - arXiv:2505.10293v3 Announce Type: replace-cross -Abstract: We study classical continuous automorphisms of the torus (cat maps) from the viewpoint of the Koopman theory. We find analytical formulae for Koopman modes defined coherently on the whole of the torus, and their decompositions associated with the partition of the torus into ergodic components. The spectrum of the Koopman operator is studied in four cases of cat maps: cyclic, quasi-cyclic, critical (transition from quasi-cyclic to chaotic behaviour) and chaotic. The synthetic spectrum associated with the ergodic decomposition is also studied. - oai:arXiv.org:2505.10293v3 - nlin.CD - math-ph - math.MP - Wed, 10 Dec 2025 00:00:00 -0500 - replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - David Viennot + Masoud Gharahi, Stefano Mancini - Understanding the Implicit Regularization of Gradient Descent in Over-parameterized Models - https://arxiv.org/abs/2505.17304 - arXiv:2505.17304v2 Announce Type: replace-cross -Abstract: Implicit regularization refers to the tendency of local search algorithms to converge to low-dimensional solutions, even when such structures are not explicitly enforced. Despite its ubiquity, the mechanism underlying this behavior remains poorly understood, particularly in over-parameterized settings. We analyze gradient descent dynamics and identify three conditions under which it converges to second-order stationary points within an implicit low-dimensional region: (i) suitable initialization, (ii) efficient escape from saddle points, and (iii) sustained proximity to the region. We show that these can be achieved through infinitesimal perturbations and a small deviation rate. Building on this, we introduce Infinitesimally Perturbed Gradient Descent (IPGD), which satisfies these conditions under mild assumptions. We provide theoretical guarantees for IPGD in over-parameterized matrix sensing and empirical evidence of its broader applicability. - oai:arXiv.org:2505.17304v2 + A Minimalist Optimizer Design for LLM Pretraining + https://arxiv.org/abs/2506.16659 + arXiv:2506.16659v2 Announce Type: replace-cross +Abstract: Training large language models (LLMs) typically relies on adaptive optimizers such as Adam, which introduce extra operations and require significant more memory to maintain first- and second-order moments than SGD. While recent works such as GaLore, Fira and APOLLO have proposed state-compressed variants to reduce memory consumption, a fundamental question remains: What are the minimum modifications to plain SGD needed to match state-of-the-art pretraining performance? We systematically investigate this question using a bottom-up approach, and identify two simple yet highly (memory- and compute-) efficient techniques: (1) column-wise gradient normalization (normalizing the gradient along the output dimension), which boosts SGD performance without momentum; and (2) applying first-order momentum only to the output layer, where gradient variance is highest. Combining these two techniques lead to SCALE (Stochastic Column-normAlized Last-layer momEntum), a simple optimizer for memory efficient pretraining. Across multiple LLaMA models (60M-1B), SCALE matches or exceeds the performance of Adam while using only 35-45% of the total memory. It also consistently outperforms memory-efficient optimizers such as GaLore, Fira and APOLLO, making it a strong candidate for large-scale pretraining under memory constraints. For LLaMA 7B model, SCALE outperforms the state-of-the-art memory-efficient methods APOLLO and Muon, in terms of both perplexity and memory consumption. + oai:arXiv.org:2506.16659v2 cs.LG + cs.AI math.OC - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 replace-cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jianhao Ma, Geyu Liang, Salar Fattahi + Athanasios Glentis, Jiaxiang Li, Andi Han, Mingyi Hong - Curse of Slicing: Why Sliced Mutual Information is a Deceptive Measure of Statistical Dependence - https://arxiv.org/abs/2506.04053 - arXiv:2506.04053v3 Announce Type: replace-cross -Abstract: Sliced Mutual Information (SMI) is widely used as a scalable alternative to mutual information for measuring non-linear statistical dependence. Despite its advantages, such as faster convergence, robustness to high dimensionality, and nullification only under statistical independence, we demonstrate that SMI is highly susceptible to data manipulation and exhibits counterintuitive behavior. Through extensive benchmarking and theoretical analysis, we show that SMI saturates easily, fails to detect increases in statistical dependence, prioritizes redundancy over informative content, and in some cases, performs worse than correlation coefficient. - oai:arXiv.org:2506.04053v3 + PROPS: Progressively Private Self-alignment of Large Language Models + https://arxiv.org/abs/2508.06783 + arXiv:2508.06783v2 Announce Type: replace-cross +Abstract: Alignment is a key step in developing Large Language Models (LLMs) using human feedback to ensure adherence to human values and societal norms. Dependence on human feedback raises privacy concerns about how much a labeler's preferences may reveal about their personal values, beliefs, and personality traits. Existing approaches, such as Differentially Private SGD (DP-SGD), provide rigorous privacy guarantees by privatizing gradients during fine-tuning and alignment but can provide more privacy than necessary as human preferences are tied only to labels of (prompt, response) pairs and can degrade model utility. This work focuses on LLM alignment with preference-level privacy, which preserves the privacy of preference labels provided by humans. We propose PROPS (PROgressively Private Self-alignment), a multi-stage privacy preserving alignment framework where privately aligned models in previous stages can serve as labelers for supplementing training data in the subsequent stages of alignment. We present theoretical guarantees for PROPS as well as comprehensive validation using multiple models (Pythia and GPT) and datasets (AlpacaEval, Anthropic HH-RLHF, truthy-dpo-v0.1) to demonstrate the utility of PROPS over existing methods while still providing high privacy. For the same privacy budget, alignment via PROPS can achieve up to 3x higher win-rates compared to DP-SGD, and 2.5x higher win-rates compared to Randomized Response (RR) based alignment. + oai:arXiv.org:2508.06783v2 cs.LG + cs.AI + cs.CR cs.IT math.IT - Wed, 10 Dec 2025 00:00:00 -0500 - replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Alexander Semenenko, Ivan Butakov, Alexey Frolov, Ivan Oseledets - - - Schauder Bases for $C[0, 1]$ Using ReLU, Softplus and Two Sigmoidal Functions - https://arxiv.org/abs/2506.07884 - arXiv:2506.07884v2 Announce Type: replace-cross -Abstract: We construct four Schauder bases for the space $C[0,1]$, one using ReLU functions, another using Softplus functions, and two more using sigmoidal versions of the ReLU and Softplus functions. This establishes the existence of a basis using these functions for the first time, and improves on the universal approximation property associated with them. We also show an $O(\frac{1}{n})$ approximation bound based on our ReLU basis, and a negative result on constructing multivariate functions using finite combinations of ReLU functions. - oai:arXiv.org:2506.07884v2 - cs.LG - math.FA - Wed, 10 Dec 2025 00:00:00 -0500 - replace-cross - http://creativecommons.org/licenses/by/4.0/ - Transactions on Machine Learning Research, November 2025 - Anand Ganesh, Babhrubahan Bose, Anand Rajagopalan - - - Sufficient digits and density estimation: A Bayesian nonparametric approach using generalized finite P\'olya trees - https://arxiv.org/abs/2506.09437 - arXiv:2506.09437v3 Announce Type: replace-cross -Abstract: This paper proposes a novel approach for statistical modelling of a continuous random variable $X$ on $[0, 1)$, based on its digit representation $X=.X_1X_2\ldots$. In general, $X$ can be coupled with a latent random variable $N$ so that $(X_1,\ldots,X_N)$ becomes a sufficient statistics and $.X_{N+1}X_{N+2}\ldots$ is uniformly distributed. In line with this fact, and focusing on binary digits for simplicity, we propose a family of generalized finite P{\'o}lya trees that induces a random density for a sample, which becomes a flexible tool for density estimation. Here, the digit system may be random and learned from the data. We provide a detailed Bayesian analysis, including closed form expression for the posterior distribution. We analyse the frequentist properties as the sample size increases, and provide sufficient conditions for consistency of the posterior distributions of the random density and $N$. We consider an extension to data spanning multiple orders of magnitude, and propose a prior distribution that encodes the so-called extended Newcomb-Benford law. Such a model shows promising results for density estimation of human-activity data. Our methodology is illustrated on several synthetic and real datasets. - oai:arXiv.org:2506.09437v3 - stat.ME - math.PR - math.ST - stat.TH - Wed, 10 Dec 2025 00:00:00 -0500 - replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Mario Beraha, Jesper M{\o}ller - - - Invariant Reduction for Partial Differential Equations. III: Poisson brackets - https://arxiv.org/abs/2507.08213 - arXiv:2507.08213v2 Announce Type: replace-cross -Abstract: We show that, under suitable conditions, finite-dimensional systems describing invariant solutions of partial differential equations (PDEs) inherit local Hamiltonian operators through the mechanism of invariant reduction, which applies uniformly to point, contact, and higher symmetries. The inherited operators endow the reduced systems with Poisson bivectors that relate constants of motion to symmetries. Applying the same mechanism to invariant conservation laws, we further show that the induced Poisson brackets agree with those of the original systems, up to sign. This is illustrated by two examples in which the inherited Poisson brackets and inherited constants of motion yield integrability of the reduced systems. - oai:arXiv.org:2507.08213v2 - nlin.SI - math.DG - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 replace-cross http://creativecommons.org/licenses/by-nc-nd/4.0/ - Kostya Druzhkov - - - Partial decidability protocol for the Wang tiling problem from statistical mechanics and chaotic mapping - https://arxiv.org/abs/2507.13268 - arXiv:2507.13268v2 Announce Type: replace-cross -Abstract: We introduce a partial decidability protocol for the Wang tiling problem (which is the prototype of undecidable problems in combinatorics and statistical physics) by constructing a suitable mapping from tilings of finite squares of different sizes. Such mapping depends on the initial family of Wang tiles (the alphabet) with which one would like to tile the plane. This allows to define effective entropy and temperature associated to the alphabet (together with the corresponding partition function). We identify a subclass of good alphabets by observing that when the entropy and temperature of a given alphabet are well-behaved in the thermodynamical sense then such alphabet is a good candidate to tile the infinite two-dimensional plane. Our proposal is tested successfully with the known available good alphabets (which produce periodic tilings, aperiodic but self-similar tilings as well as tilings which are neither periodic nor self-similar). Our analysis shows that the Kendall Tau coefficient is able to distinguish alphabets with a good thermodynamical behavior from alphabets with bad thermodynamical behavior. The transition from good to bad behavior is related to a transition from non-chaotic to chaotic regime in discrete dynamical systems of logistic type. - oai:arXiv.org:2507.13268v2 - cond-mat.stat-mech - cs.IT - hep-th - math.IT - math.LO - Wed, 10 Dec 2025 00:00:00 -0500 - replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Fabrizio Canfora, Marco Cedeno + Transactions on ML Research (TMLR) 2025 + Noel Teku, Fengwei Tian, Payel Bhattacharjee, Souradip Chakraborty, Amrit Singh Bedi, Ravi Tandon - Gaussian Approximation for Two-Timescale Linear Stochastic Approximation - https://arxiv.org/abs/2508.07928 - arXiv:2508.07928v2 Announce Type: replace-cross -Abstract: In this paper, we establish non-asymptotic bounds for accuracy of normal approximation for linear two-timescale stochastic approximation (TTSA) algorithms driven by martingale difference or Markov noise. Focusing on both the last iterate and Polyak-Ruppert averaging regimes, we derive bounds for normal approximation in terms of the convex distance between probability distributions. Our analysis reveals a non-trivial interaction between the fast and slow timescales: the normal approximation rate for the last iterate improves as the timescale separation increases, while it decreases in the Polyak-Ruppert averaged setting. We also provide the high-order moment bounds for the error of linear TTSA algorithm, which may be of independent interest. - oai:arXiv.org:2508.07928v2 - stat.ML - cs.LG - math.OC - math.PR - math.ST - stat.TH - Wed, 10 Dec 2025 00:00:00 -0500 + A comparative study of data- and image- domain LSRTM under velocity-impedance parametrization + https://arxiv.org/abs/2508.10405 + arXiv:2508.10405v2 Announce Type: replace-cross +Abstract: Least-squares reverse time migration (LSRTM) is one of the classic seismic imaging methods to reconstruct model perturbations within a known reference medium. It can be computed in either data or image domain using different methods by solving a linear inverse problem, whereas a careful comparison analysis of them is lacking in the literature. In this article, we present a comparative study for multiparameter LSRTM in data- and image- domain in the framework of SMIwiz open software. Different from conventional LSRTM for recovering only velocity perturbation with variable density, we focus on simultaneous reconstruction of velocity and impedance perturbations after logorithmic scaling, using the first-order velocity-pressure formulation of acoustic wave equation. The first 3D data-domain LSRTM example has been performed to validate our implementation, involving expensive repetition of Born modelling and migration over a number of iterations. As a more cost-effective alternative, the image-domain LSRTM is implemented using point spread function (PSF) and nonstationary deblurring filter. Dramatic disctinctions between data and image domain methods are discovered with 2D Marmousi test: (1) The data-domain multiparameter inversion provides much better reconstruction of reflectivity images than image-domain approaches, thanks to the complete use of Hessian in Krylov space; (2) The poor multiparameter image-domain inversion highlights the limitation of incomplete Hessian sampling and strong parameter crosstalks, making it difficult to work in practice; (3) In contrast, monoparameter image-domain inversion for seismic impedance is found to work well. These observations have been further validated on Viking Graben Line 12 dataset. + oai:arXiv.org:2508.10405v2 + physics.geo-ph + math-ph + math.MP + Thu, 11 Dec 2025 00:00:00 -0500 replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Bogdan Butyrin, Artemy Rubtsov, Alexey Naumov, Vladimir Ulyanov, Sergey Samsonov + http://creativecommons.org/licenses/by/4.0/ + Pengliang Yang, Zhengyu Ji - Form factors of composite branch-point twist operators in the sinh-Gordon model on a multi-sheeted Riemann surface: semiclassical limit - https://arxiv.org/abs/2508.12878 - arXiv:2508.12878v2 Announce Type: replace-cross -Abstract: Quantum sinh-Gordon model in 1+1 dimensions is one of the simplest and best-studied massive integrable relativistic quantum field theories. We consider this theory on a multi-sheeted Riemann surfaces with a flat metric, which can be seen as a pile of planes connected to each other along cut lines. The cut lines end at branch points, which are represented by a twist operator ${\cal T}_n.$ Operators of such kind are interesting in the framework of the problem of computing von Neumann and Renyi entanglement entropies in the original model on the plane. The composite branch-point twist operators (CTO) are a natural generalization of the twist operators, obtained by placing a local operator to a branch point by means of a certain limiting procedure. Correlation function in quantum field theory can be, in principle, found by means of the spectral decomposition. It allows one to express them in terms of form factors of local operators, i.e. their matrix elements in the basis of stationary states. In integrable models complete sets of exact form factors of all operators can be found exactly as solutions of a system of bootstrap equations. Nevertheless, identification of these solution to the operators in terms of the basic fields remains problematic. In this work, we develop a technique of computing form factors of a class of CTO determined in terms of the basic field in the semiclassical approximation. - oai:arXiv.org:2508.12878v2 + Necessary and sufficient conditions for correctness of complex Langevin + https://arxiv.org/abs/2508.14512 + arXiv:2508.14512v2 Announce Type: replace-cross +Abstract: We derive a family of correctness conditions for complex Langevin simulations. In particular, we show that if in a given theory the expectation values of all observables within a particular space satisfy the theory's Schwinger-Dyson equations as well as certain bounds, then these expectation values are necessarily correct. In fact, these findings are not only valid in the context of complex Langevin simulations, but they also hold for general probability densities on complex manifolds, given an initial complex density on a real manifold. We stress that, while the proposed conditions are necessary and sufficient in a mathematical sense, their practical use is not to prove the correctness of obtained simulation results. Rather, they are mainly useful for detecting incorrect convergence. In particular, we test these criteria in a few simple one- and two-dimensional toy models and find that they are indeed capable of ruling out incorrect results without the need of exact solutions. + oai:arXiv.org:2508.14512v2 + hep-lat hep-th math-ph math.MP - nlin.SI - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 replace-cross http://creativecommons.org/licenses/by/4.0/ - Michael Lashkevich, Amir Nesturov + 10.1088/1751-8121/ae2245 + J. Phys. A 58, 495202 (2025) + Michael Mandl, Erhard Seiler, D\'enes Sexty Vacuum Energy and Topological Mass from a Constant Magnetic Field and Boundary Conditions in Coupled Scalar Field Theories https://arxiv.org/abs/2508.15121 - arXiv:2508.15121v2 Announce Type: replace-cross + arXiv:2508.15121v3 Announce Type: replace-cross Abstract: We investigate the combined effects of a uniform magnetic field and boundary conditions on vacuum energy and topological mass generation in a coupled scalar field theory. The system consists of a real scalar field, subject to Dirichlet boundary conditions, interacting via self- and cross-couplings with a gauge-coupled complex scalar field obeying mixed boundary conditions between two perfectly reflecting parallel plates. The magnetic field induces Landau quantization, leading to novel contributions. Employing zeta-function regularization within the effective potential formalism, we derive the renormalized effective potential up to second order in the coupling constants without imposing a vanishing magnetic field in the renormalization scheme. Our renormalization approach preserves magnetic contributions while properly removing divergences, enabling a consistent treatment of finite-size corrections, magnetic effects, and interaction terms. We compute the vacuum energy per unit area of the plates, analyze the emergence of a topological mass from boundary and magnetic contributions, and evaluate the first-order coupling-constant corrections at two-loop order. Detailed asymptotic analysis are presented for both weak- and strong-field regimes, revealing exponential suppression at high magnetic fields and nontrivial polynomial and logarithmic behavior in the weak-field limit. - oai:arXiv.org:2508.15121v2 + oai:arXiv.org:2508.15121v3 hep-th math-ph math.MP quant-ph - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 replace-cross http://creativecommons.org/licenses/by/4.0/ A. J. D. Farias Junior, Andrea Erdas, Herondy F. Santana Mota - $su(2)$ symmetry of XX spin chains - https://arxiv.org/abs/2508.20184 - arXiv:2508.20184v3 Announce Type: replace-cross -Abstract: We show that, after suitably adjusting a uniform transverse magnetic field, the generic inhomogeneous open XX spin chain has a two-fold degeneracy, and an exact $su(2)$ symmetry whose "inhomogeneous" nonlocal generators depend on coefficients that can be explicitly computed for models associated with discrete orthogonal polynomials. - oai:arXiv.org:2508.20184v3 - cond-mat.stat-mech + A Continuous Energy Ising Machine Leveraging Difference-of-Convex Programming + https://arxiv.org/abs/2509.01928 + arXiv:2509.01928v2 Announce Type: replace-cross +Abstract: Many combinatorial optimization problems can be reformulated as finding the ground state of the Ising model. Existing Ising solvers are mostly inspired by simulated annealing. Although annealing techniques offer scalability, they lack convergence guarantees and are sensitive to the cooling schedule. We propose solving the Ising problem by relaxing the binary spins to continuous variables and introducing an attraction potential that steers the solution toward binary spin configurations. A key property of this potential is that its combination with the Ising energy produces a Hamiltonian that can be written as a difference of convex polynomials. This enables us to design efficient iterative algorithms that require a single matrix-vector multiplication per iteration and provide convergence guarantees. We implement our Ising solver on a wide range of GPU platforms, from edge devices to high-performance computing clusters, and demonstrate that it consistently outperforms existing solvers across problem sizes ranging from small ($10^3$ spins) to ultra-large ($10^8$ spins). + oai:arXiv.org:2509.01928v2 + cs.DC math-ph math.MP - Wed, 10 Dec 2025 00:00:00 -0500 + math.OC + quant-ph + Thu, 11 Dec 2025 00:00:00 -0500 replace-cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Nicolas Cramp\'e, Rafael I. Nepomechie, Luc Vinet, Nabi Zare Harofteh + Debraj Banerjee, Santanu Mahapatra, Kunal Narayan Chaudhury - A Unifying Framework for Global Optimization: From Theory to Formalization - https://arxiv.org/abs/2508.20671 - arXiv:2508.20671v2 Announce Type: replace-cross -Abstract: We introduce an abstract measure___theoretic framework that serves as a tool to rigorously study stochastic iterative global optimization algorithms as a unified class. The framework is formulated in terms of probability kernels, which, via the Ionescu--Tulcea theorem, induce probability measures on the space of sequences of algorithm iterations, endowed with two intuitive properties. This framework answers the need for a general, implementation___independent formalism in the analysis of such algorithms, providing a starting point for formalizing general results in proof-assistants. To illustrate the relevance of our tool, we show that common algorithms fit naturally in the framework, and we also use it to give a rigorous proof of a general consistency theorem for stochastic iterative global optimization algorithms (Proposition 3 of (Malherbe, et al., 2017). This proof and the entire framework are formalized in the Lean proof assistant. This formalization both ensures the correctness of the definitions and proofs, and provides a basis for future machine-assisted formalizations in the field. - oai:arXiv.org:2508.20671v2 - cs.FL - cs.LO - math.OC - math.PR - Wed, 10 Dec 2025 00:00:00 -0500 + Phase locking and multistability in the topological Kuramoto model on cell complexes + https://arxiv.org/abs/2510.05831 + arXiv:2510.05831v2 Announce Type: replace-cross +Abstract: The topological Kuramoto model generalizes classical synchronization models by including higher-order interactions, with oscillator dynamics defined on cells of arbitrary dimension within simplicial or cell complexes. In this article, we demonstrate multistability in the topological Kuramoto model and develop the topological nonlinear Kirchhoff conditions algorithm to identify all phase-locked states on arbitrary cell complexes. The algorithm is based on a generalization of Kirchhoff's laws to cell complexes of arbitrary dimension and nonlinear interactions between cells. By applying this framework to rings, Platonic solids, and simplexes, as minimal representative motifs of larger networks, we derive explicit bounds (based on winding number constraints) that determine the number of coexisting stable states. We uncover structural cascades of multistability, inherited from both lower and higher dimensions and demonstrate that cell complexes can generate richer multistability patterns than simplicial complexes of the same dimension. Moreover, we find that multistability patterns in cell complexes appear to be determined by the number of boundary cells, hinting a possible universal pattern. + oai:arXiv.org:2510.05831v2 + nlin.AO + math.DS + nlin.CD + physics.soc-ph + Thu, 11 Dec 2025 00:00:00 -0500 replace-cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Ga\"etan Serr\'e (ENS Paris Saclay, CB), Argyris Kalogeratos (CB, ENS Paris Saclay), Nicolas Vayatis (CB, ENS Paris Saclay) + Iva Ba\v{c}i\'c, Michael T. Schaub, J\"urgen Kurths, Dirk Witthaut - AoI-based Scheduling of Correlated Sources for Timely Inference - https://arxiv.org/abs/2509.01926 - arXiv:2509.01926v2 Announce Type: replace-cross -Abstract: We investigate a real-time remote inference system where multiple correlated sources transmit observations over a communication channel to a receiver. The receiver utilizes these observations to infer multiple time-varying targets. Due to limited communication resources, the delivered observations may not be fresh. To quantify data freshness, we employ the Age of Information (AoI) metric. To minimize the inference error, we aim to design a signal-agnostic scheduling policy that leverages AoI without requiring knowledge of the actual target values or the source observations. This scheduling problem is a restless multi-armed bandit (RMAB) problem with a non-separable penalty function. Unlike traditional RMABs, the correlation among sources introduces a unique challenge: the penalty function of each source depends on the AoI of other correlated sources, preventing the problem from decomposing into multiple independent Markov Decision Processes (MDPs), a key step in applying traditional RMAB solutions. To address this, we propose a novel approach that approximates the penalty function for each source and establishes an analytical bound on the approximation error. We then develop scheduling policies for two scenarios: (i) full knowledge of the penalty functions and (ii) no knowledge of the penalty functions. For the case of known penalty functions, we present an upper bound on the optimality gap that highlights the impact of the correlation parameter and the system size. For the case of unknown penalty functions and signal distributions, we develop an online learning approach that utilizes bandit feedback to learn an online Maximum Gain First policy. Simulation results demonstrate the effectiveness of our proposed policies in minimizing inference error and achieving scalability in the number of sources. - oai:arXiv.org:2509.01926v2 - cs.NI + Good quantum codes with addressable and parallelizable transversal non-Clifford gates + https://arxiv.org/abs/2510.19809 + arXiv:2510.19809v2 Announce Type: replace-cross +Abstract: In this work, we prove that for any $m>1$, there exists a family of good qudit quantum codes supporting transversal logical $\mathsf{C}^{m-1}\mathsf{Z}$ gates that can address specified logical qudits and be largely executed in parallel. Building on the family of good quantum error-correcting codes presented in He et al. (2025), which support addressable and transversal logical $\mathsf{CCZ}$ gates, we extend their framework and show how to perform large sets of gates in parallel. The construction relies on the classical algebraic geometry codes of Stichtenoth (IEEE Trans. Inf. Theory, 2006). Our results lead to a substantial reduction in the depth overhead of multi-control-$Z$ circuits. In particular, we show that the minimal depth of any logical $\mathsf{C}^{m-1}\mathsf{Z}$ circuit involving qudits from $m$ distinct code blocks is upper bounded by $O(k^{m-1})$, where $k$ is the code dimension. While this overhead is optimal for dense $\mathsf{C}^{m-1}\mathsf{Z}$ circuits, for sparse circuits we discuss how the depth overhead can be significantly reduced by exploiting the structure of the quantum code. + oai:arXiv.org:2510.19809v2 + quant-ph cs.IT math.IT - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Md Kamran Chowdhury Shisher, Vishrant Tripathi, Mung Chiang, Christopher G. Brinton + http://creativecommons.org/licenses/by/4.0/ + Virgile Gu\'emard - A Case for a "Refutations and Critiques" Track in Statistics Journals - https://arxiv.org/abs/2509.03702 - arXiv:2509.03702v3 Announce Type: replace-cross -Abstract: The statistics community, which has traditionally lacked a transparent and open peer-review system, faces a challenge of inconsistent paper quality, with some published work containing substantial errors. This problem resonates with concerns raised by Schaeffer et al. (2025) regarding the rapid growth of machine learning research. They argue that peer review has proven insufficient to prevent the publication of ``misleading, incorrect, flawed or perhaps even fraudulent studies'' and that a ``dynamic self-correcting research ecosystem'' is needed. This note provides a concrete illustration of this problem by examining two published papers, Wang, Zhou and Lin (2025) and Liu et al. (2023), and exposing striking and critical errors in their proofs. The presence of such errors in major journals raises a fundamental question about the importance and verification of mathematical proofs in our field. Echoing the proposal from Schaeffer et al. (2025), we argue that reforming the peer-review system itself is likely impractical. Instead, we propose a more viable path forward: the creation of a high-profile, reputable platform, such as a ``Refutations and Critiques'' track on arXiv, to provide visibility to vital research that critically challenges prior work. Such a mechanism would be crucial for enhancing the reliability and credibility of statistical research. - oai:arXiv.org:2509.03702v3 - stat.ME + A Practitioner's Guide to Kolmogorov-Arnold Networks + https://arxiv.org/abs/2510.25781 + arXiv:2510.25781v2 Announce Type: replace-cross +Abstract: The so-called Kolmogorov-Arnold Networks (KANs), whose design is merely inspired, rather than dictated, by the Kolmogorov superposition theorem, have emerged as a promising alternative to traditional Multilayer Perceptrons (MLPs). This review provides a systematic and comprehensive overview of the rapidly expanding KAN landscape. By collecting and categorizing a large set of open-source implementations, we map the vibrant ecosystem supporting modern KAN development. We organize the review around four core themes: + (i) presenting a precise history of Kolmogorov's superposition theory toward neural-network formulations; (ii) establishing the formal equivalence between KANs and MLPs; (iii) analyzing the critical role of basis functions; and (iv) organizing recent advancements in accuracy, efficiency, regularization, and convergence. + Finally, we provide a practical Choose-Your-KAN guide to assist practitioners in selecting appropriate architectures, and we close by identifying current research gaps and future directions. The associated GitHub repository (https://github.com/AmirNoori68/kan-review) complements this paper and serves as a structured reference for ongoing KAN research. + oai:arXiv.org:2510.25781v2 + cs.LG + cs.AI + cs.NA + cs.NE + math.NA + Thu, 11 Dec 2025 00:00:00 -0500 + replace-cross + http://creativecommons.org/licenses/by/4.0/ + Amir Noorizadegan, Sifan Wang, Leevan Ling + + + Online Price Competition under Generalized Linear Demands + https://arxiv.org/abs/2511.10718 + arXiv:2511.10718v3 Announce Type: replace-cross +Abstract: We study sequential price competition among $N$ sellers, each influenced by the pricing decisions of their rivals. Specifically, the demand function for each seller $i$ follows the single index model $\lambda_i(\mathbf{p}) = \mu_i(\langle \boldsymbol{\theta}_{i,0}, \mathbf{p} \rangle)$, with known increasing link $\mu_i$ and unknown parameter $\boldsymbol{\theta}_{i,0}$, where the vector $\mathbf{p}$ denotes the vector of prices offered by all the sellers simultaneously at a given instant. Each seller observes only their own realized demand -- unobservable to competitors -- and the prices set by rivals. Our framework generalizes existing approaches that focus solely on linear demand models. We propose a novel decentralized policy, PML-GLUCB, that combines penalized MLE with an upper-confidence pricing rule, removing the need for coordinated exploration phases across sellers -- which is integral to previous linear models -- and accommodating both binary and real-valued demand observations. Relative to a dynamic benchmark policy, each seller achieves $O(N^{2}\sqrt{T}\log(T))$ regret, which essentially matches the optimal rate known in the linear setting. A significant technical contribution of our work is the development of a variant of the elliptical potential lemma -- typically applied in single-agent systems -- adapted to our competitive multi-agent environment. + oai:arXiv.org:2511.10718v3 + cs.GT math.ST + stat.ME stat.TH - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Zhen Li + http://creativecommons.org/licenses/by/4.0/ + Daniele Bracale, Moulinath Banerjee, Cong Shi, Yuekai Sun - Hypergeometry from $\mathrm{\widehat P}$-Symmetry: Feynman Integrals in One and Two Dimensions - https://arxiv.org/abs/2509.16305 - arXiv:2509.16305v2 Announce Type: replace-cross -Abstract: Feynman integrals with generic propagator powers in one and two spacetime dimensions are investigated from various perspectives. In particular, we argue that the class of track integrals at any loop order is fixed by the recently found $\mathrm{\widehat P}$-symmetries of Yangian type. All track integrals up to six external points (and four loops) are bootstrapped explicitly as well as the full family of one-loop integrals at any multiplicity. Moreover, the triangle tracks at generic loop order, which constitute the most generic family of track-type integrals, are bootstrapped in this way. The results are compared to the direct evaluation via a `spectral transform' from the integrability toolbox that turns out to be particularly efficient for position-space tree integrals in lower dimensions. We prove that all $\mathrm{\widehat P}$-symmetries of these integrals can be derived from the framework of Aomoto--Gelfand hypergeometric functions, which applies to integrals in one and two dimensions. Finally, we also demonstrate the method's applicability to conformal integrals by deriving the complete results for all comb-channel conformal partial waves as well as the conformal double-box integral. We explicitly go through all examples of the above integrals in 1D and then provide a straightforward recipe for how to read off their 2D counterparts. - oai:arXiv.org:2509.16305v2 + The Semiclassical limit of $SU(3)$ Gauge Field Coherent States: Peakedness and Overlap Functions + https://arxiv.org/abs/2511.10969 + arXiv:2511.10969v2 Announce Type: replace-cross +Abstract: By using the heat kernel method, we construct diffeomorphism-covariant coherent states for the $SU(3)$ gauge group. We numerically demonstrate that these states exhibit the required semiclassical properties in the semiclassical limit: the peakedness property of the probability distribution and the peakedness property of the overlap function. We also provide the leading order term of the overlap amplitude in the combined limit where $t \rightarrow 0$ and $g\rightarrow g'$. This work provides the essential tool for deriving effective dynamics for $SU(3)$ gauge fields coupled to gravity via a coherent state path integral. + oai:arXiv.org:2511.10969v2 + gr-qc + hep-lat hep-th math-ph math.MP - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 replace-cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Gwena\"el Ferrando, Florian Loebbert, Amelie Pitters, Sven F. Stawinski + 10.1103/dpsm-4qyv + Phys. Rev. D 112, 124037 (2025) + Ye Zhang, Zichang Huang - Exact Taub-NUT-like Black Holes in Einstein-bumblebee gravity: their thermodynamics and thermodynamic topology - https://arxiv.org/abs/2509.17407 - arXiv:2509.17407v3 Announce Type: replace-cross -Abstract: We re-derive an exact analytic three-parameter expressions for the non-rotating metric, describing a Taub-NUT-like black hole (BH), and its associated bumblebee field that are solutions to the Einstein-bumblebee gravity. We construct a consistence thermodynamics for the Taub-NUT-like BH and determine its thermodynamic topological class. The Lorentz symmetry breaking affects the mass and temperature of the BH but does not affect its thermodynamic topological classification. - oai:arXiv.org:2509.17407v3 - gr-qc - astro-ph.GA - math-ph - math.MP - Wed, 10 Dec 2025 00:00:00 -0500 + Forgetting-MarI: LLM Unlearning via Marginal Information Regularization + https://arxiv.org/abs/2511.11914 + arXiv:2511.11914v2 Announce Type: replace-cross +Abstract: As AI models are trained on ever-expanding datasets, the ability to remove the influence of specific data from trained models has become essential for privacy protection and regulatory compliance. Unlearning addresses this challenge by selectively removing parametric knowledge from the trained models without retraining from scratch, which is critical for resource-intensive models such as Large Language Models (LLMs). Existing unlearning methods often degrade model performance by removing more information than necessary when attempting to ''forget'' specific data. We introduce Forgetting-MarI, an LLM unlearning framework that provably removes only the additional (marginal) information contributed by the data to be unlearned, while preserving the information supported by the data to be retained. By penalizing marginal information, our method yields an explicit upper bound on the unlearn dataset's residual influence in the trained models, providing provable undetectability. Extensive experiments confirm that our approach outperforms current state-of-the-art unlearning methods, delivering reliable forgetting and better preserved general model performance across diverse benchmarks. This advancement represents an important step toward making AI systems more controllable and compliant with privacy and copyright regulations without compromising their effectiveness. + oai:arXiv.org:2511.11914v2 + cs.AI + cs.CL + cs.CR + cs.IT + cs.LG + math.IT + Thu, 11 Dec 2025 00:00:00 -0500 replace-cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - 10.1016/j.nuclphysb.2025.117257 - Mustapha Azreg-A\"inou, Yassine Sekhmani + Shizhou Xu, Yuan Ni, Stefan Broecker, Thomas Strohmer - Encoding the Einstein Equations into an Algebraic Commutator Condition - https://arxiv.org/abs/2510.03048 - arXiv:2510.03048v2 Announce Type: replace-cross -Abstract: We show that the structure of the Lorentz group in four dimensions is such that unimodular (trace-free) gravity can be consistently represented as an algebraic condition on the symmetric product space of 2-forms. This condition states that the commutator between the Riemann tensor and the Hodge dual must be equal to the commutator between the Kulkarni-Nomizu product of the energy-momentum and the metric with the Hodge dual; symbolically, $[\text{Riem}, \star] = 4\pi [T\KN g, \star]$. We show that this condition is equivalent to the trace-free field equations, that the right-hand-side vanishes if and only if the energy-momentum tensor vanishes (recovering the appropriate Einstein spacetime limit) and that this condition can be solved for electrovacuum in the spherically symmetric ansatz to yield Reissner-Nordstr\"om-de Sitter uniquely. This analysis suggests that the conceptual distinction between unimodular gravity and General Relativity is one of emphasis on how irreducible representations of the Riemann tensor are constrained by the existence of energy-momentum and the associated field equations. - oai:arXiv.org:2510.03048v2 - gr-qc - math-ph - math.MP - Wed, 10 Dec 2025 00:00:00 -0500 + Geometric Solution of the Loop Equation and Quark Confinement in QCD + https://arxiv.org/abs/2511.13688 + arXiv:2511.13688v4 Announce Type: replace-cross +Abstract: We present an exact analytic confining area law for pure $\mathrm{SU}(N_c)$ Yang--Mills theory, satisfying the hierarchy of multiloop equations for arbitrary regular loops and any number of colors $N_c$. The solution is constructed using a quaternionic Hodge-dual minimal surface in a 16-dimensional auxiliary space. Unlike random surfaces, this construction defines an effectively topological string theory where the bulk dynamics reduces to the area of a conformal map of the 2D disk, with all nontrivial dynamics encoded in the boundary loop. + The Wilson loop factorizes into a confining dressing factor and a perturbative term: $W[C] = W_{\text{pert}}[C]\, e^{-\kappa S[C]}$. We show that the geometric factor $e^{-\kappa S[C]}$ is an exact multiplicative zero mode of the loop-space diffusion operator and of the full MM multiloop hierarchy for any finite $N_c$, extending the planar area law to the physical case $N_c=3$. The functional $S[C]$ obeys the inequality $S[C] \ge \sqrt{2}\,A[C]$ (where $A[C]$ is the Euclidean minimal area), providing a sufficient condition for confinement. + The area law is given explicitly by the spectral formula $S[C] = 2\sqrt{2}\,(\lambda_3 + \lambda_4)$, using the two largest eigenvalues of the Douglas--Gram matrix. We demonstrate that this functional is an exact additive zero mode of the loop diffusion operator, protected algebraically by the Bianchi identity, and globally defined for regular loops $C \in H^{1/2}(\mathbb{S}^1,\mathbb{R}^4)$. Matching this factor with the gluon condensate via the OPE determines the physical string tension $\kappa \sim \Lambda_{\text{QCD}}^2$. This framework yields a first-principles derivation of confinement in QCD and new tools for the high-lying meson spectrum. + oai:arXiv.org:2511.13688v4 + hep-th + math.CV + math.DG + Thu, 11 Dec 2025 00:00:00 -0500 replace-cross - http://creativecommons.org/licenses/by/4.0/ - Jack C. M. Hughes, Fedor V. Kusmartsev + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Alexander Migdal - Beyond Hoeffding and Chernoff: Trading conclusiveness for advantages in quantum hypothesis testing - https://arxiv.org/abs/2510.07601 - arXiv:2510.07601v2 Announce Type: replace-cross -Abstract: The ultimate limits of quantum state discrimination are often thought to be captured by asymptotic bounds that restrict the achievable error probabilities, notably the quantum Chernoff and Hoeffding bounds. Here we study hypothesis testing protocols that are permitted a probability of producing an inconclusive discrimination outcome, and investigate their performance when this probability is suitably constrained. We show that even by allowing an arbitrarily small probability of inconclusiveness, the limits imposed by the quantum Hoeffding and Chernoff bounds can be significantly exceeded. This completely circumvents the conventional trade-offs between error exponents in hypothesis testing while incurring only a vanishingly small overhead over conventional approaches. Such improvements over standard state discrimination are robust and can be obtained even when an exponentially vanishing probability of inconclusive outcomes is demanded. Relaxing the constraints on the inconclusive probability can enable even larger advantages, but this comes at a price. We show a 'strong converse' property of this setting: targeting error exponents beyond those achievable with vanishing inconclusiveness necessarily forces the probability of inconclusive outcomes to converge to one. By exactly quantifying the rate of this convergence, we give a complete characterisation of the trade-offs between error exponents and rates of conclusive outcome probabilities. Overall, our results provide a comprehensive asymptotic picture of how the allowance for inconclusive measurement outcomes reshapes optimal quantum hypothesis testing. - oai:arXiv.org:2510.07601v2 + Quantum resource degradation theory within the framework of observational entropy decomposition + https://arxiv.org/abs/2511.22350 + arXiv:2511.22350v2 Announce Type: replace-cross +Abstract: We introduce a theory of quantum resource degradation grounded in a decomposition of observational entropy, which partitions the total resource into inter-block coherence ($\mathcal{C}_{\text{rel}}$) and intra-block noise ($\mathcal{D}_{\text{rel}}$). Under free operations, the total quantum resource is transformed into classical noise while its overall quantity remains conserved. We demonstrate that the metric $\eta$ functions as a diagnostic indicator, providing a new lens on optimization stagnation, particularly the barren plateau phenomenon (BPP) in variational quantum algorithms (VQAs). We substantiate this framework through rigorous mathematical analysis and numerical simulations, and we explore how these channels can be physically implemented in real quantum systems. Our approach offers a unified viewpoint on quantum thermalization, measurement-induced disturbance, and the degradation of quantum advantage in practical devices, while also improving optimization strategies for current and near-term noisy quantum hardware. + oai:arXiv.org:2511.22350v2 quant-ph - cs.IT math-ph - math.IT math.MP - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 replace-cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Kaiyuan Ji, Bartosz Regula + Xiang Zhou - Online Energy Storage Arbitrage under Imperfect Predictions: A Conformal Risk-Aware Approach - https://arxiv.org/abs/2511.01032 - arXiv:2511.01032v2 Announce Type: replace-cross -Abstract: This work proposes a conformal approach for energy storage arbitrage to control the downside risk arising from imperfect price forecasts. Energy storage arbitrage relies solely on predictions of future market prices, while inaccurate price predictions may lead to significant profit losses. Based on conformal decision theory, we describe a controller that dynamically adjusts decision conservativeness through prediction sets without distributional assumptions. To enable online calibration when online profit loss feedback is unobservable, we establish that a temporal difference error serves as a measurable proxy. Building on this insight, we develop two online calibration strategies: prediction error-based adaptation targeting forecast accuracy, and value error-based calibration focusing on decision quality. Analysis of the conformal controller proves bounded long-term risk with convergence guarantees in temporal difference error, which further effectively manages risk exposure in potential profit losses. Case studies demonstrate superior performance in balancing risk and opportunity compared to benchmarks under varying forecast conditions. - oai:arXiv.org:2511.01032v2 + Distributionally Robust Kalman Filter + https://arxiv.org/abs/2512.06286 + arXiv:2512.06286v2 Announce Type: replace-cross +Abstract: In this work, we propose a noise-centric formulation of the distributionally robust Kalman filter (DRKF) for discrete-time linear stochastic systems with uncertain noise statistics. By placing Wasserstein ambiguity sets directly on the process and measurement noise distributions, the proposed DRKF preserves the analytical structure of the classical Kalman filter while providing a priori spectral bounds on all feasible covariances. In the time-invariant setting, we derive a steady-state DRKF from a single stationary semidefinite program, yielding a constant-gain estimator with the same per-step computational complexity as the standard Kalman filter. We establish conditions guaranteeing the existence, uniqueness, and convergence of this steady-state solution, and we prove its asymptotic minimax optimality with respect to the worst-case mean-square error. Numerical experiments validate the theory and demonstrate that the proposed DRKF improves estimation accuracy under unknown or uncertain noise models while offering computational advantages over existing robust and distributionally robust filters. + oai:arXiv.org:2512.06286v2 eess.SY cs.SY math.OC - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 replace-cross http://creativecommons.org/licenses/by-nc-nd/4.0/ - Yiqian Wu, Ming Yi, Bolun Xu, James Anderson + Minhyuk Jang, Astghik Hakobyan, Insoon Yang - Direction-of-Arrival and Noise Covariance Matrix joint estimation for beamforming - https://arxiv.org/abs/2511.10639 - arXiv:2511.10639v3 Announce Type: replace-cross -Abstract: We propose a joint estimation method for the Direction-of-Arrival (DoA) and the Noise Covariance Matrix (NCM) tailored for beamforming applications. Building upon an existing NCM framework, our approach simplifies the estimation procedure by deriving an quasi-linear solution, instead of the traditional exhaustive search. Additionally, we introduce a novel DoA estimation technique that operates across all frequency bins, improving robustness in reverberant environments. Simulation results demonstrate that our method outperforms classical techniques, such as MUSIC, in mid- to high-angle scenarios, achieving lower angular errors and superior signal enhancement through beamforming. The proposed framework was also fared against other techniques for signal enhancement, having better noise rejection and interference canceling capabilities. These improvements are validated using both theoretical and empirical performance metrics. - oai:arXiv.org:2511.10639v3 - eess.AS - math.OC - Wed, 10 Dec 2025 00:00:00 -0500 + VaR at Its Extremes: Impossibilities and Conditions for One-Sided Random Variables + https://arxiv.org/abs/2512.07787 + arXiv:2512.07787v2 Announce Type: replace-cross +Abstract: We investigate the extremal aggregation behavior of Value-at-Risk (VaR) -- that is, its additivity properties across all probability levels -- for sums of one-sided random variables. For risks supported on \([0,\infty)\), we show that VaR sub-additivity is impossible except in the degenerate case of exact additivity, which holds only under co-monotonicity. To characterize when VaR is instead fully super-additive, we introduce two structural conditions: negative simplex dependence (NSD) for the joint distribution and simplex dominance (SD) for a margin-dependent functional. Together, these conditions provide a unified and easily verifiable framework that accommodates non-identical margins, heavy-tailed laws, and a wide spectrum of negative dependence structures. All results extend to random variables with arbitrary finite lower or upper endpoints, yielding sharp constraints on when strict sub- or super-additivity can occur. + oai:arXiv.org:2512.07787v2 + q-fin.RM + math.PR + Thu, 11 Dec 2025 00:00:00 -0500 replace-cross http://creativecommons.org/licenses/by/4.0/ - Vitor Gelsleichter Probst Curtarelli, Stephan Paul, Anderson Wedderhoff Spengler + Nawaf Mohammed - Inverse Optimality for Fair Digital Twins: A Preference-based approach - https://arxiv.org/abs/2512.01650 - arXiv:2512.01650v2 Announce Type: replace-cross -Abstract: Digital Twins (DTs) are increasingly used as autonomous decision-makers in complex socio-technical systems. However, their mathematically optimal decisions often diverge from human expectations, revealing a persistent mismatch between algorithmic and bounded human rationality. This work addresses this challenge by proposing a framework that introduces fairness as a learnable objective within optimization-based Digital Twins. In this respect, a preference-driven learning workflow that infers latent fairness objectives directly from human pairwise preferences over feasible decisions is introduced. A dedicated Siamese neural network is developed to generate convex quadratic cost functions conditioned on contextual information. The resulting surrogate objectives drive the optimization procedure toward solutions that better reflect human-perceived fairness while maintaining computational efficiency. The effectiveness of the approach is demonstrated on a COVID-19 hospital resource allocation scenario. Overall, this work offers a practical solution to integrate human-centered fairness into the design of autonomous decision-making systems. - oai:arXiv.org:2512.01650v2 - cs.LG - cs.SE - math.OC - Wed, 10 Dec 2025 00:00:00 -0500 - replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Daniele Masti, Francesco Basciani, Arianna Fedeli, Girgio Gnecco, Francesco Smarra - - - The Mean-Field Dynamics of Transformers - https://arxiv.org/abs/2512.01868 - arXiv:2512.01868v2 Announce Type: replace-cross -Abstract: We develop a mathematical framework that interprets Transformer attention as an interacting particle system and studies its continuum (mean-field) limits. By idealizing attention on the sphere, we connect Transformer dynamics to Wasserstein gradient flows, synchronization models (Kuramoto), and mean-shift clustering. Central to our results is a global clustering phenomenon whereby tokens cluster asymptotically after long metastable states where they are arranged into multiple clusters. We further analyze a tractable equiangular reduction to obtain exact clustering rates, show how commonly used normalization schemes alter contraction speeds, and identify a phase transition for long-context attention. The results highlight both the mechanisms that drive representation collapse and the regimes that preserve expressive, multi-cluster structure in deep attention architectures. - oai:arXiv.org:2512.01868v2 - cs.LG + Analytical Study for Primordial Non-Gaussianity in the gravity 4D Einstein-scalar-Gauss-Bonnet Inflation + https://arxiv.org/abs/2512.08047 + arXiv:2512.08047v2 Announce Type: replace-cross +Abstract: An inflationary model can be constrained by non-gaussian statistics as a parameter in the LSS (Large Scale Structure) distribution, and in the radiation of CMB (Cosmic Microwave Background) fluctuating temperature. Data on the CMB from Planck Collaboration provide up-to-date constraints on the parameters controlling the degree of non-Gaussianity in certain inflationary models, thus supporting or not supporting the model. Setting the non-Gaussianity parameter investigated in this study can be a reference whether or not it is a good parameter in constraining cosmological inflation models. This study attempts to examine the non-Gaussianity of the 3+1-dimensional 4DEGB gravitational cosmological inflation model starting from random field statistics. The non-Gaussian signature generated by the model is quantified, and the parameters controlling the degree of non-Gaussianity are constrained using data observation of Planck Collaboration. The method used in investigating non-Gaussianity is the in-in formalism, applied after obtaining the 3-point of $\zeta$ (curvature perturbation) terms of the perturbation expansion to the third order. The 3-point correlation function helps to create a bispectrum used to investigate the non-gaussinity of the inflation model. The results of this study show that the model tested is the slow roll pressed in the squeezed limit, because it witnesses a dominant local shape function. It has such as the non-gaussianity possessed by the single scalar field inflation as confirmation that Gauss-Bonnet term within Einstein-Hilbert action is topologically invariant in $D<5$ spacetimes. + oai:arXiv.org:2512.08047v2 + gr-qc + hep-th math-ph - math.DS math.MP - math.PR - Wed, 10 Dec 2025 00:00:00 -0500 - replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Philippe Rigollet - - - Symmetry-Based Formation Control on Cycle Graphs Using Dihedral Point Groups - https://arxiv.org/abs/2512.06733 - arXiv:2512.06733v2 Announce Type: replace-cross -Abstract: This work develops a symmetry-based framework for formation control on cycle graphs using Dihedral point-group constraints. We show that enforcing inter-agent reflection symmetries, together with anchoring a single designated agent to its prescribed mirror axis, is sufficient to realize every $\mathcal{C}_{nv}$-symmetric configuration using only $n-1$ communication links. The resulting control laws have a matrix-weighted Laplacian structure and guarantee exponential convergence to the desired symmetric configuration. Furthermore, we extend the method to enable coordinated maneuvers along a time-varying reference trajectory. Simulation results are provided to support the theoretical analysis. - oai:arXiv.org:2512.06733v2 - eess.SY - cs.SY - math.OC - Wed, 10 Dec 2025 00:00:00 -0500 + Thu, 11 Dec 2025 00:00:00 -0500 replace-cross - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Zamir Martinez, Daniel Zelazo + http://creativecommons.org/licenses/by/4.0/ + A. Agung, U. Sambiri, G. Hikmawan, F. P. Zen