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" @@ -7,8903 +7,5348 @@ http://www.rssboard.org/rss-specification en-us - Tue, 09 Dec 2025 07:45:38 +0000 + Wed, 10 Dec 2025 05:00:03 +0000 rss-help@arxiv.org - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 Saturday Sunday - A simplified formula for the matched projection of an idempotent - https://arxiv.org/abs/2512.05970 - arXiv:2512.05970v1 Announce Type: new -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:2512.05970v1 - math.FA - Tue, 09 Dec 2025 00:00:00 -0500 + 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-nc-nd/4.0/ - Qingxiang Xu + http://creativecommons.org/licenses/by/4.0/ + Eun H. Park - On mathematical aspects of surface correction via ion beam etching - https://arxiv.org/abs/2512.06004 - arXiv:2512.06004v1 Announce Type: new -Abstract: Motivated by the ion beam dwell time calculation problem in Ion Beam Figuring we suggest a mathematical framework for solving a specific type of inverse problems, which appear in various areas of applied mathematics and physics. From the point of view of functional analysis we deal with a linear operator equation, which, taking advantage of the observation that the associated operator, acting from the space of dwell times into the space of measurement data, is close to a finite-dimensional one, can be solved employing the pseudoinverse operator. For the main case of interest we describe the behavior of the singular vectors inside the domain, on which measurement data are given, which turn out to be close to functions $e^{ikx}$. Heuristically, these singular vectors are similar to eigenfunctions of the infinitely deep quantum well. An alternative problem formulation, closer to practical calculations, utilizes reconstructing kernel Hilbert spaces (RKHS) and radial basis functions, which are used for pointwise approximation of measurement data and ensuing dwell time determination. Depending on the particularities of the concrete problem either framework or a suitable combination of each can be used. - oai:arXiv.org:2512.06004v1 - math-ph - math.MP - nlin.CD - Tue, 09 Dec 2025 00:00:00 -0500 + 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-nc-nd/4.0/ - 10.1088/1751-8121/ae1d35 - J. Phys. A: Math. Theor. 58 475201 (2025) - W. Pauls + http://creativecommons.org/licenses/by/4.0/ + Eun H. Park - Bounds on the Albertson Index for Trees with Given Degree Sequences - https://arxiv.org/abs/2512.06023 - arXiv:2512.06023v1 Announce Type: new -Abstract: In this paper, we presents novel and sharp bounds on the Albertson index of trees, revealing deep connections between degree sequences and graph irregularity where the Albertson index of Caterpillar tree satisfy \[ \operatorname{irr}(G)=\left( {{d_n} - 1} \right)^2 + \left( {d_1 - 1} \right)^2 + \sum\limits_{i = 2}^{n - 1} {\left( {{d_i} - 1} \right)\left( {{d_i} - 2} \right)} +\sum_{i=1}^{n-1}|d_i-d_{i+1}|. - \] - We derive powerful inequalities that precisely characterize the minimum and maximum values of the Albertson index, incorporating intricate dependencies on vertex degrees, edge counts, and the average of elements in degree sequence $\mathscr{D}=(d_1,d_2,\dots,d_n)$ where $d_n\geqslant d_{n-1}\geqslant \dots\geqslant d_2\geqslant d_1$. Our results not only improve existing extremal bounds but also uncover striking relationships between the structure of trees and their irregularity measurements. These advances open new avenues for the analysis of graph irregularity and contribute essential tools for the study of degree-based topological indices in combinatorial graph theory. - oai:arXiv.org:2512.06023v1 - math.GM - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://creativecommons.org/licenses/by/4.0/ - Jasem Hamoud, Duaa Abdullah + Selime Beyza \"Oz\c{c}ev\.ik, Abdullah Dertli - A Note About Models of Synthetic Algebraic Geometry - https://arxiv.org/abs/2512.06025 - arXiv:2512.06025v1 Announce Type: new -Abstract: We show how to build models of Synthetic Algebraic Geometry over rings k such that finitely presented k-algebra have a decidable equality. The construction is done in a constructive and weak (same proof theoretic strength as dependent type theory with universes) meta theory. - oai:arXiv.org:2512.06025v1 - math.LO - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://creativecommons.org/licenses/by/4.0/ - Thierry Coquand, Jonas Hofer, Christian Sattler + Ghaura Mahabaduge - Geometric properties of second Ricci solitons - https://arxiv.org/abs/2512.06027 - arXiv:2512.06027v1 Announce Type: new -Abstract: This paper introduce the idea of second Ricci solitons. A second Ricci soliton is nothing but a steady hyperbolic Ricci soliton. We study the geometry of closed and compact second Ricci soliton manifolds. Immersed submanifolds as second solitons also will be investigated. Finally, we investigate this structure on warped product manifolds. - oai:arXiv.org:2512.06027v1 + 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 - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/publicdomain/zero/1.0/ - Masoumeh Khalili, Ghodratallah Fasihi-Ramandi, Shahroud Azami + http://creativecommons.org/licenses/by/4.0/ + Erhan G\"uler, Magdalena Toda - The Relationship Between Euler Numbers and Bernoulli Numbers with Ordered Partitions - https://arxiv.org/abs/2512.06028 - arXiv:2512.06028v1 Announce Type: new -Abstract: In this paper, for every $n \in \mathbb{N}$, the following relationships between the functions $K_{b}(n)$ and $K_{e}(n)$ and the Bernoulli and Euler numbers are proved: \[ B_{2n} = -\,\frac{(2n)!}{2^{2n}-2}\, K_{b}(n), \qquad E_{2n} = (2n)!\, K_{e}(n). \] - The functions $K_{b}$ and $K_{e}$ are defined recursively by \[ K_{b}(0) = K_{e}(0) = 1, \] \[ K_{b}(n) = - \sum_{n'=0}^{\,n-1} \frac{K_{b}(n')}{\bigl( 2(n-n') + 1 \bigr)!}, \qquad n \ge 1, \] \[ K_{e}(n) = - \sum_{n'=0}^{\,n-1} \frac{K_{e}(n')}{\bigl( 2(n-n') \bigr)!}, \qquad n \ge 1. \] - Furthermore, we present combinatorial interpretations of these functions in terms of ordered partitions of $n$: \[ K_{b}(n) = \sum_{\lambda \vDash n} \frac{(-1)^{\ell(\lambda)}} {\displaystyle\prod_{i=1}^{\ell(\lambda)} (2b_i + 1)!}, \qquad n \ge 1, \] \[ K_{e}(n) = \sum_{\lambda \vDash n} \frac{(-1)^{\ell(\lambda)}} {\displaystyle\prod_{i=1}^{\ell(\lambda)} (2b_i)!}, \qquad n \ge 1, \] where $\lambda = (b_1,b_2,\ldots,b_k) \vDash n$ and $\ell(\lambda)=k$. - oai:arXiv.org:2512.06028v1 - math.GM - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://creativecommons.org/licenses/by/4.0/ - Kamyar Sepehri Pirayvatloo, Kazem Haghnejad Azar + Yurii Volkov, Oleksandr Volkov - Diophantine Analysis of a Digital Anomaly - https://arxiv.org/abs/2512.06056 - arXiv:2512.06056v1 Announce Type: new -Abstract: The arithmetic-digital anomaly of $5\div 2 = 2.5$ has been observed several times in the past. We generalize it to an exponential Diophantine equation and inequality in the general number base, which is the object of our analysis. First, we produce a near-parametrization of all solutions using a modification of the standard parametrization of Pythagorean triples. We use this parametrized function to find all solutions where the numerator and denominator are coprime, and we construct infinite families where they are not coprime. Next, we use a variant of Baker's theorem from transcendental number theory to prove that each number base admits only finitely many solutions. Lastly, we use the $abc$ conjecture to conditionally show that only finitely many solutions have a numerator with $k$ digits, for each $k\ge 3$. A conjecture is offered for $k=2$. - oai:arXiv.org:2512.06056v1 - math.HO - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://creativecommons.org/licenses/by/4.0/ - Samer Seraj + Anupama Ghorai, Jitraj Saha - Polymorphic Numbers with Exponential Prefix - https://arxiv.org/abs/2512.06057 - arXiv:2512.06057v1 Announce Type: new -Abstract: We observe that the computation $5^2 = 25$ has the digital property of the result being equal to the exponent concatenated directly to the left of the base. The generalization to a Diophantine equation and inequality in number bases has been articulated previously, but a comprehensive answer was not available in the literature. We classify and largely parametrize the solutions. Tools that play key roles are the Newton-Raphson method, the arithmetic-geometric means inequality, Pell's equation, and Fermat's little theorem. - oai:arXiv.org:2512.06057v1 - math.HO - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Samer Seraj + Jian-Feng Cai, Zhiqiang Xu, Zili Xu - A Kunz-type theorem for formal unramification - https://arxiv.org/abs/2512.06063 - arXiv:2512.06063v1 Announce Type: new -Abstract: We prove that for a morphism of schemes of positive characteristic whose relative Frobenius is a morphism of locally noetherian schemes, being formally unramified (resp. formally \'etale) is equivalent to its Frobenius morphism being a closed immersion (resp. an isomorphism). We also discuss the non-noetherian case. - oai:arXiv.org:2512.06063v1 - math.AG - math.AC - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Javier Carvajal-Rojas, Axel St\"abler + D. K. Durdiev, H. H. Turdiev - The Bennati-Dragulescu-Yakovenko model in the continuous setting: PDE derivation and long-time behavior - https://arxiv.org/abs/2512.06101 - arXiv:2512.06101v1 Announce Type: new -Abstract: In this manuscript, we develop and analyze a continuous version of the well-known Bennati-Dragulescu-Yakovenko (BDY) dollar-exchange discrete model. Starting from the conservative BDY exchange mechanism, we rely on kinetic theory for multi-agent systems in order to propose an analogue continuous dynamics, which does not belong to the class of other popular kinetic models for wealth exchange. We employ the quasi-invariant limit procedure to rigorously derive a nonlinear PDE on the half-line, which is a Fokker-Planck equation featuring the boundary value in the drift term. The PDE is supplemented with a nonlinear Robin-type boundary condition encoding conservation of total agents and wealth. We prove existence and uniqueness of the solution, which converges in relative entropy to the unique stationary state that is the Boltzmann-Gibbs (exponential) distribution. We determine the $L^1$ convergence (up to subsequences) of the solution toward this equilibrium: this requires us to make a step forward with respect to established arguments of entropy decay for Fokker-Planck equations. Thus, our results, which bridge the discrete stochastic dynamics with a continuous deterministic evolution equation, provide a novel and influential wealth exchange model in a PDE framework, which opens up many new applicative scenarios and methodological analytical challenges. - oai:arXiv.org:2512.06101v1 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Fei Cao, Nadia Loy + Ciro Ciliberto, Rick Miranda - From Tail Universality to Bernstein-von Mises: A Unified Statistical Theory of Semi-Implicit Variational Inference - https://arxiv.org/abs/2512.06107 - arXiv:2512.06107v1 Announce Type: new -Abstract: Semi-implicit variational inference (SIVI) constructs approximate posteriors of the form $q(\theta) = \int k(\theta | z) r(dz)$, where the conditional kernel is parameterized and the mixing base is fixed and tractable. This paper develops a unified "approximation-optimization-statistics'' theory for such families. - On the approximation side, we show that under compact L1-universality and a mild tail-dominance condition, semi-implicit families are dense in L1 and can achieve arbitrarily small forward Kullback-Leibler (KL) error. We also identify two sharp obstructions to global approximation: (i) an Orlicz tail-mismatch condition that induces a strictly positive forward-KL gap, and (ii) structural restrictions, such as non-autoregressive Gaussian kernels, that force "branch collapse'' in conditional distributions. For each obstruction we give a minimal structural modification that restores approximability. - On the optimization side, we establish finite-sample oracle inequalities and prove that the empirical SIVI objectives L(K,n) $\Gamma$-converge to their population limit as n and K tend to infinity. These results give consistency of empirical maximizers, quantitative control of finite-K surrogate bias, and stability of the resulting variational posteriors. - Combining the approximation and optimization analyses yields the first general end-to-end statistical theory for SIVI: we characterize precisely when SIVI can recover the target distribution, when it cannot, and how architectural and algorithmic choices govern the attainable asymptotic behavior. - oai:arXiv.org:2512.06107v1 - math.ST - stat.ML - stat.TH - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Sean Plummer + Paolo Aluffi - 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:2512.06109v1 Announce Type: new -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:2512.06109v1 - math.OC - cs.LG - cs.RO - cs.SY - eess.SY - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://creativecommons.org/licenses/by/4.0/ - Ajinkya Bhole, Mohammad Mahmoudi Filabadi, Guillaume Crevecoeur, Tom Lefebvre - - - A note on Johnson's rule for minimizing makespan in the Two-Machine Flow Shop scheduling problem - https://arxiv.org/abs/2512.06119 - arXiv:2512.06119v1 Announce Type: new -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:2512.06119v1 - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Federico Della Croce, Quentin Schau + Eunice Sukarto - Classification of Associative Algebras Satisfying Quadratic Polynomial Identities - https://arxiv.org/abs/2512.06125 - arXiv:2512.06125v1 Announce Type: new -Abstract: In quantum mechanics, associative algebras play an important role in understanding symmetries and operator algebras, providing new algebraic frameworks for describing physical systems. This work classifies associative algebras over a field K that are generated by a finite set G and satisfy a polynomial identity of the form X^{2} = aX+b, where a and b are elements of K and X varies either over all elements of the algebra or over all elements of the multiplicative semigroup S generated by G. One of the results obtained in this work shows that algebras satisfying X^{2}=0 over fields of characteristics different from 2 are nilpotent of index 3. - The results were computationally validated using the GAP system. - oai:arXiv.org:2512.06125v1 - math.RA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://creativecommons.org/licenses/by/4.0/ - Josimar da Silva Rocha + S. Yu. Orevkov - Polynomial identities of finite prime Universal algebras - https://arxiv.org/abs/2512.06135 - arXiv:2512.06135v1 Announce Type: new -Abstract: We prove that two finite prime $\Omega$-algebras defined over the same unital commutative ring and satisfying the same set of polynomial identities are isomorphic. - oai:arXiv.org:2512.06135v1 - math.RA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Yuri Bahturin, Daniela Martinez Correa, Diogo Diniz, Felipe Yasumura + Espen Robstad Jakobsen, Robin {\O}stern Lien, Artur Rutkowski - Data-driven Synchronization for Network Systems with Noiseless Data - https://arxiv.org/abs/2512.06136 - arXiv:2512.06136v1 Announce Type: new -Abstract: For a collection of homogeneous LTI systems that is interconnected by a protocol, given the network topology and the system model, one may obtain a feedback gain to synchronize the network. However, the model-based methods cannot be applied in case the system model is unknown. Therefore, in this paper, we study the data-driven synchronization problem for homogeneous networks. In particular, given a collection of LTI systems, we collect the input-state data from one individual system. Then, given the network topology, we provide data-based necessary and sufficient conditions for synchronizability. Once the conditions are satisfied, one can also obtain a feedback gain directly from data to synchronize the network with the corresponding design method provided in this paper. Finally, we illustrate our results with a numerical simulation. - oai:arXiv.org:2512.06136v1 - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://creativecommons.org/licenses/by/4.0/ - Yongzhang Li, M. Kanat Camlibel + Junfeng Xu, Sujoy Majumder, Lata Mahato - RationalFunctionApproximation.jl: Rational Approximation On Discrete and Continuous Domains - https://arxiv.org/abs/2512.06140 - arXiv:2512.06140v1 Announce Type: new -Abstract: Unlike polynomials, rational functions can represent functions having poles or branch cuts with root-exponential convergence and no Runge phenomenon. Recent developments of the AAA and greedy Thiele algorithms have sparked renewed interest in computational rational approximation. The \textsf{RationalFunctionApproximation} package supplies the fastest known implementations of these methods and the only arbitrary-precision ones. Combined with the \textsf{ComplexRegions} package, it can produce compact and accurate representations of a huge variety of functions over intervals, circles, or other domains in the complex plane. - oai:arXiv.org:2512.06140v1 - math.NA - cs.NA - math.CV - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://creativecommons.org/licenses/by/4.0/ - Tobin A. Driscoll + M. P. Savelov - Periodic sharpness of Miyaoka's bound for smooth rational curves - https://arxiv.org/abs/2512.06145 - arXiv:2512.06145v1 Announce Type: new -Abstract: We determine the maximal number of smooth rational degree d curves on a complex K3-surface of degree 2n provided n is sufficiently large as compared to d>1. We obtain precise characterization of configurations of rational degree d curves for which Miyaoka's bound is sharp for nd odd and n sufficiently large as compared to d. - oai:arXiv.org:2512.06145v1 + 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 + new + http://creativecommons.org/licenses/by-nc-sa/4.0/ + Rohan Goyal, Venkatesan Guruswami + + + 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 - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ Alex Degtyarev, S{\l}awomir Rams - Blow-up criterion for the compressible Navier--Stokes system with inflow-outflow boundary conditions - https://arxiv.org/abs/2512.06150 - arXiv:2512.06150v1 Announce Type: new -Abstract: We consider the compressible Navier-Stokes system in three dimensions with general inflow-outflow boundary conditions, meaning that we prescribe a boundary velocity which has non-zero normal component and accordingly the density is prescribed on the inflow part of the boundary. We establish a blow-up criterion in a class of strong solutions in the $L^p-L^q$ framework. In particular assuming the boundedness of the quantities $(\varrho^{-1}, \bu)$ and of a suitable norm of $\nabla_x \varrho$ the solution remains regular and the blow-up does not occur. We develop the condition on $\nabla_x \varrho$ because we need a new approach in order to accommodate the inhomogeneous boundary conditions, as the standard estimates on the material time derivative works when the normal component of the boundary velocity is zero. - oai:arXiv.org:2512.06150v1 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Anna Abbatiello, Mostafa Meliani + http://creativecommons.org/licenses/by/4.0/ + Krishnendu Gongopadhyay, Neelanjan Mondal - Group graded algebras and varieties with quadratic codimension growth - https://arxiv.org/abs/2512.06153 - arXiv:2512.06153v1 Announce Type: new -Abstract: Let $A$ be an associative algebra graded by a finite group $G$ over a field ${F}$ of characteristic zero. One associates to $A$ the sequence of $G$-graded codimensions $c_n^G(A)$, $n=1,2,\ldots$, which measures the growth of the polynomial identities satisfied by $A$. It is known that this sequence is either polynomially bounded or grows exponentially. In this paper, we study unitary $G$-graded varieties of polynomial codimension growth. In particular, we classify the varieties generated by unitary algebras with quadratic codimension growth and show that these varieties can be described as a direct sums of algebras that generate minimal $G$-graded varieties. - oai:arXiv.org:2512.06153v1 - math.RA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://creativecommons.org/licenses/by/4.0/ - Wesley Quaresma Cota + Daniel W. Cranston - Hybrid Beamfocusing Design for RSMA-Enabled Near-Field Wideband Communications - https://arxiv.org/abs/2512.06156 - arXiv:2512.06156v1 Announce Type: new -Abstract: Future wireless networks will utilize extremely large-scale antenna arrays (ELAAs) over high-frequency bands, which, however, produce near-field spherical wavefronts and spatial wideband effects. To exploit and mitigate these, this paper proposes a rate-splitting multiple access (RSMA)-enabled transmit scheme for wideband near-field communications (NFC). Our solution leverages true-time-delay (TTD)-based hybrid beamfocusing architectures to mitigate spatial wideband effect and reduce radio frequency chain requirements. The objective is to maximize the minimum rate by jointly optimizing frequency-dependent analog beamfocusing, frequency-independent analog beamfocusing, digital beamfocusing, and common rate allocation. To solve this complicated non-convex problem, we develop a penalty-based iterative algorithm that partitions the variables into three blocks and then employs block coordinate descent (BCD) to optimize each block alternately. This algorithm is further extended to support the sub-connected TTD-based analog beamfocusing architectures. Comprehensive simulation results indicate that our transmit scheme: 1) effectively compensates for spatial wideband effect, addressing a critical challenge in wideband operation; 2) achieves performance comparable to full digital beamfocusing while maintaining lower hardware complexity; 3) achieves substantial performance gains over the other two benchmarks. - oai:arXiv.org:2512.06156v1 - cs.IT - math.IT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jiasi Zhou, Chintha Tellambura + Alberto Enciso, Josef Greilhuber - Minimal varieties of algebras with graded involution and quadratic growth - https://arxiv.org/abs/2512.06160 - arXiv:2512.06160v1 Announce Type: new -Abstract: Subalgebras of upper triangular matrix algebras have played a fundamental role in the classification of minimal varieties of polynomial growth. Such classification has become a source of study in recent years since it leads to the more general classification of varieties of polynomial growth $n^k$, as has already been proven in many contexts for several values of $k$. In this paper, we study the asymptotic behavior of the sequence of codimensions of algebras graded by a finite group $G$ and endowed with a graded involution $*$, also called $(G,*)$-algebras. We classify the minimal varieties generated by a finite-dimensional $(G,*)$-algebra with quadratic growth. - oai:arXiv.org:2512.06160v1 - math.RA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://creativecommons.org/licenses/by/4.0/ - Wesley Quaresma Cota, Ana Cristina Vieira + http://creativecommons.org/licenses/by-nc-nd/4.0/ + Zilu Zhao, Fangqing Xiao, Dirk Slock - Isoperiodic deformations of Abelian differentials of the second kind over elliptic curves and the Boussinesq equation - https://arxiv.org/abs/2512.06162 - arXiv:2512.06162v1 Announce Type: new -Abstract: We study deformations of a genus one Riemann surface and of a second order Abelian differential on the surface which preserve the periods of the differential with respect to a chosen canonical homology basis of the surface. We call these deformations isoperiodic. We derive a second order ordinary differential equation with rational coefficients governing the variations of the position of the unique pole of the differential under the isoperiodic deformations. The obtained equation depends on the order of the pole of the differential. We characterize the solutions of the obtained ordinary differential equations that correspond to the isoperiodic deformations. We apply these results to the theory of genus one solutions to the Boussinesq equation. - oai:arXiv.org:2512.06162v1 - math.AG - math-ph + 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 - math.MP - nlin.SI - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Vladimir Dragovic, Vasilisa Shramchenko + Piotr B. Mucha, Tomasz Piasecki, Yoshihiro Shibata - On the colength sequence of algebras with graded involution - https://arxiv.org/abs/2512.06164 - arXiv:2512.06164v1 Announce Type: new -Abstract: In recent years, many results have been established regarding classifications of varieties whose colength sequences are bounded by a fixed constant. In this work, we explore this theme in the setting of algebras endowed with a graded involution, called $(G,*)$-algebras. We give an explicit description of the decomposition of the $\langle n \rangle$-cocharacter for some important $(G,*)$-algebras $A$, for every $\langle n \rangle=(n_1, \ldots, n_{2t})$. For each algebra $A$, the $n$th colength is defined as the number of irreducible components that appear in these decompositions. Our aim is to classify varieties whose $n$th colengths are bounded by a fixed constant. - oai:arXiv.org:2512.06164v1 - math.RA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://creativecommons.org/licenses/by/4.0/ - Wesley Quaresma Cota, Rafael Bezerra dos Santos, Ana Cristina Vieira + http://creativecommons.org/licenses/by-sa/4.0/ + Gustavo Amilcar Salda\~na Moncada - Graph morphisms as groupoid actors - https://arxiv.org/abs/2512.06165 - arXiv:2512.06165v1 Announce Type: new -Abstract: We describe proper actors from the underlying groupoid of a graph C*-algebra to another \'etale groupoid in terms of bisections. This allows to understand graph morphisms and the *-homomorphisms that they induce more conceptually. More generally, we describe actors from the groupoid model of a groupoid correspondence to any \'etale groupoid. This also covers the groupoids associated to self-similar groups and self-similar graphs, among others. - oai:arXiv.org:2512.06165v1 - math.OA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Gilles G. de Castro, Ralf Meyer + http://creativecommons.org/licenses/by-nc-nd/4.0/ + Saieed Akbari, Jonathan Aloni, Maxwell Levit, Bojan Mohar, Steven Xia - A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners - https://arxiv.org/abs/2512.06166 - arXiv:2512.06166v1 Announce Type: new -Abstract: We investigate the dimension dependence of Bramble--Pasciak--Xu (BPX) preconditioners for high-dimensional partial differential equations and establish that the condition numbers of BPX-preconditioned systems grow only polynomially with the spatial dimension. Our analysis requires a careful derivation of the dimension dependence of several fundamental tools in the theory of finite element methods, including the elliptic regularity, Bramble--Hilbert lemma, trace inequalities, and inverse inequalities. We further introduce a new quasi-interpolation operator into finite element spaces, a variant of the classical Scott--Zhang interpolation, whose associated constants scale polynomially with the dimension. Building on these ingredients, we prove a multilevel norm equivalence theorem and derive a BPX preconditioner with explicit polynomial bounds on its dimensional dependence. This result has notable implications for emerging quantum computing methodologies: recent studies indicate that polynomial dependence of BPX preconditioners on dimension can yield exponential speedups for quantum-algorithmic approaches over their classical counterparts. - oai:arXiv.org:2512.06166v1 - math.NA - cs.NA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Boou Jiang, Jongho Park, Jinchao Xu + 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 + + + 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 + new + http://creativecommons.org/licenses/by/4.0/ + Alexis Lucas - Deformations of the Hill curves and isoperiodicity in the KdV and the sine-Gordon equations - https://arxiv.org/abs/2512.06168 - arXiv:2512.06168v1 Announce Type: new -Abstract: We consider a family of genus $g$ hyperelliptic curves as double ramified coverings over the Riemann sphere with the set of branch points of the form $\{0, \infty, x_1, \dots, x_g, u_1, \dots, u_g\}$. The branch point at infinity $P_\infty$ is selected to be a marked point on the Riemann surfaces. A meromorphic differential $\Omega$ with a unique pole being of order two at $P_\infty$, is completely defined by the values of half of its periods, the $a$-periods. Fixing values of $a$-periods of $\Omega$, we then find a continuous subfamily in the considered family of hyperelliptic curves along which all the periods of $\Omega$ are constant. This subfamily is defined by the functions $u_j(x_1, \dots, x_g)$, while $x_1, \dots, x_g$ are independent parameters. We derive a system of differential equations for the functions $u_j(x_1, \dots, x_g)$, which, remarkably, has rational coefficients. We call this subfamily the isoperiodic deformations of the hyperelliptic curves relative to the given differential of the second kind $\Omega.$ We deduce necessary and sufficient conditions for the existence and uniqueness of isoperiodic deformations. We discuss reality conditions as well. Using the obtained results, we solve the following problem for the Korteweg-de Vries and sine-Gordon equations: starting from an algebro-geometric data which generate a real periodic solution of a period $T$, how to deform the data, so that the associated solutions remain periodic with the same period $T$. - oai:arXiv.org:2512.06168v1 + 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.AP math.MP - nlin.SI - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Vladimir Dragovic, Vasilisa Shramchenko + http://creativecommons.org/publicdomain/zero/1.0/ + John Alexander Cruz Morales - The effects of individual versus community-influenced isolation on SIS epidemic persistence on finite random graphs - https://arxiv.org/abs/2512.06175 - arXiv:2512.06175v1 Announce Type: new -Abstract: The contact process, or SIS epidemic, is a continuous-time Markov process used to model the spread of infection on a graph. Each vertex is either healthy or infected, and each infected vertex independently infects each of its healthy neighbors at rate $\lambda$ and recovers at rate $1$. We study the contact process in the presence of additional intervention measures by introducing a third possible state for vertices, which we call isolated. Vertices may enter the isolated state either because of individual decisions or due to community-influenced decisions, which leads to two distinct models that we call the isolation model and the vigilance model, respectively. In the isolation model, infected vertices self-isolate at rate $\alpha$. In the vigilance model, each healthy vertex causes each of its infected neighbors to isolate at rate $\alpha$. Unlike the usual contact process, these models lack the key features of attractiveness and existence of a dual, which makes analyzing them more challenging. We study the persistence times of the infection on large, finite, degree-heterogeneous random graphs. We show that the infection in the isolation model persists for at least stretched exponential time in the size of the graph for all values of $\alpha$ and $\lambda$. By contrast, in the vigilance model, for every fixed $\alpha$ the persistence time of the infection exhibits a phase transition in $\lambda$: for small $\lambda$ the infection persists for at most a linear time in the size of the graph, while for large $\lambda$ the infection persists exponentially long. This contrast demonstrates that individual versus community-influenced isolation can substantially affect the persistence of an epidemic. - oai:arXiv.org:2512.06175v1 - math.PR - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Shirshendu Chatterjee, David Sivakoff, Matthew Wascher + Hannah Cairo, Ruixiang Zhang - Potential theory and applications in conformal geometry - https://arxiv.org/abs/2512.06188 - arXiv:2512.06188v1 Announce Type: new -Abstract: In this paper, we want to give an exposition of our recent work on linear and nonlinear potential theory and their applications in conformal geometry. We use potential theory to study linear and quasilinear equations arising from conformal geometry. We establish the asymptotic behavior near singularities and derive applications in conformal geometry. In particular, we establish some Huber's type theorems and Hausdorff dimension estimates of the ends in conformal geometry in general dimensions. - oai:arXiv.org:2512.06188v1 - math.DG - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://creativecommons.org/licenses/by/4.0/ - 10.1285/i15900932v45s1p147 - Shiguang Ma, Jie Qing + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Emmanuel Balderas, David Chodounsk\'y, Osvaldo Guzm\'an - A geometric view of formation control with application to directed sensing - https://arxiv.org/abs/2512.06195 - arXiv:2512.06195v1 Announce Type: new -Abstract: We propose a geometric approach to distance-based formation control modeled on a minimum-norm lifting of Riemannian gradient descent in edge-space to node-space. This yields a unified family of controllers, including the classical gradient controller and its directed variant. For the directed case, we give a simple numerical test for local convergence that applies to any directed graph and target. We show that persistence is neither necessary nor sufficient for local convergence of our directed controller and propose an alternative that is necessary and more easily checked. - oai:arXiv.org:2512.06195v1 - math.OC - math.MG - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.NA + cs.CV + cs.IT + cs.NA + math.IT + Wed, 10 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Louis Theran, Daniel Zelazo, Jessica Sidman + Matthias Beckmann, Robert Beinert, Jonas Bresch - On Graded Deformations of The universal Enveloping Algebra of a Color Lie Algebra - https://arxiv.org/abs/2512.06197 - arXiv:2512.06197v1 Announce Type: new -Abstract: Let $\mathfrak{g}$ be a Color Lie Algebra and $\mathcal{U}(\mathfrak{g})$ its the universal Enveloping Algebra. We define the notion of graded deformations and we give explicit graded deformations of the universal Enveloping Algebra of $\mathfrak{g}$. - oai:arXiv.org:2512.06197v1 - math.RA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Toukaiddine Petit + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Cec\'ilia Salgado, Lara Vicino - A geophysical free-boundary system modeling an ice-sheet interacting with an ocean - https://arxiv.org/abs/2512.06202 - arXiv:2512.06202v1 Announce Type: new -Abstract: We consider a free-boundary model for the ice-sheet interacting with an ocean. The model captures the coupling between a viscous geophysical fluid and an elastic interface through kinematic and dynamic boundary conditions that account for hydrodynamic loading. Using the ALE formulation, we derive a system on a fixed reference domain and establish local-in-time a priori estimates for strong solutions with initial data in $H^2$. The main analytical difficulties arise from the nonlinear terms involving vertical derivatives and from high-order pressure contributions on the interface. - oai:arXiv.org:2512.06202v1 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Matthias Hieber, Igor Kukavica, Amjad Tuffaha, Qi Xu + http://creativecommons.org/licenses/by/4.0/ + Enrique Garc\'ia-S\'anchez, David de Hevia - A Front Fixing Crank-Nicolson Finite Deference for the American Put Options Model - https://arxiv.org/abs/2512.06214 - arXiv:2512.06214v1 Announce Type: new -Abstract: In this paper, we present a novel approach to solving the American put options pricing model by hugely relying on a front-fixing Crank-Nicolson finite difference method. Since the American put option pricing model is a widely used financial model for valuing an option with the right to sell an underlying asset at a fated price which generally decided in advance. The method we proposed here, solves the problem of early exercise by introducing a front-fixing technique that permits for efficient and accurate valuation of an American put option. As in the comparison to other approaches in the existing literature, we can assert that this method is stable, accurate, consistent, and efficient. The results that we obtained here from the numerical experiments demonstrate not only the efficacy of the proposed method but also in consistently and accurately pricing American put options with a stable scheme. Under some appropriate conditions on the step size discretization, we also show the positivity and monotonicity of the coefficient involved in the numerical scheme used. - oai:arXiv.org:2512.06214v1 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://creativecommons.org/licenses/by/4.0/ - Z. I. Ali, M. A. Abebe + Enrique Garc\'ia-S\'anchez, David de Hevia, Mitchell Taylor - Diffusion bridge with misspecification: theory construction and application to high-resolution fish count data - https://arxiv.org/abs/2512.06216 - arXiv:2512.06216v1 Announce Type: new -Abstract: Stochastic processes of bridge types having pinned initial and terminal conditions have been widely used in applied research areas, but they all have a common drawback in that the model at hand is possibly misspecified owing to its stochastic nature; namely, parameter values and coefficients are distorted compared to the ground truth. We consider a pair of novel exactly-solvable optimization problems that provide both the lower and upper bounds of the performance index of a diffusion bridge. Our formulation is based on the Girsanov transformation, in which the model uncertainty is measured through relative entropy. We provide a sufficient condition under which these optimization problems are well-posed, and hence admit the corresponding maximizer/minimizer that achieves the worst-case lower and upper bounds given the ambiguity aversion or uncertainty size. We apply the proposed method to the latest 10-min, high-resolution fish count data of a migratory fish in a river and discuss the influence of model uncertainty on the estimation of the total fish count, which is an important problem in resource and environmental management. - oai:arXiv.org:2512.06216v1 - math.PR - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Hidekazu Yoshioka + Satoru Odake - A linear upper bound on the zero-sum Ramsey number of forests in $\mathbb{Z}_p$ - https://arxiv.org/abs/2512.06229 - arXiv:2512.06229v1 Announce Type: new -Abstract: Let $m$ be a positive integer and let $G$ be a graph. The zero-sum Ramsey number $R(G,\mathbb{Z}_m)$ is the least integer $N$ (if it exists) such that for every edge-coloring $\chi \, : \, E(K_N) \, \rightarrow \, \mathbb{Z}_m$ one can find a copy of $G$ in $K_N$ such that $\sum_{e \, \in \, E(G)}{\chi(e)} \, = \, 0$. - In this paper, we show that, for every prime $p$, $$R(F,\mathbb{Z}_p)\leq n+9p-12$$ for every forest $F$ in $n\geq 3p^2-12p+11$ vertices with $p\mid e(F)$. - oai:arXiv.org:2512.06229v1 - math.CO - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://creativecommons.org/licenses/by/4.0/ - Lucas Colucci, Marco D'Emidio + Amy de Castro, Hyesuk Lee - New Results on the Polyak Stepsize: Tight Convergence Analysis and Universal Function Classes - https://arxiv.org/abs/2512.06231 - arXiv:2512.06231v1 Announce Type: new -Abstract: In this paper, we revisit a classical adaptive stepsize strategy for gradient descent: the Polyak stepsize (\texttt{PolyakGD}), originally proposed in \cite{polyak1969minimization}. We study the convergence behavior of \texttt{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 \texttt{PolyakGD} by explicitly constructing worst-case functions. In particular, we show that the $\mathcal{O}((1-\frac{1}{\kappa})^K)$ rate for smooth strongly convex functions and the $\mathcal{O}(1/K)$ rate for smooth convex functions are both tight. Moreover, we theoretically show that \texttt{PolyakGD} automatically exploits floating-point errors to escape the worst-case behavior. Our second main result provides new convergence guarantees for \texttt{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:2512.06231v1 - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Chang He, Wenzhi Gao, Bo Jiang, Madeleine Udell, Shuzhong Zhang + http://creativecommons.org/licenses/by/4.0/ + Milan Rosko + + + 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 + new + http://creativecommons.org/licenses/by/4.0/ + Jeremie Brieussel, Ryokichi Tanaka - Non-Asymptotic Error Bounds for Causally Conditioned Directed Information Rates of Gaussian Sequences - https://arxiv.org/abs/2512.06238 - arXiv:2512.06238v1 Announce Type: new -Abstract: Directed information and its causally conditioned variations are often used to measure causal influences between random processes. In practice, these quantities must be measured from data. Non-asymptotic error bounds for these estimates are known for sequences over finite alphabets, but less is known for real-valued data. This paper examines the case in which the data are sequences of Gaussian vectors. We provide an explicit formula for causally conditioned directed information rate based on optimal prediction and define an estimator based on this formula. We show that our estimator gives an error of order $O\left(N^{-1/2}\log(N)\right)$ with high probability, where $N$ is the total sample size. - oai:arXiv.org:2512.06238v1 + 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 - math.ST - stat.TH - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Yuping Zheng, Andrew Lamperski + Lei Xie, Hengtao He, Yifeng Xiong, Fan Liu, Shi Jin - Quadratic Formula-based Nonlinear Approximation - https://arxiv.org/abs/2512.06246 - arXiv:2512.06246v1 Announce Type: new -Abstract: This paper presents a quadratic formula-based nonlinear representation for a given single-variable function f(x), $-1 \leq x \leq 1$. First, we construct the explicit polynomial coefficient functions a(x), b(x), and c(x) using a least-squares approach. Then, f is reconstructed by solving the degree-2 polynomial equation a(x) f^2 - b(x) f - c(x)=0 for any $x \in [-1,1]$, where an index function is used to select the correct sign in the quadratic formula. The quadratic formula-based nonlinear approximation (degree-2 in f) outperforms classical orthogonal polynomial-based least-squares approximation (degree-0 in f) and rational approximation (degree-1 in f) for functions with sharp transitions or discontinuities. As a potential application, we apply the degree-2 representation to data denoising. Instead of relying on more complex "edge-preserving" metric-based optimization techniques, the smooth coefficient functions a(x), b(x), and c(x) enable effective least-squares-based denoising on the low-dimensional manifold described by the algebraic variety a(x) f^2 - b(x) f - c(x)=0. Denoising the index function, which determines the appropriate root to select, can be achieved using classical statistical or modern classification/clustering techniques. Numerical results and data denoising examples are provided to demonstrate the effectiveness of the degree-2 nonlinear approximation technique. The new nonlinear, quadratic formula-based representation also raises theoretical and numerical questions, including strategies for identifying numerically stable representations, developing optimal algorithms to construct the polynomial coefficient functions a(x), b(x), and c(x), and achieving economical representation and denoising of the index function. - oai:arXiv.org:2512.06246v1 - math.NA - cs.NA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Ziqin He, Can Chen, Min Hyung Cho, Jingfang Huang, Yichao Wu + Yao Yu - Impartial Avoidance Games on Convex Geometries - https://arxiv.org/abs/2512.06267 - arXiv:2512.06267v1 Announce Type: new -Abstract: We analyze a two-player game in which players take turns avoiding the selection of certain points within a convex geometry. The objective is to prevent the convex closure of all chosen points from encompassing a predefined set. The first player forced into a move that results in the inclusion of this set loses the game. We redevelop a theoretical framework for these avoidance games and determine their nim numbers, including cases involving vertex geometries of trees, edge geometries of trees, and scenarios where the predefined set consists of extreme points. - oai:arXiv.org:2512.06267v1 - math.CO - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://creativecommons.org/licenses/by/4.0/ - Seomgeun Shim + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Alexander Rogozin, Nhat Trung Nguyen, Hamed Azami Zenuzagh, Alexander Gasnikov - Crystal skeleton polynomials with major index, charge and depth - https://arxiv.org/abs/2512.06273 - arXiv:2512.06273v1 Announce Type: new -Abstract: We introduce a new family of polynomials, crystal skeleton polynomials, to better understand enumeration of standard Young tableaux, quasi-Yamanouchi tableaux and interactions with Gessel's expansion of a Schur function, quasi-crystals and crystal skeletons as Maas-Gari\'{e}py introduced in 2023. After developing calculus of those polynomials, we organize thoughts on major index, charge, depth, inversions with RSK correspondence and a bivariate factorial. Also, we revisit the theorem on internal zeros of fake degree polynomials by Billey--Konvalinka--Swanson (2020). These results altogether improve Gessel's expansion. - oai:arXiv.org:2512.06273v1 + 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 - Tue, 09 Dec 2025 00:00:00 -0500 + math.AG + Wed, 10 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Masato Kobayashi + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Christian Gaetz, Yibo Gao - Weak exponential metrics for high-dimensional log-correlated Gaussian fields - https://arxiv.org/abs/2512.06292 - arXiv:2512.06292v1 Announce Type: new -Abstract: For log-correlated Gaussian fields on $\mathbb{R}^d$ with $d \geq 2$, Ding-Gwynne-Zhuang (2023) established the existence of subsequential limits of exponential metrics obtained from appropriate approximations. For $\gamma \in (0,\sqrt{2d})$, we define a \textit{weak $\gamma$-exponential metric} to be a map $h \mapsto D_h$ that assigns to a sample of a log-correlated Gaussian field $h$ a continuous metric on $\mathbb{R}^d$ satisfying a list of axioms. We prove that every subsequential limit of exponential metrics built from appropriate approximations of $h$ is a weak $\gamma$-exponential metric in this sense. Moreover, we establish general properties that hold for any weak exponential metric: (1). sharp moment bounds for several natural distances; (2). optimal H\"older exponents when comparing $D_h$ and the Euclidean metric; and (3). Hausdorff dimension and a KPZ relation. These results extend the two-dimensional Liouville quantum gravity metric theory to higher dimensions. Along the way we derive several useful properties for log-correlated Gaussian fields including the equivalence between white-noise decomposition and convolution, and a shell independence lemma. - oai:arXiv.org:2512.06292v1 + 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 - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Andres A. Contreras Hip, Zijie Zhuang + Zhi-Hao Cui, Hao Wu, Wei Xu - Band-unknotting numbers and connected sums of knots - https://arxiv.org/abs/2512.06299 - arXiv:2512.06299v1 Announce Type: new -Abstract: We study the band-unknotting number $u_{nb}(K)$ of a knot $K$, and how it behaves with respect to connect sums. We show that this sub-additive function is not additive under connected sums, by finding infinitely many examples of knots $K_1, K_2$ with $u_{nb}(K_1\#K_2) < u_{nb}(K_1) + u_{nb}(K_2)$. Even more surprisingly, there are infinitely many examples of knots $K_1, K_2$ such that $u_{nb}(K_1\#K_2) < u_{nb}(K_i)$, $i=1,2$. Our work is motivated by the recent analogous results for the Gordian unknotting number by Brittenham and Hermiller \cite{BrittenhamHermiller}. - We also prove new lower and upper bounds on the topological and smooth non-orientable 4-genus of a knot $K$. - oai:arXiv.org:2512.06299v1 - math.GT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://creativecommons.org/licenses/by/4.0/ - Nakisa Ghanbarian, Stanislav Jabuka + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Haonan Gu - Knots in $S_{g} \times S^{1}$, their essential diagrams and virtual knots - https://arxiv.org/abs/2512.06300 - arXiv:2512.06300v1 Announce Type: new -Abstract: In \cite{Kim} it is shown that knots in $S_{g} \times S^{1}$ can be presented by virtual diagrams with a decoration, so called, {\em double lines}. In this paper, we study the essential diagram for each knot in $S_{g} \times S^{1}$, which has the minimal number of double lines. We prove that virtual knot theory is embedded in the theory of knots in $S_{g}\times S^{1}$. In the same time, one can obtain knots in $S^{2}\times S^{1}$ from 2-component links $L = K\sqcup T$ where $T$ is a trivial knot. By using knots in $S^{2} \times S^{1}$, we study the minimality and separability of such classical links. - oai:arXiv.org:2512.06300v1 - math.GT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.NT + Wed, 10 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Seongjeong Kim + http://creativecommons.org/licenses/by/4.0/ + Kazuhide Matsuda - A Simple Construction of Lefschetz Fibrations on Compact Stein Surfaces - https://arxiv.org/abs/2512.06302 - arXiv:2512.06302v1 Announce Type: new -Abstract: Loi-Piergallini, Akbulut-Ozbagci, and Akbulut-Arikan showed that every compact Stein surface admits a positive allowable Lefschetz fibration over the disk $D^2$ with bounded fibers (PALF in short), and they provided constructions of PALF's corresponding to compact Stein surfaces. - In this paper, we present a simple method for constructing a PALF from a 2-handlebody decomposition of any given compact Stein surface. Our method yields PALF's whose regular fibers have small genus, and it provides an alternative constructive proof of the above result. - We also define the minimal genus of a regular fiber of a PALF on the knot trace of a knot $K$ with framing one less than its maximal Thurston-Bennequin number as an invariant of $K$. When the grid number of $K$ is $N$, our construction produces a PALF whose regular fiber has genus at most $(N - 1)/2$, showing that the defined invariant is bounded above by $(N - 1)/2$. - oai:arXiv.org:2512.06302v1 - math.GT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Atsushi Tanaka + Jaime Negrete - Performance Bounds on Pliable Index Coding Using Absent Receivers - https://arxiv.org/abs/2512.06312 - arXiv:2512.06312v1 Announce Type: new -Abstract: We characterise bounds on the optimal broadcast rate for a few classes of pliable-index-coding instances. Unlike the majority of currently solved instances, which belong to a special class where all receivers with a certain side-information cardinality are either present or absent, we consider more general instances without this constraint. We devise a novel algorithm that constructs a decoding chain by iteratively adding a message that can be decoded by a receiver whose side information is already in the chain. If the decoding chain cannot proceed due to the absence of a receiver with the required messages, we skip a message by adding it to the chain regardless. We prove that a lower bound on the optimal broadcast rate is a function of the number of skipped messages, across all possible decoding choices of the receivers and any realisation of the algorithm for each decoding choice. While this result is not computationally feasible in isolation, it serves as a basis for deriving explicit lower bounds on the broadcast rate for specific classes of pliable-index-coding instances. These lower bounds depend on the number of absent receivers or the pattern of their side-information sets. Specifically, we explicitly characterise the optimal broadcast rate for instances with up to and including four absent receivers with any side-information pattern, as well as instances where the side-information sets are nested in particular ways. - oai:arXiv.org:2512.06312v1 - cs.IT - math.IT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - 10.1109/TIT.2025.3632399 - IEEE Transactions on Information Theory, 2025 - Lawrence Ong, Badri N. Vellambi, Parastoo Sadeghi, J\"org Kliewer + Umberto L. Hryniewicz, Pedro A. S. Salom\~ao, Richard Siefring - Approximation property in terms of Lipschitz maps via tensor product approach - https://arxiv.org/abs/2512.06317 - arXiv:2512.06317v1 Announce Type: new -Abstract: This article explores the extension of the classical approximation property and its variants to the nonlinear framework of Lipschitz operator theory. Building on Grothendieck's tensor product methodology, we characterize the Lipschitz approximation property of Banach spaces using Lipschitz finite-rank operators and tensor products. Furthermore, inspired by the $p$-approximation property defined via $p$-compact sets, we introduce and examine the Lipschitz $p$-approximation property. We also establish a factorization theorem for dual Lipschitz $p$-compact operators, mirroring known linear results. This paper looks more closely at how the Lipschitz approximation property and the $p$-approximation property of a Banach space are related to those of its Lipschitz-free space. - oai:arXiv.org:2512.06317v1 - math.FA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Arindam Mandal + Jie Li, Chao Zhang - Horofunction compactifications and local Gromov model domains - https://arxiv.org/abs/2512.06321 - arXiv:2512.06321v1 Announce Type: new -Abstract: We explore the horofunction compactification of complete hyperbolic domains in complex Euclidean space equipped with the Kobayashi distance. We provide a sufficient condition under which, given a domain $\Omega$ as above, the identity map from $\Omega$ to itself extends to an embedding of $\overline{\Omega}$ into the horofunction compactification of $(\Omega,k_\Omega)$, with $k_\Omega$ denoting the Kobayashi distance on $\Omega$. Notably, this condition admits unbounded domains that are not Gromov hyperbolic relative to the Kobayashi distance. We also provide a large class of planar hyperbolic domains satisfying the above condition. - oai:arXiv.org:2512.06321v1 - math.CV - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://creativecommons.org/licenses/by/4.0/ - Vikramjeet Singh Chandel, Sushil Gorai, Anwoy Maitra, Amar Deep Sarkar + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Jo\~ao Vitor da Silva, Feida Jiang, Jiangwen Wang - Partial Tower Sealing - https://arxiv.org/abs/2512.06323 - arXiv:2512.06323v1 Announce Type: new -Abstract: The main result of this paper shows that a weak form of Tower Sealing holds in a generic extension of hod mice with a strong cardinal and a proper class of Woodin cardinals. We show Tower Sealing fails in such extensions in general. We show that this weak form of Tower Sealing (called Partial Tower Sealing) implies Sealing and that its consistency strength is below that of ZFC + there is a Woodin limit of Woodin cardinals. - oai:arXiv.org:2512.06323v1 - math.LO - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://creativecommons.org/licenses/by/4.0/ - Grigor Sargsyan, Nam Trang + Zhanqiang Bai, William Q. Erickson, Markus Hunziker, Jing Jiang - Subsampling Confidence Bound for Persistent Diagram via Time-delay Embedding - https://arxiv.org/abs/2512.06324 - arXiv:2512.06324v1 Announce Type: new -Abstract: Time-delay embedding is a fundamental technique in Topological Data Analysis (TDA) for reconstructing the phase space dynamics of time-series data. While persistent homology effectively identifies topological features, such as cycles associated with periodicity, a rigorous statistical framework for quantifying the uncertainty of these features has been lacking in this context. In this paper, we propose a subsampling based method to construct confidence sets for persistence diagrams derived from time-delay embeddings. We establish finite sample guarantees for the validity of these confidence bounds under regularity conditions specifically for $C^{1,1}$ functions with positive reach and prove their asymptotic convergence as the embedding dimension tends to infinity. This framework provides a principled statistical test for periodicity, enabling the distinction between true periodic signals and non-periodic approximations. Simulation studies demonstrate that our method achieves detection performance comparable to the Generalized Lomb-Scargle periodogram on periodic data while exhibiting superior robustness in distinguishing non-periodic signals with time-varying frequencies, such as chirp signals. - oai:arXiv.org:2512.06324v1 + 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 - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Donghyun Park, Junhyun An, Taehyoung Kim, Jisu Kim + http://creativecommons.org/licenses/by-nc-nd/4.0/ + Andrew T. A. Wood - Limit theorems for the Wiener process with resetting - https://arxiv.org/abs/2512.06325 - arXiv:2512.06325v1 Announce Type: new -Abstract: We establish a large deviation principle for the trajectories of Wiener processes subject to random resets to the origin occurring according to a Poisson process. In addition to the pathwise large deviation principle, we identify the rate function and establish a large deviation principle for the supremum of the process over long time intervals. - oai:arXiv.org:2512.06325v1 - math.PR - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.OC + Wed, 10 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - A. V. Logachov, O. M. Logachova, A. A. Yambartsev, K. A. Zaykov + Xiushan Jiang, Dong Wang, Weihai Zhang, Daniel W. C. Ho, Yuanqing Wu - Curves in hyperspaces obtained by intersection of $r$-neighborhoods with a fixed subset - https://arxiv.org/abs/2512.06327 - arXiv:2512.06327v1 Announce Type: new -Abstract: The present paper generalizes the result from one of the papers by Galstyan. Namely, we consider two nonempty subsets $A$ and $B$ of a metric space $X$, and construct one-parametric family $F_r$ of subsets obtained by intersection between $B$ and closed $r$-neighborhood of $A$, where $r$ is bigger than the infimum distance between the sets $A$ and $B$. In the case where $B$ is compact, we show that this intersection, considered as a mapping, is right semicontinuously on $r$ in the topology generated by Hausdorff distance. Moreover, if $A$ and $B$ are convex subsets of a normed space $X$, then we prove that $F_r$ depends continuously on $r$ in such topology if and only if the Hausdorff distance between different sets $F_r$ is finite. We also show that for normed spaces $X$ of dimension $2$ or less, the latter condition is automatically fulfilled. For dimension $3$ and hence for bigger ones, we construct an example in which the Hausdorff distance between different $F_r$ is always infinite. - oai:arXiv.org:2512.06327v1 - math.MG - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.NA + cs.NA + Wed, 10 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Arsen Galstyan, Alexey Tuzhilin + Jerem\'ias Garay, David Nolte, Crist\'obal Bertoglio - Polar Decomposition for Non-Adjointable Maps - https://arxiv.org/abs/2512.06335 - arXiv:2512.06335v1 Announce Type: new -Abstract: We give conditions when not necessarily adjointable operators between Hilbert modules allow for a polar decomposition involving not necessarily adjointable partial isometries. While the latter have been introduced and discussed by Shalit and Skeide [SS23,Ske25], here we are led, as a basic new ingredient, to the notion of not necessarily adjointable operators $a$ that admit a modulus $|a|$, so-called modular operators. - oai:arXiv.org:2512.06335v1 - math.OA - math.FA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Michael Skeide + George Dunn, Elizabeth Stojanovski, Bishnu Lamichhane, Hadi Charkhgard, Ali Eshragh - Suggestion of a definition of the twisted affine Yangian of type $D$ - https://arxiv.org/abs/2512.06340 - arXiv:2512.06340v1 Announce Type: new -Abstract: We suggest a definition of the twisted affine Yangian $TY_{\hbar,\varepsilon}(\widehat{\mathfrak{so}}(2n))$. We show that $TY_{\hbar,\varepsilon}(\widehat{\mathfrak{so}}(2n))$ coincides with the universal enveloping algebra of a subalgebra of the universal central extension of $\mathfrak{sl}(2n)[u^{\pm1},v]$ when we set two parameters $\hbar=\varepsilon=0$. We also construct a homomorphism from $TY_{\hbar,\varepsilon}(\widehat{\mathfrak{so}}(8))$ to the universal enveloping algebra of the rectangular $W$-algebra $\mathcal{W}^k(\mathfrak{sp}(16),(2^8))$. - oai:arXiv.org:2512.06340v1 - math.RA - Tue, 09 Dec 2025 00:00:00 -0500 + 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://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Mamoru Ueda + http://creativecommons.org/licenses/by-nc-nd/4.0/ + Peter Jaehyun Cho, Jinjoo Yoo - Linear resolution of connected graph ideals and their powers - https://arxiv.org/abs/2512.06346 - arXiv:2512.06346v1 Announce Type: new -Abstract: For a finite simple graph $G$ and an integer $r \ge 1$, the $r$-connected ideal $I_r(G)$ is the squarefree monomial ideal generated by the vertex sets of connected induced subgraphs of size $r+1$, extending the classical edge ideal. We investigate the linearity of the minimal free resolutions of $I_r(G)$ via structural features of the associated clutter $\mathcal{C}_r(G)$. We introduce the class of co-chordal-cactus graphs and prove that $I_r(G)$ has a linear resolution for all $r \ge 2$ whenever $G$ lies in this family. The result further extends to $(2K_2, C_4)$-free graphs and co-grid graphs. For $r=1$, we show that the edge ideal $I_1(G)$ has Castelnuovo-Mumford regularity at most $3$ for all co-chordal-cactus and co-grid graphs. We also examine powers of connected ideals and establish that $I_r(G)^q$ has a linear resolution for every $q \ge 1$ in several natural graph families, including complements of trees with bounded degree, complete multipartite graphs, complements of cycles, graphs obtained by gluing complete graphs along cliques, and certain subclasses of split graphs. - oai:arXiv.org:2512.06346v1 - math.AC - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.ST + math.PR + stat.ME + stat.TH + Wed, 10 Dec 2025 00:00:00 -0500 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Arka Ghosh, S Selvaraja + http://creativecommons.org/licenses/by/4.0/ + Sohom Bhattacharya, Subhabrata Sen - Stabilizing Rate of Stochastic Control Systems with Multiplicative Noise - https://arxiv.org/abs/2512.06349 - arXiv:2512.06349v1 Announce Type: new -Abstract: This paper develops a quantitative framework for analyzing the mean-square exponential stabilization of stochastic linear systems with multiplicative noise, focusing specifically on the optimal stabilizing rate, which characterizes the fastest exponential stabilization achievable under admissible control policies. -Our contributions are twofold. First, we extend norm-based techniques from deterministic switched systems to the stochastic setting, deriving a verifiable necessary and sufficient condition for the exact attainability of the optimal stabilizing rate, together with computable upper and lower bounds. Second, by restricting attention to state-feedback policies, we reformulate the optimal stabilizing rate problem as an optimal control problem with a nonlinear cost function and derive a Bellman-type equation. Since this Bellman-type equation is not directly tractable, we recast it as a nonlinear matrix eigenvalue problem whose valid solutions require strictly positive-definite matrices. To ensure the existence of such solutions, we introduce a regularization scheme and develop a Regularized Normalized Value Iteration (RNVI) algorithm, which in turn generates strictly positive-definite fixed points for a perturbed version of original nonlinear matrix eigenvalue problem while producing feedback controllers. Evaluating these regularized solutions further yields certified lower and upper bounds for the optimal stabilizing rate, resulting in a constructive and verifiable framework for determining the fastest achievable mean-square stabilization under multiplicative noise. - oai:arXiv.org:2512.06349v1 - math.OC - cs.SY - eess.SY - Tue, 09 Dec 2025 00:00:00 -0500 + $0$-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 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Hui Jia, Yuan-Hua Ni, Guangchen Wang + http://creativecommons.org/licenses/by/4.0/ + You-Hung Hsu - Riesz potential estimates under co-canceling constraints - https://arxiv.org/abs/2512.06352 - arXiv:2512.06352v1 Announce Type: new -Abstract: Inequalities for Riesz potentials are well-known to be equivalent to Sobolev inequalities of the same order for domain norms ``far" from $L^1$, but to be weaker otherwise. Recent contributions by Van Schaftingen, by Hernandez, Rai\c{t}\u{a} and Spector, and by Stolyarov proved that this gap can be filled in Riesz potential inequalities for vector-valued functions in $L^1$ fulfilling a co-canceling differential condition. The present work demonstrates that such a property is not just peculiar to the space $L^1$. As a consequence, Riesz potential inequalities under the co-canceling constraint are offered for general families of rearrangement-invariant spaces, such as the Orlicz spaces and the Lorentz-Zygmund spaces. Especially relevant instances of inequalities for domain spaces neighboring $L^1$ are singled out. - oai:arXiv.org:2512.06352v1 - math.FA - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - D. Breit, A. Cianchi, D. Spector + http://creativecommons.org/licenses/by/4.0/ + Xiaojun Huang, Scott James, Xiaoshan Li - A Low-rank Augmented Lagrangian Method for Polyhedral-SDP and Moment-SOS Relaxations of Polynomial Optimization - https://arxiv.org/abs/2512.06359 - arXiv:2512.06359v1 Announce Type: new -Abstract: Polynomial optimization problems (POPs) can be reformulated as geometric convex conic programs, as shown by Kim, Kojima, and Toh (SIOPT 30:1251-1273, 2020), though such formulations remain NP-hard. In this work, we prove that several well-known relaxations can be unified under a common polyhedral-SDP framework, which arises by approximating the intractable cone by tractable intersections of polyhedral cones with the positive semidefinite matrix cone. Although effective in providing tight lower bounds, these relaxations become computationally expensive as the number of variables and constraints grows at the rate of $\Omega(n^{2\tau})$ with the relaxation order $\tau$. To address this challenge, we propose RiNNAL-POP, a low-rank augmented Lagrangian method (ALM) tailored to solve large-scale polyhedral-SDP relaxations of POPs. To efficiently handle the $\Omega(n^{2\tau})$ nonnegativity and consistency constraints, we design a tailored projection scheme whose computational cost scales linearly with the number of variables. In addition, we identify a hidden facial structure in the polyhedral-SDP relaxation, which enables us to eliminate a large number of linear constraints by restricting the matrix variable to affine subspaces corresponding to exposed faces of the semidefinite cone. The latter enables us to efficiently solve the factorized ALM subproblems over the affine subspaces. At each ALM iteration, we additionally carry out a single projected gradient step with respect to the original matrix variable to automatically adjust the rank and escape from spurious local minima when necessary. We also extend our RiNNAL-POP algorithmic framework to solve moment-SOS relaxations of POPs. Extensive numerical experiments on various benchmark problems demonstrate the robustness and efficiency of RiNNAL-POP in solving large-scale polyhedral-SDP relaxations. - oai:arXiv.org:2512.06359v1 - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://creativecommons.org/licenses/by/4.0/ - Di Hou, Tianyun Tang, Kim-Chuan Toh + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Takuya Yanagisawa - A geometric perspective on Amitsur's conjecture - https://arxiv.org/abs/2512.06360 - arXiv:2512.06360v1 Announce Type: new -Abstract: Roquette proved Amitsur's conjecture for Severi-Brauer varieties associated with cyclic algebras using algebraic methods. We present a geometric proof of Roquette's result, providing simple and explicit birational isomorphisms. - oai:arXiv.org:2512.06360v1 - math.AG - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Divyasree C Ramachandran + 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 + new + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Anubhav Gupta - Compressed Momentum-based Single-Point Zero-Order Algorithm for Stochastic Distributed Nonconvex Optimization - https://arxiv.org/abs/2512.06366 - arXiv:2512.06366v1 Announce Type: new -Abstract: This paper studies a compressed momentum-based single-point zeroth-order algorithm for stochastic distributed nonconvex optimization, aiming to alleviate communication overhead and address the unavailability of explicit gradient information. In the developed framework, each agent has access only to stochastic zeroth-order information of its local objective function, performs local stochastic updates with momentum, and exchanges compressed updates with its neighbors. We theoretically prove that the proposed algorithm can achieve the exact solution with diminishing step sizes and can achieve a sublinear convergence rate towards a neighborhood of the stationary point with fixed step sizes. Numerical experiments validate the effectiveness and communication efficiency of the proposed algorithm. - oai:arXiv.org:2512.06366v1 - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Linjing Chen, Antai Xie, Xinlei Yi, Xiaoqiang Ren, Xiaofan Wang + Francesco D'Andrea, Piotr M. Hajac, Tomasz Maszczyk, Bartosz Zieli\'nski - 3-Coloring $P_t$-Free Graphs With Only One Prescribed Induced Odd Cycle Length - https://arxiv.org/abs/2512.06367 - arXiv:2512.06367v1 Announce Type: new -Abstract: A graph is $P_t$-free if it contains no induced subgraph isomorphic to a $t$-vertex path. A graph is not bipartite if and only if it contains an induced subgraph isomorphic to a $k$-vertex cycle, where $k$ is odd. We focus on the 3-coloring problem for $P_t$-free graphs that have only one prescribed induced odd cycle length. For any integer $t$ and any odd integer $k$, let $\mathcal{G}_{t,k}$ be the class of graphs that are $P_{t}$-free and all their induced odd cycles must be $C_k$. In this paper, we present a polynomial-time algorithm that solves the 3-coloring problem for any graph in $\mathcal{G}_{10,7}$. - oai:arXiv.org:2512.06367v1 - math.CO - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://creativecommons.org/licenses/by/4.0/ - Yidong Zhou, Mingxian Zhong, Shenwei Huang + Wee Teck Gan - Secondary Stiefel-Whitney numbers and corresponding cobordism groups - https://arxiv.org/abs/2512.06371 - arXiv:2512.06371v1 Announce Type: new -Abstract: For every relation $R$ between Stiefel-Whitney numbers of closed $(n+1)$-manifolds we consider an associated invariant $\varkappa_R$ of null-cobordant $n$-manifolds with a certain additional structure. For $n=2k-1$ and $R = w_{n+1}+v_k^2$ the invariant $\varkappa_R$ equals the Kervaire semi-characteristic. In addition, we construct the cobordism group $\Omega_n^R$, which extends the unoriented cobordism group $\Omega_n^O$. We show that $\varkappa_R$ is a complete invariant of $R$-cobordism classes of null-cobordant $n$-manifolds. We prove that our invariant $\varkappa_R$ and $R$-cobordism class of manifold are quadratic in the sense of Gusarov-Vassiliev-Podkorytov. - oai:arXiv.org:2512.06371v1 - math.AT - math.GT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://creativecommons.org/publicdomain/zero/1.0/ - Viktor Lavrukhin + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Hamilton Wan - Extended Argmin-Theorems for multiple nets of multivariate c\`adl\`ag stochastic processes - https://arxiv.org/abs/2512.06375 - arXiv:2512.06375v1 Announce Type: new -Abstract: Consider finitely many nets of multivariate c\`adl\`ag stochastic processes. We show that the vectors consisting of the respective minimizing points converge in distribution to a random closed set. This set is given as a cartesian product with factors which are equal to the set of all minimizing points of stochastic processes occurring as functional limits of the respective nets. If these limit processes have almost surely exactly one minimizer, then the vectors converge classically in distribution to the vector of these minimizers. - oai:arXiv.org:2512.06375v1 - math.PR - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://creativecommons.org/licenses/by/4.0/ - Dietmar Ferger, Niklas Rosar + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Sung Hoon Lim, Daewon Seo - Model theory of tame valued fields and beyond: recent developments and open questions - https://arxiv.org/abs/2512.06386 - arXiv:2512.06386v1 Announce Type: new -Abstract: We give a survey on recent developments in the model theory of valued fields since the introduction of the notion of ``tame valued field'', and of the modifications and generalizations of this notion. - oai:arXiv.org:2512.06386v1 - math.LO - math.AC - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Franz-Viktor Kuhlmann + Miguel Ballesteros, Gerardo Franco Cordova, Hermann Schulz-Baldes - Convergence analysis of max-product and max-min Durrmeyer-type exponential sampling operators in Mellin Orlicz space - https://arxiv.org/abs/2512.06388 - arXiv:2512.06388v1 Announce Type: new -Abstract: In the present study, we establish both pointwise and uniform convergence in the space of logarithmically uniformly continuous and bounded functions for the max-product and max-min Durrmeyer-type exponential sampling operators. Furthermore, the modular convergence of these operators is demonstrated within the framework of Orlicz space. In addition to the theoretical results, we provide numerical and graphical analyses for various kernel pairs, illustrating the convergence rates and approximation behavior of the proposed operators. - oai:arXiv.org:2512.06388v1 - math.FA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://creativecommons.org/licenses/by/4.0/ - Satyaranjan Pradhan, H. M. Srivastava, Madan Mohan Soren + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Jianquan Ge, Huixin Tan, Wenjiao Yan, Yunheng Zhang - On certain definable coarsenings of valuation rings and their applications - https://arxiv.org/abs/2512.06391 - arXiv:2512.06391v1 Announce Type: new -Abstract: We show how suitable extensions $(L|K,v)$ of prime degree of valued fields give rise to definable coarsenings of the valuation rings of $L$ and $K$. In the case of Artin-Schreier and Kummer extensions with wild ramification, we can also define the ramification ideal. We demonstrate the use of the coarsenings on $L$, their maximal ideals, and the ramification ideals for the classification of defects and for the presentation of the K\"ahler differentials of the extension of the valuation rings of $(L|K,v)$, and their annihilators. Finally, we give a construction that realizes predescribed convex subgroups of suitable value groups as those that are associated with Galois extensions of degree $p$ with independent defect, which in turn give rise to definable coarsenings. - oai:arXiv.org:2512.06391v1 - math.LO - math.AC - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Franz-Viktor Kuhlmann + Zhendong Fang, Kunlun Qi - Optimal domain of Volterra operators in classes of Banach spaces of analytic functions - https://arxiv.org/abs/2512.06398 - arXiv:2512.06398v1 Announce Type: new -Abstract: A thorough investigation is made of the optimal domain space of generalized Volterra operators, Ces\`aro operators and other operators when they act in various Banach spaces of analytic functions. Of particular interest is the situation when the operators act in Hardy spaces, Korenblum growth spaces and more general weighted spaces. The optimal domain space may be genuinely larger than the initial domain of the operator, or not. In the former case, the initial space may or may not be dense in the optimal domain space. Sometimes the optimal domain space can be identified with a known Banach space of analytic functions, on other occasions it determines a new space. - oai:arXiv.org:2512.06398v1 + 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 - Tue, 09 Dec 2025 00:00:00 -0500 + math.CA + Wed, 10 Dec 2025 00:00:00 -0500 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Angela A. Albanese, Jos\'e Bonet, Werner J. Ricker + http://creativecommons.org/licenses/by/4.0/ + Biagio Ricceri - Emergent behaviors of the singular continuum Kuramoto model and its graph limit - https://arxiv.org/abs/2512.06399 - arXiv:2512.06399v1 Announce Type: new -Abstract: We study the emergent dynamics of the singular continuum Kuramoto model (in short, SCKM) and its graph limit. The SCKM takes the form of an integro-differential equation exhibiting two types of nonlocal singularities: a nonlocal singular interaction weight and a nonlocal singular alignment force. The natural frequency function determines the emergent dynamics of the SCKM, and we emphasize that singularity plays a crucial role in the occurrence of sticking phenomena. For the identical natural frequency function, we derive the complete phase synchronization in finite time under a suitable set of conditions for system parameters and initial data. In contrast, for a nonidentical natural frequency function, we show the emergence of practical synchronization, meaning that the phase diameter is proportional to the inverse of coupling strength asymptotically. Furthermore, we rigorously establish a graph limit from the singular Kuramoto model with a finite system size to the SCKM. We also provide several numerical simulations to illustrate our theoretical results. - oai:arXiv.org:2512.06399v1 - math.DS - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Li Chen, Seung-Yeal Ha, Xinyu Wang, Valeriia Zhidkova + Ying Zhang, Fan Liu, Yifeng Xiong, Weijie Yuan, Shuangyang Li, Le Zheng, Tony Xiao Han, Christos Masouros, Shi Jin - Hardness of Planarity for Weak Temporal Sequences of 2-Connected Graphs - https://arxiv.org/abs/2512.06403 - arXiv:2512.06403v1 Announce Type: new -Abstract: A weak deletion sequence is a sequence $(G_1,\ldots,G_n)$ of graphs so that for each $i\in[n-1]$ either $G_i$ is isomorphic to a subgraph of $G_{i+1}$, or vice versa: $G_{i+1}$ is isomorphic to a subgraph of $G_i$. We prove that determining the simultaneous planar embeddability of weak deletion sequences of $2$-connected graphs is NP-hard. - oai:arXiv.org:2512.06403v1 - math.CO - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.OC + Wed, 10 Dec 2025 00:00:00 -0500 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Johannes Carmesin, Will J. Turner + http://creativecommons.org/publicdomain/zero/1.0/ + Ruo Li, Haoyang Liu, Jun Yin - Gevrey well-posedness of the hydrostatic MHD-wave system - https://arxiv.org/abs/2512.06405 - arXiv:2512.06405v1 Announce Type: new -Abstract: This paper investigates the well-posedness of the hydrostatic MHD-wave system. Unlike the standard hydrostatic MHD equations, the tangential magnetic field equation in this system is degenerate hyperbolic rather than parabolic, which leads to substantial mathematical difficulties. Using the boundary decomposition method, we establish local well-posedness in Gevrey $\frac{7}{6}$ space for convex initial data. - oai:arXiv.org:2512.06405v1 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Wei-Xi Li, Zhan Xu + Thomas Blomme, Francesca Carocci - A Factorization of the Log-Concavity Operator for Pascal Determinantal Arrays and Their Infinite Row-Wise Log-Concavity - https://arxiv.org/abs/2512.06414 - arXiv:2512.06414v1 Announce Type: new -Abstract: We study the Pascal determinantal arrays $\PD_k$, whose entries $\PD_k(i,j)$ are the $k\times k$ minors of the lower-triangular Pascal matrix $P=( \binom{a}{b} )_{a,b\ge 0}$. - We prove an exact factorization of the row-wise log-concavity operator: - \[ - \LC(\PD_k)=\PD_{k-1}\Had\PD_{k+1}, - \] - where $\LC(a)_j=a_j^2-a_{j-1}a_{j+1}$ and $\Had$ denotes the Hadamard (entrywise) product. - This identity is established by an elementary manipulation of the Desnanot--Jacobi (Dodgson) identity in two adjacent positions. - We further prove a general inequality asserting that the log-concavity operator is submultiplicative under Hadamard products of log-concave arrays: - $\LC(A\Had X)\ge\LC(A)\Had\LC(X)$. - Combining the factorization with this inequality yields a uniform algebraic proof that every row of every array $\PD_k$ ($k\ge 1$) is infinitely log-concave, extending the celebrated theorem of McNamara and Sagan from Pascal's triangle ($\PD_1$) to the entire determinantal hierarchy. - Applications include the log-convexity of $\{\PD_k(i,j)\}_{k\ge 0}$ in the determinantal order $k$ and a family of determinantal Hadamard inequalities. - oai:arXiv.org:2512.06414v1 - math.CO - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://creativecommons.org/licenses/by-sa/4.0/ - Hossein Teimoori Faal, Hasan Khodakarami + http://creativecommons.org/licenses/by/4.0/ + Erich Novak, Friedrich Pillichshammer - Multidimensional analogues of the improved Bohr's inequality - https://arxiv.org/abs/2512.06419 - arXiv:2512.06419v1 Announce Type: new -Abstract: The main aim of this article is to establish a sharp improvement of the classical Bohr inequality for bounded holomorphic mappings in the polydisk $\mathbb{P}\Delta(0;1_n)$. We also prove two other sharp versions of the Bohr inequality in the setting of several complex variables by replacing the constant term with the absolute value of the function and the square of the absolute value of the function, respectively. All the results are shown to be sharp. - oai:arXiv.org:2512.06419v1 - math.CV - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://creativecommons.org/licenses/by/4.0/ - Molla Basir Ahamed, Sujoy Majumder, Nabadwip Sarkar, Ming-Sheng Liu + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Xi Chen, Lang Fu, Jiajie Ruan - On the Dynamics of Weighted Composition Operators II - https://arxiv.org/abs/2512.06425 - arXiv:2512.06425v1 Announce Type: new -Abstract: We establish complete characterizations of various notions of expansivity for weighted composition operators on a very general class of locally convex spaces of continuous functions. This class includes several classical classes of continuous function spaces, such as the Banach spaces $C_0(X)$ of continuous scalar-valued functions vanishing at infinity on a Hausdorff locally compact space $X$, endowed with the sup norm, and the locally convex spaces $C(X)_c$ of continuous scalar-valued functions on a completely regular space $X$, endowed with the compact-open topology. We also obtain complete characterizations of various notions of expansivity for weighted composition operators on $L^p(\mu)$ spaces, thereby complementing and extending previously known results in the unweighted case. Finally, we establish a conjugation between weighted and unweighted composition operators in the case of dissipative systems on $L^p(\mu)$ spaces and apply it to the study of several dynamical properties. - oai:arXiv.org:2512.06425v1 - math.DS + 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 - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Nilson C. Bernardes Jr., Antonio Bonilla, Jo\~ao V. A. Pinto - - - Questions on the Chow ring of complete intersections - https://arxiv.org/abs/2512.06430 - arXiv:2512.06430v1 Announce Type: new -Abstract: We state several questions, and prove some partial results, about the Chow ring $A^\ast(X)$ of complete intersections in projective space. For one thing, we prove that if $X$ is a general Calabi-Yau hypersurface, the intersection product $A^2(X)\cdot A^i(X)$ is one-dimensional, for any $i>0$. We also show that quintic threefolds have a multiplicative Chow-K\"unneth (MCK) decomposition. We wonder whether all Calabi-Yau hypersurfaces might have an MCK decomposition, and prove this is the case conditional to a conjecture of Voisin. - oai:arXiv.org:2512.06430v1 - math.AG - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Robert Laterveer + Fernanda M. Ba\^eta - On Christophersen's problem - https://arxiv.org/abs/2512.06436 - arXiv:2512.06436v1 Announce Type: new -Abstract: Let $A$ be a finite-dimensional (Artinian) Gorenstein algebra, and let $\operatorname{Aut}(A)^{\circ}$ denote the connected component of the identity in the automorphism group of $A$. We introduce a new subclass of Gorenstein algebras and prove that for any algebra $A$ in this subclass, the group $\operatorname{Aut}(A)^{\circ}$ is solvable. This result is closely related to the Christophersen problem in the theory of local algebras. - oai:arXiv.org:2512.06436v1 - math.AC - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.PR + Wed, 10 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Roman Stasenko + Marcus Sch\"onfelder - The Joint Range of Quadratic Mapping on Hilbert Space - https://arxiv.org/abs/2512.06437 - arXiv:2512.06437v1 Announce Type: new -Abstract: We present a novel technical method for analyzing the hidden convex structure embedded in the joint range of a quadratic mapping defined on a Hilbert space. Our approach stands out by relying exclusively on elementary mathematical principles. - oai:arXiv.org:2512.06437v1 - math.OC - math.FA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.AP + Wed, 10 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Huu-Quang Nguyen + Xinzhi Cai, Hongmei Cao, Chao-jiang Xu - Existence and multiplicity of normalized solutions for $L^2$-supercritical Schr\"odinger equations on noncompact metric graphs with nonlinear point defects - https://arxiv.org/abs/2512.06445 - arXiv:2512.06445v1 Announce Type: new -Abstract: In this paper, we study the existence and multiplicity of normalized solutions for the following $L^2$-supercritical Schr\"odinger equation on noncompact metric graph $\G=(\V,\E)$ with nonlinear point defects \begin{equation*} - \begin{cases} u'' = \lambda u & \text{on every }\e \in \E, \\ \|u\|_{L^2(\mathcal{G})}^2 = \mu & \\ \displaystyle\sum_{\e \succ \vv} u'_\e(\vv) = -|u(\vv)|^{p-2}u(\vv) & \text{at every }\vv \in \V, \end{cases} \end{equation*} where $p>4$, $\G$ has finitely many edges, $\mu>0$ is a given constant, the parameter $\lambda$ is a part of the unknown which arises as a Lagrange multiplier, $\e \succ \vv$ means that the edge $\e$ is incident at $\vv$, and the notation $u'_\e(\vv)$ stands for $u'_\e(0)$ or $-u'_\e(\ell_\e)$, according to whether the vertex $\vv$ is identified with $0$ or $\ell_\e$. This work complements the study initiated by Boni, Dovetta, and Serra [J. Funct. Anal. 288 (2025), 110760], which addressed only the existence of normalized solutions for the $L^2$-subcritical ($2<p<4$) Schr\"{o}dinger equation on metric graphs with nonlinear point defects. - oai:arXiv.org:2512.06445v1 + 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 - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Zhentao He, Chao Ji, YIfan Tao + Fessel Achhoud, Hichem Khelifi - Uniform Bounds for Digit-Appending Fibonacci Walks - https://arxiv.org/abs/2512.06446 - arXiv:2512.06446v1 Announce Type: new -Abstract: Building on the work of Miller et al. [Fibonacci Quarterly, 2022], we show that it is impossible to "walk to infinity" along the Fibonacci sequence in any integer base $b\geq 2$ when at most $N$ digits are appended per step. Our proof method is base-independent, yielding the bound \[L \;\leq\; 2N\log_\varphi b \,+\, O(1),\] uniformly in the starting term, without relying on base-specific periodicity computations (here, $\varphi=\frac{1+\sqrt{5}}{2}$). Our approach extends to certain Lucas sequences. - oai:arXiv.org:2512.06446v1 - math.NT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Scott Duke Kominers + http://creativecommons.org/licenses/by/4.0/ + Lloren\c{c} Balada Gaggioli, Didier Henrion, Milan Korda - Trajectory Optimization for Cellular-Connected UAV in Complex Environment with Partial CKM - https://arxiv.org/abs/2512.06452 - arXiv:2512.06452v1 Announce Type: new -Abstract: Cellular-connected unmanned aerial vehicles (UAVs) are expected to play an increasingly important role in future wireless networks. To facilitate the reliable navigation for cellular-connected UAVs, channel knowledge map (CKM) is considered a promising approach capable of tackling the non-negligible co-channel interference resulting from the high line-of-sight (LoS) probability of air-ground (AG) channels. Nevertheless, due to measurement constraints and the aging of information, CKM is usually incomplete and needs to be regularly updated to capture the dynamic nature of complex environments. In this paper, we propose a novel trajectory design strategy in which UAV navigation and CKM completion are incorporated into a common framework, enabling mutual benefits for both tasks. Specifically, a cellular-connected UAV deployed in an urban environment measures the radio information during its flight and completes the CKM with Kriging interpolation. Based on the method of grid discretization and spherical approximation, a mixed-integer multi-objective optimization problem is formulated. The problem falls into the category of combinatorial mathematics and is essentially equivalent to determining an optimum sequence of grid points to traverse. Through proper mathematical manipulation, the problem is reformulated as variants of two classic models in graph theory, namely the shortest-path problem (SPP) and the traveling salesman problem (TSP). Two navigation strategies based on the two different models are proposed and thoroughly compared based on numerical results to provide implementable methods for engineering practice and reveal the trade-offs between UAV navigation and CKM completion. Simulation results reveal that the proposed navigation strategies can quickly expand the Pareto boundary of the problem and approach the performance of fully-known CKM. - oai:arXiv.org:2512.06452v1 - cs.IT - math.IT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Yuxuan Song, Haiquan Lu, Chiya Zhang, Beixiong Zheng, Yong Zeng + Simon Pietig - A two-stage explicit/implicit approach combined with mixed finite element methods for a radiation-conduction model in optically thick anisotropic media - https://arxiv.org/abs/2512.06456 - arXiv:2512.06456v1 Announce Type: new -Abstract: This paper develops a two-stage explicit/impicit computational technique combined with a mixed finite element method for solving a nonlinear radiation-conduction problem in anisotropic media, subject to suitable initial and boundary conditions. The space derivatives are approximated by the mixed finite element method ($\mathcal{P}_{p}/\mathcal{P}_{p-1}/\mathcal{P}_{p-1}$), while the interpolation technique is employed in two stages to approximate the time derivative. The proposed strategy is so-called, a two-stage explicit/implicit computational technique combined with mixed finite element method. Specifically, the new algorithm should be observed as a predictor-corrector numerical scheme. Additionally, it efficiently treats the time derivative term and provides a necessary requirement on time step for stability. Under this time step limitation, the stability is deeply analyzed whereas the convergence order is numerically obtained in the $L^{2}$-norm. The theoretical results suggest that the developed approach is spatial fourth-order convergent and temporal second-order accurate. Some numerical experiments are carried out to confirm the theoretical results and to demonstrate the practical applicability of the new algorithm. - oai:arXiv.org:2512.06456v1 - math.NA - cs.NA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://creativecommons.org/licenses/by-sa/4.0/ - Eric Ngondiep + http://creativecommons.org/licenses/by-nc-nd/4.0/ + Vanni Noferini - On groupoid-graded C*-algebras and equivalent subcategories linked via monads and comonads - https://arxiv.org/abs/2512.06461 - arXiv:2512.06461v1 Announce Type: new -Abstract: We present a new method, involving monads and comonads from category theory, to help establish a certain type of equivalence of subcategories. As a case study we consider the category of topological gradings of $C^*$-algebras over a fixed Hausdorff \'etale groupoid. - oai:arXiv.org:2512.06461v1 - math.OA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Erik B\'edos, S. Kaliszewski, John Quigg + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Adrien Dubouloz (LMA), Kento Fujita, Takashi Kishimoto - Convolution operators preserving the set of totally positive sequences - https://arxiv.org/abs/2512.06468 - arXiv:2512.06468v1 Announce Type: new -Abstract: A real sequence $(a_k)_{k=0}^\infty$ is called {\it totally positive} if all minors of the infinite Toeplitz matrix $ \left\| a_{j-i} \right\|_{i, j =0}^\infty$ are nonnegative (here $a_k=0$ for $k<0$). In this paper, which continues our earlier work \cite{kv}, we investigate the set of real sequences $(b_k)_{k=0}^\infty$ with the property that for every totally positive sequence $(a_k)_{k=0}^\infty,$ the sequense of termwise products $(a_k b_k)_{k=0}^\infty$ is also totally positive. In particular, we show that for every totally positive sequence $(a_k)_{k=0}^\infty$ the sequence $\left(a_k a^{-k (k-1)}\right)_{k=0}^\infty$ is totally positive whenever $a^2\geq 3{.}503.$ We also propose several open problems concerning convolution operators that preserve total positivity. - oai:arXiv.org:2512.06468v1 - math.CV + 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 - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Olga Katkova, Anna Vishnyakova + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Juli\'an L\'opez-G\'omez, Juan Carlos Sampedro - Formal power series solutions with coefficients defined on shrinking discs for some partial differential equations - https://arxiv.org/abs/2512.06470 - arXiv:2512.06470v1 Announce Type: new -Abstract: In this paper conditions, under which an integro-differential operator is a linear automorphism, are provided. Alternatively, the problem can be considered in terms of existence of a unique formal power series solution for a linear Cauchy problem, where the coefficients of the solution are of a certain Gevrey order on progressively shrinking domains. - oai:arXiv.org:2512.06470v1 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 + 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-nd/4.0/ - Alberto Lastra, S{\l}awomir Michalik, Maria Suwi\'nska + http://creativecommons.org/licenses/by-nc-sa/4.0/ + Felix Schremmer - Generalizing quadratic $\mathbb{R}$-Algebraic sets in $\mathbb{CP}^{n}$ - https://arxiv.org/abs/2512.06472 - arXiv:2512.06472v1 Announce Type: new -Abstract: The images of a ball under complex linear transformations are complex ellipsoids. So, they are the unit balls of finite dimensional Hilbert spaces over the complex numbers. The analog of segments in the real line, are discs in the complex line. So, the analog of convex bodies in $\mathbb R^n$ should be what we called ``\emph{bombons}'' in $\mathbb C^n$: bodies whose non-trivial sections with complex lines are disks. Clearly, a complex ellipsoid is a bombon in this sense. We first introduced bombons in \cite{ABM1} motivated by our study of the complex Banach conjecture \cite{BM}; A little later, they turned out to be an unexpected characterization of complex ellipsoids with no analog over the real numbers. Namely, if every complex line that intersects a convex body in $\mathbb C^n$ does so in a disk or a point, then the convex body is a complex ellipsoid. This characterization naturally leads to the main question of this paper. What are those closed sets of $\mathbb{CP}^n$ with the property that any complex line that intersects them does so either at a single point, at the boundary of a complex disk, or along the entire line? - oai:arXiv.org:2512.06472v1 - math.GT - math.CV - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.OC + Wed, 10 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/publicdomain/zero/1.0/ - Javier Bracho, Luis Montejano + 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) - An Operator Theoretical Approach to Mercer's Theorem - https://arxiv.org/abs/2512.06475 - arXiv:2512.06475v1 Announce Type: new -Abstract: This is a survey article on Mercer's Theorem in its most general form and its relations with the theory of reproducing kernel Hilbert spaces and the spectral theory of compact operators. We provide a modern introduction to the basics of the theory of reproducing kernel Hilbert spaces, an overview on Weyl's kernel and the Gaussian kernels, and finally an approach to Mercer's Theorem within the theory of reproducing kernel Hilbert spaces and the spectral theory of integral operators. This approach is reverse to the known approaches to Mercer's Theorem and sheds some light on the intricate relations between different domains in analysis. - oai:arXiv.org:2512.06475v1 - math.FA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Aurelian Gheondea + Giuseppe Buttazzo, Juan Casado-D\'iaz, Faustino Maestre - Algebra in Algorithmic Coding Theory - https://arxiv.org/abs/2512.06478 - arXiv:2512.06478v1 Announce Type: new -Abstract: We survey the notion and history of error-correcting codes and the algorithms needed to make them effective in information transmission. We then give some basic as well as more modern constructions of, and algorithms for, error-correcting codes that depend on relatively simple elements of applied algebra. While the role of algebra in the constructions of codes has been widely acknowledged in texts and other writings, the role in the design of algorithms is often less widely understood, and this survey hopes to reduce this difference to some extent. - oai:arXiv.org:2512.06478v1 - cs.IT - cs.CC - math.IT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://creativecommons.org/licenses/by/4.0/ - Madhu Sudan + Maximilian Pierer von Esch, Andreas V\"olz, Knut Graichen - Weyl-Type Algebras over Exponential-Polynomial Rings: Structure, Representations, and Deformations - https://arxiv.org/abs/2512.06479 - arXiv:2512.06479v1 Announce Type: new -Abstract: This paper introduces and studies a class of Weyl-type algebras \(A_{p,t,\cA} = \Weyl{e^{\pm x^{p} e^{t x}},\; e^{\cA x},\; x^{\cA}}\) constructed over exponential-polynomial rings, where \(\FF\) is a field of characteristic zero, \(\cA\) is a finitely generated additive subgroup of \(\FF\), and \(p \in \mathbb{N}^n\), \(t \in \FF\). We investigate their structural properties, proving simplicity, establishing faithful infinite-dimensional irreducible representations, and demonstrating the failure of the Noetherian property. A natural filtration by exponential order is introduced, with the associated graded algebra shown to be commutative. We also examine the corresponding Witt-type Lie algebra \(\mathfrak{g}_{p,t,\cA} = \Der_{\mathrm{gr}}(R_{p,t,\cA})\) and prove the vanishing of its second cohomology group with adjoint coefficients, implying rigidity under formal deformations. Furthermore, we construct explicit deformation quantizations of the underlying exponential-polynomial rings, compute Hochschild and cyclic homology groups, and relate them to the topology of the parameter space. The deformation rigidity of \(A_{p,t,\cA}\) is classified in terms of the rank of \(\cA\), and a Gerstenhaber algebra structure on the Hochschild cohomology is described. Several open problems concerning representation classification and geometric realization are proposed. - oai:arXiv.org:2512.06479v1 - math.RA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.FA + math.PR + Wed, 10 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Mohammad H. M. Rashid + http://creativecommons.org/licenses/by/4.0/ + Joseph Lehec - Rogers-Ramanujan type identities at $\Lambda_0$ from perfect crystals of exceptional quantum affine algebras - https://arxiv.org/abs/2512.06480 - arXiv:2512.06480v1 Announce Type: new -Abstract: We derive Rogers--Ramanujan type partition identities at the fundamental weight $\Lambda_0$ for the exceptional affine types $G_2^{(1)}$, $D_4^{(3)}$, $F_4^{(1)}$, $E_6^{(2)}$, $E_6^{(1)}$, $E_7^{(1)}$ and $E_8^{(1)}$. Our starting point is the Dousse--Konan reformulation of the $(\mathrm{KMN})^2$ crystal character formula, applied to the level-one perfect crystal $B=B(\theta)\sqcup B(0)$ of Benkart--Frenkel--Kang--Lee with ground element $\phi\in B(0)$. This realizes the normalized character $e^{-\Lambda_0}\mathrm{ch} L(\Lambda_0)$ as generating functions of grounded $B$-colored partitions governed locally by the crystal energy. After principal specialization, we obtain a colored partition model subject to explicit difference, congruence, and initial conditions. On the product side, under the same specialization, the Weyl--Kac character formula yields an explicit Euler-type product, equivalently the generating function for partitions with parts in a concrete allowed set. Comparing the two specializations gives coefficientwise equalities of generating functions. A key computational feature is that the difference matrix can be produced from the crystal data without explicitly computing the energy function. For each type we tabulate the congruence data, forbidden initial parts, and the full difference matrix, and we provide reproducible coefficient checks. - oai:arXiv.org:2512.06480v1 - math.RT + 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 math.CO - Tue, 09 Dec 2025 00:00:00 -0500 + math.NT + Wed, 10 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Shaolong Han + Weiwen Zhang - Structure and Invariants of Weyl-Type Algebras with Exponential Generators - https://arxiv.org/abs/2512.06491 - arXiv:2512.06491v1 Announce Type: new -Abstract: This paper introduces and systematically studies a class of Weyl-type algebras enriched with exponential and power generators over a field of characteristic zero, defined as $A_{p,t,\cA} = \Weyl{e^{\pm x^{p} e^{t}},\; e^{\cA x},\; x^{\cA}}$ in the associative setting and $\Nass{e^{\pm x^{p} e^{t}},\; e^{\cA x},\; x^{\cA}}$ in a non-associative framework. We establish fundamental structural properties, including the triviality of the center for the non-associative version and the explicit description $Z(A_{p,t,\cA}) = \FF[e^{\pm x^{p} e^{t}}]$ for the associative one, proving that $A_{p,t,\cA}$ is an Azumaya algebra over its center and represents a nontrivial class in the Brauer group $\Br(\FF(y))$. Furthermore, we compute the Gelfand--Kirillov dimension for relevant examples and demonstrate its key properties, such as additivity under tensor products and the growth dichotomy. We completely characterize the automorphism group of $A_{p,t,\cA}$ as a semidirect product of a torus with a discrete group, and provide a sharp isomorphism criterion showing that the parameter $t$ is a complete invariant in the family. The paper concludes with two open problems concerning the GK dimension of non-associative exponential algebras and the classification of their deformations, pointing toward future research directions in non-associative growth theory and deformation rigidity. - oai:arXiv.org:2512.06491v1 - math.RA - math.QA - math.RT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Mohammad H. M Rashid + http://creativecommons.org/licenses/by-nc-nd/4.0/ + Jari Taskinen, Zhan Zhang - Structural and Classification Theorems for Weyl-Type Algebras over Expolynomial Rings - https://arxiv.org/abs/2512.06497 - arXiv:2512.06497v1 Announce Type: new -Abstract: This paper introduces and systematically studies Weyl-type, Witt-type, and non-associative algebras defined over expolynomial rings -- commutative rings generated by exponential functions $e^{\alpha x}$, exponentials of exponentials $e^{\pm x^p e^{t}}$, and power functions $x^{\alpha}$ for $\alpha$ in an additive subgroup $\cA$ of a characteristic zero field $\FF$. We establish several fundamental structural results: scalar extensions preserve both the algebraic structure and simplicity; intermediate subalgebras associated with subgroups $\ZZ \subseteq \cB \subseteq \cA$ remain simple; the algebra of graded derivations is isomorphic to a semidirect product $\Weyl{e^{\pm x^p e^{t}},\; e^{\cA x},\; x^{\cA}} \rtimes \FF^n$; tensor products over disjoint variable sets decompose naturally into larger algebras; and a complete isomorphism criterion is given, showing that isomorphism depends precisely on the orbit of the parameter $p$ under the automorphism group of $\cA$ and the equality of the deformation parameter $t$. These theorems generalize classical results on Weyl and Witt algebras, provide new families of simple algebras, and offer a foundation for further research in deformation theory, representation theory, and cohomology. - oai:arXiv.org:2512.06497v1 - math.RA - math.QA - math.RT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Mohammad H. M Rashid + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Paulo Andr\'es Soto Moreno - Finite-rank conformal quantum mechanics - https://arxiv.org/abs/2512.06501 - arXiv:2512.06501v1 Announce Type: new -Abstract: In this work, we study the simplest example of the landscape of conformal field theories: one-dimensional CFTs with finite-dimensional state space. Following the definition of quantum field theory given by G. Segal, we formulate the condition under which a one-dimensional QFT (quantum mechanics) possesses conformal symmetry, and we give a complete classification of conformal Hamiltonians with finite rank. It turns out that correlation functions in such theories are polynomial functions of the underlying geometric data. Moreover, the one-dimensional conformal Ward identities determine their scaling behavior, so that the correlators of the conformal observables are, in fact, homogeneous polynomials. - oai:arXiv.org:2512.06501v1 - math-ph - hep-th - math.MP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://creativecommons.org/publicdomain/zero/1.0/ - Maxim Gritskov, Saveliy Timchenko + http://creativecommons.org/licenses/by-nc-nd/4.0/ + Sinem S\"onmez, Jari Taskinen - Betti numbers of the moduli space of Higgs bundles over a real curve - https://arxiv.org/abs/2512.06527 - arXiv:2512.06527v1 Announce Type: new -Abstract: We produce a formula for the $\mathbb{Z}_2$-Betti numbers of the moduli space $M_r^d$ of stable real Higgs bundles over a real projective curve, with coprime rank $r$ and degree $d$. Our approach relies on the motivic formula for the moduli space due to Mellit, Fedorov-Soibelman-Soibelman, and Schiffman , and the fact that the virtual $\mathbb{Z}_2$ Poincar\'e polynomial is a motivic measure over $\mathbb{R}$. - oai:arXiv.org:2512.06527v1 - math.AG - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Thomas John Baird + Emmanuel Audusse (LAGA), S\'ebastien Boyaval (MATHERIALS, LHSV), Virgile Dubos (UMA), Minh-Hoang Le (LHSV) - Generalized Connes-Kreimer Hopf algebras on decorated rooted forests by weighted cocycles - https://arxiv.org/abs/2512.06538 - arXiv:2512.06538v1 Announce Type: new -Abstract: The Connes-Kreimer Hopf algebra of rooted trees is an operated Hopf algebra whose coproduct satisfies the classical Hochschild 1-cocycle condition. In this paper, we extend the setting from rooted trees to the space $H_{\rm RT}(X,\Omega)$ of $(X,\Omega)$-rooted trees, in which internal vertices are decorated by a set $\Omega$ and leafs are decorated by $X \cup \Omega$. We introduce a new coalgebra structure on $H_{\rm RT}(X,\Omega)$ whose coproduct satisfies a weighted Hochschild 1-cocycle condition involving multiple operators, thereby generalizing the classical condition. A combinatorial interpretation of this coproduct is also provided. We then endow $H_{\rm RT}(X,\Omega)$ with a Hopf algebra structure. Finally, we define weighted $\Omega$-cocycle Hopf algebras, characterized by a Hochschild 1-cocycle condition with weights, and show that $H_{\rm RT}(X,\Omega)$ is the free object in the category of $\Omega$-cocycle Hopf algebras. - oai:arXiv.org:2512.06538v1 - math.QA - math.CO - math.RA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Fei Wang, Li Guo, Yi Zhang + http://creativecommons.org/licenses/by/4.0/ + Amandine Boucart, Sonia Fliss, Laure Giovangigli - An Approach to the Joint Rapid and Slow Transit Network Design Problem - https://arxiv.org/abs/2512.06540 - arXiv:2512.06540v1 Announce Type: new -Abstract: The increase in congestion in surface traffic, airborne pollution, and other environmental issues have motivated the transit authorities to promote public transit worldwide. In big cities and large metropolitan areas, adding new rapid transit lines attracts more commuters to the public system, as they frequently allow saving travel time as compared to the private mode (car) that faces high congestion. In addition, the travel time has less variability with respect to preset schedules, and rapid lines are more efficient than slow modes operated by buses. When a new rapid transit line is constructed, it partially replaces the traffic of existing slow transit lines. As a consequence, some of the slow-mode lines have to be either canceled or their routes modified to collaborate properly with the new rapid transit line. This process is usually carried out in a sequential way, thus leading to suboptimal solutions. - In this paper, we consider an integrated model for simultaneously designing rapid and redesigning slow networks. The aim of the model is community-oriented, that is, to maximize the demand covered (or captured) by both modes. We present a mathematical programming formulation that is solved by using a specially improved Benders decomposition. For this purpose, we include a partial decomposition to speed up the computation. The computational experiments are done on a case study based on real data obtained from a survey of mobility among transportation zones in the city of Seville. - oai:arXiv.org:2512.06540v1 - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Natividad Gonz\'alez-Blanco, Antonio J. Lozano, Vladimir Marianov, Juan A. Mesa + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Xiaodong Yi - Frame Numbers and Jacobson Radicals for Partial Geometries and Related Coherent Configurations - https://arxiv.org/abs/2512.06541 - arXiv:2512.06541v1 Announce Type: new -Abstract: We study the modular representation theory of rank $3$ association schemes arising from partial geometries with parameters $(s,t,\alpha)$. First, we obtain an explicit closed formula for the Frame number of the point scheme in terms of the number of points $v$ and the parameter $s+t+1-\alpha$, and use it to characterize the primes $p$ for which the adjacency algebra over $\mathbb{F}_p$ is not semisimple. We then give a complete case-by-case description of the Jacobson radical of this algebra in four arithmetic situations and determine the generic $p$-ranks of the adjacency matrices. - As a step toward understanding the modular representation theory of coherent configurations of type $[3,2;3]$ associated with strongly regular designs, we analyze the relationship between the modular structure of the point scheme and that of the design algebra. For the generalized quadrangle $\mathrm{GQ}(2,2)$ we obtain partial results on the structure of the $2$-modular adjacency algebra $\mathbb{F}_2 \mathfrak{X}$, and we explain the representation-theoretic difficulties that prevent a complete determination of its Wedderburn decomposition and Gabriel quiver, which remains open and is formulated as Problem~6.8. - oai:arXiv.org:2512.06541v1 - math.CO - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Osamu Shimabukuro + Atef Lechiheb - The Hurwitz existence problem and the prime-degree conjecture: A computational perspective - https://arxiv.org/abs/2512.06545 - arXiv:2512.06545v1 Announce Type: new -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:2512.06545v1 - math.GR - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.FA + Wed, 10 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Yiru Wang, Bingqian Li, Yi Zhou, Zhiqiang Wei, Yu Ye, Yiqian Shi, Bin Xu + Jian Li, Qijing Liao, Yonghang Ruan - Suborbital graphs obtained by the modular congruence subgroup $\Gamma_0(L,M)$ - https://arxiv.org/abs/2512.06546 - arXiv:2512.06546v1 Announce Type: new -Abstract: In the suborbital graphs studies, there has been a research gap in the sense that the Modular group is connected to two numbers. Thus, this paper attempts to contribute to the studies developed by Gauss, Bolyai, Lobachevsky and Riemann. However, this study mainly concentrates on the action of suborbital graphs obtained with the Modular congruence subgroup $\Gamma_0(L,M)$, making this study sui generis since it deals with the Modular group, connected to two numbers. In developing our graph action, we utilized the theories of non-Euclidean geometry. Investigating the congruence relation other than identity and universal relation, the number of congruence relation, transitive act on vertices and edges, edge condition for the congruence group $\Gamma_0(L,M)$, based on previously-obtained studies, we concluded with new theorems in this study. So, the results are obtained in this paper related to a different congruence modular subgroup provides various aspects of the same structure in mathematics and adapting it to such as algebraic geometry, number theory, differential geometry, topology and physics. Keywords: Modular group, Mobius transforms, suborbital graph - oai:arXiv.org:2512.06546v1 - math.GM - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.OA + math-ph + math.MP + Wed, 10 Dec 2025 00:00:00 -0500 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Ibrahim Gokcan, Ali Hikmet Deger + http://creativecommons.org/licenses/by/4.0/ + Krzysztof Szczygielski - Semidefinite hierarchies for diagonal unitary invariant bipartite quantum states - https://arxiv.org/abs/2512.06551 - arXiv:2512.06551v1 Announce Type: new -Abstract: We investigate questions about the cone $\mathrm{SEP}_n$ of separable bipartite states, consisting of the Hermitian matrices acting on $\mathbb{C}^n\otimes\mathbb{C}^n$ that can be written as conic combinations of rank one matrices of the form $xx^*\otimes yy^*$ with $x,y\in\mathbb{C}^n$. Bipartite states that are not separable are said to be entangled. Detecting quantum entanglement is a fundamental task in quantum information and a hard computational problem. We explore the Doherty-Parrilo-Spedaglieri (DPS) hierarchy of semidefinite conic approximations for $\mathrm{SEP}_n$ when the bipartite states have some additional structural properties: first, (i) for states with diagonal unitary invariance, and second (ii) for states with Bose symmetry. In case (i) we show that the DPS hierarchy can be block diagonalized, which, combining with its moment reformulation, leads to a substantially more efficient implementation. In case (ii), we give a characterization of the dual hierarchy, in terms of sums of squares of Hermitian complex polynomials, extending a known result in the generic case. It turns out that the completely positive cone $\mathrm{CP}_n$, its dual cone $\mathrm{COP}_n$, and their sums-of-squares based conic approximations $\mathcal{K}^{(t)}_n$, play a central role in these two settings (i),(ii). We clarify these connections and test the block diagonal relaxations on classes of examples. - oai:arXiv.org:2512.06551v1 - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://creativecommons.org/licenses/by/4.0/ - Jonas Britz, Monique Laurent + Oscar Kivinen - On Wiener-Hopf operators over linearly ordered diskrete Abelian groups - https://arxiv.org/abs/2512.06552 - arXiv:2512.06552v1 Announce Type: new -Abstract: Let $X$ denotes a discrete linearly ordered Abelian group, and let $X_+$ be the positive cone in $X$. In this note we compute the Fredholm index and study spectral properties of Wiener-Hopf operators $W_kg=1_{X_+}(k\ast g)$, $k\in l_2(X_+)$ in the space $l_2(X_+)$ in terms of their symbols $\check k$ where $\check k$ stands for the inverse Fourier transform of $k$. - oai:arXiv.org:2512.06552v1 - math.FA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://creativecommons.org/licenses/by/4.0/ - Adolf Mirotin + http://creativecommons.org/licenses/by-nc-nd/4.0/ + Etna Lindy, Vanni Noferini - Switched Linear Ensemble Systems and Structural Controllability - https://arxiv.org/abs/2512.06561 - arXiv:2512.06561v1 Announce Type: new -Abstract: This paper introduces and solves a structural controllability problem for ensembles of switched linear systems. All individual subsystems in the ensemble are sparse, governed by the same sparsity pattern, and undergo switching at the same sequence of time instants. The controllability of an ensemble system describes the ability to use a common control input to simultaneously steer every individual system. A sparsity pattern is called structurally controllable for pair \((k,q)\) if it admits a controllable ensemble of \(q\) individual systems with at most \(k\) switches. We derive a necessary and sufficient condition for a sparsity pattern to be structurally controllable for a given \((k,q)\), and characterize when a sparsity pattern admits a finite \(k\) that guarantees structural controllability for \((k,q)\) for arbitrary $q$. Compared with the linear time-invariant ensemble case, this second condition is strictly weaker. We further show that these conditions have natural connections with maximum flow, and hence can be checked by polynomial algorithms. Specifically, the time complexity of deciding structural controllability is \(O(n^3)\) and the complexity of computing the smallest number of switches needed is \(O(n^3 \log n)\), with \(n\) the dimension of each individual subsystem. - oai:arXiv.org:2512.06561v1 - math.OC - cs.SY - eess.SY - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Haoyu Yin, Yi Li, Ouyang Du, Bruno Sinopoli, Xudong Chen + Haoyuan Sun - A potentialist conception of ultrafinitism - https://arxiv.org/abs/2512.06564 - arXiv:2512.06564v1 Announce Type: new -Abstract: I shall explore various senses in which ultrafinitism can be fruitfully understood as engaging with a potentialist perspective in mathematics. First, I explain that every model $M$ of the theory of finite arithmetic -- arithmetic with a largest number, in which addition and multiplication are merely partial functions -- is bi-interpretable with a strictly taller model $M^+$, in which the arithmetic operations on objects taken from the original base model $M$ are totally defined in the extended world $M^+$. More generally, I explain how ultrafinitist ideas emerge in the modal potentialist system consisting of all models of arithmetic under end-extension. - oai:arXiv.org:2512.06564v1 - math.LO - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://creativecommons.org/licenses/by/4.0/ - Joel David Hamkins + Gilles Poncelet, Jonathan Lambrechts, Thomas Gillis, Philippe Chatelain - Boundary structure of gauge fields on asymptotically AdS spaces - https://arxiv.org/abs/2512.06576 - arXiv:2512.06576v1 Announce Type: new -Abstract: We study boundary structure of asymptotically AdS gravity and (gauge) fields defined on this background by employing the gauge PDE approach. The essential step of the construction is the incorporation of the boundary-defining function among the fields of the theory, which allows us to realise the asymptotic boundary as a space-time submanifold by employing the gauge PDE implementation of Penrose's concept of asymptotically-simple space. In so doing the gauge PDE describing the boundary structure is obtained by restricting to the boundary of spacetime and simultaneously restricting to the boundary of the field space by setting the boundary defining function to zero. To implement this step systematically we introduce a notion of $Q$-boundary which seems to be new. The main concrete result of this work is the construction of the efficient boundary calculus, which gives a recursive procedure to obtain the explicit form of the equations satisfied by the boundary fields and their gauge transformations for boundary dimension $d \geq 3$. These include obstruction equations (such as Bach equation or Yang-Mills equation for $d=4$) and generalised conservation equations in the subleading sector. In particular, we derive the explicit form of the higher conformal Yang-Mills equation for $d=8$. The approach is very general and, in principle, applies to generic (gauge) fields on the Einstein gravity background producing a conformally-invariant gauge theory on the boundary, which describes their boundary structure. It can be considered as an extension of the Fefferman-Graham construction that takes into account both the leading and the subleading sector of the bulk fields. - oai:arXiv.org:2512.06576v1 - math-ph - gr-qc - hep-th - math.DG - math.MP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.AP + Wed, 10 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Maxim Grigoriev, Mikhail Markov + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Zhen Lu, Shou-Fu Tian - On masas of the Calkin algebra generated by projections - https://arxiv.org/abs/2512.06580 - arXiv:2512.06580v1 Announce Type: new -Abstract: First, assuming the continuum hypothesis CH, for every compact totally disconnected Hausdorff space $K$ of weight not exceeding the continuum and without $G_\delta$ points, we construct a masa of the Calkin algebra $\mathcal Q(\ell_2)$ which is $*$-isomorphic to the algebra $C(K)$ of complex-valued continuous functions on $K$. This is sharp in two ways: (1) there cannot be other $*$-isomorphic types of masas of $\mathcal Q(\ell_2)$ generated by projections and so, this result gives a complete $*$-isomorphic classification of masas of $\mathcal Q(\ell_2)$ generated by projections, (2) some additional set-theoretic hypothesis, like CH, is necessary to have all these C*-algebras as masas of $\mathcal Q(\ell_2)$. - This shows that masas of the Calkin algebras could have rather unexpected properties compared to the previously known three $*$-isomorphic types of them generated by projections: $\ell_\infty/c_0$, $L_\infty$ and $\ell_\infty/c_0\oplus L_\infty$. - Secondly, without making any additional set-theoretic assumptions we construct a family of maximal possible cardinality (of the power set of $\mathbb R$) of pairwise non-$*$-isomorphic masas of $\mathcal Q(\ell_2)$ generated by projections which (a) are not SAW*-algebras unlike the liftable masas (Gelfand spaces in this group of our masas are not $F$-spaces) (b) do not admit conditional expectations. This improves the results which required additional set-theoretic hypotheses to construct a single masa of $\mathcal Q(\ell_2)$ generated by projections without a commutative lift. - oai:arXiv.org:2512.06580v1 - math.OA - math.GN - math.LO - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Piotr Koszmider + http://creativecommons.org/licenses/by/4.0/ + Yorgo Chamoun, Samuel Mimram - Proof of a combinatorial conjecture posed in "The Blimpy Shape of Heady-s and Taily-s Bit Strings" - https://arxiv.org/abs/2512.06587 - arXiv:2512.06587v1 Announce Type: new -Abstract: We demonstrate three properties conjectured to hold for a certain function by Levin (2025) in a study of the blimpy graphical shape of the number of bit strings with a given score under an interesting scoring system. The properties include discrete convexity, a simple formula for the greatest argument at which the function is negative, and a positive expectation under a certain probability function. A new set of inequalities which imply the latter is presented and proved under some monotonicity assumptions. - oai:arXiv.org:2512.06587v1 - math.CO - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Bruce Levin + http://creativecommons.org/licenses/by/4.0/ + Hannah Bakker, Gianfranco Guastaroba, Stefan Nickel, M. Grazia Speranza - On Jacobi sums arising from the classical doubling method - https://arxiv.org/abs/2512.06588 - arXiv:2512.06588v1 Announce Type: new -Abstract: We define the notion of a non-abelian Jacobi sum $\mathcal{J}^{\mathrm{dbl}}\left(\pi, \chi\right)$ attached to an irreducible representation $\pi$ of a general linear group or a classical group over a finite field and a character $\chi$ of the multiplicative group of the finite field or its quadratic extension. These sums emerge in the study of the doubling method of Piatetski-Shapiro--Rallis and Lapid--Rallis. For general linear groups, we express these non-abelian Jacobi sums in terms of Kondo's non-abelian Gauss sums. For classical groups and for characters that are not conjugate-dual, we give an explicit formula for these non-abelian Jacobi sums in terms of Gauss sums attached to the Deligne--Lusztig data of the representation, and we prove that these Jacobi sums are constant on geometric Lusztig series. Our results rely on a multiplicativity result of non-abelian Jacobi sums obtained by Girsch--Zelingher. - oai:arXiv.org:2512.06588v1 - math.NT - math.RT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.LO + math.QA + Wed, 10 Dec 2025 00:00:00 -0500 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Calvin Yost-Wolff, Elad Zelingher + http://creativecommons.org/licenses/by/4.0/ + Silvia Properzi, Yufei Qin - Improved Interactive Protocol for Synchronizing From Deletions - https://arxiv.org/abs/2512.06606 - arXiv:2512.06606v1 Announce Type: new -Abstract: Data synchronization is a fundamental problem with applications in diverse fields such as cloud storage, genomics, and distributed systems. This paper addresses the challenge of synchronizing two files, one of which is a subsequence of the other and related through a constant rate of deletions, using an improved communication protocol. Building upon prior work, we integrate advanced multi-deletion correction codes into an existing baseline protocol, which previously relied on single-deletion correction. Our proposed protocol reduces communication cost by leveraging more general partitioning techniques as well as multi-deletion error correction. We derive a generalized upper bound on the expected number of transmitted bits, applicable to a broad class of deletion correction codes. Experimental results demonstrate that our approach outperforms the baseline in communication cost. These findings establish the efficacy of the improved protocol in achieving low-redundancy synchronization in scenarios where deletion errors occur. - oai:arXiv.org:2512.06606v1 - cs.IT - math.IT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Haolun (Michael), Ni, Lev Tauz, Ryan Gabrys, Lara Dolecek + http://creativecommons.org/licenses/by/4.0/ + Huali Zhang - Optimal Preconditioning is a Geodesically Convex Optimization Problem - https://arxiv.org/abs/2512.06618 - arXiv:2512.06618v1 Announce Type: new -Abstract: We introduce a unified framework for computing approximately-optimal preconditioners for solving linear and non-linear systems of equations. We demonstrate that the condition number minimization problem, under structured transformations such as diagonal and block-diagonal preconditioners, is geodesically convex with respect to unitarily invariant norms, including the Frobenius and Bombieri--Weyl norms. This allows us to introduce efficient first-order algorithms with precise convergence guarantees. -For linear systems, we analyze the action of symmetric Lie subgroups $G \subseteq \GL_m(\CC) \times \GL_n(\CC)$ on the input matrix and prove that the logarithm of the condition number is a smooth geodesically convex function on the associated Riemannian quotient manifold. We obtain explicit gradient formulas, show Lipschitz continuity, and prove convergence rates for computing the optimal Frobenius condition number: $\widetilde{O}(1/\eps^2)$ iterations for general two-sided preconditioners and $\widetilde{O}(\kappa_F^2 \log(1/\eps))$ for strongly convex cases such as left preconditioning. We extend our framework to consider preconditioning of polynomial systems $\f(x) = 0$, where $\f$ is a system of multivariate polynomials. We analyze the local condition number $\mu(\f, \xi)$, at a root $\xi$ and prove that it also admits a geodesically convex formulation under appropriate group actions. We deduce explicit formulas for the Riemannian gradients and present convergence bounds for the corresponding optimization algorithms. To the best of our knowledge, this is the first preconditioning algorithm with theoretical guarantees for polynomial systems. - oai:arXiv.org:2512.06618v1 - math.OC - cs.CC - cs.NA - math.AG - math.NA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - M. Levent Do\u{g}an, Alperen Erg\"ur, Elias Tsigaridas + Mikhail V. Bludov, Sergei Vad. Fomin, Oleg R. Musin - Stable Brauer-Thrall II' conjecture for finite-dimensional Jacobian algebras - https://arxiv.org/abs/2512.06623 - arXiv:2512.06623v1 Announce Type: new -Abstract: We prove that finite-dimensional Jacobian algebras associated with non-degenerate quivers with potentials satisfy the stable Brauer-Thrall II' conjecture. In particular, this implies that the brick Brauer-Thrall II' conjecture (also known as the $\tau$-Brauer-Thrall II' conjecture) holds for finite-dimensional Jacobian algebras. - oai:arXiv.org:2512.06623v1 - math.RT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Mohamad Haerizadeh, Toshiya Yurikusa + http://creativecommons.org/licenses/by-nc-sa/4.0/ + Peter W. Michor, Praful Rahangdale - Thermoelastic plates with type I heat conduction with second gradient - https://arxiv.org/abs/2512.06625 - arXiv:2512.06625v1 Announce Type: new -Abstract: This paper investigates the qualitative properties of thermoelastic plates modeled by the second-gradient theory with a Type I heat equation. We establish the exponential stability of the solutions. Our main contribution is to prove that the semigroup is non-differentiable when the bi-Laplacian operator appears in the heat equation. Additionally, we analyze the case where the elastic parameter is negative, demonstrating the uniqueness and instability of the solutions. Finally, in the one-dimensional quasi-static case, we demonstrate the existence and exponential decay of the solutions under specific conditions. - oai:arXiv.org:2512.06625v1 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.DS + Wed, 10 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - 10.58997/ejde.2025.94 - Electronic Journal of Differential Equations 2025 (2025) 1-11 - Jaime Mu\~noz Rivera, Elena Ochoa Ochoa, Ram\'on Quintanilla + Ferdinand Verhulst - B-spline periodization of Fourier pseudo-spectral method for non-periodic problems - https://arxiv.org/abs/2512.06631 - arXiv:2512.06631v1 Announce Type: new -Abstract: Spectral methods are renowned for their high accuracy and efficiency in solving partial differential equations. The Fourier pseudo-spectral method is limited to periodic domains and suffers from Gibbs oscillations in non-periodic problems. The Chebyshev method mitigates this issue but requires edge-clustered grids, which does not match the characteristics of many physical problems. To overcome these restrictions, we propose a B-spline-periodized Fourier (BSPF) method that extends to non-periodic problems while retaining spectral-like accuracy and efficiency. The method combines a B-spline approximation with a Fourier-based residual correction. The B-spline component enforces the smooth matching of boundary values and derivatives, while the periodic residual is efficiently treated by Fourier differentiation/integration. This construction preserves spectral convergence within the domain and algebraic convergence at the boundaries. Numerical tests on differentiation and integration confirm the accuracy of the BSPF method superior to Chebyshev and finite-difference schemes for interior-oscillatory data. Analytical mapping further extends BSPF to non-uniform meshes, which enables selective grid refinement in regions of sharp variation. Applications of the BSPF method to the one-dimensional Burgers' equation and two-dimensional shallow water equations demonstrate accurate resolution of sharp gradients and nonlinear wave propagation, proving it as a flexible and efficient framework for solving non-periodic PDEs with high-order accuracy. - oai:arXiv.org:2512.06631v1 - math.NA - cs.NA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Dongan Li, Mou Lin, Shunxiang Cao, Shengli Chen + http://creativecommons.org/publicdomain/zero/1.0/ + Rohan Sarkar - FEALPy v3: A Cross-platform Intelligent Numerical Simulation Engine - https://arxiv.org/abs/2512.06632 - arXiv:2512.06632v1 Announce Type: new -Abstract: In resent years, the software ecosystem for numerical simulation still remains fragmented, with different algorithms and discretization methods often implemented in isolation, each with distinct data structures and programming conventions. This fragmentation is compounded by the growing divide between packages from different research fields and the lack of a unified, universal data structure, hindering the development of integrated, cross-platform solutions. In this work, we introduce FEALPy, a numerical simulation engine built around a unified tensor abstraction layer in a modular design. It enables seamless integration between diverse numerical methods along with deep learning workflows. By supporting multiple computational backends such as NumPy, PyTorch, and JAX, FEALPy ensures consistent adaptability across CPU and GPU hardware systems. Its modular architecture facilitates the entire simulation pipeline, from mesh handling and assembly to solver execution, with built-in support for automatic differentiation. In this paper, the versatility and efficacy of the framework are demonstrated through applications spanning linear elasticity, high-order PDEs, moving mesh methods, inverse problems and path planning. - oai:arXiv.org:2512.06632v1 + 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 - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Yangyang Zheng, Huayi Wei, Yunqing Huang, Chunyu Chen, Tian Tian, Hanbin Liu, Wenbin Wang, Liang He + Hao Dong, Liqun Cao - PG-Flow: Deterministic implicit policy gradients for geometric product-form queueing networks - https://arxiv.org/abs/2512.06633 - arXiv:2512.06633v1 Announce Type: new -Abstract: Product-form queueing networks (PFQNs) admit steady-state distributions that factorize into local terms, and in many classical PFQNs including Jackson, BCMP, G-networks, and Energy Packet Networks, these marginals are geometric and parametrized by local flow variables satisfying balance equations. While this structure yields closed-form expressions for key performance metrics, its use for deterministic steady-state optimization remains limited. We introduce PG-Flow, a deterministic policy-gradient framework that differentiates through the steady-state flow fixed-point equations, providing exact gradients via implicit differentiation and a local adjoint system while avoiding trajectory sampling and Poisson equations. We establish global convergence under structural assumptions (affine flow operators and convex local costs), and show that acyclic networks admit linear-time computation of both flows and gradients. Numerical experiments on routing control in Jackson networks and energy-arrival control in Energy Packet Networks demonstrate that PG-Flow provides a principled and computationally efficient approach to deterministic steady-state optimization in geometric product-form networks. - oai:arXiv.org:2512.06633v1 - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.NT + Wed, 10 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Youssef Ait El Mahjoub + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Qingshen Lv, Bingyong Xie - On the regularity for thermoelastic systems of phase-lag parabolic type - https://arxiv.org/abs/2512.06634 - arXiv:2512.06634v1 Announce Type: new -Abstract: In this article, we investigate the maximal smoothness (infinite differentiability) of solutions to thermoelastic models, specifically those where the heat equation is of the ``phase-lag'' or ``parabolic'' type. We derive optimal regularity results for two distinct models. The first model addresses the transverse oscillations of a fully thermoelastic plate, for which we prove that the associated semigroup is analytic. The second model considers a partially thermoelastic plate composed of two components: a thermoelastic component with nonzero temperature differences and an elastic component unaffected by temperature variations. For this model, we demonstrate that the semigroup \( S(t) \) belongs to the Gevrey class of order 4, provided the solutions are radial and symmetric. Both analyticity and Gevrey class membership are qualitative properties that intricately link regularity and stability, driven by robust dissipative mechanisms. These properties are significantly stronger than standard regularity conditions, such as belonging to the class \( C^k \) or a Sobolev space \( H^s \). - oai:arXiv.org:2512.06634v1 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://creativecommons.org/licenses/by/4.0/ - 10.1080/01495739.2025.2514482 - Journal of Thermal Stresses (48) 2025 - Jaime Mu\~noz Rivera, Elena Ochoa Ochoa, Ram\'on Quintanilla + Alessandro Neri, Paolo Santonastaso - Existence and sharpness of the phase transition for the Frog Model on transitive graphs - https://arxiv.org/abs/2512.06640 - arXiv:2512.06640v1 Announce Type: new -Abstract: We consider a slight modification of the frog model. For a given graph, each vertex has $\mathrm{Poisson}(\lambda)$ particles (or frogs). At time zero, only the particles at the origin are active, and all the other particles are sleeping. Each active particle performs an independent, continuous-time simple random walk, becoming inactive after time $t$. Once an active frog jumps to a vertex, it activates all of its particles. The survival of active particles can be studied as a dependent percolation model with two parameters $\lambda$ and $t$. In the present work, we establish the existence of a phase transition with respect to each parameter for non-amenable graphs of bounded degrees and quasi-transitive graphs of superlinear polynomial growth, as well as prove the sharpness of the phase transition for transitive graphs. - oai:arXiv.org:2512.06640v1 - math.PR - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Omer Angel, Daniel de la Riva, Jonathan Hermon, Yuliang Shi + Arpit Babbar, Hendrik Ranocha - Totally nonnegative Peterson variety and strongly dominant weight polytope - https://arxiv.org/abs/2512.06646 - arXiv:2512.06646v1 Announce Type: new -Abstract: We study the totally nonnegative part of the Peterson variety in arbitrary Lie type and establish its connection to the strongly dominant weight polytope. In particular, we prove that the totally nonnegative part of the Peterson variety is a regular CW-complex, which is homeomorphic to a cube as a cell-decomposed space. This confirms a conjecture of Rietsch for all Lie types. - oai:arXiv.org:2512.06646v1 + 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 math.AG - math.CO - math.RT - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Hiraku Abe, Tao Gui, Haozhi Zeng + http://creativecommons.org/licenses/by/4.0/ + Nathan H. Morris - Local structure of the Hilbert scheme of conics in quintic del Pezzo varieties - https://arxiv.org/abs/2512.06670 - arXiv:2512.06670v1 Announce Type: new -Abstract: Let $X$ be the quintic del Pezzo $4$-fold. It is very well-known that $X$ is realized by a smooth linear section of Grassmannian $\mathrm{Gr}(2,5)$. In this paper, we prove that the Hilbert scheme of conics in $X$ is a smooth variety of dimension $7$ by using a torus action on $X$, which provides a more direct proof about the first named author's previous result. - oai:arXiv.org:2512.06670v1 - math.AG - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Kiryong Chung, Bomyeong Kim, Minseong Kwon + http://creativecommons.org/licenses/by/4.0/ + Xue-Mei Li, Colin Piernot, Szymon Sobczak, Kexing Ying - Some explicit values of a $q$-multiple zeta function whose denominator power is not uniform - https://arxiv.org/abs/2512.06672 - arXiv:2512.06672v1 Announce Type: new -Abstract: One of the generalizations of multiple zeta values is the $q$-version, and in the case of finite sums, they may be expressed explicitly in polynomial form. Several results have been found when the powers of the factors in the denominator are equal and when they are small. In this paper, we give explicit formulas for the case when the powers are unequal and are small. - oai:arXiv.org:2512.06672v1 + 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 math.NT - math.CO - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Yuri Bilu, Hideaki Ishikawa, Takao Komatsu + http://creativecommons.org/licenses/by-nc-nd/4.0/ + Desir\'ee Gij\'on G\'omez - Berge Hamilton cycles in a random sparsification of dense hypergraphs - https://arxiv.org/abs/2512.06675 - arXiv:2512.06675v1 Announce Type: new -Abstract: In the standard random graph process, edges are added to an initially empty graph one by one uniformly at random. A classic result by Ajtai, Koml\'os, and Szemer\'edi, and independently by Bollob\'as, states that in the standard random graph process, with high probability, the graph becomes Hamiltonian exactly when its minimum degree becomes $2$; this is known as a \emph{hitting time} result. Johansson extended this result by showing the following: For a graph $G$ with $\delta(G) \geq (1/2+\varepsilon)n$, in the random graph process constrained to the host graph $G$, the hitting times for minimum degree $2$ and Hamiltonicity still coincide with high probability. - In this paper, we extend Johansson's result to Berge Hamilton cycles in hypergraphs. We prove that if an $r$-uniform hypergraph $H$ satisfies either $\delta_1(H) \geq (\frac{1}{2^{r-1}} + \varepsilon)\binom{n-1}{r-1}$ or $\delta_2(H) \geq \varepsilon n^{r-2}$, then in the random process generated by the edges of $H$, the time at which the hypergraph reaches minimum degree $2$ coincides with the time at which it contains a Berge Hamilton cycle with high probability. This generalizes the work of Bal, Berkowitz, Devlin, and Schacht, who established the result for the case where $H$ is a complete $r$-uniform hypergraph. - oai:arXiv.org:2512.06675v1 - math.CO - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Seonghyuk Im, Minseo Kim + http://creativecommons.org/licenses/by/4.0/ + Chris Lambie-Hanson, Pedro Marun - On Poisson superalgebras in characteristic 2 - https://arxiv.org/abs/2512.06680 - arXiv:2512.06680v1 Announce Type: new -Abstract: This paper is devoted to the study of Poisson superalgebras over fields of characteristic $2$. We investigate their representations, semidirect products, cohomology, formal deformations, and universal enveloping algebras. We also introduce Lie-Rinehart superalgebras in characteristic $2$ and clarify their connections with Poisson superalgebras. In particular, we show that the universal enveloping algebra of a Poisson superalgebra coincides with the universal enveloping algebra of an associated Lie-Rinehart superalgebra. We also compute examples and initiate the study of pre-Poisson superalgebras. - oai:arXiv.org:2512.06680v1 - math.RT - math.RA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://creativecommons.org/licenses/by/4.0/ - Quentin Ehret + Shengkui Ye, Kejia Zhu - Faithfully flat quotient morphisms by $G_a$-actions on factorial affine varieties - https://arxiv.org/abs/2512.06687 - arXiv:2512.06687v1 Announce Type: new -Abstract: Let $X$ be a factorial complex affine variety of dimension $\ge 3$ with an algebraic action of the additive group $G_a$. Let $\pi : X \to Y$ be the algebraic quotient morphism where we assume $Y$ is an affine variety. When $\pi$ is faithfully flat, we investigate $\pi$ by $G_a$-equivariant affine modifications and give criteria for $\pi$ to be a trivial $\mathbb A^1$-bundle. For a smooth acyclic fourfold $X$ with a free $G_a$-action and a $G_a$-equivariant $\mathbb A^3$-fibration $f : X \to \mathbb A^1$ where $G_a$ acts trivially on $\mathbb A^1$, we give a criterion for the algebraic quotient $Y$ to be isomorphic to $\mathbb A^3$ with $f$ as a coordinate. Together with a criterion for $\pi : X \to Y$ to be a trivial $\mathbb A^1$-bundle, we obtain a sufficient condition for $X\cong Y\times \mathbb A^1\cong \mathbb A^4$. - oai:arXiv.org:2512.06687v1 - math.AG - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Kayo Masuda + http://creativecommons.org/licenses/by/4.0/ + Soumitra Ghara, Surjit Kumar, Shailesh Trivedi - The 2-local homotopy types of G_2-gauge groups - https://arxiv.org/abs/2512.06696 - arXiv:2512.06696v1 Announce Type: new -Abstract: We determine the 2-local homotopy types of G_2-gauge groups over S^4. - oai:arXiv.org:2512.06696v1 - math.AT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Masaki Kameko + Reinder Meinsma, Riccardo Moschetti - Clairaut semi-slant/hemi-slant Riemannian maps to K\"ahler manifolds - https://arxiv.org/abs/2512.06698 - arXiv:2512.06698v1 Announce Type: new -Abstract: The aim of this paper is to study Clairaut semi-slant(hemi-slant) Riemannian maps to K\"ahler manifolds. - oai:arXiv.org:2512.06698v1 - math.DG - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Jyoti Yadav, Gauree Shanker + http://creativecommons.org/licenses/by/4.0/ + Ulrich Bauer, Tamal K. Dey, Michael Kerber, Florian Russold, Matthias S\"ols - Boundary regularity of weakly coupled vectorial almost-minimizers for Alt-Caffarelli functionals with non-standard growth - https://arxiv.org/abs/2512.06703 - arXiv:2512.06703v1 Announce Type: new -Abstract: For a fixed constant $\lambda > 0$ and a bounded Lipschitz domain $\Omega \subset \mathbb{R}^n$ with $n \geq 2$, we establish that almost-minimizers (functions satisfying a sort of variational inequality) of the Alt-Caffarelli type functional \[ \mathcal{J}_G({\bf v};\Omega) \coloneqq \int_\Omega \left(\sum_{i=1}^mG\big(|\nabla v_i(x)|\big) + \lambda \chi_{\{|{\bf v}|>0\}}(x)\right) dx , \] where ${\bf v} = (v_1, \dots, v_m)$ and $m \in \mathbb{N}$, exhibit optimal (up-to-the boundary) Lipschitz continuity, where $G$ is a $\mathcal{N}$-function satisfying specific growth conditions. Our work extends the recent regularity results for weakly coupled vectorial almost-minimizers for the $p$-Laplacian addressed in \cite{BFS24}, thereby providing new insights and approaches applicable to a wide class of non-linear one or two-phase free boundary problems with non-standard growth. Our findings remain novel and significant even in the scalar setting and for minimizers of the type considered by Mart\'{i}nez--Wolanski \cite{MW08} and da Silva \textit{et al.} \cite{daSSV2024}. - oai:arXiv.org:2512.06703v1 + 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 - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Pedro Fellype Pontes, Jo\~ao Vitor da Silva, Minbo Yang + Giada Cianfarani Carnevale - GPU-Accelerated Optimization Solver for Unit Commitment in Large-Scale Power Grids - https://arxiv.org/abs/2512.06715 - arXiv:2512.06715v1 Announce Type: new -Abstract: This work presents a GPU-accelerated solver for the unit commitment (UC) problem in large-scale power grids. The solver uses the Primal-Dual Hybrid Gradient (PDHG) algorithm to efficiently solve the relaxed linear subproblem, achieving faster bound estimation and improved crossover and branch-and-bound convergence compared to conventional CPU-based methods. These improvements significantly reduce the total computation time for the mixed-integer linear UC problem. The proposed approach is validated on large-scale systems, including 4224-, 6049-, and 6717-bus networks with long control horizons and computationally intensive problems, demonstrating substantial speed-ups while maintaining solution quality. - oai:arXiv.org:2512.06715v1 - math.OC - cs.AR - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Hussein Sharadga, Javad Mohammadi + http://creativecommons.org/licenses/by/4.0/ + Krishna Menon, Emil Verkama - Randomness before Probability, Quantised Gas Laws Directly from Objective Martin-Lof Randomness of Detailed Data - https://arxiv.org/abs/2512.06717 - arXiv:2512.06717v1 Announce Type: new -Abstract: We show that objective Martin-Lof randomness and Kolmogorov complexity of instantaneous detailed data lists for $N$ helium gas atoms on $M$ possible energies is necessary and sufficient to directly write down its Helmholtz free energy and thus all thermostatics of the gas. We show that such theory formally precedes application of probability and statistics. Each datum in a list is distinct if $N,M$ are formally well defined and with passive monitoring of thermostatic variables only, each is to be intrinsic. In this introductory paper we consider a low density cool gas of noninteracting He atoms in quantum and classical regimes. Objective definitions of detailed disorder and of thermostatic entropy arise for gas in spontaneous detailed motion along with new insights into irreversible processes and an objective Second Law. Algorithmic probability is rigorously associated with Kolmogorov complexity. A condition for equal a priori probability naturally arises and Fermi-Dirac quantum statistics follows from Martin-Lof randomness. - oai:arXiv.org:2512.06717v1 - math-ph - math.MP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://creativecommons.org/licenses/by/4.0/ - David Sherwell + A. Colesanti, M. Focardi, P. Guan, P. Salani - Determining Modes, State Reconstruction, and Intertwinement: Existence of Self-Synchronizing Intertwinements - https://arxiv.org/abs/2512.06720 - arXiv:2512.06720v1 Announce Type: new -Abstract: In the companion paper of the authors, a general synchronization framework was developed in the paradigmatic context of the 2D Navier-Stokes equations that allows one to precisely study the relation between the determining modes property of the corresponding dynamical system and the ability of certain continuous data assimilation algorithms to reconstruct unobserved state variables from sufficiently many observed state variables in this system, i.e., the reconstruction property. In this framework, the determining modes property and the reconstruction property can be viewed in a unified way as the ability of certain couplings of the Navier-Stokes equations to self-synchronize; due to the bi-directionality of coupling, the coupled system is referred to as an "intertwinement." A central achievement of this framework is to deduce a conceptual equivalence between the determining modes property and the reconstruction property of continuous data assimilation algorithms. In this paper, we prove that there are at least two non-trivial classes of intertwinements to which this framework applies. Moreover, these intertwinements encompass the continuous data assimilation algorithms studied in (Olson, Titi 2003) and (Azouani, Olson, Titi 2014) as special cases. Specifically, we show that there exist two types of intertwinements that are globally well-posed and we identify conditions under which these intertwinements self-synchronize. We emphasize that the intertwinements studied here can be induced by nonlinear perturbations of the underlying system, which are subsequently coupled bi-directionally to a copy of itself. Thus, establishing global well-posedness and suitable global-in-time uniform bounds, which are crucial to proving the claimed synchronization phenomenon, requires careful consideration. - oai:arXiv.org:2512.06720v1 - math.AP - math.DS - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.CO + math.CA + math.NT + Wed, 10 Dec 2025 00:00:00 -0500 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Elizabeth Carlson, Aseel Farhat, Vincent R. Martinez, Collin Victor + http://creativecommons.org/licenses/by/4.0/ + Dung The Tran - Well-posedness of parabolic KWC-systems with variable-dependent mobilities - https://arxiv.org/abs/2512.06723 - arXiv:2512.06723v1 Announce Type: new -Abstract: In this paper, we deal with the parabolic KWC system, associated with the mathematical model of grain boundary motion. The goal of this paper is to guarantee the well-posedness of the parabolic KWC system. However, such results have not been reported under the setting where the mobility of grain boundary motion depends on the unknown. To overcome this difficulty, results for the pseudo-parabolic type KWC system in [Antil et al., SIAM J. Math. Anal. \textbf{56}(5), 6422--6445](2024) suggest that the $H^1$-regularity of the time-derivative of the solution plays an essential role in verifying the uniqueness of the solution. In this light, we consider the pseudo-parabolic KWC system as an approximating system of the parabolic one, and focus on the improvements of regularity of solution to the parabolic system. By virtue of this regularity result, we establish the well-posedness theory on the parabolic KWC system. - oai:arXiv.org:2512.06723v1 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://creativecommons.org/licenses/by/4.0/ - Daiki Mizuno, Ken Shirakawa + Mayara Antunes, Bernardo Carvalho, Welington Cordeiro - Central elements and evaluation map for the quantum queer superalgebras - https://arxiv.org/abs/2512.06724 - arXiv:2512.06724v1 Announce Type: new -Abstract: We construct central elements in the quantum queer superalgebra $U_q(q_n)$ and in its affine counterpart $U_q(\widehat q_n)$. We also produce an epimorphism $ev:U_q(\widehat q_n)\to U_q(q_n)$ identical on the subalgebra isomorphic to $U_q(q_n)$. - oai:arXiv.org:2512.06724v1 - math.QA - math.RT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Ming Liu, Alexander Molev, Jian Zhang + Baosen Wu - Overdetermined Steklov eigenvalue problems on compact surfaces - https://arxiv.org/abs/2512.06740 - arXiv:2512.06740v1 Announce Type: new -Abstract: We consider the overdetermined problem given by - \begin{equation*} - \Delta u=0 \mbox{ in } \Omega,\quad \frac{\partial u}{\partial\nu} =\sigma_1 u \mbox{ on } \partial \Omega, \quad |\nabla u|=\mbox{constant on } \partial \Omega, - \end{equation*} where $\Omega$ is a connected, orientable, compact Riemannian surface with smooth boundary $\partial \Omega$, and $\sigma_1$ is the first non-zero Steklov eigenvalue of $\Omega$. We give a complete characterization of $\Omega$ when the overdetermined problem is solvable. Precisely, we prove that the overdetermined problem above admits a (nontrivial) solution if and only if $\Omega$ is conformally equivalent to either the flat unit disk or a flat cylinder $[-L,L]\times S^1$ for certain $L\ge L_0$ by a conformal transformation which (up to scaling) is an isometry on the boundary. In particular, we completely determine the compact domains in $\mathbb{R}^2$ or in $\mathbb{H}^2$ such that the overdetermined problem is solvable. - oai:arXiv.org:2512.06740v1 - math.DG - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Hang Chen, Bohan Wu + http://creativecommons.org/licenses/by/4.0/ + Alexey Gordeev, Lars-Daniel \"Ohman - Hausdorff dimension of the Cartesian product of exact approximation set in $\beta$-expansions - https://arxiv.org/abs/2512.06741 - arXiv:2512.06741v1 Announce Type: new -Abstract: In this paper, we study the metrical theory of Cartesian products of exact approximation sets in $\beta$-expansions. More precisely, for an integer $d \ge 2$ and real numbers $\beta_i > 1$ $(1 \le i \le d)$, we consider the set of points $x_i \in [0,1)$ is approximable by its convergents in the $\beta_i$-expansion to order $\psi_i$, but not to any better order. For any non-increasing functions $\psi_i$, we determine the Hausdorff dimension of the Cartesian product of these sets. - oai:arXiv.org:2512.06741v1 - math.NT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Wanjin Cheng, Xinyun Zhang + http://creativecommons.org/licenses/by-nc-nd/4.0/ + Rico Z\"ollner, Konrad Handrich - Non-continuous valuations on convex bodies and a new characterization of volume - https://arxiv.org/abs/2512.06745 - arXiv:2512.06745v1 Announce Type: new -Abstract: This paper investigates the use of automatic continuity techniques in the context of valuations on convex bodies. We first provide an automatic continuity theorem for valuations restricted to parallelotopes with respect to a fixed basis. This result in combination with a counting argument provides a strengthened version of a classical characterization of volume due to Hadwiger. As a byproduct of the proof it is shown that $[0,n-1]\cup\{n\}$ are precisely the possible degrees of homogeneity of bounded translation invariant valuations on $n$-dimensional convex bodies. - oai:arXiv.org:2512.06745v1 - math.MG - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://creativecommons.org/licenses/by/4.0/ - Jorge S. Ib\'a\~nez Marcos, Pedro Tradacete, Ignacio Villanueva + Masoud Khalkhali, Nathan Pagliaroli - The Lipschitz Liouville Property, Affine Rigidity, and Coarse Harmonic Coordinates on Groups of Polynomial Growth - https://arxiv.org/abs/2512.06753 - arXiv:2512.06753v1 Announce Type: new -Abstract: We develop a quantitative theory of Lipschitz harmonic functions (LHF) on finitely generated groups, with emphasis on the Lipschitz Liouville property, affine rigidity, and quasi-isometric invariance for groups of polynomial growth. On finitely generated nilpotent groups we prove an affine rigidity theorem: for any adapted, smooth, Abelian-centered probability measure $\mu$, every Lipschitz $\mu$-harmonic function is affine, $f(x)=c+\varphi([x])$. For any finite generating set $S$ this yields a canonical isometric identification $$ - \mathrm{LHF}(G,\mu)/\mathbb{C} \cong \mathrm{Hom}(G_{\mathrm{ab}},\mathbb{C}),\qquad - \|\nabla_S f\|_\infty=\max_{s\in S}|\varphi([s])|, $$ independent of the choice of centered measure. Next, for any finite-index subgroup $H\le G$ and adapted smooth $\mu$ we prove a quantitative induction-restriction principle: restriction along $H$ and an explicit averaging operator give a linear isomorphism $\mathrm{LHF}(G,\mu)\cong\mathrm{LHF}(H,\mu_H)$, where $\mu_H$ is the hitting measure, with two-sided control of the Lipschitz seminorms. For groups of polynomial growth equipped with SAS measures we then show that $\mathrm{LHF}$ is a quasi-isometry invariant, and use this to construct coarse harmonic coordinates that straighten quasi-isometries up to bounded error. Finally, within the Lyons-Sullivan / Ballmann-Polymerakis discretization framework, we prove a quantitative discrete-to-continuous extension theorem: Lipschitz harmonic data on an orbit extend to globally Lipschitz $L$-harmonic functions on the ambient manifold, with gradient bounds controlled by the background geometry. - oai:arXiv.org:2512.06753v1 - math.GR - math.MG - math.PR - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Mayukh Mukherjee, Soumyadeb Samanta, Soumyadip Thandar + http://creativecommons.org/licenses/by/4.0/ + Nathan Dalaklis, Yan Mary He - The Intersection Cohomology of a Fan and the Hodge Conjecture for Toric Varieties - https://arxiv.org/abs/2512.06755 - arXiv:2512.06755v1 Announce Type: new -Abstract: We formulate a combinatorial version of the Intersection Hodge Conjecture for projective toric varieties. The conjecture asserts that the subspace of rational Hodge classes in the intersection cohomology $IH^*(X_\Sigma)$ is generated by the classes of algebraic cycles. We define the space of combinatorial Hodge classes, $Hdg^k_{\mathrm{comb}}(\Sigma) \subset IH^{2k}_{\mathrm{comb}}(\Sigma, \mathbb{Q})$, using the combinatorial intersection cohomology theory for fans developed by Barthel, Brasselet, Fieseler, and Kaup. We conjecture that this space is spanned by the combinatorial cycle classes corresponding to torus-invariant subvarieties. We verify this conjecture for all projective toric varieties of dimension $n \le 3$ and for the class of simplicial projective toric varieties. Finally, we provide an algorithmic framework to verify the conjecture for arbitrary rational fans. - oai:arXiv.org:2512.06755v1 - math.AG + 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 - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Rizwan Jahangir + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Mikhail V. Bludov - Higher-dimensional Teter rings via the canonical trace - https://arxiv.org/abs/2512.06761 - arXiv:2512.06761v1 Announce Type: new -Abstract: We study Puthenpurakal's higher-dimensional Teter rings via the canonical trace ideal. We give a sufficient criterion for Teterness and show that, in the standard graded case, it is also necessary, yielding a characterization. Consequently, several nearly Gorenstein families are Teter; moreover, under certain hypotheses, the Cohen--Macaulay type of nearly Gorenstein rings is bounded by the codimension. We also analyze Teterness for fiber products, Veronese subrings, and numerical semigroup rings. - oai:arXiv.org:2512.06761v1 - math.AC - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Sora Miyashita, Taiga Ozaki + Aram Dermenjian - The $\psi$-$\omega$-Mellin transform - https://arxiv.org/abs/2512.06767 - arXiv:2512.06767v1 Announce Type: new -Abstract: This manuscript introduces a generalization of the Mellin integral transform within the framework of weighted fractional calculus with respect to an increasing function. The proposed transform is much more suitable for working with fractional operators that involve a weight and are defined with respect to a function. This work also explores the connections between the Laplace and Fourier integral transforms in the same context. To achieve this, a new formulation of the weighted Fourier integral transform with respect to a function is presented, along with a new version of the bilateral Laplace transform. We study some of the properties of these new operators, obtain an inversion formula and a convolution theorem, and also present a practical application as an illustrative example. - oai:arXiv.org:2512.06767v1 - math.FA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + new + http://creativecommons.org/licenses/by/4.0/ + Shah Faisal + + + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Gustavo Dorrego, Luciano Luque y Rub\'en Cerutti + Wilberclay G. Melo, Cilon Perusato, Thyago S. R. Santos - Geometrical representation and dependence structure of three-dimensional Bernoulli distributions - https://arxiv.org/abs/2512.06786 - arXiv:2512.06786v1 Announce Type: new -Abstract: This paper fully characterizes the geometrical structure of the class of distributions of three-dimensional Bernoulli random variables with equal means, $p$. We find all the geometrical generators in closed form as functions of $p$. This result stems from an algebraic representation of the class that encodes the statistical properties of Bernoulli distributions. We study extremal negative dependence within the class and provide an application example by finding the impact of negative dependence to minimal aggregate risk. The application relies on a game theory approach. - oai:arXiv.org:2512.06786v1 - math.PR - math.ST - stat.TH - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Roberto Fontana, Patrizia Semeraro + B. Wolnik, D. M. Falkiewicz, W. Bo{\l}t, A. Rutkowski, B. De Baets - Global existence of solutions for semilinear damped wave equation with nonlinearities of derivative type - https://arxiv.org/abs/2512.06789 - arXiv:2512.06789v1 Announce Type: new -Abstract: In this paper, we consider the semilinear damped wave equation with nonlinearities of derivative type $|u_t|^p$. We observe that this problem admits a unique global (in time) solution with small initial data for all $p > 1$ in low spatial dimensions $n=1,2$. This result provides new insights into semilinear damped wave equations and complements the existing literature. - oai:arXiv.org:2512.06789v1 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.NA + cs.DC + cs.NA + Wed, 10 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Dinh Van Duong, Tuan Anh Dao + http://creativecommons.org/licenses/by-nc-sa/4.0/ + Teoman Toprak, Florian Kummer - On the Monotonicity and Rate of Convergence of the Markovian Persuasion Value - https://arxiv.org/abs/2512.06794 - arXiv:2512.06794v1 Announce Type: new -Abstract: We study a dynamic Bayesian persuasion model called Markovian persuasion. In such a model, the belief of the receiver regarding the current state of a Markov chain $(X_n)_{n\geq 1}$, over a finite state space $K$, is controlled through signals she obtains from a sender, who observes $(X_n)_{n\geq 1}$ in real time. At each stage $n\geq 1$, the receiver takes an action based on his current belief, which together with the realized state of $X_n$, determines the $n$'th stage payoff of the sender. The sender's goal in a Markovian persuasion game is to find a signaling policy that maximizes her expected $\delta$-discounted sum of stage payoffs for a discount factor $\delta \in [0,1)$. We show that starting from any invariant distribution $(X_n)_{n\geq 1}$ the trajectory of the $\delta$-discounted value is a monotone decreasing in $\delta$. By combining this result with the opposite increasing monotone trajectories found in Lehrer and S.\ (2025, GEB), we are able to derive an upper bound on the rate of convergence of the $\delta$-discounted values (as $\delta \to 1^-$) in the case where $(X_n)_{n\geq 1}$ is ergodic. The results for the Markovian persuasion model are then extended to the Markov chain games model of Renault (2006, MOR). - oai:arXiv.org:2512.06794v1 + 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 math.OC - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by/4.0/ - Dimitry Shaiderman + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Dylan Possama\"i, Chiara Rossato - Optimal and Diffusion Transports in Machine Learning - https://arxiv.org/abs/2512.06797 - arXiv:2512.06797v1 Announce Type: new -Abstract: Several problems in machine learning are naturally expressed as the design and analysis of time-evolving probability distributions. This includes sampling via diffusion methods, optimizing the weights of neural networks, and analyzing the evolution of token distributions across layers of large language models. While the targeted applications differ (samples, weights, tokens), their mathematical descriptions share a common structure. A key idea is to switch from the Eulerian representation of densities to their Lagrangian counterpart through vector fields that advect particles. This dual view introduces challenges, notably the non-uniqueness of Lagrangian vector fields, but also opportunities to craft density evolutions and flows with favorable properties in terms of regularity, stability, and computational tractability. This survey presents an overview of these methods, with emphasis on two complementary approaches: diffusion methods, which rely on stochastic interpolation processes and underpin modern generative AI, and optimal transport, which defines interpolation by minimizing displacement cost. We illustrate how both approaches appear in applications ranging from sampling, neural network optimization, to modeling the dynamics of transformers for large language models. - oai:arXiv.org:2512.06797v1 + 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 math.OC - cs.AI - cs.LG - stat.ML - Tue, 09 Dec 2025 00:00:00 -0500 + cs.SY + eess.SY + Wed, 10 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Gabriel Peyr\'e + Ujjwal Pratap, Steffen Hofmann - Related Hom-rhizaform algebras and Rota-Baxter Operators, Hom-Rhizaform Family Algebras - https://arxiv.org/abs/2512.06798 - arXiv:2512.06798v1 Announce Type: new -Abstract: This paper explores the link between Hom-rhizaform algebras and Rota-Baxter operators. We define a new structure, the Hom-rhizaform family algebra, which is a more general version of the Hom-rhizaform algebra. The main finding is that Rota-Baxter operators can be used to construct new Hom-rhizaform algebras. This work expands the theory of Hom-algebras by showing a new way to apply Rota-Baxter operators. Finally, we establish the classification of these algebras as well as their corresponding cocycle cones. - oai:arXiv.org:2512.06798v1 - math.RA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://creativecommons.org/licenses/by/4.0/ - Imed Basdouri, Mariem Jendoubi, Ahmed Zahari Abdou Damdji + Martin Burger, Samira Kabri, Gitta Kutyniok, Yunseok Lee, Lukas Weigand - A Volterra equation approach to the local limit of nonlocal traffic models - https://arxiv.org/abs/2512.06805 - arXiv:2512.06805v1 Announce Type: new -Abstract: We consider a class of nonlocal conservation laws modeling traffic flow, given by $ \partial_t u_\varepsilon + \partial_x(V(u_\varepsilon \ast \gamma_\varepsilon)\, u_\varepsilon) = 0 $ with $ \gamma_\varepsilon(\cdot) := \varepsilon^{-1}\gamma(\cdot/\varepsilon) $ for a suitable convex convolution kernel $\gamma$. Since the work of Colombo et al. (Arch. Ration. Mech. Anal., 2023), thanks to uniform $ \mathrm{L}^\infty $- and TV-estimates, it is known that $ w_\varepsilon := u_\varepsilon \ast \gamma_\varepsilon $ converges to the entropy solution of the local scalar conservation law $ \partial_t u + \partial_x(V(u)\, u) = 0 $ as $\varepsilon \searrow 0$. However, the convergence of $ \{u_\varepsilon\}_{\varepsilon > 0} $ itself has not been fully addressed so far. In this direction, a known result applies specifically to the case of an exponential kernel, where the identity $ \varepsilon \partial_x w_\varepsilon = w_\varepsilon - u_\varepsilon $ is fundamental. In this work, we address this gap in the literature and prove that $ \{u_\varepsilon\}_{\varepsilon > 0} $ converges to the same limit $u$ under the mild additional assumption that the initial datum belongs to $\mathrm L^1(\mathbb{R})$. Our analysis exploits, through a Fourier approach, the stability properties of the more general Volterra-type equation $\partial_xw_\varepsilon=\gamma'_\varepsilon\ast u_\varepsilon-\gamma_\varepsilon(0)u_\varepsilon$, thereby deducing the convergence of $u_\varepsilon$ from that of $w_\varepsilon$. - oai:arXiv.org:2512.06805v1 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Nicola De Nitti, Kuang Huang + 10.1007/s10479-025-06968-z + Stuart M. Harwood, Dimitri J. Papageorgiou - Urgent Samples in Clinical Laboratories: Stochastic Batching to Minimize Patient Turnaround Time - https://arxiv.org/abs/2512.06820 - arXiv:2512.06820v1 Announce Type: new -Abstract: This paper addresses the problem of batching laboratory samples in hospital laboratories where samples of different priorities are received continuously with uncertain transportation times. The focus is on optimizing the control strategy for loading a centrifuge to minimize patient turnaround time (TAT). While focusing on samples of patients in life-threatening situations (i.e., vital samples), we propose several online and offline methods, including a stochastic mixed-integer quadratic programming model integrated within a discrete-event system simulation. This paper aims to enhance patient care by providing timely laboratory results through improved batching strategies. The case study, which uses real data from a university hospital, demonstrates that incorporating distributional knowledge of transport times into our decision policy can reduce the median patient TAT of vital samples by 4.9 minutes and the 0.95 quantile by 9.7 minutes, but has no significant effect on low-priority samples. In addition, we show that this is essentially an optimal result by comparison with the upper bound obtained by a perfect-knowledge offline algorithm. - oai:arXiv.org:2512.06820v1 - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Antonin Novak, Andrzej Gnatowski, Premysl Sucha + http://creativecommons.org/licenses/by/4.0/ + Patr\'icia Gon\c{c}alves, Martin Hairer, Maria Chiara Ricciuti - Representation of quasi-periodic functions and Hausdorff-Young inequalities for Besicovitch almost periodic functions - https://arxiv.org/abs/2512.06821 - arXiv:2512.06821v1 Announce Type: new -Abstract: For a class of $\mathbb{R}^d$-ations and $\mathbb{Z}^d$-actions on the $n$-dimensional torus $\mathbb{T}^n$, we characterize their unique ergodicity and establish a theorem of Weyl type. This result allows us to establish an isomorphism between the Banach algebra of quasi-periodic functions with spectrum in a given $\mathbb{Z}$-module and the Banach algebra of periodic functions on a torus. This, in return, allows us to give a very simple proof of Hausdorff-Young inequalities for Besicovitch almost periodic functions. The regularity of the parent function of a quasi-periodic function is also studied. - oai:arXiv.org:2512.06821v1 - math.CA - math.DS - math.NT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Aihua Fan, Kai Jiang, Pingwen Zhang + 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 - Double Local-to-Unity: Estimation under Nearly Nonstationary Volatility - https://arxiv.org/abs/2512.06823 - arXiv:2512.06823v1 Announce Type: new -Abstract: This article develops a moderate-deviation limit theory for autoregressive models with jointly persistent mean and volatility dynamics. The autoregressive coefficient is allowed to drift toward unity slower than the classical 1/n rate, while the volatility persistence parameter also converges to one at an even slower, logarithmic order, so that the conditional variance process is itself nearly nonstationary and its unconditional moments may diverge. This double localization allows the variance process to be nearly nonstationary and to evolve slowly, as observed in financial data and during asset price bubble episodes. Under standard regularity conditions, we establish consistency and distributional limits for the OLS estimator of the autoregressive coefficient that remains valid in the presence of highly persistent stochastic volatility. We show that the effective normalization for least squares inference is governed by an average volatility scale, and we derive martingale limit theorems for the OLS estimator under joint drift and volatility dynamics. In a mildly stationary regime (where the autoregressive root approaches one from below), the OLS estimator is asymptotically normal. In a mildly explosive regime (where the root approaches one from above), an OLS based self normalized statistic converges to a Cauchy limit. Strikingly, in both regimes, the limiting laws of our statistics are invariant to the detailed specification of the volatility process, even though the conditional variance is itself nearly nonstationary. Overall, the results extend moderate-deviation asymptotics to settings with drifting volatility persistence, unify local to unity inference with nearly nonstationary stochastic volatility, and deliver practically usable volatility robust statistics for empirical work in settings approaching instability and exhibiting bubbles. - oai:arXiv.org:2512.06823v1 - math.ST - stat.TH - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Abir Sarkar, Martin T. Wells + http://creativecommons.org/licenses/by/4.0/ + Zengo Tsuboi - OEF (Proximal) Newton-type Method with Inexact Derivatives for Unconstrained Optimization - https://arxiv.org/abs/2512.06825 - arXiv:2512.06825v1 Announce Type: new -Abstract: In this paper, we propose objective-evaluation-free (OEF) variants of the proximal Newton method for nonconvex composite optimization problems and the regularized Newton method for unconstrained optimization problems, respectively, using inexact evaluations of gradients and Hessians. Theoretical analysis demonstrates that the global/local convergence rates of the proposed algorithms are consistent with those achieved when both objective function and derivatives are evaluated exactly. Additionally, we present an OEF regularized Newton and negative curvature algorithm that uses inexact derivatives to find approximate second-order stationary points for unconstrained optimization problems. The worst-case iteration/(sample) operation complexity of the proposed algorithm matches the optimal results reported in the literature. - oai:arXiv.org:2512.06825v1 - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.MG + Wed, 10 Dec 2025 00:00:00 -0500 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Hong Zhu + http://creativecommons.org/publicdomain/zero/1.0/ + Yaoying Fu, Evgeniya Lagoda, Shiying Li, Tom Needham, Lander Ver Hoef, Morgan Weiler - Nonstandard Calder\'on-type theorems - https://arxiv.org/abs/2512.06826 - arXiv:2512.06826v1 Announce Type: new -Abstract: We establish Calder\'on-type theorems for operators bounded on nonstandard end-point Lorentz spaces \begin{equation*} T\colon L^{p_0, q_0}\to L^{p_1, q_1}\quad\text{and}\quad T\colon L^{q, 1}\to L^\infty \end{equation*} and the improvement of target spaces which is intimately connected with this. The emphasis will be placed on the cases $q_0=q_1$ and $q_1=\infty$. - oai:arXiv.org:2512.06826v1 - math.FA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - David Kub\'i\v{c}ek + Alessandro Proserpio, Ian A. B. Strachan - Quaternionic Carleson measures - https://arxiv.org/abs/2512.06831 - arXiv:2512.06831v1 Announce Type: new -Abstract: In this paper we provide a general construction of a quaternionic Banach space of slice regular functions from a given Banach space of holomorphic functions, which we call its quaternionic lift. To the best of our knowledge, this construction encompasses all known examples of quaternionic Banach spaces of slice regular functions in the literature. Our main result is a characterization of Carleson and vanishing Carleson measures for such quaternionic Banach function spaces in terms of the corresponding Carleson measures of the underlying holomorphic function space. This offers a unified approach to a problem that so far has been treated on a case-by-case basis. - oai:arXiv.org:2512.06831v1 - math.FA - math.CV - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Nikolaos Chalmoukis, Giulia Sarfatti + http://creativecommons.org/licenses/by/4.0/ + Francesca La Piana - Real split hyperplane sections on smooth polarized $K3$-surfaces - https://arxiv.org/abs/2512.06833 - arXiv:2512.06833v1 Announce Type: new -Abstract: We find upper bounds, sharp in most cases, on the number of real hyperplane sections of real smooth polarized $K3$-surfaces that split into lines. Most bounds coincide with their complex counterparts. - oai:arXiv.org:2512.06833v1 - math.AG - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://creativecommons.org/licenses/by/4.0/ - Alex Degtyarev + Christof Kuelske, Niklas Schubert - Noncommutative weak type $(1,1)$ estimates for Calder\'on-Zygmund operators with $L_2$-mean H\"ormander conditions - https://arxiv.org/abs/2512.06843 - arXiv:2512.06843v1 Announce Type: new -Abstract: We construct a slightly new noncommutative Calder\'on-Zygmund decomposition by further splitting the bad function. - Using this tool, we prove the weak type (1,1) boundedness of noncommutative Calder\'on-Zygmund operators under $L_2$-mean H\"older conditions, which improves the previous result. - oai:arXiv.org:2512.06843v1 + 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 - math.OA - Tue, 09 Dec 2025 00:00:00 -0500 + cs.NA + math.NA + Wed, 10 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Xudong Lai, Lingxin Xu + Daniel Freeman, Mitchell A. Taylor - A note on the RAGE Theorem and phase-averaged dispersion for the Fibonacci Hamiltonian - https://arxiv.org/abs/2512.06844 - arXiv:2512.06844v1 Announce Type: new -Abstract: We find a weaker condition on spectral measures, "eventual absolute continuity", that ensure quantum delocalization as in the RAGE Theorem in the case of purely absolutely continuous spectrum. We then adapt these idea to strongly improve some phase-averaged delocalization bounds for the Fibonacci quasicrystal. - oai:arXiv.org:2512.06844v1 - math.SP - math-ph - math.DS - math.FA - math.MP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://creativecommons.org/licenses/by/4.0/ - Ga\'etan Leclerc + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Dengjun Guo, Xiaoyutao Luo - On stable equivalences of Morita type with twisted diagonal vertices - https://arxiv.org/abs/2512.06856 - arXiv:2512.06856v1 Announce Type: new -Abstract: We give a new proof, by using simplified terminology and notation, to a result of Puig stating that if a bimodule of two block algebras of finite groups over an algebraically closed field induces a stable equivalence of Morita type and has a twisted diagonal vertex, then it has an endopermutation module as a source. We also extend this result to arbitrary fields under a mild assumption. - oai:arXiv.org:2512.06856v1 + 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 - math.GR - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Xin Huang + Pranav Enugandla, Christian Gaetz - On Laplace transform on semitattices - https://arxiv.org/abs/2512.06857 - arXiv:2512.06857v1 Announce Type: new -Abstract: The aim of this work is to prove inverse formulas for Laplace transform on semilattices of open-and-compact sets in a both discrete and non-discrete cases. These are partial answers to a question posed by Yu.~I.~Lyubich. - oai:arXiv.org:2512.06857v1 - math.FA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://creativecommons.org/licenses/by/4.0/ - A. R. Mirotin + Elena Kulinskaya, David C. Hoaglin - Stability of Superposition of Viscous Contact Wave and Rarefaction Waves for Compressible Navier-Stokes System with Degenerate Heat-Conductivity and Large-Data - https://arxiv.org/abs/2512.06861 - arXiv:2512.06861v1 Announce Type: new -Abstract: This paper is concerned with the large-time behavior of solutions for the compressible Navier-Stokes system with degenerate heat-conductivity describing the one-dimensional motion of a viscous heat-conducting perfect polytropic gas. We proved that for the one-dimensional compressible system with temperature-dependent heat conductivity, the combination of viscous contact wave with rarefaction waves for the non-isentropic polytropic gas is asymptotically stable under large initial perturbation, provided the strength of the combination waves is suitably small. - oai:arXiv.org:2512.06861v1 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Manyu Liu + Mohammad Javaheri - On planar Schrodinger-Poisson systems with repulsive interactions in the mass supercritical regime - https://arxiv.org/abs/2512.06863 - arXiv:2512.06863v1 Announce Type: new -Abstract: In this paper, we investigate solutions with prescribed $L^{2}$-norm (i.e., prescribed mass) for the planar Schr\"{o}dinger-Poisson (SP) equation% \begin{equation*} -\Delta u+\lambda u+\alpha \left( \log |\cdot |\ast |u|^{2}\right) u=|u|^{p-2}u,\ \text{in}\ \Omega_{R} , \end{equation*}% where $\lambda \in \mathbb{R}$ is unknown, $\alpha <0,p>4$ and $\Omega_{R} \subseteq \mathbb{R}^{2}$ is a domain. First, we prove that the energy functional $J$ corresponding to the SP equation in $\mathbb{R}^{2}$ is unbounded both above and below on the Pohozaev manifold $\mathcal{P}$; this explains the reason why the minimax level of $J$ is difficult to determine, as referenced in [Cingolani and Jeanjean, SIAM J. Math. Anal., 2019]. Second, we establish the existence of a ground state and a high-energy solution, both with positive energy in a large bounded domain $\Omega_{R} $, which is a substantial advancement in addressing an open problem proposed in [Cingolani and Jeanjean, SIAM J. Math. Anal., 2019]. Finally, we analyze the asymptotic behavior of solutions as the domain $\Omega_{R} $ is extended to the entire space $\mathbb{R}^{2}$. - oai:arXiv.org:2512.06863v1 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://creativecommons.org/licenses/by/4.0/ - Juntao Sun, Shuai Yao, He Zhang + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Francesco Tesolin - Inverse problems for infinite-dimensional transport PDEs on Wasserstein space - https://arxiv.org/abs/2512.06871 - arXiv:2512.06871v1 Announce Type: new -Abstract: We develop a foundational framework for inverse problems governed by evolutionary partial differential equations (PDEs) on the Wasserstein space of probability measures. While the forward problems for such transport-type PDEs have been extensively and intensively studied, their corresponding inverse problems--which aim to reconstruct unknown operators, cost functions, or interaction kernels from observed solution data--remain largely unexplored at this level of generality. - The cornerstone of our theory is a systematic approach featuring high-order calculus on the Wasserstein space and a progressive variational scheme. This methodology is specifically designed to address the challenges inherent in inverse problems for infinite-dimensional, nonlinear, and nonlocal transport PDEs. - We demonstrate the power and versatility of our theory through two canonical examples: inverse problems for both the Mean Field Control (MFC) Dynamic Programming Equation and the Mean Field Game (MFG) Master Equation. Our work provides, for the first time, a unified foundation for identifying cost functions and interaction kernels from value function data. This establishes a new and fertile field of mathematical research with significant implications for both theory and applications in stochastic control and mean field games. - oai:arXiv.org:2512.06871v1 - math.OC - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Hongyu Liu, Jianliang Qian, Shen Zhang + Issam Naghmouchi - Stationary list colorings - https://arxiv.org/abs/2512.06876 - arXiv:2512.06876v1 Announce Type: new -Abstract: Komjath studied the list chromatic number of infinite graphs and introduced the notion of restricted list chromatic number. For a graph $X=(V_X,E_X)$ and a cardinal $\kappa$, we say that $X$ is restricted list colorable for $\kappa$ if for every $L:V_X\to[\kappa]^\kappa$ there is a choice function $c$ of $L$ such that $c(v)\neq c(w)$ whenever ${v,w}\in E_X$. In this paper, we discuss a variation, stationary list colorability for $\kappa$, obtained by replacing $[\kappa]^\kappa$ with the set of all stationary subsets of $\kappa$. We compare the stationary list colorability with other coloring properties. Among other things, we prove that the stationary list colorability is essentially different from other coloring properties including the restricted list colorability. We also prove the consistency result showing that for some $\kappa<\lambda$, restricted and stationary list colorability at $\kappa$ do not imply the corresponding properties at $\lambda$. - oai:arXiv.org:2512.06876v1 - math.LO + 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 - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Yusuke Hayashi + Richard Lang, Nicol\'as Sanhueza-Matamala - Circular Chromatic Numbers, Balanceability, Relation Algebras, and Network Satisfaction Problems - https://arxiv.org/abs/2512.06878 - arXiv:2512.06878v1 Announce Type: new -Abstract: In this paper, we characterize graphs with circular chromatic number less than 3 in terms of certain balancing labellings studied in the context of signed graphs. In fact, we construct a signed graph which is universal for all such labellings of graphs with circular chromatic number less than $3$, and is closely related to the generic circular triangle-free graph studied by Bodirsky and Guzm\'an-Pro. Moreover, our universal structure gives rise to a representation of the relation algebra $56_{65}$. We then use this representation to show that the network satisfaction problem described by this relation algebra belongs to NP. This concludes the full classification of the existence of a universal square representation, as well as the complexity of the corresponding network satisfaction problem, for relation algebras with at most four atoms. - oai:arXiv.org:2512.06878v1 - math.CO - cs.DM - math.RA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Manuel Bodirsky, Santiago Guzm\'an-Pro, Moritz Jahn, Mat\v{e}j Kone\v{c}n\'y, Paul Winkler + Andreas Bode - The Multi-set Allocation Occupancy function and inequality (MAO function and MAO inequality): the foundation of Generalized hypergeometric distribution theory - https://arxiv.org/abs/2512.06880 - arXiv:2512.06880v1 Announce Type: new -Abstract: In our previous work, we studied the Generalized Hypergeometric Distribution (GHGD), which we refer to as the Multi-set Allocation Occupancy (MAO) distribution. We derived formulas for its expectation and variance for any number of subsets $T$ and overlap count $t$ ($1 \le t \le T$), and established an asymptotic property. However, these formulas were complex, and higher moments were not derived. Through further study, we have established a novel function that describes all higher moments of the MAO distribution with a unified, elegant formula. The core definitions are the MAO function $g(A_1, A_2, \dots, A_r) = \prod_{i=1}^{T} (m_i)_{k_i} \cdot (n-m_i)_{r-k_i}$ and the MAO norm $\|(p_1, \dots, p_r)\|_T = \frac{\sum_{A_1, \dots, A_r \subseteq [T] \; : \; |A_j|=p_j} g(A_1, \dots, A_r)}{((n)_r)^{T-1}}$, where $p_i$ is the size of subset $A_i$, $m_i < n$, and $(x)_r$ is the falling factorial. Using these definitions, the intricate moment relations simplify into a unified form: the $\nu$-th raw moment of $p(x_{=t})$ and $p(x_{\ge t})$ can be calculated as $E(x_{=t}^\nu) = \sum_{1 \le i \le \nu} s_{\nu,i} \|t^i\|$ and $E(x_{\ge t}^\nu) = \sum_{1 \le i \le \nu} s_{\nu,i} \|[t, T]^i\|$, where $s_{\nu,i}$ are Stirling numbers of the second kind and $[t,T] = \{t, t+1, \dots, T\}$. Furthermore, based on the MAO norm, we formulate a novel MAO inequality under the proximity condition $\max(p_i) - \min(p_i) \le 1$: $\prod_{1\le i \le r} \|(p_i)\|_T \ge \|(p_1, \dots, p_r)\|_T$. A direct corollary is the asymptotic property of the MAO distribution: $E(X) > \text{Var}(X)$ and $E(X) - \text{Var}(X) = o(E(X))$ as $E(X) \to 0$. - oai:arXiv.org:2512.06880v1 - math.PR - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Xing-gang Mao, Xiao-yan Xue + Justin Holmer, Panayotis G. Kevrekidis, Dmitry E. Pelinovsky - Stochastic integral representations for the Ray-Knight theorem of the Levy forest - https://arxiv.org/abs/2512.06884 - arXiv:2512.06884v1 Announce Type: new -Abstract: We present a simple stochastic integral representation for the local times of the height process of a spectrally positive Levy process stopped at a hitting time. From the representation we derive a strong stochastic equation for the local time process of the type of Bertoin and Le Gall (Illinois J. Math., 2006) and Dawson and Li (Ann. Probab., 2012). This leads to a representation of the Ray-Knight theorem of Le Gall and Le Jan (Ann. Probab., 1998) and Duquesne and Le Gall (Asterisque, 2002), which codes the genealogical forest of a continuous-state branching process. The results extend those in the recent work of Aidekon et al. (Sci. China Math., 2024) for a Brownian motion with a local time drift. - oai:arXiv.org:2512.06884v1 - math.PR - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://creativecommons.org/licenses/by/4.0/ - Pei-Sen Li, Zenghu Li, Wenjing Zhang + Mukthesh Mahadev, Marc Gerritsma - On mutual arrangements of a plane real curve relative to an $M$-quartic with an oval-snake - https://arxiv.org/abs/2512.06907 - arXiv:2512.06907v1 Announce Type: new -Abstract: An oval $O$ of a plane real algebraic quartic curve $S$ is called a snake coiling around a real curve $C_k$ of degree $k$ if $O\cup\mathbb{R}C_k$ is isotopic to $O'\cup\mathbb{R}C_k$, where $O'$ is the boundary of a thickening of the embedded segment that transversally intersects $\mathbb{R}C_k$ at $2k$ points. In this article we prove that in this case $\mathbb{R}C_k\cup\mathbb{R}S$ is isotopic to $\mathbb{R}C_k\cup\mathbb{R}Q$, where $Q$ is a perturbation of the doubled conic. We prove analogs of this statement for real pseudoholomorphic curves under some additional assumptions. - oai:arXiv.org:2512.06907v1 - math.AG - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math-ph + math.MP + math.OA + Wed, 10 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - S. Yu. Orevkov, N. D. Puchkova + Lucas Hataishi - Quantum Elliptic Curves I: Algebraic Case - https://arxiv.org/abs/2512.06936 - arXiv:2512.06936v1 Announce Type: new -Abstract: A complex elliptic curve $E$ can be defined as the quotient of the analytic space $\mathbb{C}^*$ by a discrete action of the cyclic group $q^{\mathbb{Z}}$ for $\vert q\vert \neq 1$. We study the boundary case when $\vert q\vert =1$, which leads to the notion of a quantum elliptic curve and a conjectural equivalence of categories that one might call a noncommutative GAGA. - oai:arXiv.org:2512.06936v1 + 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 - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Michael J. Larsen, Valery Lunts + http://creativecommons.org/licenses/by/4.0/ + Srijan Ghosh - Continued fraction expansions of complex numbers, Lagrange's theorem, and badly approximable numbers - https://arxiv.org/abs/2512.06937 - arXiv:2512.06937v1 Announce Type: new -Abstract: This paper concerns extension of the classical Lagrange theorem, on the eventual periodicity of continued fraction expansions of quadratic surds, and the versions of it found in the literature in the case of complex numbers. In this respect, firstly, we adopt a more general notion of continued fraction expansions, in place of those arising from the nearest integer algorithms. Secondly, the issue is formulated in terms of zeros of quadratic and Hermitian forms, and a result is proved in terms of certain sequences of matrices associated with them, via continued fraction expansions. The result may be considered as a matrix analogue of Lagrange's theorem in the general framework. The unified approach leads to generalizations of the Lagrange theorem on one hand, and an extended version of a result of Hines (2019) on badly approximable complex numbers, on the other hand. - oai:arXiv.org:2512.06937v1 - math.NT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://creativecommons.org/licenses/by/4.0/ - S. G. Dani, Ojas Sahasrabudhe + Mohamed Benelmekki, Brahim Boulayat - Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties - https://arxiv.org/abs/2512.06939 - arXiv:2512.06939v1 Announce Type: new -Abstract: We study energy minimization problems in quantum chemistry through the lens of computational algebraic geometry. We focus on minimizing the Rayleigh quotient of a Hamiltonian over a tensor train variety. The complex critical points of this problem approximate eigenstates of the quantum system, with the global minimum approximating the ground state. We call the number of critical points the Rayleigh-Ritz degree. - After introducing tensor train varieties, we identify instances when they are Segre products of projective spaces. We also report what we know about the defining ideals of tensor trains. We present a birational parametrization of them from products of Grassmannians. Along the way, we study the Rayleigh-Ritz degree, and we introduce the Rayleigh-Ritz discriminant, which describes Hamiltonians that lead to deficient number of critical points. We use homotopy continuation to compute all critical points of this optimization problem over various tensor train and determinantal varieties. Finally, we use these results to benchmark state-of-the-art methods, the Alternating Linear Scheme and Density Matrix Renormalization Group. - oai:arXiv.org:2512.06939v1 - math.AG + 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 - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 new http://creativecommons.org/licenses/by/4.0/ - Viktoriia Borovik, Hannah Friedman, Serkan Ho\c{s}ten, Max Pfeffer + Hadi Salloum, Roland Hildebrand, Nhat Trung Nguyen, Vitali Pirau, Amer Al Badr, Mohammad Alkousa, Alexander Gasnikov - Analytic matrix descriptions with application to time-delay systems - https://arxiv.org/abs/2512.06957 - arXiv:2512.06957v1 Announce Type: new -Abstract: A polynomial matrix description(PMD) of a rational matrix $G(\lambda)$ is a matrix polynomial of the form $$ \mathbf{P}(\lambda) := \left[\begin{array}{c|c} A(\lambda) & B(\lambda) \\ \hline -C(\lambda) & D(\lambda)\end{array}\right] \text{ such that } G(\lambda) = D(\lambda) + C(\lambda) A(\lambda)^{-1} B(\lambda),$$ where $A(\lambda)$ is regular and called the state matrix. PMDs have been studied extensively in the context of higher order linear time-invariant systems. An analytic matrix description(AMD) of a meromorphic matrix $ M(\lambda)$ is a holomorphic matrix (i.e., a holomorphic matrix-valued function) of the form $$ \mathbf{H}(\lambda) := \left[\begin{array}{c|c} A(\lambda) & B(\lambda) \\ \hline -C(\lambda) & D(\lambda)\end{array}\right] \text{ such that } M(\lambda) = D(\lambda) + C(\lambda) A(\lambda)^{-1} B(\lambda),$$ where $A(\lambda)$ is regular and called the state matrix. AMDs arise in the study of linear time-invariant time-delay systems (TDS). Our aim is to develop a framework for analysis of AMDs analogous to the framework for PMDs and discuss the extent to which results of PMDs can be generalized to AMDs. We show that important results (e.g., coprime matrix-fraction descriptions (MFDs), least order PMDs, equivalence of PMDs, canonical forms, characterization of PMDs by transfer functions, structural indices of zeros and poles) which hold for PMDs can be generalized to AMDs which in turn can be utilized to analyze time-delay systems. - oai:arXiv.org:2512.06957v1 - math.SP - math.DS - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Rafikul Alam, Jibrail Ali + http://creativecommons.org/licenses/by/4.0/ + Yairon Cid-Ruiz - Isometries of the Ebin metric - https://arxiv.org/abs/2512.06958 - arXiv:2512.06958v1 Announce Type: new -Abstract: We study the space of Riemannian metrics over a compact manifold equipped with the Ebin metric. We characterize its self-isometries and prove that two such spaces are isometric if and only if their underlying manifolds are diffeomorphic. - oai:arXiv.org:2512.06958v1 - math.MG - math.DG - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - David Lenze + Nazar Arakelian, Pietro Speziali - A brief overview of spectral perturbation Theory - https://arxiv.org/abs/2512.06962 - arXiv:2512.06962v1 Announce Type: new -Abstract: The aim of this article is to present a brief overview of spectral perturbation theory for matrices, bounded linear operators and holomorphic operator-valued functions. We focus on bounds for perturbed eigenvalues, eigenvectors and invariant subspaces and provide simplified proofs of some well known results. We present a comprehensive perturbation analysis of invariant subspaces of matrices. For bounded linear operators we discuss, among other things, the effect of analytic perturbation on the discrete eigenvalues and spectral projections. We also briefly discuss analytic spectral perturbation theory for holomorphic operator-valued functions. - oai:arXiv.org:2512.06962v1 - math.SP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Rafikul Alam + Felix Joos, Let\'icia Mattos - On Quasinormality of compact perturbations of the isometries - https://arxiv.org/abs/2512.06967 - arXiv:2512.06967v1 Announce Type: new -Abstract: We study the compact perturbations of an isometry on a separable Hilbert space and provide a complete characterization of when they are quasinormal. Based on that, we present a complete classification for a rank-one perturbation of a unilateral shift of finite multiplicity to be quasinormal in the setting of the Hardy space. The result can also be generalized for a separable Hilbert space. As an application, we provide a complete characterization for quasinormality of a rank-one perturbation of the Hardy shift. - oai:arXiv.org:2512.06967v1 - math.FA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.GT + Wed, 10 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Susmita Das + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Stepan Alexandrov - Alternating Weighted Residual Flows and the Non-Commutative Gap - https://arxiv.org/abs/2512.06968 - arXiv:2512.06968v1 Announce Type: new -Abstract: This work develops a nonlinear analogue of alternating projections on Hilbert space, based on iterating a weighted residual transformation that removes the portion of an operator detected by a projection after conjugation by its square root. Although this map is neither linear nor variational and falls outside classical operator-mean frameworks, the alternating flow between two fixed projections is shown to be monotone and to converge strongly to a positive limit supported on their common kernel. The analysis identifies an intrinsic representation of this limit inside the operator range of the initial datum, which makes it possible to compare the nonlinear limit with the shorted operator of Anderson-Duffin-Trapp. The nonlinear flow always produces an operator dominated by the shorted operator, with equality precisely in the commuting regime. A global energy identity describes how mass is dissipated at each step of the iteration, and a factorized description localizes the gap between the nonlinear limit and the classical shorted operator. - oai:arXiv.org:2512.06968v1 - math.FA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new - http://creativecommons.org/licenses/by/4.0/ - James Tian + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Eric Bucher, Elizabeth Howard - On the Chow group of elliptic surfaces over number fields - https://arxiv.org/abs/2512.06970 - arXiv:2512.06970v1 Announce Type: new -Abstract: Let $X$ be a smooth projective surface over a number field $K$. Assume that $X$ has an elliptic fibration over $\mathbb{P}^1_K$ with at least one singular fibre and a section. Let $\mathcal{X}/U$ be a smooth projective model of $X$ over some open subset $U \subset \mathrm{Spec}(\mathcal{O}_K)$. We show that $\ker\bigl(\mathrm{CH}^2(\mathcal{X}) \rightarrow \mathrm{CH}^2(X)\bigr)$ is a finitely generated group. - oai:arXiv.org:2512.06970v1 - math.AG - math.NT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 new http://creativecommons.org/licenses/by/4.0/ - Domenico Valloni + Gabriele Benomio, Rita Teixeira da Costa - On-line Pick-Freeze Mirror algorithm for Sensitity Analysis - https://arxiv.org/abs/2512.06974 - arXiv:2512.06974v1 Announce Type: new -Abstract: The main objective of this paper is to propose a new approach for estimating the entire collection of Sobol' indices simultaneously. - Our approach exploits the fact that Sobol' indices can be rewritten as solutions to an optimization problem over the simplex of $\R^d$, to construct an online sequence of estimators using a stochastic mirror descent algorithm. We prove that our estimation procedure is consistent and provide a non-asymptotic upper bound for its rate of convergence. Furthermore, we demonstrate the numerical accuracy of our method and compare it with other classical estimation procedures. - oai:arXiv.org:2512.06974v1 - math.ST - stat.TH - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.FA + Wed, 10 Dec 2025 00:00:00 -0500 new http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Manon Costa, S\'ebastien Gadat, Xavier Gendre, Thierry Klein + Solesne Bourguin, Simon Campese - A duality approach to gradient H\"older estimates for linear divergence form elliptic equations - https://arxiv.org/abs/2512.06979 - arXiv:2512.06979v1 Announce Type: new -Abstract: We prove a sparse bound in the context of Schauder theory for divergence form elliptic partial differential equations. In addition, we show how an iteration argument inspired by sparse domination bounds can be used to deduce gradient reverse H\"older inequalities for equations with non-constant coefficients from the theory for constant coefficient equations. We deal with coefficient matrices whose entries are either H\"older continuous or just uniformly continuous, leading to different results. The purpose of the approach is to highlight the connection between Schauder theory and duality of local Hardy spaces and local H\"older spaces. - oai:arXiv.org:2512.06979v1 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Olli Saari, Yuanlin Sun, Hua-Yang Wang, Yuanhong Wei - - - Bell Numbers and Stirling Numbers of the Mycielskian of Trees - https://arxiv.org/abs/2512.06980 - arXiv:2512.06980v1 Announce Type: new -Abstract: We establish explicit formulas for Bell numbers and graphical Stirling numbers of complete multipartite graphs, complete bipartite graphs with removed perfect matchings, and Mycielskian trees. For complete multipartite graphs $K(n_1,\ldots,n_\ell)$, we provide a simplified proof that $B(G) = \prod_{i=1}^\ell \bell{n_i}$. We derive $B(K_{n,n} - M) = \sum_{k=0}^{n} \binom{n}{k} \bell{k}^2$ for removed perfect matching $M$, and for Mycielskian star graphs, $B(M(St_n); 3) = 2^n + 1$ and $B(M(St_n); 2n) = 2n^2 - 3n + 3$. Results extend to Mycielskians of arbitrary trees. Our computational verifications establish links between graphical Bell numbers and fundamental sequences in combinatorics and pattern avoidance, including identification of several OEIS entries: A000051, A096376, A116735, A384980, A384981, A384988, A385432, and A385437. - oai:arXiv.org:2512.06980v1 - math.CO - cs.DM - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - J. Allagan, G. Morgan, D. Sinclair + Shi Chen, Michael V. Klibanov, Kevin McGoff, Trung Truong, Wangjiaxuan Xin, Shuhua Yin - Infinite Dimensional Multifractal Analysis of the Wiener measure - https://arxiv.org/abs/2512.06984 - arXiv:2512.06984v1 Announce Type: new -Abstract: We present a multifractal formalism for measures on infinite dimensional metric spaces, in terms of scales instead of dimensions in the classical multifractal analysis. We prove a multifractal formalism with a suitable scaling, called order, for the Wiener measure, which is the probability law of the standard Brownian motion. We also prove the fundamental Frostman Lemma on a large class of Polish spaces, for which the increasing sets lemma holds. - oai:arXiv.org:2512.06984v1 + 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 - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 new - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Aihua Fan, Mathieu Helfter + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Martin Friesen, Stefan Gerhold, Kristof Wiedermann - Exploring baby Julia sets in parameter space slices for Generalized McMullen Maps - https://arxiv.org/abs/2512.06992 - arXiv:2512.06992v1 Announce Type: new -Abstract: For the family of complex rational functions of the form R(z)= z^n + a/z^n+b, known as "Generalized McMullen maps", for non-zero a, and integer n fixed and at least 3, we describe the apparent phenomena of baby Julia sets in parameter space appearing both in slices with independent critical orbits and a slice defined by imposing a critical orbit relation. - Specifically, we introduce the subfamily where one of two critical orbits is set to be a super-attracting fixed point, provide some general results on this subfamily and describe how Julia set copies in the parameter space slice occur--due to parameters for which the other critical orbit is in the (not immediate) basin of attraction of this fixed critical point. We provide several conjectures on this intriguing phenomena to catalyze further study. - oai:arXiv.org:2512.06992v1 - math.DS - Tue, 09 Dec 2025 00:00:00 -0500 + 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://creativecommons.org/licenses/by-nc-sa/4.0/ - Suzanne Boyd, Kelsey Brouwer, Matthew Hoeppner + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Guanjun Pan, Hong-Ming Yin - Cell-free ISAC for Drone Detection Considering Coverage and Age of Sensing - https://arxiv.org/abs/2512.06998 - arXiv:2512.06998v1 Announce Type: new -Abstract: The growing presence of unauthorized drones poses significant threats to public safety, underscoring the need for aerial surveillance solutions. This work proposes a cell-free integrated sensing and communication (ISAC) framework enabling drone detection within the existing communication network infrastructure, while maintaining communication services. The system exploits the spatial diversity and coordination of distributed access points (APs) in a cell-free massive MIMO architecture to detect aerial passive targets. To evaluate sensing performance, we introduce two key metrics: age of sensing (AoS), capturing the freshness of sensing information, and sensing coverage. The proposed AoS metric includes not only the transmission delays as in the existing models, but also the processing for sensing and networking delay, which are critical in dynamic environments like drone detection. We introduce an ambiguity parameter quantifying the similarity between the target-to-receiver channels for two hotspots and develop a novel network configuration strategy, including hotspot grouping, AP clustering, and sensing pilot assignment, leveraging simultaneous multi-point sensing to minimize AoS. Our results show that the best trade-off between AoS and sensing coverage is achieved when the number of hotspots sharing the same time/frequency resource matches the number of sensing pilots, indicating ambiguity as the primary factor limiting the sensing performance. - oai:arXiv.org:2512.06998v1 - cs.IT - math.IT - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Zinat Behdad, Ozan Alp Topal, Cicek Cavdar + 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 + 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 - On formal deformations and degenerations of evolution algebras - https://arxiv.org/abs/2512.07002 - arXiv:2512.07002v1 Announce Type: new -Abstract: The main purpose of this paper is to study formal deformations of evolution algebras, determining their existence and classifying them up to equivalence. In addition, we examine degenerations in this setting and provide Hasse diagrams that describe the degeneration relations among nilpotent evolution algebras of dimensions up to four. - oai:arXiv.org:2512.07002v1 - math.RA - Tue, 09 Dec 2025 00:00:00 -0500 - new + 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/ - Abdenacer Makhlouf, Andr\'es P\'erez-Rodr\'iguez + Quentin Vigneron, Hamed Barzegar - Extreme Values in Closed Networks - https://arxiv.org/abs/2512.07003 - arXiv:2512.07003v1 Announce Type: new -Abstract: For a widely used hub-and-spoke closed product-form network consisting of an infinite-server node and several single-server queues, we characterize the maximum queue-length distribution in various operational regimes by leveraging a novel probabilistic representation of the joint queue-length distribution and scaling where the number of customers grows. In these limiting regimes, we derive explicit characterizations of the maximum that are asymptotically equivalent to the maximum of independent random variables with the same geometric marginal distribution as queue lengths. In particular, when both the number of customers and queues grow, the parameters of the marginal distribution depend on the global characteristics of the network and are explicitly computed from a quadratic equation that arises from the corresponding large-deviation rate functions. Explicit computation of global characteristics of product-form distribution beyond the marginals, e.g., the maximum, appears novel, and our methodology may apply to other global measures of interest. - oai:arXiv.org:2512.07003v1 + 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 - Tue, 09 Dec 2025 00:00:00 -0500 - new + stat.CO + Wed, 10 Dec 2025 00:00:00 -0500 + cross http://creativecommons.org/licenses/by/4.0/ - Predrag Jelenkovic, Petar Momcilovic + Daniele Avitabile, Gabriel J. Lord, Khadija Meddouni - Combinatorial proofs of totals of some statistics on Catalan words - https://arxiv.org/abs/2512.07008 - arXiv:2512.07008v1 Announce Type: new -Abstract: A Catalan word is one on the alphabet of positive integers starting with $1$ in which each subsequent letter is at most one more than its predecessor. Let $\mathcal{C}_n$ denote the set of Catalan words of length $n$. In this paper, we give combinatorial proofs of explicit formulas for the sums of several parameter values taken over all the members of $\mathcal{C}_n$. In particular, we find such proofs for the parameters tracking the number of symmetric or $\ell$-valleys, which was previously requested by Baril et al. Further, we find a combinatorial explanation of a related Catalan number identity whose proof was also requested. To carry out our arguments, we consider corresponding statistics on Dyck paths and find the cardinality of certain sets of marked Dyck paths wherein one or more of the steps is distinguished from all others. - oai:arXiv.org:2512.07008v1 - math.CO - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Mark Shattuck + 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 + cross + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Tao Wang, Cyril Touz\'e, Haiqin Li, Qian Ding - Some unipotent Arthur packets for p-adic split F4 - https://arxiv.org/abs/2512.07014 - arXiv:2512.07014v1 Announce Type: new -Abstract: Let $G(k)$ be the split form of the simple exceptional p-adic group of type $F_4$, and let $\mathcal O = F_4(a_3)$ be the minimal distinguished nilpotent orbit. Our main result concerns the class of unipotent representations with cuspidal support at infinitesimal character $\Lambda$ determined by $\mathcal O$. These representations are parameterized by local systems, $\{(S, \mathcal L)\}$. We compute the characteristic cycles of the perverse sheaves $\text{IC}(S, \mathcal L)$ and determine all micro-packets in the sense of [Vo93]. In [CMBO24], the authors introduced a notion of weak Arthur packets in the p-adic setting. They conjectured that weak Arthur packets are unions of Arthur packets, in an appropriate sense. We verify that weak Arthur packets are unions of micro-packets. - oai:arXiv.org:2512.07014v1 - math.RT - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Leticia Barchini, Andr\'as C. L\H{o}rincz + 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 - Some inequalities for Gurland's ratio of the gamma functions - https://arxiv.org/abs/2512.07028 - arXiv:2512.07028v1 Announce Type: new -Abstract: This paper investigates the classical Gurland ratio of the gamma function and introduces its modified form, $\mathcal{G}^{\star}(x,y)$, which is particularly amenable to analytic expansions. By utilizing the Weierstrass product representation of the gamma function, we derive a finite expansion for the logarithm of $\mathcal{G}^{\star}(x,y)$ involving the Hurwitz zeta function. Explicit upper bounds for the remainder term are established, providing a rigorous basis for convergence analysis. As a direct consequence, we obtain new bilateral inequalities for the Gurland ratio and demonstrate the existence of a specific parameter $t(x,y)$ related to the Mean Value Theorem. Furthermore, we formulate open problems regarding the optimal localization of this parameter. These results extend the classical works of Gurland, Gautschi, and Merkle, offering new insights into the asymptotic behavior of gamma function ratios. - oai:arXiv.org:2512.07028v1 - math.CA - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Halina Wisniewska - - - Flexibility of affine spherical varieties - https://arxiv.org/abs/2512.07031 - arXiv:2512.07031v1 Announce Type: new -Abstract: We prove that the automorphism group $\mathrm{Aut}(X)$ of an affine spherical variety $X$ acts transitively on the set of smooth points $X^{reg}.$ If every invertible regular function on $X$ is constant, we prove that $X$ is flexible, i.e., the subgroup of $\mathrm{Aut}(X)$ generated by all $\mathbb{G}_a$-subgroups acts transitively on $X^{reg}.$ - oai:arXiv.org:2512.07031v1 - math.AG - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Anton Shafarevich - - - A toolbox for left-orders of low complexity - https://arxiv.org/abs/2512.07035 - arXiv:2512.07035v1 Announce Type: new -Abstract: This thesis explores how concepts of formal language theory can be used to study left-orderable groups. It analyses the languages formed by their positive cones and demonstrates how the abstract families of languages (AFLs) in the Chomsky hierarchy (in particular regular and context-free languages) interact with core group-theoretic constructions under subgroups, extensions, finite generation and taking direct products with $\mathbb{Z}$. These investigations yield new insights into the interplay between decidability and geometry in group theory. - Some results which may be improvements to the existing literature are included in the thesis. There is a classification of the complexity of positive cones of $\mathbb{Z}^2$, a more constructive proof on finding regular positive cone languages of language-convex subgroups compared to a result of Su (2020), a construction of countably infinite many regular positive cones of $\mathrm{BS}(1,q)$ for $q \geq -1$ which are all automorphic to each other extending a result of Antol\'in, Rivas, and Su (2022), and a construction of positive cones with finite generating set for groups of the form $F_{2n} \times \mathbb{Z}$ extending a result of Malicet, Mann, Rivas, and Triestino (2019). - oai:arXiv.org:2512.07035v1 - math.GR - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Hang Lu Su - - - Anisotropic min-max via phase transitions - https://arxiv.org/abs/2512.07039 - arXiv:2512.07039v1 Announce Type: new -Abstract: We develop a PDE-based approach to the min-max construction of nontrivial integer rectifiable varifolds that are stationary with respect to anisotropic surface energies on closed Riemannian manifolds, in codimension one. Specifically, we study the anisotropic analogue of the Allen-Cahn energy and establish a Modica-type gradient bound for its critical points. Using this in conjunction with certain estimates for stable solutions, we then prove that the energy densities of stable or bounded-Morse-index critical points of its rescalings concentrate along an integer rectifiable varifold that is stationary for the underlying anisotropic integrand. As a consequence, we construct a (possibly singular) anisotropic min-max hypersurface via Allen-Cahn, obtaining an analogue of the result of Hutchinson-Tonegawa in the anisotropic setting. - oai:arXiv.org:2512.07039v1 - math.DG - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Antonio De Rosa, Alessandro Pigati - - - Set-based Optimal, Robust, and Resilient Control with Applications to Autonomous Precision Landing - https://arxiv.org/abs/2512.07043 - arXiv:2512.07043v1 Announce Type: new -Abstract: We present a real-time-capable set-based framework for closed-loop predictive control of autonomous systems using tools from computational geometry, dynamic programming, and convex optimization. The control architecture relies on the offline precomputation of the controllable tube, i.e, a time-indexed sequence of controllable sets. Sets are represented using constrained zonotopes (CZs), which are efficient encodings of convex polytopes that support fast set operations and enable tractable dynamic programming in high dimensions. Online, we obtain a globally optimal control profile by solving a series of one-step optimal control problems. Our key contributions are: (1) free-final-time optimality: we devise an optimal horizon computation algorithm to achieve global optimality; (2) robustness: we handle stochastic uncertainty in both the state and control, with probabilistic guarantees, by constructing bounded disturbance sets; (3) resilience: we develop (i) an optimization-free approach to computing the instantaneous reachable set, i.e., the reachable set from the current state, to enable, for example, large/maximal divert maneuvers, and (ii) an approach to achieving maximal decision-deferral, i.e., maintaining reachability/divert-feasibility to multiple targets for as long as possible. By means of an autonomous precision landing case study, we demonstrate globally optimal free-final-time guidance, robustness to navigation and actuation uncertainties, instantaneous divert envelope computation, and maximal decision-deferral. - oai:arXiv.org:2512.07043v1 - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Abhinav G. Kamath, Abraham P. Vinod, Purnanand Elango, Stefano Di Cairano, Avishai Weiss - - - A new improvement to the Overfull Conjecture - https://arxiv.org/abs/2512.07044 - arXiv:2512.07044v1 Announce Type: new -Abstract: Let $G$ be a simple graph with order $n$, maximum degree $\D(G)$, minimum degree $\delta(G)$ and chromatic index $\chi'(G)$, respectively. A graph $G$ is called {\em $\D$-critical} if $\chi'(G)=\D(G)+1$ and $\chi'(H)\textless \chi'(G)$ for every proper subgraph $H$ of $G$, and $G$ is overfull if $\left|E(G)\right|>\Delta(G)\lfloor n/2\rfloor$. In 1986, Chetwynd and Hilton proposed the Overfull Conjecture: Every $\D$-critical graph $G$ with $\D(G)\textgreater\frac{n}{3}$ is overfull. The Overfull Conjecture has many implications, such as that it implies a polynomial-time algorithm for determining the chromatic index of graphs $G$ with $\D(G)\textgreater\frac{n}{3}$, and implies several longstanding conjectures in the area of graph edge coloring. Recently, Cao, Chen, Jing and Shan (SIAM J. Discrete Math. 2022) verified the Overfull Conjecture for $\D(G)-7\delta(G)/4\ge (3n-17)/4$. In this paper, we improve it for $\D(G)-5\delta(G)/3\ge (2n-7)/3$. - oai:arXiv.org:2512.07044v1 - math.CO - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Xuli Qi, Chunhui Ge, Yanrui Feng - - - Minimizing Control Attention:The Linear Gauss-Markov paradigm - https://arxiv.org/abs/2512.07046 - arXiv:2512.07046v1 Announce Type: new -Abstract: We revisit the concept of `attention' as a technical term to quantify the effort in calibrating control action based on available data. While Wiener, in his work on Cybernetics, anticipated key principles on prioritizing task-relevant signals, it was not until the late 1990's when Brockett first formulated pertinent optimization problems that have inspired subsequent as well as the present work. `Attention,' as a technical term, is defined so as to quantify the dependence of the control law on the time and space/state coordinate; a control law that is independent of time and space, assuming it meets specifications, requires vanishing attention. In the present work we focus on Linear-Markovian dynamics with Gaussian state uncertainty so as to analyze the structure of minimal-attention control schemes that steer the dynamics between terminal states with Gaussian uncertainty profile. - oai:arXiv.org:2512.07046v1 - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Ralph Sabbagh, Asmaa Eldesoukey, Mahmoud Abdelgalil, Tryphon T. Georgiou - - - A Geometric Theory of Surface Elasticity and Anelasticity - https://arxiv.org/abs/2512.07056 - arXiv:2512.07056v1 Announce Type: new -Abstract: In this paper we formulate a geometric theory of elasticity and anelasticity for bodies containing material surfaces with their own elastic energies and distributed surface eigenstrains. Bulk elasticity is written in the language of Riemannian geometry, and the framework is extended to material surfaces by using the differential geometry of hypersurfaces in Riemannian manifolds. Within this setting, surface kinematics, surface strain measures, surface material metric, and the induced second fundamental form follow naturally from the embedding of the material surface in the material manifold. The classical theory of surface elasticity of Gurtin and Murdoch (1975) is revisited and reformulated in this geometric framework, and then extended to anelastic bodies with anelastic material surfaces. Constitutive equations for isotropic and anisotropic material surfaces are formulated systematically, and bulk and surface anelasticity are introduced by replacing the elastic metrics with their anelastic counterparts. The balance laws are derived variationally using the Lagrange-d'Alembert principle. These include the bulk balance of linear momentum together with the surface balance of linear momentum, whose normal component gives a generalized Laplace's law. As an application, we obtain the complete solution for a spherical incompressible isotropic solid ball containing a cavity filled with a compressible hyperelastic fluid, where the cavity boundary is an anelastic material surface with distributed surface eigenstrains. The analytical and numerical results quantify the effects of surface and fluid eigenstrains on the pressure-stretch response and residual stress. - oai:arXiv.org:2512.07056v1 - math-ph - math.MP - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Arash Yavari - - - Blown-up singular Riemannian foliations - https://arxiv.org/abs/2512.07069 - arXiv:2512.07069v1 Announce Type: new -Abstract: In this paper we investigate new properties of the blow-up desingularization method in the context of singular Riemannian foliations. First, we relate the dynamics of such a foliation, which is governed by the so called Molino sheaf, with that of its blow-up. In the particular case of singular Killing foliations, this leads to a strong constraint under mild topological assumptions: namely, the leaves of such foliations are all closed, provided the Euler characteristic of its ambient manifold is non-vanishing and its singular strata are all odd-codimensional. Next, we relate the basic cohomology of a singular Riemannian foliation with that of its blow-up, generalizing well-known, classical analogous results in algebraic and complex geometry. Finally, we show that the space of leaf closures of a singular Killing foliation is the Gromov--Hausdorff limit of a sequence of orbifolds, whose dimensions are the codimension of the foliation. - oai:arXiv.org:2512.07069v1 - math.DG - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Francisco C. Caramello Jr., Laura Ribeiro dos Santos - - - Left regular bands with symmetry - https://arxiv.org/abs/2512.07070 - arXiv:2512.07070v1 Announce Type: new -Abstract: The representation theory of left regular band semigroup algebras is well-studied and known to have close connections with combinatorial topology, as established in the work of Margolis--Saliola--Steinberg ('15, '21). In this paper, we investigate the representation theory of the invariant subalgebras of left regular band semigroup algebras carrying the action of a finite group through the lens of group-equivariant combinatorial topology. - We characterize when the invariant subalgebra is semisimple or commutative and examine the equivariant structure of the Peirce components of the semigroup algebra. For CW left regular bands, we interpret these Peirce components in terms of the equivariant topology of intervals in the support semilattice, yielding the Cartan invariants of the invariant subalgebras of left regular bands associated to CAT(0)-cube complexes. We also give a topological formula for the Peirce components for left regular bands with hereditary algebras. Finally, in specializing to left regular bands associated to geometric lattices, we explore generalizations of the Desarm\'{e}ni\'{e}n--Wachs derangement representation and their connections to Markov chains. - oai:arXiv.org:2512.07070v1 - math.CO - math.GR - math.RT - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Patricia Commins, Benjamin Steinberg - - - Modulation approximation for the non-isentropic Euler-Poisson system - https://arxiv.org/abs/2512.07071 - arXiv:2512.07071v1 Announce Type: new -Abstract: As a formal approximation, the nonlinear Schr\"{o}dinger (NLS) equation can be derived to describe the evolution of the envelopes of small oscillating wave packets-like solutions to the Euler-Poisson system. In this paper we rigorously justify that the wave packets for the non-isentropic Euler-Poisson system can be approximated by solutions of the NLS equation over a physically relevant $\mathcal{O}(\epsilon^{-2})$ time scale. Besides the difficulties such as resonances at $k=0$ and $k=\pm k_0$ and loss of derivatives arising in the modulation approximation problem in the isentropic Euler-Poisson system, new difficulties arise in the non-isentropic case. In the non-isentropic Euler-Poisson system, new resonances at wave number $k=\pm 2k_0$ appear which necessitate rescaling the correction to the modulation approximation differently for different wave numbers. In addition, it is more difficult to obtain the uniform estimates for the error $(R_{0},R_{1},R_{-1})$ between the real solutions and the approximate solutions, due to the extra interactions with the temperature. To overcome the difficulties aroused by resonances and loss of derivatives, we find several important structural identities between the diagonalized unknowns and apply a series of normal-form transforms, to obtain uniform estimates for the error over the desired $\mathcal{O}(\epsilon^{-2})$ long time scale. - oai:arXiv.org:2512.07071v1 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Huimin Liu, Xueke Pu - - - Lipschitz stability for an inverse problem of a fully-discrete stochastic hyperbolic equation - https://arxiv.org/abs/2512.07072 - arXiv:2512.07072v1 Announce Type: new -Abstract: In this paper, we investigate a discrete inverse problem of determining three unknowns, i.e. initial displacement, initial velocity and random source term, in a fully discrete approximation of one-dimensional stochastic hyperbolic equation. We firstly prove a new Carleman estimate for the fully-discrete stochastic hyperbolic equation. Based on this Carleman estimate, we then establish a Lipschitz stability for this discrete inverse problem by the discrete spatial derivative data at the left endpoint and the measurements of the solution and its time derivative at the final time. Owing to the discrete setting, an extra term with respect to mesh size arises in the right-hand side of the stability estimate. - oai:arXiv.org:2512.07072v1 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Bin Wu, Xu Zhu, Wenwen Zhou, Zewen Wang - - - A new generalization of the McKay conjecture for $p$-solvable groups - https://arxiv.org/abs/2512.07073 - arXiv:2512.07073v1 Announce Type: new -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 heavily depend on the theory of self-stabilizing pairs developed by M. L. Lewis, as well as some results of $p$-special characters due to I. M. Isaacs. - oai:arXiv.org:2512.07073v1 - math.GR - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/publicdomain/zero/1.0/ - Huimin Chang, Ping Jin - - - Degenerate Complex Hessian type equations on compact Hermitian manifolds and Applications - https://arxiv.org/abs/2512.07084 - arXiv:2512.07084v1 Announce Type: new -Abstract: The aim of this paper is to further develop the theory of the degenerate complex Hessian equations on compact Hermitian manifolds. Building upon the generalization of the Bedford-Taylor pluripotential theory to complex Hessian equations by Ko\l odziej-Nguyen, we solve these equations in the $(\omega, m)$-positive cone, $(\omega, m)$-big classes and in nef classes, where $\omega$ is a reference Hermitian metric. These results are also new in the K\"ahler case. Moreover, we adapt our techniques to solve complex Monge-Amp\`ere equations in nef classes with mild singularities. The solutions we obtain, in the compact K\"ahler case, coincide with those for the complex Monge-Amp\`ere equations in the sense of the non-pluripolar product introduced by Boucksom-Eyssidieux-Guedj-Zeriahi. One of the key ingredients in the proof is the adaption, to the Hermitian setting, of a new a priori $L^\infty$-estimate established by Guo-Phong-Tong and Guo-Phong-Tong-Wang. - oai:arXiv.org:2512.07084v1 - math.CV - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Kai Pang, Haoyuan Sun, Zhiwei Wang, Xiangyu Zhou - - - An Accelerated Primal Dual Algorithm with Backtracking for Decentralized Constrained Optimization - https://arxiv.org/abs/2512.07085 - arXiv:2512.07085v1 Announce Type: new -Abstract: We propose a distributed accelerated primal-dual method with backtracking (D-APDB) for cooperative multi-agent constrained consensus optimization problems over an undirected network of agents, where only those agents connected by an edge can directly communicate to exchange large-volume data vectors using a high-speed, short-range communication protocol, e.g., WiFi, and we also assume that the network allows for one-hop simple information exchange beyond immediate neighbors as in LoRaWAN protocol. The objective is to minimize the sum of agent-specific composite convex functions over agent-specific private constraint sets. Unlike existing decentralized primal-dual methods that require knowledge of the Lipschitz constants, D-APDB automatically adapts to local smoothness by employing a distributed backtracking step-size search. Each agent relies only on first-order oracles associated with its own objective and constraint functions and on local communications with the neighboring agents, without any prior knowledge of Lipschitz constants. We establish $\mathcal{O}(1/K)$ convergence guarantees for sub-optimality, infeasibility and consensus violation, under standard assumptions on smoothness and on the connectivity of the communication graph. To our knowledge, when nodes have private constraints, especially when they are nonlinear convex constraints onto which projections are not cheap to compute, D-APDB is the first distributed method with backtracking that achieves the optimal convergence rate for the class of constrained composite convex optimization problems. We also provide numerical results for D-APDB on a distributed QCQP problem illustrating the potential performance gains that can be achieved by D-APDB. - oai:arXiv.org:2512.07085v1 - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Qiushui Xu, Necdet Serhat Aybat, Mert G\"urb\"uzbalaban - - - The Equational Theories Project: Advancing Collaborative Mathematical Research at Scale - https://arxiv.org/abs/2512.07087 - arXiv:2512.07087v1 Announce Type: new -Abstract: We report on the Equational Theories Project (ETP), an online collaborative pilot project to explore new ways to collaborate in mathematics with machine assistance. The project successfully determined all 22 028 942 edges of the implication graph between the 4694 simplest equational laws on magmas, by a combination of human-generated and automated proofs, all validated by the formal proof assistant language Lean. As a result of this project, several new constructions of magmas satisfying specific laws were discovered, and several auxiliary questions were also addressed, such as the effect of restricting attention to finite magmas. - oai:arXiv.org:2512.07087v1 - math.RA - cs.LO - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Matthew Bolan, Joachim Breitner, Jose Brox, Nicholas Carlini, Mario Carneiro, Floris van Doorn, Martin Dvorak, Andr\'es Goens, Aaron Hill, Harald Husum, Hern\'an Ibarra Mejia, Zoltan Kocsis, Bruno Le Floch, Amir Livne Bar-on, Lorenzo Luccioli, Douglas McNeil, Alex Meiburg, Pietro Monticone, Pace P. Nielsen, Emmanuel Osalotioman Osazuwa, Giovanni Paolini, Marco Petracci, Bernhard Reinke, David Renshaw, Marcus Rossel, Cody Roux, J\'er\'emy Scanvic, Shreyas Srinivas, Anand Rao Tadipatri, Terence Tao, Vlad Tsyrklevich, Fernando Vaquerizo-Villar, Daniel Weber, Fan Zhen - - - Incompressible 2D Euler equations with non-decaying random initial vorticity - https://arxiv.org/abs/2512.07096 - arXiv:2512.07096v1 Announce Type: new -Abstract: Consider a random initial vorticity $\omega_0(x) = \sum_{n\in \mathbb{Z}^2} a_n \phi(x-n)$, where $\phi$ is bounded and compactly supported and $\{a_n\}$ are independent, uniformly bounded, mean $0$, variance $1$ random variables (i.e. $\omega_0$ is an array of randomly weighted vortex blobs). We prove global well-posedness of weak solutions to the Euler equations in $\mathbf{R}^2$ for almost every such initial vorticity. The main contribution of our work is the construction of a corresponding initial velocity field that grows slowly at infinity, which enables us to apply a recent well-posedness result of Cobb and Koch. - oai:arXiv.org:2512.07096v1 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Gautam Iyer, Milton C. Lopes Filho, Helena J. Nussenzveig Lopes - - - Regular Functions on Formal-Analytic Arithmetic Surfaces - https://arxiv.org/abs/2512.07098 - arXiv:2512.07098v1 Announce Type: new -Abstract: In this paper, we prove for a broad class of pseudo convex formal-analytic arithmetic surfaces, those which admit a nonconstant monic such regular function, a conjecture of Bost-Charles that the ring of regular functions has continuum cardinality. A key feature of the proof is a new formula for the pushforward of the equilibrium Green's functions for our bordered Riemann surface with boundary by a holomorphic function, a formula which has constant term related to Arakelov degree. A Fekete-Sz\"ego-type approximation argument then produces a polynomial "large" relative to the regular function, which in turn yields continuum many distinct regular functions. - oai:arXiv.org:2512.07098v1 - math.CV - math.NT - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Samuel Goodman - - - Dynamics of multiplicative groups over fields and Folner-Kloosterman sums - https://arxiv.org/abs/2512.07106 - arXiv:2512.07106v1 Announce Type: new -Abstract: For two countably infinite fields whose multiplicative groups are isomorphic, we examine invariant couplings between the actions that these groups induce on the additive Pontryagin duals of the fields. We show that the actions are disjoint unless the fields themselves are isomorphic and the group isomorphism extends (possibly after a finite twist) to a field isomorphism. As an application, we establish equidistribution of F\o lner-Kloosterman sums - an extension of classical Kloosterman sums to infinite fields. Unlike the classical case over algebraic closures of finite fields, these averages exhibit an inherent multiplicative asymmetry, revealing new and fundamentally different behavior. Finally, we derive several combinatorial consequences, including results on sum-product phenomena and a Furstenberg--S\'ark\"ozy-type theorem for Laurent polynomials over general fields. - oai:arXiv.org:2512.07106v1 - math.DS - math.NT - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Michael Bj\"orklund, Alexander Fish - - - Compactness of Extremals for Singular Anisotropic Trudinger-Moser functionals on bounded domain - https://arxiv.org/abs/2512.07118 - arXiv:2512.07118v1 Announce Type: new -Abstract: In this paper, we investigate the compactness of extremal functions for a critical singular anisotropic Trudinger-Moser inequality established by Lu-Shen-Xue-Zhu\cite{ref1}. We prove by means of blow-up analysis that the extremals $u_{\beta}$ converge in $W_{0}^{1,n}(\Omega)\cap C^{1}(\overline{\Omega})$ to some function $u_{0}$ which achieves the supremum - \begin{equation} - \sup\limits_{u\in W_{0}^{1,n}(\Omega),\Vert u\Vert_{F(\Omega)}\leq1}\int_{\Omega}^{}e^{\tau_{n}\vert u\vert^{\frac{n}{n-1}}}dx,\notag - \end{equation} as $\beta\to 0$, where $\tau_{n}=n^{\frac{n}{n-1}}\kappa_{n}^{\frac{1}{n-1}}$, $\kappa_{n}$ denotes the volume of the unit Wulff ball in $\mathbb{R}^{n}$ and $\Vert u\Vert_{F(\Omega)}$ is the anisotropic norm of $u$. - oai:arXiv.org:2512.07118v1 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Weiwei Shan, Minbo Yang, Jiazheng Zhou - - - A revisit on the critical blow-up for semilinear wave equations in low space dimensions with slicing method - https://arxiv.org/abs/2512.07119 - arXiv:2512.07119v1 Announce Type: new -Abstract: In this reviewing paper, we are interested in the proof of estimating the lifespan of classical solutions of semilinear wave equations with the critical exponent from above especially in low space dimensions. There are a few ways to show the result by comparison argument with ODE via point-wise estimates, or by functional method via a weak form with a special choice of test functions. But in order to make a good much with the numerical analysis, we show a simple proof by iteration argument of a point-wise estimate of the solution with a slicing technique. - oai:arXiv.org:2512.07119v1 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Hiroyuki Takamura - - - A Newton-Okounkov Body Viewpoint on the SOS Conjecture - https://arxiv.org/abs/2512.07133 - arXiv:2512.07133v1 Announce Type: new -Abstract: Let $z\in \mathbb C^n$ be the complex coordinates on $\mathbb C^n$, and $A(z,\bar z)$ be a real-valued Hermitian polynomial. The famous Ebenfelt's SOS conjecture asks for the minimum rank of $A(z,\bar z)\|z\|^2$ under the restriction that $A(z,\bar z)\|z\|^2$ is an SOS. Assume that $A(z,\bar z)$ is bihomogeneous. In the present note, we establish a connection between Ebenfelt's (Weak) SOS Conjecture and the theory of Newton-Okounkov bodies. By reformulating the conjecture in terms of lattice semigroups and their associated Newton-Okounkov convex bodies, we transform the problem of finding the minimal rank of a prolonged sum-of-squares polynomial into an extremal problem in convex geometry. In particular, we prove that this minimal rank is attained at the extreme points of a specific Newton-Okounkov body. Furthermore, if $A(z,\bar z)$ is moreover diagonal, we demonstrate that the relevant extreme points are finitely many rational points, thereby reducing the verification of the conjecture to a computationally tractable problem. This work provides a new tool for attacking the SOS Conjecture. - oai:arXiv.org:2512.07133v1 - math.CV - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Zhiwei Wang, Chenlong Yue, Xiangyu Zhou - - - Rational points in Cantor sets in the complex plane - https://arxiv.org/abs/2512.07139 - arXiv:2512.07139v1 Announce Type: new -Abstract: Let $K$ be an imaginary quadratic field and let $\mathcal{O}_K$ be the ring of algebraic integers of $K$. For $\alpha \in \mathcal{O}_K$ with $|\alpha| > 1$, define \[ \mathcal{D}_\alpha = \bigcup_{n=0}^\infty \frac{\mathcal{O}_K}{\alpha^n}. \] For $\beta \in \mathcal{O}_K$ with $|\beta|>1$ and a finite subset $A \subset \mathcal{O}_K$, define \[ S_{\beta,A} = \bigg\{ \sum_{k=1}^{\infty} \frac{a_k}{\beta^k}: \; a_k \in A \;\forall k \in \mathbb{N} \bigg\}. \] Suppose that $\alpha$ and $\beta$ are relatively prime. In this paper, we show that if $\dim_{\mathrm{H}} S_{\beta,A} < 1$, then the intersection $\mathcal{D}_\alpha \cap S_{\beta,A}$ is a finite set. In general, the threshold for the Hausdorff dimension of $S_{\beta,A}$ is sharp. If we further assume that $\mathcal{O}_K$ is a unique factorization domain and that $\overline{\alpha}$ and $\alpha$ are relatively prime, then we establish the finiteness of the intersection under the weaker condition $\dim_{\mathrm{H}} S_{\beta,A} < 2$. This extends the previously known results on the real line. - oai:arXiv.org:2512.07139v1 - math.NT - math.CA - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Wenxia Li, Zhiqiang Wang, Jiuzhou Zhao - - - Toeplitz operators on weighted Fock spaces with $A_{\infty}$-type weights - https://arxiv.org/abs/2512.07145 - arXiv:2512.07145v1 Announce Type: new -Abstract: By establishing some reproducing kernel estimates, we characterize the bounded, compact and Schatten $p$-class Toeplitz operators with positive measure symbols on the weighted Fock space $F^2_{\alpha,w}$ for $p\geq1$, where $w$ is a weight on the complex plane satisfying an $A_{\infty}$-type condition. Applications to Volterra operators and weighted composition operators are given. - oai:arXiv.org:2512.07145v1 - math.FA - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jiale Chen - - - Recent Results On The Modulated Cubic Nonlinear Schr\"odinger Equation On $\mathbb{T}^2$ - https://arxiv.org/abs/2512.07147 - arXiv:2512.07147v1 Announce Type: new -Abstract: New Strichartz estimates for the modulated cubic nonlinear Schr\"{o}dinger equation are proved. These Strichartz estimates allow us to show that this equation is pathwise locally well-posed. We also show that improved Strichartz estimates are available in the case where the modulation is white noise. Additionally, we comment on a few basic properties of the modulated cubic nonlinear Schr\"{o}dinger equation such as conservation of mass and convergence of its linear flow as time tends to zero. - oai:arXiv.org:2512.07147v1 - math.AP - math.PR - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Josh Messing - - - Higgs bundle, isomonodromic leaves and minimal surfaces - https://arxiv.org/abs/2512.07152 - arXiv:2512.07152v1 Announce Type: new -Abstract: In this paper we give a gauge theoretic construction of the joint moduli space of stable G-Higgs bundles on closed Riemann surfaces, where the Riemann surface structure is allowed to vary in the Teichm\"uller space of the underlying smooth surface. This joint moduli space has many interesting structures that are preserved by the mapping class group of the surface. We describe a surprising relationship between four key objects: the isomonodromic foliation, a canonical hermitian form arising from the Atiyah-Bott-Goldman symplectic structure on the character variety, a canonical holomorphic form which vertically lifts vector fields on Teichm\"uller space, and the energy function for equivariant harmonic maps. One consequence of this work is the construction of pseudo-K\"ahler metrics on many examples of components of character varieties which include rank two higher Teichm\"uller spaces. This recovers some of the recent work on the subject by various authors. - oai:arXiv.org:2512.07152v1 - math.DG - math.AG - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Brian Collier, J\'er\'emy Toulisse, Richard Wentworth - - - Lorenz ordering of parasite loads across hosts in Isham's model of Host-Macroparasite Interaction - https://arxiv.org/abs/2512.07156 - arXiv:2512.07156v1 Announce Type: new -Abstract: In Isham's model of host-macroparasite interaction, parasite-induced host mortality increases parasite aggregation in the sense of the Lorenz order and related measures when the distribution of the number of parasites entering the host at infectious contacts is log-concave. Furthermore, in the presence of parasite-induce host mortality, the rate of parasite mortality may no longer have a monotone effect on aggregation. - oai:arXiv.org:2512.07156v1 - math.PR - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - R. McVinish - - - Top dickson class and annihilators of cohomology over invariant rings - https://arxiv.org/abs/2512.07157 - arXiv:2512.07157v1 Announce Type: new -Abstract: Let $\mathbb{F}_q$ denote the finite field with $q = p^r$ elements. Let $V$ be a finite dimensional vector space of dimension $d$ over $\mathbb{F}_q$ and let $G \subseteq GL(V)$ be a group. Let $R = \mathbb{F}_q[V] = \text{Sym}(V^*)$ and let $S = R^G$. - Let $\mathbf{d}_{d,0} $ be the top Dickson class, i.e., $\mathbf{d}_{d,0} = \prod_{0\neq v \in V^*}v$. Surprisingly (a power of) $\mathbf{d}_{d,0}$ annihilates many cohomological modules. - (a) Let $H^i(G, R)$ be the $i^{th}$-group cohomology of $R$ considered as a $S$-module. Set $J_i = \text{ann}_S \ H^i(G, R)$. We show that $\mathbf{d}_{d,0} \in \sqrt{J_i}$ for all $i \geq 1$. - (b) We also show that $\mathbf{d}_{d,0} \in \sqrt{ \text{ann}_S \ H^j_{S_+}(S)}$ for all $ 0 \leq j \leq d - 1$ (here $H^j_{S_+}(S)$ is the $j^{th}$ local cohomology of $S$ with respect to $S_+$). - As an application we get that there exists a fixed power of $\mathbf{d}_{d,0} $ which works as a cohomological annihilator. - oai:arXiv.org:2512.07157v1 - math.AC - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Tony J. Puthenpurakal - - - Stability for Strichartz inequalities: Existence of minimizers - https://arxiv.org/abs/2512.07174 - arXiv:2512.07174v1 Announce Type: new -Abstract: We study the quantitative stability associated to the adjoint Fourier restriction inequality, focusing on the paraboloid and two-dimension sphere cases. We show that these Strichartz-stability inequalities admit minimizers attaining their sharp constants, on the condition that these sharp constants are strictly smaller than the corresponding spectral-gap constants. Furthermore, for the two-dimension sphere case, we obtain the existence of minimizers. - oai:arXiv.org:2512.07174v1 - math.CA - math.AP - math.FA - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Boning Di, Dunyan Yan - - - Coarse spaces for virtual element methods on irregular 3D subdomain decompositions - https://arxiv.org/abs/2512.07181 - arXiv:2512.07181v1 Announce Type: new -Abstract: We present a two-level overlapping Schwarz preconditioner for three-dimensional problems discretized with the Virtual Element Method. Our approach handles general polyhedral meshes and irregular subdomains, extending the applicability of previous methods. Numerical experiments show robust performance with respect to the number of subdomains and mesh parameters, with condition-number bound comparable to classical finite element results. While alternative methods such as FETI-DP and BDDC are available, the simplicity and competitiveness of overlapping additive Schwarz methods underscore the practical significance of our contribution. - oai:arXiv.org:2512.07181v1 - math.NA - cs.NA - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Ana Aguilar-Pineda, Luis F. Amey, Adrian Angulo-Paniagua, Juan G. Calvo - - - Hitting Probabilities for Hypoelliptic Differential Equations Driven by Fractional Brownian Motion - https://arxiv.org/abs/2512.07202 - arXiv:2512.07202v1 Announce Type: new -Abstract: The main goal of this article is to derive a two-sided estimate for hitting probabilities of a hypoelliptic stochastic differential equation (SDE) driven by fractional Brownian motion (fBM) with Hurst parameter $H\in(1/4,1)$ in terms of Newtonian-type capacities that are defined with respect to the (sub-Riemannian) control distance associated with the vector fields. As a starting point, we first establish the existence and smoothness of joint densities for the finite-dimensional distributions of the solution in the general context of hypoellitpic SDEs driven by Gaussian rough paths. We then turn to the fBM setting and derive a local upper bound for the joint density in terms of the control distance. As an application of these results, we establish our main estimate on hitting probabilities which generalises a well-known elliptic result of \cite{BNOT} to the hypoelliptic case. - oai:arXiv.org:2512.07202v1 - math.PR - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/publicdomain/zero/1.0/ - Xi Geng, Sheng Wang - - - Metric diophantine approximation on fractals - https://arxiv.org/abs/2512.07204 - arXiv:2512.07204v1 Announce Type: new -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:2512.07204v1 - math.NT - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - James Wyatt - - - Automorphisms of Sedenions - https://arxiv.org/abs/2512.07210 - arXiv:2512.07210v1 Announce Type: new -Abstract: This paper extends the seven-dimensional Fano plane to a 15-dimensional Fano volume, which is related to sedenions. The Fano plane visualises the octonions and their structure as seven quaternions and is derived from a calibration in differential geometry. Clifford algebra allows the Spin and Pin groups to fully analyse calibrations and a new calibration is created that derives the Fano volume, which provides a visualisation of the complete subalgebra structure of sedenions. - This new 15-dimensional calibration, along with the existing one containing 35 quaternions, enables an explicit derivation of the automorphisms of sedenions matching Schafer's result and hence addresses a discrepancy in the literature. Also, Gresnigt has suggested extending Furey's work on quark and lepton families using octonions to three octonion subalgebras of sedenions. The Fano volume allows this process to avoid the power-associative subalgebras of sedenions. It is conjectured that Fano hyper-volumes will uncover the complete subalgebra structure of all Cayley-Dickson algebras. - oai:arXiv.org:2512.07210v1 - math.RA - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by-nc-sa/4.0/ - G. P. Wilmot - - - Iterative Switching Time Optimization for Mixed-integer Optimal Control Problems - https://arxiv.org/abs/2512.07213 - arXiv:2512.07213v1 Announce Type: new -Abstract: This paper proposes an iterative method to solve Mixed-Integer Optimal Control Problems arising from systems with switched dynamics. The so-called relaxed problem plays a central role within this context. Through a numerical example, it is shown why relying on the relaxed problem can lead the solution astray. As an alternative, an iterative Switching Time Optimization method is proposed. The method consists of two components that iteratively interact: a Switching Time Optimization (STO) problem and a sequence optimization. Each component is explained in detail, and the numerical example is resolved, the results of which shows the efficiency of the proposed algorithm. Finally, the advantages and disadvantages of the method are discussed and future lines of research are sketched. - oai:arXiv.org:2512.07213v1 - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - 10.23919/ECC57647.2023.10178419 - Ramin Abbasi-Esfeden, Wim Van Roy, Jan Swevers - - - Sterile Insect Technique in a n-patch system with Allee effect and mass trapping: modeling, analysis and simulations - https://arxiv.org/abs/2512.07225 - arXiv:2512.07225v1 Announce Type: new -Abstract: The sterile insect technique (SIT) is a biological control method aimed at reducing or eliminating populations of pests or disease vectors. This technique involves releasing sterilised insects which, by mating with wild individuals, will reduce the target population. In this study, we take into account the spatial dimension by modelling the pest/vector population as being distributed over several plots, with wild insects and sterile insects migrating between these plots. The main objective is to identify the critical plots for intervention, using the network connectivity and potential intervention constraints. - Using results from monotone systems theory, we first derive a sufficient condition guaranteeing the elimination of the wild population through SIT, which relies on the sign of the Perron value of a certain Metzler matrix. When an Allee effect is naturally present, releases are finite in time, and an upper bound of the control time is provided. We then formulate an optimisation problem aimed at minimising the total daily number of sterile insects released to ensure population elimination. We focus in particular on the oriental fruit fly, which significantly impacts mango orchards in La R\'eunion. - Through numerical simulations, we illustrate our theoretical results and study different scenarios, including some where releases are limited to certain orchards. Indeed, when implementing SIT in the field, some owners may be reluctant to allow releases on their property. We also consider additional control by mass trapping, which can affect the sterile insects entering trapped areas, and show that although it increases the critical number of sterile insects to be released daily, it reduces the duration of the SIT program. Mass trapping may thus decrease the total number of sterile insects released over the entire elimination program. - oai:arXiv.org:2512.07225v1 - math.DS - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Pierre-Alexandre Bliman, Manon de la Tousche, Yves Dumont - - - Disjointly almost trivial unbounded functionals - https://arxiv.org/abs/2512.07227 - arXiv:2512.07227v1 Announce Type: new -Abstract: We show that there exist unbounded functionals on the spaces of sequences that take at most one nonzero value on an arbitrary family of elements whose supports are pairwise disjoint. - oai:arXiv.org:2512.07227v1 - math.FA - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Konstantin Storozhuk - - - Isometric Embeddings of Conformally Compact Manifolds into Hyperbolic Spaces - https://arxiv.org/abs/2512.07231 - arXiv:2512.07231v1 Announce Type: new -Abstract: The celebrated Nash Embedding Theorem asserts that every closed Riemannian manifold can be isometrically embedded into a sufficiently high-dimensional Euclidean space. In this paper, we prove an analogous result in the conformally compact context. Let $\left(M,g\right)$ be a conformally compact manifold whose sectional curvature at infinity is strictly bounded below by a negative constant $-\lambda^{2}$. We prove that $\left(M,g\right)$ can be realized as a submanifold, transverse to the sphere at infinity, of a sufficiently high-dimensional rescaled hyperbolic space of constant curvature $-\lambda^{2}$. - oai:arXiv.org:2512.07231v1 - math.DG - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Marco Usula - - - On $\pi_1$-injectivity of self-maps in low dimensions - https://arxiv.org/abs/2512.07238 - arXiv:2512.07238v1 Announce Type: new -Abstract: We show that all self-maps of non-zero degree of $3$-manifolds not covered by $S^3$ and of Thurston geometric $4$-manifolds and their connected sums not covered by $N\#(\#_{p\geq0}S^2\times S^2)\#(\#_{q\geq0}\mathbb C P^2)$, where $N$ is an $S^2\times\mathbb X^2$ or $S^3\times\mathbb R$ manifold, are $\pi_1$-injective. We thus determine when these maps induce $\pi_1$-isomorphisms. The results in dimension three were previously established by Shicheng Wang. We give a uniform group theoretic proof in all cases based only on the residual finiteness of the fundamental groups for the $\pi_1$-injectivity and then only on numerical invariants for the $\pi_1$-isomorphisms. - oai:arXiv.org:2512.07238v1 - math.GT - math.AT - math.GR - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Christoforos Neofytidis - - - Function-Correcting Codes for Insertion-Deletion Channel - https://arxiv.org/abs/2512.07243 - arXiv:2512.07243v1 Announce Type: new -Abstract: In coding theory, handling errors that occur when symbols are inserted or deleted from a transmitted message is a long-standing challenge. Optimising redundancy for insertion and deletion channels remains a key open problem with significant importance for applications in DNA data storage and document exchange. Recently, a coding framework known as function-correcting codes has been proposed to address the challenge of minimising redundancy while preserving specific functions of the message. This framework has gained attention due to its potential applications in machine learning systems and long-term archival data storage. Motivated by the problem of redundancy optimisation for insertion and deletion channels, we propose a new framework called function-correcting codes for insdel channels. In this paper, we introduce the notions of function-correcting insertion codes, function-correcting deletion codes, and function-correcting insdel codes, and we show that these three formulations are equivalent. We then define insdel distance matrices and irregular insdel-distance codes, and derive lower and upper bounds on the optimal redundancy achievable by function-correcting codes for insdel channels. In addition, we establish Gilbert-Varshamov and Plotkin-like bounds on the length of irregular insdel-distance codes. Using the relation between optimal redundancy and the length of such codes, we obtain a simplified lower bound on optimal redundancy. Finally, we derive bounds on the optimal redundancy of function-correcting insdel codes for several classes of functions, including locally bounded functions, VT syndrome functions, the number-of-runs function, and the maximum-run-length function. - oai:arXiv.org:2512.07243v1 - cs.IT - math.IT - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Anamika Singh, Abhay Kumar Singh - - - Short Brooms in Edge-chromatic Critical Graphs - https://arxiv.org/abs/2512.07252 - arXiv:2512.07252v1 Announce Type: new -Abstract: This paper studies short brooms in edge-chromatic critical graphs. We prove that for any short broom in a $\Delta$-critical graph, at most one color is missing at more than one vertex. Moreover, this color (if exists) is missing at exactly two vertices. Applying this result, we verify the Vertex-splitting Conjecture for graphs with $\Delta \geq 2(n-1)/3$ and the Overfull Conjecture for $\Delta$-critical graphs satisfying $\Delta \geq (2n+5\delta-12)/3$. - oai:arXiv.org:2512.07252v1 - math.CO - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Yonglei Chen, Yan Cao - - - Non-weight modules over generalized Heisenberg-Virasoro algebra of rank two - https://arxiv.org/abs/2512.07254 - arXiv:2512.07254v1 Announce Type: new -Abstract: In this paper, we study a class of non-weight modules over the generalized Heisenberg-Virasoro algebra of rank two $\widetilde{L}(p_1, p_2)$. We construct a family of irreducible - $\widetilde{L}(p_1, p_2)$-modules, determine the isomorphism classes and show that these modules exhaust all the $\widetilde{L}(p_1, p_2)$-modules that are free modules of rank one over the Cartan subalgebra. - oai:arXiv.org:2512.07254v1 - math.RT - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - 10.1063/5.0281897 - J. Math. Phys. 66, 121701 (2025) - Yi Wen, Naihuan Jing, Jiancai Sun, Honglian Zhang - - - Improved bounds and optimal constructions of pure quantum locally recoverable codes - https://arxiv.org/abs/2512.07256 - arXiv:2512.07256v1 Announce Type: new -Abstract: By incorporating the concept of locality into quantum information theory, quantum locally recoverable codes (qLRCs) have been proposed, motivated by their potential applications in large-scale quantum data storage and their relevance to quantum LDPC codes. Despite the progress in optimal quantum error-correcting codes (QECCs), optimal constructions of qLRCs remain largely unexplored, partly due to the fact that the existing bounds for qLRCs are not sufficiently tight. In this paper, we focus on pure qLRCs derived from the Hermitian construction. We provide several new bounds for pure qLRCs and demonstrate that they are tighter than previously known bounds. Moreover, we show that a variety of classical QECCs, including quantum Hamming codes, quantum GRM codes, and quantum Solomon-Stiffler codes, give rise to pure qLRCs with explicit parameters. Based on these constructions, we further identify many infinite families of optimal qLRCs with respect to different bounds, achieving code lengths much larger than those of known optimal qLRCs. - oai:arXiv.org:2512.07256v1 - cs.IT - math.IT - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Yang Li, Shitao Li, Gaojun Luo, San Ling - - - Mass and volume of four-dimensional Einstein metrics - https://arxiv.org/abs/2512.07257 - arXiv:2512.07257v1 Announce Type: new -Abstract: Let $(M^4,\bar{g})$ be an Einstein manifold, where $M^4$ is a smooth, closed, oriented four-manifold $M^4$ and $\bar{g}$ has positive Einstein constant. Given a point $0 \in M^4$, let $G$ denote the (positive) Green's function $G$ of the conformal laplacian $L_{\bar{g}}$; then $g = G^2 \bar{g}$ is a complete, scalar-flat, asymptotically flat metric on $\widehat{M} = M \setminus \{ 0 \}$. We first show that the ADM mass of $g$ can be expressed as an integral over $\widehat{M}$, then use this identity to prove a lower bound for the mass of $g$ in terms of the volume of $\bar{g}$. As corollaries, we prove a 'mass times volume' inequality, plus various mass gap theorems characterizing the round metric on $S^4$ and the Fubini-Study metric on $\mathbb{CP}^2$. - oai:arXiv.org:2512.07257v1 - math.DG - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Matthew Gursky, Andrea Malchiodi - - - Optimal asymptotic expansion of entire solutions to Monge-Amp\`{e}re equation with $C^\alpha$ perturbed periodic data - https://arxiv.org/abs/2512.07260 - arXiv:2512.07260v1 Announce Type: new -Abstract: We consider the asymptotic behavior at infinity of solution $u$ to Monge-Amp\`{e}re equation $\det(D^2u)=f$ in $\rn$, where $f$ is a perturbation of a periodic function and is only assumed to be H\"{o}lder continuous, compared to the previous work that $f$ is at least $C^{1,\az}$. The consequence established in this paper, by a nonlocal method, is that the difference between $u$ and a quadratic polynomial is asymptotically close to a periodic function. - oai:arXiv.org:2512.07260v1 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Shuai Qi, Jiguang Bao - - - Escaping the native space of Sobolev kernels by interpolation - https://arxiv.org/abs/2512.07262 - arXiv:2512.07262v1 Announce Type: new -Abstract: Classical convergence analysis for kernel interpolation typically assumes that the target function $f$ lies in the reproducing kernel Hilbert space $\mathcal{H}_k\!\left(\Omega\right)$ induced by a kernel on a domain $\Omega\subset\mathbb{R}^N$. For many applications, however, this assumption is overly restrictive. We develop a general framework for analyzing the convergence of kernel interpolation {beyond the native space}. Let $A(\Omega)$ and $B(\Omega)$ be Banach spaces with continuous embeddings $\mathcal{H}_k\!\left(\Omega\right) \hookrightarrow A(\Omega)\hookrightarrow B(\Omega)$, assume point evaluation is continuous on $A(\Omega)$, and that $\mathcal{H}_k\!\left(\Omega\right)$ is dense in $A(\Omega)$. For a nested sequence of node sets $(X_n)_{n\ge1}\subset\Omega$ with $\bigcup_n X_n$ dense, we characterize convergence of the kernel interpolants in the $B(\Omega)$-norm for all target functions in $A(\Omega)$ via the uniform boundedness of the interpolation operators $\Pi^{\,n}_{A,B}:A(\Omega)\to B(\Omega)$. This yields a necessary and sufficient condition under which kernel interpolation extends beyond $\mathcal{H}_k\!\left(\Omega\right)$. Specializing to Sobolev kernels of order $\tau>N/2$ on bounded Lipschitz domains, we show that every $f \in C(\overline{\Omega})$ can be approximated in the $L^2(\Omega)$-norm by interpolation using quasi-uniform nested centers. Moreover, for a subclass of Sobolev kernels (including integer-order Mat\'ern kernels), we prove that the Lebesgue constant is uniformly bounded on $[a,b]\subset\mathbb{R}$ under quasi-uniform centers; within our framework this implies supremum norm convergence of the interpolants for every target functions $f \in C([a,b])$. - oai:arXiv.org:2512.07262v1 - math.NA - cs.NA - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Tobias Ehring, Max-Paul Vogel, Bernard Haasdonk - - - The first nonzero eigenvalue of the weighted p-Laplacian on differential forms - https://arxiv.org/abs/2512.07263 - arXiv:2512.07263v1 Announce Type: new -Abstract: We introduce the weighted p-Laplace operator acting on differential forms on a metric measure space, which is a natural generalization of the p-Laplace operator defined by Seto [32]. We obtain some sharp lower bounds of the first nonzero eigenvalue for the weighted p-Laplacian. Our results extend an estimate of Seto [32], as well as the eigenvalue estimates derived by Cui-Sun [8] for closed submanifolds. - oai:arXiv.org:2512.07263v1 - math.DG - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Mingzhu Miao, Xuerong Qi, Jiabin Yin - - - A remark on the Beurling-Malliavin theorem in several variables - https://arxiv.org/abs/2512.07271 - arXiv:2512.07271v1 Announce Type: new -Abstract: We use a lifting trick to show that the Beurling-Malliavin multiplier theorem extends to radial functions in several variables in a straightforward way. This simplifies an argument of Vasilyev and also answers a question of Vasilyev on the Cartwright version of the theorem. - oai:arXiv.org:2512.07271v1 - math.CV - math.CA - math.FA - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Alex Bergman - - - Rigidity of the gradient estimate for Einstein manifolds - https://arxiv.org/abs/2512.07278 - arXiv:2512.07278v1 Announce Type: new -Abstract: We study the rigidity of Ricci-flat manifolds with quadratic curvature decay under conditions on the Green function. We show that if the gradient of the Green function is uniformly bounded from below, then the manifold is flat. Furthermore, we prove that for a Ricci-flat manifold with quadratic curvature decay and Euclidean volume growth, the curvature is in $L^p$ for any $p \ge 2$. Combining with Cheeger-Tian \cite{CT} and Kr\"oncke-Szab\'o \cite{KS}, we obtain that the manifold must be ALE of optimal order. - oai:arXiv.org:2512.07278v1 - math.DG - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Sanghoon Lee, Jiewon Park - - - Reproducing Kernel Hilbert Spaces for Virtual Persistence Diagrams - https://arxiv.org/abs/2512.07282 - arXiv:2512.07282v1 Announce Type: new -Abstract: A persistence diagram is a finite multiset of birth-death pairs representing the lifetimes of topological features across a filtration. Persistence diagrams do not carry intrinsic spectral or kernel structures, so applications typically use auxiliary vectorizations of diagrams. Virtual persistence diagrams, given by the Grothendieck completion of finite diagrams with the $W_1$ metric, yield a group structure with additive cancellation and a translation-invariant metric. For a finite metric pair $(X,d,A)$ we use the identification $K(X,A)\cong \mathbb Z^{|X\setminus A|}$ and parametrize its Pontryagin dual torus. The Lipschitz seminorms of characters in the $W_1$ geometry are expressed in terms of edgewise phase differences on the quotient $X/A$. A weighted graph Laplacian on $X/A$ determines a Dirichlet symbol $\lambda(\theta)$, and the corresponding heat spectral multipliers induce translation-invariant kernels and their reproducing-kernel Hilbert spaces. We obtain explicit global $W_1$-Lipschitz bounds for all functions in these spaces. Random Fourier feature maps are constructed by sampling from the heat measures; they are unbiased kernel approximations and satisfy asymptotic Lipschitz estimates based on the same spectral quantities. We apply these kernels and their finite-dimensional approximations in a synthetic segmentation experiment that compares baseline, Wasserstein, and Reproducing Kernel Hilbert Space (RKHS)-based losses. - oai:arXiv.org:2512.07282v1 - math.AT - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Charles Fanning, Mehmet Aktas - - - Investigation and Development of the Methodologies for Simulating Self-similar Processes - https://arxiv.org/abs/2512.07296 - arXiv:2512.07296v1 Announce Type: new -Abstract: This paper is devoted to the study of simulating a large class of self-similar processes. Since most current simulation approaches are limited to case-by-case studies, every existing approach has its constraints and flaws; hence a general and efficient simulation approach is in demand. Our study sheds some light in this direction. The paper's contributions are bi-fold. First, reviews and improvements are made to some existing methods for simulating specific self-similar processes. Second, we propose a novel method to simulate a general self-similar process, where we use a modified inverse Lamperti transformation to transform self-similarity to stationarity. Successful applications are made to simulate fractional Brownian motion and sub-fractional Brownian motion. - oai:arXiv.org:2512.07296v1 - math.PR - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Qidi Peng, William Wu - - - Quantitative unique continuation for Neumann problem in planar $C^{1,\alpha}$ domains - https://arxiv.org/abs/2512.07297 - arXiv:2512.07297v1 Announce Type: new -Abstract: In this paper, we study the quantitative unique continuation property of the second-order elliptic operators under the vanishing Neumann boundary condition over $C^{1,\alpha}$ or convex domains in two dimensions. We establish the optimal estimates of the number of critical points, doubling index and the total length of level curves. The key idea is to reduce the Neumann problem to the Dirichlet problem, which has been understood better, by a classical duality between an $A$-harmonic function and its stream function. - oai:arXiv.org:2512.07297v1 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Yingying Cai, Jiuyi Zhu, Jinping Zhuge - - - Non-asymptotic convergence bounds of modified EM schemes for non-dissipative SDEs - https://arxiv.org/abs/2512.07298 - arXiv:2512.07298v1 Announce Type: new -Abstract: In this paper, we address the issue on non-asymptotic convergence bounds of Euler-type schemes associated with non-dissipative SDEs. On the one hand, for non-degenerate SDEs with super-linear drifts, we propose a novel modified Euler scheme and establish the corresponding non-asymptotic convergence bound under the multiplicative type quasi-Wasserstein distance - by the aid of the asymptotic reflection by coupling. As a direct application of the theory derived, we explore the non-asymptotic convergence bound of the modified tamed/truncated Euler scheme - and, as a byproduct, furnish the associated non-asymptotic convergence rate under the $L^1$-Wasserstein distance although the - dissipativity at infinity is not in force. On the other hand, we tackle the non-asymptotic convergence analysis of the Euler scheme corresponding to a kind of degenerate SDEs, where the underdamped Langevin SDE is a typical candidate. To handle such setting, we also appeal to a carefully tailored coupling approach, where the ingredient in the coupling construction lies in that a proper metric and a suitable substitute in the cut-off function and the reflection matrix need to be chosen appropriately. In addition, as a consequent application, the non-asymptotic convergence bound and the $L^1$-Wasserstein convergence rate are revealed for the kinetic Langevin sampler. - oai:arXiv.org:2512.07298v1 - math.PR - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jianhai Bao, Jiaqing Hao, Panpan Ren - - - Estimation of the elasticity for CKLS model from high-frequency observations - https://arxiv.org/abs/2512.07301 - arXiv:2512.07301v1 Announce Type: new -Abstract: We investigate parametric estimation of the elasticity parameter in the CKLS diffusion based on high-frequency data. First, we transform the CKLS diffusion to a CIR-type one via a smooth state-space mapping and the general Girsanov change of measure. This transformation enables the applications of existing inference tools for CIR processes while ensuring possibilities of transferring the resulting limit theorems back to the original probability space. However, because Feller's condition fails, many existing high-frequency likelihood-based procedures cannot be applied directly, since their discretization schemes approximate likelihood terms involving the reciprocal of the process by Riemann sums that are no longer well-defined once the paths are allowed to hit zero. Instead, we estimate the drift coefficient of the transformed CIR-type model via a procedure based on its positive Harris recurrence, which is valid in the high-frequency regime. Exploiting the drift-elasticity relationship implied by the CKLS--CIR transformation, with the help of an initial estimation, we obtain an estimator of the CKLS elasticity from the CIR drift estimator in the transformed model. This yields a closed-form estimator of the elasticity parameter with an explicit asymptotic variance. We establish its $p$-consistency, stable convergence in law, and asymptotic normality. Finally, we show that stable convergence in law is invariant under equivalent changes of measure, thereby guaranteeing that the Gaussian limit remains invariant under the original measure. - oai:arXiv.org:2512.07301v1 - math.ST - stat.TH - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Boyuan Ning, Yasutaka Shimizu - - - Radiance-Field Reinforced Pretraining: Scaling Localization Models with Unlabeled Wireless Signals - https://arxiv.org/abs/2512.07309 - arXiv:2512.07309v1 Announce Type: new -Abstract: Radio frequency (RF)-based indoor localization offers significant promise for applications such as indoor navigation, augmented reality, and pervasive computing. While deep learning has greatly enhanced localization accuracy and robustness, existing localization models still face major challenges in cross-scene generalization due to their reliance on scene-specific labeled data. To address this, we introduce Radiance-Field Reinforced Pretraining (RFRP). This novel self-supervised pretraining framework couples a large localization model (LM) with a neural radio-frequency radiance field (RF-NeRF) in an asymmetrical autoencoder architecture. In this design, the LM encodes received RF spectra into latent, position-relevant representations, while the RF-NeRF decodes them to reconstruct the original spectra. This alignment between input and output enables effective representation learning using large-scale, unlabeled RF data, which can be collected continuously with minimal effort. To this end, we collected RF samples at 7,327,321 positions across 100 diverse scenes using four common wireless technologies--RFID, BLE, WiFi, and IIoT. Data from 75 scenes were used for training, and the remaining 25 for evaluation. Experimental results show that the RFRP-pretrained LM reduces localization error by over 40% compared to non-pretrained models and by 21% compared to those pretrained using supervised learning. - oai:arXiv.org:2512.07309v1 - cs.IT - cs.AI - math.IT - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Guosheng Wang, Shen Wang, Lei Yang - - - On the Orbits of Similarity Classes of Tetrahedra Generated by the Longest-Edge Bisection Algorithm - https://arxiv.org/abs/2512.07315 - arXiv:2512.07315v1 Announce Type: new -Abstract: In this work, we study the dynamics of similarity classes of tetrahedra generated by the longest-edge bisection (LEB) algorithm. Building on the normalization strategy introduced by Perdomo and Plaza for triangles, we construct a canonical representation of tetrahedra in a normalized space embedded in the product of the hyperbolic half-plane and the hyperbolic half-space model. This representation allows us to define the left and right refinement maps, $\Phi_L$ and $\Phi_R$, acting on the space of normalized tetrahedral shapes, and to study their iterative orbits as discrete dynamical systems. Using these maps, we show that the orbit of the space-filling Sommerville tetrahedron contains only 4 similarity classes, 3 of which form an attractive cycle corresponding to the orbit of the path tetrahedron. We also show that small perturbations of elements in those orbits still lead to finite orbits. In addition, we study small perturbations of the regular tetrahedron and show that their orbits are also finite. Extensive numerical exploration of orbits for the other types of tetrahedra suggests that the LEB algorithm does not produce degenerating tetrahedra. Our framework provides a geometric and dynamical foundation for analyzing the shape evolution of tetrahedral meshes and offers a possible route toward an analytic proof of the non-degeneracy property for the tetrahedral partitions generated by the LEB refinements. This property is highly desired in e.g. the finite element methods (FEMs). - oai:arXiv.org:2512.07315v1 - math.NA - cs.NA - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by-nc-nd/4.0/ - J\'er\^ome Michaud, Sergey Korotov - - - Midpoints and critical points - https://arxiv.org/abs/2512.07322 - arXiv:2512.07322v1 Announce Type: new -Abstract: For a degree $5$ real polynomial with roots $x_1\leq \cdots \leq x_5$ and roots $\xi_1\leq \cdots \leq \xi_4$ of its derivative, we set $z_j:=(x_j+x_{j+1})/2$, $1\leq j\leq 4$. We prove that one cannot have at the same time $\min_{1\leq j\leq 3}(z_{j+1}-z_j)\geq \min_{1\leq j\leq 3}(\xi_{j+1}-\xi_j)$ and $\max_{1\leq j\leq 3}(z_{j+1}-z_j)\geq \max_{1\leq j\leq 3}(\xi_{j+1}-\xi_j)$. The result settles a general question about midpoints and critical points of hyperbolic polynomials. - oai:arXiv.org:2512.07322v1 - math.CA - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/publicdomain/zero/1.0/ - Yousra Gati, Vladimir Petrov Kostov - - - Nash Equilibrium of Bi-objective Optimal Control of Fractional Space-Time Parabolic PDE - https://arxiv.org/abs/2512.07327 - arXiv:2512.07327v1 Announce Type: new -Abstract: This work investigates the existence and uniqueness of the Nash equilibrium (solutions to competitive problems in which individual controls aim at separate desired states) for a bi-objective optimal control problem governed by a fractional space-time parabolic partial differential equation. The governing equation involves a Caputo fractional derivative with respect to time of order $\gamma$ in (0,1) and a fractional Laplacian in the spatial variables of order $s$ in (0,1). The system is associated with two independent controls, each aiming at different targets. The problem is formulated as a distributed optimal control system with quadratic cost functionals. Existence and uniqueness of the Nash equilibrium are established under convexity and coercivity assumptions. The solution is computed using conjugate gradient algorithms applied iteratively to the discretized optimal control problems. The numerical experiments agree with the theoretical estimates and demonstrate the efficiency of the proposed scheme. - oai:arXiv.org:2512.07327v1 - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Kedarnath Buda, B. V. Rathish Kumar, Anil Rathi - - - Multiple Mertens theorems for arithmetic progressions - https://arxiv.org/abs/2512.07336 - arXiv:2512.07336v1 Announce Type: new -Abstract: We establish asymptotic formulas for sums of reciprocals of primes in arithmetic progressions, generalizing recent results on multiple Mertens evaluations by Tenenbaum, Qi, and Hu. Specifically, for any fixed constant $K>0$, we derive asymptotic expansions for the sums $ -\sum_{\substack{p_1\cdots p_n\leq x \\ p_i\equiv h_i \pmod{m_i} \\ i=1,\dots, n}}\frac{1}{p_1\cdots p_n} $ -and the corresponding log-weighted sums. A key feature of our results is that the error terms hold \emph{uniformly} for moduli satisfying $m_i \le (\log x)^K$, a range accessible via the Siegel-Walfisz theorem. Furthermore, we identify the coefficients of the asymptotic expansion with the Taylor series of the reciprocal Gamma function, $1/\Gamma(z)$, providing a structural explanation for the lower-order terms. - oai:arXiv.org:2512.07336v1 - math.NT - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Zhen Chen, Junrong Luo - - - Lyapunov maximizing measures for balanced pairs of matrices - https://arxiv.org/abs/2512.07340 - arXiv:2512.07340v1 Announce Type: new -Abstract: We show that every balanced pair (see Definition 1.1) of real $2\times 2$ matrices admits a unique Lyapunov maximizing measure, and the measure is always Sturmian. - oai:arXiv.org:2512.07340v1 - math.DS - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Rui Gao - - - Linear codes over $\frac{\mathbb{F}_q[u]}{\langle u^2 \rangle}$ with mixed-alphabet defining sets and their Gray images: Constructions of projective few-weight, distance-optimal and minimal codes - https://arxiv.org/abs/2512.07343 - arXiv:2512.07343v1 Announce Type: new -Abstract: Let $\mathcal{R}=\frac{\mathbb{F}_q[u]}{\langle u^2 \rangle}\times \mathbb{F}_q$ be the mixed alphabet ring. In this paper, we construct four infinite families of linear codes over the ring $\frac{\mathbb{F}_q[u]}{\langle u^2 \rangle}$ whose defining sets are certain nonempty subsets of $\mathcal{R}^m$ associated with three simplicial complexes of $\mathbb{F}_q^m,$ each possessing a single maximal element. We explicitly determine the parameters and Lee weight distributions of these codes. We also study their Gray images and obtain three infinite families of few weight, near Griesmer, distance optimal and minimal codes over $\mathbb{F}_q$ with new parameters. We also provide two constructions of infinite families of projective few weight codes over $\mathbb{F}_q$ with new parameters, and observe that these codes are self orthogonal for $q=2$ or $3.$ Additionally, we obtain two infinite families of binary distance optimal projective codes and an infinite family of dimension optimal projective codes over $\mathbb{F}_q$ with new parameters. Apart from this, we construct an infinite family of quaternary projective $3$-weight codes whose non zero Hamming weights sum to $\frac{9}{4}$ times the code length, which give rise to strongly walk regular graphs. As an application of our newly constructed minimal codes over $\mathbb{F}_q$, we examine the minimal access structures of Massey's secret sharing schemes based on their duals and determine the number of dictatorial participants in these schemes. Finally, we investigate the locality properties of our newly constructed projective codes. - oai:arXiv.org:2512.07343v1 - cs.IT - math.IT - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Leijo Jose, Lavanya G., Anuradha Sharma - - - Self-adjoint realization of the harmonic oscillator in polar coordinates and some consequences - https://arxiv.org/abs/2512.07347 - arXiv:2512.07347v1 Announce Type: new -Abstract: We consider spectral decomposition of the harmonic oscillator in $\mathbb R^n$ in terms of two different orthonormal bases in $L^2(\mathbb R^n)$ consisting of its eigenfunctions. Then, using purely functional analysis tools we provide simple proofs of rotational symmetry of the Hermite projection operators studied by Kochneff, and Thangavelu's Hecke-Bochner type identity. - oai:arXiv.org:2512.07347v1 - math.FA - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/publicdomain/zero/1.0/ - Krzysztof Stempak - - - Dualities of dihedral and generalised quaternion codes and applications to quantum codes - https://arxiv.org/abs/2512.07354 - arXiv:2512.07354v1 Announce Type: new -Abstract: Let $\mathbb{F}_q$ be a finite field of $q$ elements, for some prime power $q$, and let $G$ be a finite group. A (left) group code, or simply a $G$-code, is a (left) ideal of the group algebra $\mathbb{F}_q[G]$. In this paper, we provide a complete algebraic description for the hermitian dual code of any $D_n$-code over $\mathbb{F}_{q^2}$, where $D_n$ is a dihedral group of order $2n$ with $\gcd(q,n)=1$, through a suitable Wedderburn-Artin's decomposition of the group algebra $\mathbb{F}_{q^2}[D_n]$, and we determine all distinct hermitian self-orthogonal $D_n$-codes over $\mathbb{F}_{q^2}$. We also present a thorough representation of the euclidean dual code of any $Q_n$-code over $\mathbb{F}_q$, where $Q_n$ is a generalised quaternion group of order $4n$ with $\gcd(q,4n)=1$, via the Wedderburn-Artin's decomposition of the group algebra $\mathbb{F}_q[Q_n]$. In particular, since the semisimple group algebras $\mathbb{F}_{q^2}[Q_n]$ and $\mathbb{F}_{q^2}[D_{2n}]$ are isomorphic, then the hermitian dual code of any $Q_n$-code has also been fully described. As application of the hermitian dualities computed, we give a systematic construction, via the structure of the group algebra, to obtain quantum error-correcting codes, and in fact we rebuild some already known optimal quantum codes with this methodical approach. - oai:arXiv.org:2512.07354v1 - cs.IT - math.IT - math.QA - math.RA - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Miguel Sales-Cabrera, Xaro Soler-Escriv\`a, V\'ictor Sotomayor - - - Traveling Wave Solutions For A Singular Diffusive Prey-Predator Model With Nonlocal Dispersal - https://arxiv.org/abs/2512.07362 - arXiv:2512.07362v1 Announce Type: new -Abstract: We study a singular diffusive prey-predator system with nonlocal dispersal for which the carrying capacity of the predator is proportional to the density of prey. We show the existence of positive one-dimensional traveling waves connecting the predator-free state and the constant co-existence state. The set of admissible wave speeds is proved to be equal to the semi-infinite interval $[s^*,\infty)$, for some $s^*>0$ which is characterized by a variational formula. - oai:arXiv.org:2512.07362v1 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jong-Shenq Guo (TKU), Fran\c{c}ois Hamel (I2M), Chin-Chin Wu (NCHU) - - - On semi-separability and differentiation matrices - https://arxiv.org/abs/2512.07365 - arXiv:2512.07365v1 Announce Type: new -Abstract: The theory of spectral methods for partial differential equations leads to infinite-dimensional matrices which represent the derivative operator with respect to an underlying orthonormal basis. Favourable properties of such differentiation matrices are crucial in the design of good spectral methods. It is known that bases using Laguerre and ultraspherical polynomials lead to semi-separable differentiation matrices of rank 1. In this paper we consider orthonormal bases constructed from Jacobi polynomials and prove that the underlying differentiation matrices are semi-separable of rank 2. This requires new results on semi-separable matrices which might be interesting in a wider context. - oai:arXiv.org:2512.07365v1 - math.NA - cs.NA - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Arieh Iserles - - - Non-Intrusive Data-Free Parametric Reduced Order Model for Geometrically Nonlinear Structures - https://arxiv.org/abs/2512.07366 - arXiv:2512.07366v1 Announce Type: new -Abstract: We present a fully non-intrusive parametric reduced-order modeling (PROM) framework for geometrically nonlinear structures subject to geometric variations. The method builds upon equation-driven Galerkin ROMs constructed from vibration modes and modal-derivative companion vectors, while nonlinear reduced tensors are identified from standard finite element outputs. A database of such ROMs is generated over a set of training samples, and all reduced operators-including the linear stiffness matrix, the quadratic and cubic nonlinear tensors, the Rayleigh damping parameters, and the reduction basis-are interpolated using Radial Basis Functions (RBFs). A global reduced basis is obtained through a two-level POD compression, combined with a MAC-guided reordering strategy to ensure parametric smoothness. The resulting PROM preserves the symmetry and polynomial structure of the reduced equations, enabling robust and efficient adaptation to new parameter values. Analytical parameter sensitivities follow directly from the interpolation model. The approach is demonstrated on a parametrically curved panel and a wing-box with geometric variations, showing excellent agreement with high-fidelity simulations and enabling substantial reductions in computational cost for parametric analyses. - oai:arXiv.org:2512.07366v1 - math.NA - cs.NA - physics.comp-ph - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Alexander Saccani, Paolo Tiso - - - Alperin's weight conjecture, Galois automorphisms, alternating sums, and functorial equivalences - https://arxiv.org/abs/2512.07369 - arXiv:2512.07369v1 Announce Type: new -Abstract: We show that functorial equivalences can offer new insight into the blockwise Galois Alperin weight conjecture (BGAWC). Inspired by Kn\"orr and Robinson's work, we first formulate the BGAWC in terms of alternating sums indexed by chains of $p$-subgroups, and we also give a functorial reformulation in the Grothendieck group of diagonal $p$-permutation functors. We prove that these formulations are equivalent. We further show that if a functorial equivalence between a block with abelian defect group and its Brauer correspondent descends to the minimal field of the block, then the BGAWC holds for that block. Finally, we prove that Galois conjugate blocks are functorially equivalent over an algebraically closed field of characteristic zero. - oai:arXiv.org:2512.07369v1 - math.RT - math.GR - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Xin Huang, Deniz Y{\i}lmaz - - - Copositivity, discriminants and nonseparable signed supports - https://arxiv.org/abs/2512.07373 - arXiv:2512.07373v1 Announce Type: new -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:2512.07373v1 - math.AG - math.CO - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Elisenda Feliu, Joan Ferrer, M\'at\'e L. Telek - - - Control and Reinforcement Learning through the Lens of Optimization: An Algorithmic Perspective - https://arxiv.org/abs/2512.07377 - arXiv:2512.07377v1 Announce Type: new -Abstract: The connection between control algorithms for Markov decision processes and optimization algorithms has been implicitly and explicitly exploited since the introduction of dynamic programming algorithm by Bellman in the 1950s. Recently, this connection has attracted a lot of attention for developing new control algorithms inspired by well-established optimization algorithms. In this paper, we make this analogy explicit across four problem classes with a unified solution characterization. This novel framework, in turn, allows for a systematic transformation of algorithms from one domain to the other. In particular, we identify equivalent optimization and control algorithms that have already been pointed out in the existing literature, but mostly in a scattered way. We also discuss the issues arising in providing theoretical convergence guarantees for these new control algorithms and provide simple yet effective techniques to solve them. The provided framework and techniques then lay out a concrete methodology for developing new convergent control algorithms. - oai:arXiv.org:2512.07377v1 - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Tolga Ok, Arman Sharifi Kolarijani, Mohamad Amin Sharif Kolarijani, Peyman Mohajerin Esfahani - - - Nonparametric optimal density estimation for censored circular data - https://arxiv.org/abs/2512.07380 - arXiv:2512.07380v1 Announce Type: new -Abstract: We consider the problem of estimating the probability density function of a circular random variable observed under censoring. To this end, we introduce a projection estimator constructed via a regression approach on linear sieves. We first establish a lower bound for the mean integrated squared error in the case of Sobolev densities, thereby identifying the minimax rate of convergence for this estimation problem. We then derive a matching upper bound for the same risk, showing that the proposed estimator attains the minimax rate when the underlying density belongs to a Sobolev class. Finally, we develop a data-driven version of the procedure that preserves this optimal rate, thus yielding an adaptive estimator. The practical performance of the method is demonstrated through simulation studies. - oai:arXiv.org:2512.07380v1 - math.ST - stat.TH - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Nicolas Conanec (LAGA), Claire Lacour (LAMA), Thanh Mai Pham Ngoc (LAGA) - - - Gradient estimates and Liouville properties for the drifted Laplacian - https://arxiv.org/abs/2512.07389 - arXiv:2512.07389v1 Announce Type: new -Abstract: In this paper, we discuss the validity of the Liouville property for $X$-harmonic functions, i.e. positive solution to $\Delta_{X}u=0$, where $X$ is a vector field on a complete, non-compact Riemannian manifold and $\Delta_{X}$ is the drifted Laplacian. In particular, we show that if the $X$-Bakry-\'Emery-Ricci curvature $\mathrm{Ric}_{X}$ is non-negative and the norm of $X$ decays to zero at infinity, then the manifold has the Liouville property for the $X$-Laplacian. The proof exploits a local gradient estimate for positive solutions to the semilinear equation $\Delta_{X}u+F(u)=0$, which holds when $F$ satisfies the structural conditions $tF'(t)-F(t)\le\alpha$ and $\vert F(t)\vert\le\beta t$, and the manifold has $\mathrm{Ric}_{X}\ge-(n-1)K$. - oai:arXiv.org:2512.07389v1 - math.DG - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Salvatore Lincastri - - - A new scale of function spaces characterizing homogeneous Besov spaces - https://arxiv.org/abs/2512.07399 - arXiv:2512.07399v1 Announce Type: new -Abstract: We introduce and study a new scale of function spaces that characterize the homogeneous Besov spaces $\mathrm{\dot B}^{\beta}_{p,q}$, hence completing earlier work by Ullrich. These new spaces include the ones introduced by Barton and Mayboroda, and systematically studied by Amenta under the name of weighted $\mathrm{Z}$-spaces, for the purpose of boundary value problems with $\mathrm{\dot B}^{\beta}_{p,p}$ data. They are the counterparts to the weighted tent spaces with Whitney averages, developed by Huang, and arise as their real interpolants. We describe their functional analytic properties: completeness, duality, embeddings, as well as their real and complex interpolants. - oai:arXiv.org:2512.07399v1 - math.CA - math.FA - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Pascal Auscher, Sebastian Bechtel, Luca Haardt - - - Orbit recovery under the rigid motions group - https://arxiv.org/abs/2512.07405 - arXiv:2512.07405v1 Announce Type: new -Abstract: We study the orbit recovery problem under the rigid-motion group SE(n), where the objective is to reconstruct an unknown signal from multiple noisy observations subjected to unknown rotations and translations. This problem is fundamental in signal processing, computer vision, and structural biology. - Our main theoretical contribution is bounding the sample complexity of this problem. We show that if the d-th order moment under the rotation group SO(n) uniquely determines the signal orbit, then orbit recovery under SE(n) is achievable with $N\gtrsim \sigma^{2d+4}$ samples as the noise variance $\sigma^2 \to \infty$. The key technical insight is that the d-th order SO(n) moments can be explicitly recovered from (d+2)-order SE(n) autocorrelations, enabling us to transfer known results from the rotation-only setting to the rigid-motion case. We further harness this result to derive a matching bound to the sample complexity of the multi-target detection model that serves as an abstract framework for electron-microscopy-based technologies in structural biology, such as single-particle cryo-electron microscopy (cryo-EM) and cryo-electron tomography (cryo-ET). - Beyond theory, we present a provable computational pipeline for rigid-motion orbit recovery in three dimensions. Starting from rigid-motion autocorrelations, we extract the SO(3) moments and demonstrate successful reconstruction of a 3-D macromolecular structure. Importantly, this algorithmic approach is valid at any noise level, suggesting that even very small macromolecules, long believed to be inaccessible using structural biology electron-microscopy-based technologies, may, in principle, be reconstructed given sufficient data. - oai:arXiv.org:2512.07405v1 - cs.IT - eess.SP - math.IT - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Amnon Balanov, Tamir Bendory, Dan Edidin - - - Structure preserving discretization method for 1D and 2D port-Hamiltonian systems using finite differences on staggered grids - https://arxiv.org/abs/2512.07406 - arXiv:2512.07406v1 Announce Type: new -Abstract: This paper extends previous work on finitedifference schemes over staggered grids for infinite-dimensional port-Hamiltonian systems. In the one-dimensional setting, it generalizes the discretization approach originally developed for the wave equation to a broader class of systems characterized by interconnection operators that include both differential and non-differential terms, such as the Timoshenko beam equation. The paper then introduces a discretization strategy for the two-dimensional case that requires only two grids, thereby accommodating a wider range of systems, including those whose interconnection operators contain non-differential components, such as the Mindlin plate model. - oai:arXiv.org:2512.07406v1 - math.NA - cs.NA - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Ignacio Diaz Alastuey (UMLP, ENSMM, FEMTO-ST), Yann Le Gorrec (UMLP, ENSMM, FEMTO-ST), Yongxin Wu (UMLP, ENSMM, FEMTO-ST) - - - Open qubit parameter identification with bounded pulses - https://arxiv.org/abs/2512.07409 - arXiv:2512.07409v1 Announce Type: new -Abstract: We address the problem of parameter identification for a single open qubit subjected to relaxation and dephasing. Our approach is based on selecting a minimal set of carefully chosen qubit configurations that can be reliably prepared and measured in order to provide an interpretable methodology of parameter identification while potentially minimizing experimental overhead. The protocol relies on saturating control pulses to generate these configurations. In an idealized regime of infinite-amplitude pulses, we demonstrate that the parameters can be reconstructed analytically from the measured observables. We then consider large but finite pulses as a perturbation of this ideal regime and provide bounds on the estimation error introduced by the practical implementation. This framework allows us to separate the sources of uncertainty in the estimation procedure, distinguishing between statistical fluctuations arising from repeated measurements and modeling errors due to deviations from the ideal pulse regime. - oai:arXiv.org:2512.07409v1 - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Ghaieth Aloui (McTAO), Ivan Beschastnyi (McTAO), Ludovic Sacchelli (McTAO) - - - Harmonic Geometric Polynomials via Geometric Polynomials and Their Applications - https://arxiv.org/abs/2512.07416 - arXiv:2512.07416v1 Announce Type: new -Abstract: The aim of this study is to show that harmonic geometric polynomials can be represented in terms of geometric polynomials. This problem was first considered by Keller [14]; however, the corresponding coefficients were not fully determined. In the present work, we provide several explicit representations of harmonic geometric polynomials in terms of geometric polynomials. Moreover, several applications of one of these representations are subsequently developed. In particular, we obtain a generalization of the classical identity for the harmonic numbers, compute an integral involving harmonic geometric polynomials and an integral involving products of harmonic geometric and geometric polynomials in terms of Bernoulli numbers. These integral formulas lead to new explicit expressions for Bernoulli numbers. In addition, we give several recurrence relations for harmonic geometric polynomials and evaluate a finite sum involving harmonic numbers and positive powers of integers. - oai:arXiv.org:2512.07416v1 - math.NT - math.CO - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by-sa/4.0/ - P{\i}nar Akkanat, Levent Karg{\i}n - - - A weighted Reilly type integral formula for differential forms and its applications - https://arxiv.org/abs/2512.07418 - arXiv:2512.07418v1 Announce Type: new -Abstract: In this paper, we derive a weighted Reilly type integral formula for differential forms on a compact smooth metric measure space with boundary. As applications, a lower bound of the spectrum for the weighted Hodge Laplacian acting on differential forms on the boundary, and some special properties for p-th absolute cohomology space with respect to the lowest p-curvatures of the boundary have been obtained, respectively. Furthermore, we obtain a lower bound for the first positive eigenvalue of the Steklov eigenvalue problem on differential forms which is related to the lowest principal curvature of the boundary, and a comparison result between the eigenvalues of the Steklov eigenvalue problem and the Hodge Laplacian on the boundary. On the other hand, for closed submanifolds of weighted Euclidean space, we derive universal inequalities for the sum of eigenvalues with respect to the weighted Hodge Laplacian, which can be seen as a generalization of Levitin-Parnovski inequality. - oai:arXiv.org:2512.07418v1 - math.DG - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Cao Liyi, Huang Guangyue, Song Hongru - - - A model-free Screening procedure - https://arxiv.org/abs/2512.07423 - arXiv:2512.07423v1 Announce Type: new -Abstract: In this article, we propose a generic screening method for selecting explanatory variables correlated with the response variable Y . We make no assumptions about the existence of a model that could link Y with a subset of explanatory variables, nor about the distribution of the variables. Our procedure can therefore be described as ''model-free'' and can be applied in a wide range of situations. In order to obtain precise theoretical guarantees (Sure Screening Property and control of the False Positive Rate), we establish a Berry-Esseen type inequality for the studentized statistic of the slope estimator. We illustrate our selection procedure using two simulated examples and a real data set. - oai:arXiv.org:2512.07423v1 - math.ST - stat.TH - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - J Dedecker (MAP5 - UMR 8145), M L Taupin (LaMME), A S Tocquet (LaMME) - - - A tropical formula for non-Archimedean local heights - https://arxiv.org/abs/2512.07431 - arXiv:2512.07431v1 Announce Type: new -Abstract: We introduce delta-forms on tropical toric varieties generalizing the construction of Mihatsch for $R^n$. These delta-forms will be used to define the star-product with Green functions of piecewise smooth type on a tropical toric variety. As an application, we show that non-archimedean local heights of projective varieties can be computed using the star-product on a suitable complete tropical toric variety. - On the way, we show that open subsets of a simplicial tropical toric variety have a locally finite simplicial decomposition which is constant towards the boundary. - oai:arXiv.org:2512.07431v1 - math.AG - math.NT - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jos\'e Ignacio Burgos Gil, Walter Gubler, Klaus K\"unnemann - - - On the number of $k$-full integers between three successive $k$th powers - https://arxiv.org/abs/2512.07438 - arXiv:2512.07438v1 Announce Type: new -Abstract: Let $k\geq2$ be an integer. The aim of this paper is to investigate the distribution of $k$-full integers in consecutive intervals determined by three successive $k$th powers. More precisely, for any integers $\ell,m\ge0$, we establish the explicit asymptotic density for the set of integers $n$ such that the intervals $(n^k, (n+1)^k)$ and $((n+1)^k, (n+2)^k)$ contain exactly $\ell$ and $m$ $k$-full integers, respectively. As an application, we prove that there are infinitely many integers $n$ for which the interval $(n^k,(n+2)^k)$ contains no $k$-full integer other than the central $k$th power $(n+1)^k$, thereby providing a more general answer to Shiu's question. - oai:arXiv.org:2512.07438v1 - math.NT - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Shusei Narumi, Yohei Tachiya - - - Absence of the analytic continuation of elastic transmission eigenfunctions at rectangular corners - https://arxiv.org/abs/2512.07440 - arXiv:2512.07440v1 Announce Type: new -Abstract: We study time harmonic scattering problems in linear elasticity in $\mathbb{R}^{2}$. We show that certain penetrable scatterers with rectangular corners scatter every incident wave nontrivially. Even though these scatterers have interior transmission eigenvalues, the far field operator has a trivial kernel at every real frequency. Our approach relies on a special decomposition of the elastic Lam\'e operator and also provides an alternative idea for treating inverse elastic medium problems with a general polygonal support. - oai:arXiv.org:2512.07440v1 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jianli Xiang, Guanghui Hu - - - A multivariate extension of Azadkia-Chatterjee's rank coefficient - https://arxiv.org/abs/2512.07443 - arXiv:2512.07443v1 Announce Type: new -Abstract: The Azadkia-Chatterjee coefficient is a rank-based measure of dependence between a random variable $Y \in \mathbb{R}$ and a random vector ${\boldsymbol Z} \in \mathbb{R}^{d_Z}$. This paper proposes a multivariate extension that measures dependence between random vectors ${\boldsymbol Y} \in \mathbb{R}^{d_Y}$ and ${\boldsymbol Z} \in \mathbb{R}^{d_Z}$, based on $n$ i.i.d. samples. The proposed coefficient converges almost surely to a limit with the following properties: i) it lies in $[0, 1]$; ii) it equals zero if and only if ${\boldsymbol Y}$ and ${\boldsymbol Z}$ are independent; and iii) it equals one if and only if ${\boldsymbol Y}$ is almost surely a function of ${\boldsymbol Z}$. Remarkably, the only assumption required by this convergence is that ${\boldsymbol Y}$ is not almost surely a constant. We further prove that under the same mild condition, the coefficient is asymptotically normal when ${\boldsymbol Y}$ and ${\boldsymbol Z}$ are independent and propose a merge sort based algorithm to calculate this coefficient in time complexity $O(n (\log n)^{d_Y})$. Finally, we show that it can be used to measure conditional dependence between ${\boldsymbol Y}$ and ${\boldsymbol Z}$ conditional on a third random vector ${\boldsymbol X}$, and prove that the measure is monotonic with respect to the deviation from an independence distribution under certain model restrictions. - oai:arXiv.org:2512.07443v1 - math.ST - stat.ME - stat.TH - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Wenjie Huang, Zonghan Li, Yuhao Wang - - - Expansivity of algebraic semigroup actions - https://arxiv.org/abs/2512.07445 - arXiv:2512.07445v1 Announce Type: new -Abstract: For a semigroup $S$ and a right $\mathbb{Z}[S]$-submodule $J\leq \mathbb{Z}[S]^n$, we study expansivity of the algebraic action of $S$ induced on the Pontryagin dual of $\mathbb{Z}[S]^n/J$. We completely determine the class of semigroups for which expansivity of this action is characterized by the triviality of $J^\perp$, in terms of the existence of a finite subset $K\subseteq S$ such that $S=KS$. This condition is satisfied in particular by every monoid, and more generally by every semigroup with a left unital convolution Banach algebra, in which case we are able to extend the characterization of expansivity in terms of an invertibility condition when $J$ is finitely generated. We also exhibit examples of non-unital semigroups satisfying the hypotheses of our results. - oai:arXiv.org:2512.07445v1 - math.DS - math.FA - math.GR - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Miguel Donoso-Echenique - - - A lower bound theorem for $d$-polytopes with at most $3d-1$ vertices - https://arxiv.org/abs/2512.07456 - arXiv:2512.07456v1 Announce Type: new -Abstract: We prove a lower bound theorem for the number of $k$-faces ($1\le k\le d-2$) in a $d$-dimensional polytope $P$ (or $d$-polytope) with up to $3d-1$ vertices. Previous lower bound theorems for $d$-polytopes with few vertices concern those with at most $2d$ vertices, $2d+1$ vertices, and $2d+2$ vertices. - If $P$ has exactly $d+2$ facets and $2d+\ell$ vertices ($\ell\ge 1$), the lower bound is tight for certain combinations of $d$ and $\ell$. When $P$ has at least $d+3$ facets and $2d+\ell$ vertices ($\ell\ge 1$), the lower bound remains tight up to $\ell=d-1$, and equality for some $1\le k\le d-2$ is attained only when $P$ has precisely $d+3$ facets. - We exhibit at least one minimiser for each number of vertices between $2d+1$ and $3d-1$, including two distinct minimisers with $2d+2$ vertices and three with $3d-2$ vertices. - oai:arXiv.org:2512.07456v1 - math.CO - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Guillermo Pineda-Villavicencio, Jie Wang - - - On local holomorphic maps between Hermitian manifolds preserving $(p,p)$-forms - https://arxiv.org/abs/2512.07460 - arXiv:2512.07460v1 Announce Type: new -Abstract: In this article, we generalize some results in Chan-Yuan (2025) to local holomorphic maps between Hermitian manifolds preserving $(p,p)$-forms. In particular, we obtain further rigidity theorems and non-existence theorems for such maps. - oai:arXiv.org:2512.07460v1 - math.DG - math.CV - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Shan Tai Chan - - - Estimates for Dirichlet Eigenvalues of the Schrodinger operator with the Kronig-Penney Model - https://arxiv.org/abs/2512.07470 - arXiv:2512.07470v1 Announce Type: new -Abstract: In this paper, first, we improve the asymptotic formulas obtained in [13] and obtain sharp asymptotic formulas explicitly expressed by the potential. For the potentials of bounded variation, we obtain asymptotic formulas in which the first and second terms are explicitly determined and separated from the error terms. In addition, we illustrate these formulas for the Kronig-Penney potential. We then provide estimates for the small Dirichlet eigenvalues of the one-dimensional Schrodinger operator in the Kronig-Penney model. Using Rouches theorem, we derive several useful equations from certain iteration formulas for computing these Dirichlet eigenvalues, and we estimate the eigenvalues numerically. Moreover, we present error estimates and include a numerical example. - oai:arXiv.org:2512.07470v1 - math.SP - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Cemile Nur, Oktay Veliev - - - Recovery of the optimal control value function in reproducing kernel Hilbert spaces from verification conditions - https://arxiv.org/abs/2512.07477 - arXiv:2512.07477v1 Announce Type: new -Abstract: Approximating the optimal value function $v^*$ for infinite-horizon, nonlinear, autonomous optimal control problems is both challenging and essential for synthesizing real-time optimal feedback. We develop an abstract optimal recovery framework in reproducing kernel Hilbert spaces (RKHS) for reconstructing unknown target functions from mixed equality and inequality functional constraints. Within this framework, the approximation of $v^*$ is cast as a collocation-type problem derived from verification conditions for optimality -- most prominently, the Hamilton-Jacobi-Bellman (HJB) equation -- that uniquely characterizes $v^*$. As the set of collocation points becomes dense in the ambient domain $\Omega$, we establish convergence of the RKHS approximants to $v^*$: globally on $\Omega$ in the RKHS norm when $v^*$ is analytic, and locally (in a neighborhood of the origin) in the RKHS norm when $v^*$ is bounded from above and below by quadratic functions. Furthermore, we show that a practical numerical realization of the abstract scheme reduces to the classical policy iteration algorithm. Numerical experiments support the effectiveness of the proposed approach. - oai:arXiv.org:2512.07477v1 - math.OC - cs.NA - math.NA - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Tobias Ehring, Behzad Azmi, Bernard Haasdonk - - - Entire Functions on Lie Groups - https://arxiv.org/abs/2512.07479 - arXiv:2512.07479v1 Announce Type: new -Abstract: Every Lie group $G$ carries a distinguished algebra of particularly well-behaved real-analytic mappings: The entire functions $\mathcal{E}(G)$. They were introduced for the purposes of strict deformation quantization. This paper establishes a one-to-one correspondence between entire functions and holomorphic mappings $\mathcal{H}(G_\mathbb{C})$ on the universal complexification $G_\mathbb{C}$ of $G$ as Fr\'{e}chet algebras. Methodically, this is achieved by porting aspects of classical complex analysis into a left-invariant guise and by studying the geometry of $G_\mathbb{C}$. As a byproduct, we obtain a strict deformation quantization of the holomorphic cotangent bundle of any universal complexification. - oai:arXiv.org:2512.07479v1 - math.CV - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Michael Heins - - - Interior $C^{1,\alpha}$ regularity of mixed local-nonlocal $(p,q)$-energy minimizers for $p\leq sq$ - https://arxiv.org/abs/2512.07481 - arXiv:2512.07481v1 Announce Type: new -Abstract: We establish the local $C^{1, \alpha}$ regularity of minimizers for functionals of the form $$w\to \int_{\Omega}(|\nabla w|^p-fw) dx + \int_{\mathbb{R}^n}\int_{\mathbb{R}^n} \frac{|w(x)-w(y)|^q}{|x-y|^{n+sq}}dx\, dy,$$ where $s \in (0, 1)$, $1 < p \leq sq$, and $f \in L^\infty(\Omega)$. This result complements the work of De Filippis and Minigione in \cite{DFM}, thereby completing the proof of $C^{1,\alpha}$ regularity for all $p, q \in (1, \infty)$ and $s \in (0, 1)$ with locally bounded source term. - oai:arXiv.org:2512.07481v1 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Anup Biswas, Erwin Topp - - - Mod-$\ell$ monodromy of double covers of $\mathbb{P}^n$ branched along hyperplane arrangements - https://arxiv.org/abs/2512.07488 - arXiv:2512.07488v1 Announce Type: new -Abstract: We determine the mod-$\ell$ geometric monodromy group of the universal family of double covers of projective space branched along hyperplane arrangements in general position. - oai:arXiv.org:2512.07488v1 - math.AG - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Xiaopeng Xia, Jinxing Xu - - - Enumeration of Finite Distance Monoids - https://arxiv.org/abs/2512.07499 - arXiv:2512.07499v1 Announce Type: new -Abstract: Building on the work of Gabriel Conant, we investigate the enumeration problems of finite distance monoids by applying the decomposition of Archimedean classes and studying their internal arithmetic progressions. Specifically, we first determine the exact value of $DM(n,2)$, which denotes the number of distance monoids on $n$ non-zero elements with Archimedean complexity $2$. This computation allows us to resolve a conjecture of Conant, establishing that the total number $DM(n)$ of distance monoids grows at least exponentially in $n$. Furthermore, we study the asymptotic behavior of $DM(n,n-k)$ for fixed $k$, proving that $DM(n,n-k) = O(n^k)$ and providing an exact formula for $DM(n,n-2)$. - oai:arXiv.org:2512.07499v1 - math.CO - math.LO - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Yunjie Luo, Jie Sheng - - - A foliated viewpoint on homotopy Brouwer theory - https://arxiv.org/abs/2512.07510 - arXiv:2512.07510v1 Announce Type: new -Abstract: Brouwer homeomorphisms are fixed-point-free, orientation-preserving homeomorphisms of the plane. In recent years, their dynamics have been mostly studied through two complementary approaches, one introduced by Handel and the other by Le Calvez, each offering a distinct perspective on the behavior of Brouwer homeomorphisms. In this work, we present a unified framework that allows Le Calvez's foliated methods to recover, and in some cases improve, the classical results of Handel's theory. - oai:arXiv.org:2512.07510v1 - math.DS - math.GT - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Nelson Schuback - - - Compressible Euler equations with time-dependent damping in the critical regularity setting: global well-posedness and strong relaxation limit - https://arxiv.org/abs/2512.07516 - arXiv:2512.07516v1 Announce Type: new -Abstract: We investigate the relaxation problem and the diffusion phenomenon for the compressible Euler system with a time-dependent damping coefficient of the form $\tfrac{\mu}{(1+t)^{\lambda}}$ in $\mathbb{R}^d$ $(d \geq 1)$. We establish uniform regularity estimates with respect to the relaxation parameter $\varepsilon$ and prove the global well-posedness of classical solutions to the Cauchy problem. In addition, we justify the global-in-time strong convergence of the solutions towards those of a general porous medium-type diffusion system, with an explicit rate of convergence, and for ill-prepared initial data. The core of our proof relies on a refined hypocoercivity framework combined with a new time-dependent frequency decomposition, both adapted to handle damping terms with time-dependent coefficients. This enables us to treat the overdamped regime $\lambda \in (-\infty,0)$ and the underdamped regime $\lambda \in (0,1)$ for any $\mu>0$, and also the borderline critical case $\lambda=1$ under the improved condition $\mu>2\varepsilon^2$. - oai:arXiv.org:2512.07516v1 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Timoth\'ee Crin-Barat, Xinghong Pan, Ling-Yun Shou, Qimeng Zhu - - - A linear MARS method for three-dimensional interface tracking - https://arxiv.org/abs/2512.07524 - arXiv:2512.07524v1 Announce Type: new -Abstract: For explicit interface tracking in three dimensions, we propose a linear MARS method that (a) represents the interface by a partially ordered set of glued surfaces and approximates each glued surface with a triangular mesh, (b) maintains an $(r,h,\theta)$-regularity on each triangular mesh so that the distance between any pair of adjacent markers is within the range $[rh,h]$ and no angle in any triangle is less than $\theta$, (c) applies to three-dimensional continua with arbitrarily complex topology and geometry, (d) preserves topological structures and geometric features of moving phases under diffeomorphic and isometric flow maps, and (e) achieves second-order and third-order accuracy in terms of the Lagrangian and Eulerian length scales, respectively. Results of classic benchmark tests verify the effectiveness of the novel mesh adjustment algorithms in enforcing the $(r,h,\theta)$-regularity and demonstrate the high accuracy and efficiency of the proposed linear MARS method. - oai:arXiv.org:2512.07524v1 - math.NA - cs.NA - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Yunhao Qiu, Qinghai Zhang - - - Variet\`a di Jacobi parziali - https://arxiv.org/abs/2512.07529 - arXiv:2512.07529v1 Announce Type: new -Abstract: The notion of partial Jacobi manifold is introduced in the convenient ($c^\infty$-complete) framework of Fr\"olicher, Kriegl, and Michor. Explicit examples are provided in both finite and infinite dimensions, and the characteristic distribution associated with this structure is analysed. Several research directions that would merit further study are indicated. - oai:arXiv.org:2512.07529v1 - math.DG - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Patrick Cabau - - - Chaotic and Predictable Representations for Markov Additive Processes with Levy Modulator - https://arxiv.org/abs/2512.07534 - arXiv:2512.07534v1 Announce Type: new -Abstract: Our main result is the martingale representations for Markov additive processes where the modulator is a Levy process. These processes have three parts: the modulator, the jumps of the ordinate triggered by the modulator, and the semimartingale part of the ordinate with parameters depending on the modulator. We orthogonalize Teugels martingales constructed from these parts to give a chaotic representation of square-integrable random variables as a sum of stochastic integrals with respect to the orthogonal sequence obtained. Consequently, a predictable representation of square-integrable martingales is derived in terms of the ordinate and the Teugels martingales. - oai:arXiv.org:2512.07534v1 - math.PR - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Celal Umut Yaran, Mine \c{C}a\u{g}lar - - - Intersection problems for linear codes and polynomials over finite fields - https://arxiv.org/abs/2512.07547 - arXiv:2512.07547v1 Announce Type: new -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:2512.07547v1 - math.CO - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Sam Adriaensen - - - An Infinite Transitivity Theorem - https://arxiv.org/abs/2512.07549 - arXiv:2512.07549v1 Announce Type: new -Abstract: In this note, we promote an infinite Kadison transitivity theorem on massive $C^*$-algebras, including the Calkin algebra. This transitivity stems from the analog of countable degree-1 saturation on pure states which is inherited from these algebras via excision. We show this saturation to be equivalent to several order-theoretic properties on the quantum filter associated to the state, in particular the property of being a quantum P-point. While we show their existence is independent from ZFC, under basic set theoretic assumptions, we produce a plethora of these states. Finally, we find an irreducible representation of the Calkin algebra which fails infinite transitivity. - oai:arXiv.org:2512.07549v1 - math.OA - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Miles Gould - - - Universal Hitchin moduli spaces - https://arxiv.org/abs/2512.07553 - arXiv:2512.07553v1 Announce Type: new -Abstract: We study metric aspects of the universal moduli space of solutions to Hitchin's equations as the complex structure $J$ varies over the Teichm\"uller space $\mathcal{T}$ of a closed surface $\Sigma$. Our approach is gauge theoretical and builds on the theory of K\"ahler fibrations and the moment map interpretation of constant scalar curvature K\"ahler metrics. Our first main result establishes that, over the moduli space of cscK metrics, the universal moduli space of solutions to Hitchin's equations carries a natural complex structure together with a family of pseudo-K\"ahler metrics forming a K\"ahler fibration with a K\"ahler Ehresmann connection. - We then investigate a second universal moduli space, constructed from the space of flat $G$-connections over $\mathcal{T}$, which admits a nontrivial $J$-dependent K\"ahler fibration structure discovered by Hitchin. Using symplectic reduction, we build universal moduli spaces of solutions to the harmonicity equations depending on a coupling constant $\alpha$, obtaining natural complex and pseudo-K\"ahler structures and an explicit K\"ahler potential. The main novelty here is that this moduli space is defined by a system coupling the scalar curvature with a cubic term in the Higgs field. Finally, we propose a conjectural relationship between the two resulting families of moduli spaces in the weak-coupling limit $\alpha\to 0$, inspired by the twistor geometry of Hitchin's hyperk\"ahler moduli space. - oai:arXiv.org:2512.07553v1 - math.DG - math.AG - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Luis \'Alvarez-C\'onsul, Mario Garcia-Fernandez, Oscar Garc\'ia-Prada, Samuel Trautwein - - - A simple proof of exponential decay for the near-critical planar Ising model - https://arxiv.org/abs/2512.07554 - arXiv:2512.07554v1 Announce Type: new -Abstract: For the Ising model defined on $a\mathbb{Z}^2$ at critical temperature with external field $a^{15/8}h$, we give a simple and elementary proof that its truncated two-point function decays exponentially. The proof combines the high temperature expansion, random-cluster and random current representations. A new input in the proof is that, in the near-critical sourceless single current measure, there are many loops formed by a path on $a\mathbb{Z}^2$ with diameter of order $1$, together with two external edges that connect the path's endpoints to the ghost. - oai:arXiv.org:2512.07554v1 - math.PR - math-ph - math.MP - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Jianping Jiang, Frederik Ravn Klausen - - - Monotonicity of the period function for planar Hamiltonian vector fields: A Generalization of Chicone's Criterion - https://arxiv.org/abs/2512.07556 - arXiv:2512.07556v1 Announce Type: new -Abstract: This paper investigates the monotonicity of the period function associated with planar Hamiltonian systems of the form $H(x,y) = F(x) + G(y)$. We establish sufficient conditions ensuring the monotonicity of the period function corresponding to a nondegenerate center, expressed explicitly in terms of the functions F and G. Our approach extends Chicone's classical criterion, originally formulated for systems of the type $x' = y$, $y' = -F'(x)$, to a broader Hamiltonian framework. As a main application, we analyze the monotonicity of the period function associated with the center at (0,0) of the polynomial Hamiltonian system $$H(x,y) = (1/2)x^2 + (a/3)x^3 + (b/4)x^4 + (1/2)y^2 + (c/4)y^4,$$ as a function of the parameters $a, b, c \in \mathbb{R}$. - oai:arXiv.org:2512.07556v1 - math.DS - math.CA - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - F. J. S. Nascimento - - - An effective criterion for multiple positive zeros of vertically parametrized polynomial systems - https://arxiv.org/abs/2512.07560 - arXiv:2512.07560v1 Announce Type: new -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:2512.07560v1 - math.AG - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Carles Checa, Elisenda Feliu - - - Renewal Hawkes Processes: Expectations and Applications - https://arxiv.org/abs/2512.07563 - arXiv:2512.07563v1 Announce Type: new -Abstract: Hawkes processes are point processes with self-exciting and clustering properties that are popular in applications. In recent years, renewal Hawkes processes have gained attention, due to their versatility such as the capability of capturing dependence between clusters. In this paper, three classes of novel renewal Hawkes processes are introduced after incorporating exogenous and endogenous renewal factors. The relationship among five related Hawkes processes is studied. The expectations of the three classes of renewal Hawkes processes are derived by establishing a set of integral equations. A general common renewal equation for these expectations is derived and further discussions are provided. The special case of constant exogenous factor is discussed as well for the three proposed Hawkes processes. Finally, we apply our proposed models to study the optimization problems that arise in a periodic replacement policy for systems with cascading failures and provide numerical illustrations. The numerical solutions rely on computing the expectations of the proposed renewal Hawkes processes that can be efficiently obtained by using the direct Riemann integration method. - oai:arXiv.org:2512.07563v1 - math.PR - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Lirong Cui, Yongji Zhang, Lingjiong Zhu - - - On the Integral Cohomology of Fano Varieties of Linear Subspaces - https://arxiv.org/abs/2512.07572 - arXiv:2512.07572v1 Announce Type: new -Abstract: For each $n$, each dimension $r$, and each subscheme $X \subset \mathbb{P}^n$ defined as the common zero-locus of $s$ hypersurfaces, of degrees $\mathbf{d} = (d_1, \ldots , d_s)$ say, the Fano variety $F_r(X)$ of projective $r$-spaces contained in $X$ is a subvariety of the Grassmannian $G(r + 1, n + 1)$. We prove that the inclusion $F_r(X) \subset G(r + 1, n + 1)$ induces an isomorphism $H^i(G(r + 1, n + 1); \mathbb{Z}) \rightarrow H^i(F_r(X); \mathbb{Z})$ on integral cohomology for certain indices $i$ (i.e., depending only on $n$, $r$, $s$ and $\mathbf{d}$). Our result extends to the integral setting a result proved for rational cohomology by Debarre and Manivel (Math. Ann. '98), and answers a question of Benoist and Voisin. Our techniques adapt ones introduced by Tu (Trans. Am. Math. Soc. '89) for a different purpose. - oai:arXiv.org:2512.07572v1 - math.AG - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Benjamin E. Diamond - - - The index of $t\mathcal{{C}}_{3}^{-}$-free signed graphs - https://arxiv.org/abs/2512.07579 - arXiv:2512.07579v1 Announce Type: new -Abstract: The classical spectral Tur\'{a}n problem is to determine the maximum spectral radius of an $F$-free graph of order $n$. This paper extends this framework to signed graphs. Let $\mathcal{C}_r^-$ be the set of all unbalanced signed graphs with underlying graphs $C_r$. Wang, Hou and Li [Linear Algebra Appl, 681 (2024) 47-65] previously determined the spectral Tur\'{a}n number of $\mathcal{C}_{3}^{-}$. In the present work, we characterize the extremal graphs that achieve the maximum index among all unbalanced signed graphs of order $n$ that are $t\mathcal{C}{3}^{-}$-free for $t\geq 2$. Furthermore, for $t\geq 3$, we identify the graphs with the second maximum index among all $t\mathcal{C}{3}^{-}$-free unbalanced signed graphs of fixed order $n$. - oai:arXiv.org:2512.07579v1 - math.CO - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Dan Li, Mingsong Qin - - - A Difference Formula for Tensor-power Multiplicities - https://arxiv.org/abs/2512.07586 - arXiv:2512.07586v1 Announce Type: new -Abstract: A novel combinatorial formula is developed for for tensor product multiplicities in representation theory. We introduce a difference formula linking these multiplicities to restricted occupancy coefficients via a shifted operator. This method is extended to derive branching rules for subalgebras and is conjecturally applied to A-type Lie superalgebras. - oai:arXiv.org:2512.07586v1 - math.RT - hep-th - math-ph - math.MP - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Hongfei Shu, Peng Zhao, Rui-Dong Zhu, Hao Zou - - - A note on proper asymptotic uniqueness for semifinite factors - https://arxiv.org/abs/2512.07587 - arXiv:2512.07587v1 Announce Type: new -Abstract: Let $\mathcal{A}$ be a separable nuclear C*-algebra, and let $\mathcal{M}$ be a semifinite von Neumann factor with separable predual. Let $\phi, \psi: \mathcal{A} \rightarrow \mathcal{M}$ be essential trivial extensions with $\phi(a) - \psi(a) \in \mathcal{K}_{\mathcal{M}}$ for all $a \in \mathcal{A}$ such that either both $\phi$ and $\psi$ (and hence $\mathcal{A}$) are unital or both $\phi$ and $\psi$ have large complement. Then $\phi$ and $\psi$ are properly asymptotically unitarily equivalent if and only if $[\phi, \psi]_{CS} = 0$ in $KK(\mathcal{A}, \mathcal{C}(S \mathcal{K}_{\mathcal{M}}))$. - oai:arXiv.org:2512.07587v1 - math.OA - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Ping Wong Ng, Cangyuan Wang - - - A Closed-form Solution to the Wahba Problem for Pairwise Similar Quaternions - https://arxiv.org/abs/2512.07597 - arXiv:2512.07597v1 Announce Type: new -Abstract: We present a closed-form solution to Wahba's problem in the quaternion domain for the special case of two vector observations. Existing approaches, including Davenport's $q$-method, QUEST, Horn's method, and ESOQ algorithms, recover the optimal quaternion through the eigendecomposition of a $4\times4$ matrix or iterative numerical methods. Consequently, these methods do not reveal the analytic structure of the optimal quaternion. - In this work, we derive an explicit analytical characterization of all quaternions that yield zero Wahba cost for the case $\ell=2$. Our approach builds on a connection between quaternion similarity, the singular Sylvester equation $aq=qb$, and quaternion square roots established in our previous work [1]. We provide (i) necessary and sufficient conditions under which the Wahba's cost function is zero and (ii) a closed-form parameterization of all such quaternions. This eliminates the need for eigenvalue computations and enables a direct algebraic understanding of the underlying geometry of Wahba's problem. - oai:arXiv.org:2512.07597v1 - math.RA - cs.NA - math.NA - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Hristina Radak, Christian Scheunert, Frank H. P. Fitzek - - - Homological Methods in the Generalization of Drinfeld Modules - https://arxiv.org/abs/2512.07607 - arXiv:2512.07607v1 Announce Type: new -Abstract: We introduce and study a natural class of Anderson t- modules, called triangular t-modules, characterized by having Drinfeld modules as their $\tau$-composition factors. They form a homologically meaningful generalization of Drinfeld modules and exhibit rich arithmetic structure.\smallskip - We establish criteria for purity, strict and almost strict, and develop a reduction procedure that lowers the degrees of the defining biderivations. As a consequence, every almost strictly pure triangular t-module becomes strictly pure after a finite base extension. - We then investigate morphisms and isogenies between triangular t-modules, provide a characterization of triangular isogenies, and describe the algebra of endomorphisms, including a criterion for commutativity. On the analytic side, we show that all triangular t- modules are uniformizable and establish finiteness and purity criteria with consequences for Taelman's conjecture. - Finally, we develop a duality theory for triangular t- modules and their biderivations, proving compatibility with $\tau$-composition series and establishing analogues of the Cartier-Nishi theorem and the Weil-Barsotti formula. - oai:arXiv.org:2512.07607v1 - math.NT - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Dawid E. K\k{e}dzierski, Piotr Kraso\'n - - - Well-posedness of the 3-D compressible Navier-Stokes equations with density-dependent viscosities in exterior domains with far-field vacuum - https://arxiv.org/abs/2512.07614 - arXiv:2512.07614v1 Announce Type: new -Abstract: This paper investigates the local existence and uniqueness of strong solutions to the three-dimensional compressible Navier-Stokes equations with density-dependent viscosities in exterior domains. When both the shear and bulk viscosity coefficients depend on the density in a power law ($\rho^{\delta}$ with $0<\delta<1$) and Navier-slip boundary condition on the velocity is imposed, base on a reformulation of the problem using new variables to handle the degeneracy near vacuum, we establish the local well-posedness of regular solutions with far-field vacuum in inhomogeneous Sobolev spaces. Compared to the Cauchy problem, the initial-boundary value problem requires establishing non-standard weighted estimates and handling the unavailability of boundary conditions for higher-order terms. Our approach addresses these challenges via the conormal space technique. - oai:arXiv.org:2512.07614v1 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Hairong Liu, Hua Zhong - - - Long- and short-time behavior of hypocoercive evolution equations with higher index via modal decompositions - https://arxiv.org/abs/2512.07617 - arXiv:2512.07617v1 Announce Type: new -Abstract: Hypocoercivity emerged in kinetic transport theory, allowing to derive exponential long-time estimates for evolution equations. Recently, the short-time asymptotics for equations with dissipative generators were obtained using the hypocoercivity index that is in finite dimensions surprisingly given by a Kalman-type rank condition well-known in control theory. However, the situation for unbounded generators is only understood for index one if modal decompositions are available. Here, we prove long- and short-time estimates for unbounded generators with higher index admitting a modal decomposition. Additionally, an explicit Lyapunov functional is constructed. The result is applied to a class of port-Hamiltonian systems with distributed dissipation. - oai:arXiv.org:2512.07617v1 - math.AP - math.FA - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Marco Roschkowski, Hannes Gernandt - - - Approximating sub-riemannian structures by Riemannian metrics and spectral convergence - https://arxiv.org/abs/2512.07621 - arXiv:2512.07621v1 Announce Type: new -Abstract: We construct an approximating sequence of Riemannian metrics tailored to a given sub-Riemannian structure. We prove that the sequence of associated Riemannian volumes converge to Popp's volume and we then proceed to study the spectral convergence of the associated Laplace operators. - oai:arXiv.org:2512.07621v1 - math.DG - math.AP - math.SP - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Leo Harakeh, Luc Hillairet - - - Location and scatter halfspace median under {\alpha}-symmetric distributions - https://arxiv.org/abs/2512.07634 - arXiv:2512.07634v1 Announce Type: new -Abstract: In a landmark result, Chen et al. (2018) showed that multivariate medians induced by halfspace depth attain the minimax optimal convergence rate under Huber contamination and elliptical symmetry, for both location and scatter estimation. We extend some of these findings to the broader family of {\alpha}-symmetric distributions, which includes both elliptically symmetric and multivariate heavy-tailed distributions. For location estimation, we establish an upper bound on the estimation error of the location halfspace median under the Huber contamination model. An analogous result for the standard scatter halfspace median matrix is feasible only under the assumption of elliptical symmetry, as ellipticity is deeply embedded in the definition of scatter halfspace depth. To address this limitation, we propose a modified scatter halfspace depth that better accommodates {\alpha}-symmetric distributions, and derive an upper bound for the corresponding {\alpha}-scatter median matrix. Additionally, we identify several key properties of scatter halfspace depth for {\alpha}-symmetric distributions. - oai:arXiv.org:2512.07634v1 - math.ST - stat.ME - stat.TH - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - 10.1080/10485252.2025.2600417 - Filip Bo\v{c}inec, Stanislav Nagy - - - Factorization envelopes and enveloping vertex algebras - https://arxiv.org/abs/2512.07635 - arXiv:2512.07635v1 Announce Type: new -Abstract: We construct a factorization algebra, via the factorization envelope, starting from a Lie conformal algebra, and prove that the associated vertex algebra is isomorphic to its enveloping vertex algebra. Our construction generalizes the Kac--Moody factorization algebra of Costello--Gwilliam and the Virasoro factorization algebra of Williams. Moreover, by considering the super analogue of this construction, we obtain new factorization algebras corresponding to vertex superalgebras, such as the Neveu--Schwarz vertex superalgebra and the $N=2$ vertex superalgebra. - oai:arXiv.org:2512.07635v1 - math.QA - math-ph - math.MP - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Yusuke Nishinaka - - - Kru\v{z}kov-type uniqueness theorem for a non-monotone flow function case with application to Riemann problem solutions - https://arxiv.org/abs/2512.07639 - arXiv:2512.07639v1 Announce Type: new -Abstract: We generalize the previously obtained Kru\v{z}kov-type uniqueness result for the initial-boundary value problem for the chemical flood conservation law system to the case of an almost arbitrary flow function, not restricted by the S-shaped condition or the monotonicity with respect to the chemical agent concentration. The result is applied to the analysis of the Riemann problem solutions for an S-shaped flow function changing monotonicity with respect to the chemical concentration exactly once. All possible Riemann problem solution structures are classified, including certain unique structures that have not been described in earlier studies. - Keywords: Initial-boundary value problem; Riemann problem; first-order hyperbolic system; conservation laws; shock waves; uniqueness theorem; vanishing viscosity; chemical flood. - oai:arXiv.org:2512.07639v1 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Yulia Petrova, Nikita Rastegaev - - - On the singular elliptic problem involving the variable order fractional Musielak $g_{x,y}$-Laplacian - https://arxiv.org/abs/2512.07645 - arXiv:2512.07645v1 Announce Type: new -Abstract: In this paper, we investigate the existence of positive weak solutions to a nonlocal singular elliptic problem under Dirichlet boundary condition. Problem is settled in fractional Musielak-Sobolev spaces with variable order. The main tool is variational approach, however, various auxiliary tools from the theory of nonlinear functional analysis, convex analysis - and critical point theory are also applied. - oai:arXiv.org:2512.07645v1 - math.AP - math.FA - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Azeddine Baalal, Mohamed Berghout, El-Houcine Ouali - - - Energy-Aware Aggregation of Input Data for the Optimisation of Heat Supply of Municipal Districts - https://arxiv.org/abs/2512.07646 - arXiv:2512.07646v1 Announce Type: new -Abstract: In the context of municipal heat planning, it is imperative to consider the numerous buildings, numbering in the hundreds or thousands, that are involved. This poses particular challenges for model-based energy system optimization, as the number of variables increases with the number of buildings under consideration. In the worst case, the computational complexity of the models experiences an exponential increase with the number of variables. Furthermore, within the context of heat transition, it is often necessary to map extended periods of time (i.e., the service life of systems) with high resolution (particularly in the case of load peaks that occur at the onset of the day). In response to these challenges, the aggregation of input data is a common practice. In general, building blocks or other geographical and urban formations, such as neighbourhoods, are combined. This article explores the potential of incorporating energy performance indicators into the grouping of buildings. The case study utilizes authentic data from the Neu-Schwachhausen district, grouped based on geographical location, building geometry, and energy performance indicators. The selection of energy indicators includes the annual heat consumption as well as the potential for solar energy generation. To this end, a methodology is hereby presented that considers not only the anticipated annual energy quantity, but also its progression over time. We present a full workflow from geodata to a set of techno-socio-economically Pareto-optimal heat supply options. Our findings suggest that it is beneficial to find a balance between geographical position and energy properties when grouping buildings for the use in energy system models. - oai:arXiv.org:2512.07646v1 - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Patrik Sch\"onfeldt, Elif Turhan - - - Convergence of weighted branching processes - https://arxiv.org/abs/2512.07653 - arXiv:2512.07653v1 Announce Type: new -Abstract: We study the long-term behavior of weighted multi-type branching processes, focusing on extending classical laws of large numbers and martingale convergence to settings with infinitely many weighted particles, arbitrary type spaces and non-geometric rescaling. We demonstrate applications to Galton-Watson trees indexed by random weights and by random kernels, convergence in Wasserstein distance of the underlying mean semi-group, and convergence of ergodic averages along lineages. - oai:arXiv.org:2512.07653v1 - math.PR - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Denis Villemonais, Nicolas Zalduendo - - - $\mathcal{M}$-points of bounded height - https://arxiv.org/abs/2512.07654 - arXiv:2512.07654v1 Announce Type: new -Abstract: We initiate a general quantitative study of sets of $\mathcal{M}$-points, which are special subsets of rational points, generalizing Campana points, Darmon points, and squarefree solutions of Diophantine equations. We propose an asymptotic formula for the number of $\mathcal{M}$-points of bounded height on rationally connected varieties, extending Manin's conjecture as well as its generalization to Campana points by Pieropan, Smeets, Tanimoto and V\'arilly-Alvarado. Finally, we show that the conjecture explains several previously established results in arithmetic statistics. - oai:arXiv.org:2512.07654v1 - math.NT - math.AG - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Boaz Moerman - - - A quantitative dynamical Zhang fundamental inequality and Bogomolov-type problems - https://arxiv.org/abs/2512.07655 - arXiv:2512.07655v1 Announce Type: new -Abstract: We prove a quantitative version of Zhang's fundamental inequality for heights attached to polarizable endomorphisms. As an application, we obtain a gap principle for the N\'eron-Tate height on abelian varieties over function fields of arbitrary transcendence degree and characteristic zero, extending the result of Gao-Ge-K\"uhne. We also establish instances of effective gap principles for regular polynomial endomorphisms of $\mathbb{P}^2$, in the sense that all constants can are explicit. These yield effective instances of uniformity in the dynamical Bogomolov conjecture in both the arithmetic and geometric settings, including examples in prime characteristic. - oai:arXiv.org:2512.07655v1 - math.NT - math.AG - math.DS - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Niki Myrto Mavraki, Jit Wu Yap - - - Entropy--Smooth Structures on Topological Manifolds - https://arxiv.org/abs/2512.07660 - arXiv:2512.07660v1 Announce Type: new -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:2512.07660v1 - math.DG - math.GN - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Amandip Sangha - - - Neural Compress-and-Forward for the Primitive Diamond Relay Channel - https://arxiv.org/abs/2512.07662 - arXiv:2512.07662v1 Announce Type: new -Abstract: The diamond relay channel, where a source communicates with a destination via two parallel relays, is one of the canonical models for cooperative communications. We focus on the primitive variant, where each relay observes a noisy version of the source signal and forwards a compressed description over an orthogonal, noiseless, finite-rate link to the destination. Compress-and-forward (CF) is particularly effective in this setting, especially under oblivious relaying where relays lack access to the source codebook. While neural CF methods have been studied in single-relay channels, extending them to the two-relay case is non-trivial, as it requires fully distributed compression without any inter-relay coordination. We demonstrate that learning-based quantizers at the relays can harness input correlations by operating remote, yet in a collaborative fashion, enabling effective distributed compression in line with Berger-Tung-style coding. Each relay separately compresses its observation using a one-shot learned quantizer, and the destination jointly decodes the source message. Simulation results show that the proposed scheme, trained end-to-end with finite-order modulation, operates close to the known theoretical bounds. These results demonstrate that neural CF can scale to multi-relay systems while maintaining both performance and interpretability. - oai:arXiv.org:2512.07662v1 - cs.IT - math.IT - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Ozan Ayg\"un, Ezgi Ozyilkan, Elza Erkip - - - On Borel orbits of quadratic forms in characteristic 2 - https://arxiv.org/abs/2512.07669 - arXiv:2512.07669v1 Announce Type: new -Abstract: We consider the spherical variety of quadratic forms over a quadratically closed field of characteristic 2, and determine its orbits for the action of the Borel subgroup of upper triangular matrices. We exhibit a connection between these orbits and the Catalan triangle numbers. In addition, we describe explicitly a natural Weyl group action on the set of Borel orbit double covers - oai:arXiv.org:2512.07669v1 - math.AG - math.CO - math.RT - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Yasmine B. Sanderson - - - Equidistant dimension of Cartesian product graphs - https://arxiv.org/abs/2512.07672 - arXiv:2512.07672v1 Announce Type: new -Abstract: Given a connected graph $G$, the equidistant dimension of $G$ represents the cardinality of the smallest set of vertices $S$ of $G$ such that for any two vertices $x,y\notin S$ there is at least one vertex in $S$ equidistant to both $x,y$ in terms of distances. In this article, we compute the equidistant dimension of some Cartesian product graphs including two-dimensional Hamming graphs, some hypercubes, prisms of cycle, and squared grid graphs. - oai:arXiv.org:2512.07672v1 - math.CO - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Adria Gispert-Fernandez, Juan A. Rodriguez-Velazquez, Ismael G. Yero - - - On the Poles of Real Archimedean Zeta Functions - https://arxiv.org/abs/2512.07679 - arXiv:2512.07679v1 Announce Type: new -Abstract: This paper studies the poles of the real Archimedean zeta function for a weighted homogeneous polynomial $f \in \mathbb{R}[x, y]$ with an isolated singularity at the origin. By applying a weighted blow-up, we derive the meromorphic continuation of $Z_{f,\varphi}$ to $\text{Re }s > -1$. This explicit expression yields a necessary and sufficient condition for a root $s \in (-1, 0)$ of the Bernstein-Sato polynomial $b_f(s)$ to be a pole of $Z_{f,\varphi}$. Unlike the complex case established by F. Loeser (1985), this condition may fail in certain obvious cases -- such as when $f$ is odd or even in $x$, $y$, or $(x, y)$ -- so not all such roots necessarily become poles. - oai:arXiv.org:2512.07679v1 - math.AG - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Zhikuang Chen, Huaiqing Zuo - - - Optimal Control of a Higher-Order Cahn-Hilliard Equation Coupled with Brinkman Equation - https://arxiv.org/abs/2512.07682 - arXiv:2512.07682v1 Announce Type: new -Abstract: In this work, we investigate optimal control of a Brinkman equation couple with sixth-order Cahn-Hilliard equation. The Cahn-Hilliard equation is endowed with a source term accounting for mass exchange and the velocity equation contains a non divergence-free forcing term, which act as distributed control variable. We consider the aforementioned system with constant mobility, viscosity and nonlinearity of double-well shape is regular. The cost functional of the optimal control problem contains a nondifferentiable term like the $L^1$-norm with sparsity constant $\kappa$, which leads to sparsity of optimal controls. We study the first order necessary optimality condition for both the case $\kappa=0$ and $\kappa>0.$ When the cost functional is differentiable, first order necessary optimality conditions are characterized by Lagrange multiplier method and for nondifferentiable case we have used the idea of Casas and Tr\"oltzsch from the paper (Math. control Relat. Fields, 10(3):527-546, 2020). - oai:arXiv.org:2512.07682v1 - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Manika Bag - - - Generalized Higman's Theorem and iterated ideals - https://arxiv.org/abs/2512.07685 - arXiv:2512.07685v1 Announce Type: new -Abstract: Generalized Higman's Theorem is the direct counterpart of Higman's Theorem that asserts the closure of the class of \emph{better} quasi-orders, instead of the class of \emph{well} quasi-orders, under the construction $P\mapsto P^{<\omega}$ of the embeddability order on finite sequences. Traditionally, this result is obtained as a consequence of very powerful and general techniques of Nash-Williams. In this paper, we propose a new proof of this result that is based on an explicit characterization of the underlying orders. In particular, this new technique allows us to formalize the proof of the result in the formal theory $\mathsf{atr}_0$, thus resolving a long-standing open problem in the field of reverse mathematics. - The main ingredient of our proof is the introduction of a transfinite hierarchy of orders $\dot I^*_\alpha(P)$ starting with $\dot I^*_0(P)=P$ and $\dot I^*_{\alpha+1}(P)$ being the inclusion order on ideals of $\dot I^*_{\alpha}(P)$. On one hand, we show that a quasi-order $P$ is a bqo if and only if all $\dot I^*_\alpha(P)$ are wqos. On the other hand, under the assumption that $P$ is a bqo, we show that the $\dot I^*_\alpha(P^{<\omega})$ are wqos, and furthermore give a characterization of their structure in terms of a transfinite iteration of a Higman-like construction. The sufficiently explicit character of this proof allows us to formalize it in a rather straightforward manner. - oai:arXiv.org:2512.07685v1 - math.LO - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Fedor Pakhomov, Giovanni Sold\`a - - - A winning approach to the intersections of twisted non-recurrent sets with fractals - https://arxiv.org/abs/2512.07686 - arXiv:2512.07686v1 Announce Type: new -Abstract: In this paper, we prove that if $S\subseteq\mathbb{R}^d$ is hyperplane absolute winning on a closed hyperplane diffuse set $L\subseteq\mathbb{R}^d$, then $\mathrm{dim}_H S\cap K=\mathrm{dim}_H K$ for any irreducible self-conformal set $K\subseteq L$ without assuming any separation condition on $K$. The result is then applied to obtain the Hausdorff dimension of intersections between irreducible self-conformal sets and twisted non-recurrent sets $\mathrm{N}(T,\mathcal{G})$ defined as - $$ - \mathrm{N}(T,\mathcal{G}):=\left\{\mathbf{x}\in[0,1]^d:\liminf_{n\to\infty}\|T^n(\mathbf{x})-g_n(\mathbf{x})\|>0\right\}, - $$ - where $T:[0,1]^d\to[0,1]^d$ belongs to a broad class of product maps, $\mathcal{G}:=\{g_n\}_{n\in\mathbb{N}}$ is a sequence of self-maps on $[0,1]^d$ with uniform Lipschitz constant and $\|\cdot\|$ denotes the maximal norm in $\mathbb{R}^d$. When $T$ is the $\beta$-transformation on $[0,1]$, it provides a positive answer to a question raised informally by Broderick, Bugeaud, Fishman, Kleinbock and Weiss (Math. Res. Lett., 2010). For the case $T$ is a $d\times d$ diagonal matrix transformations, our results provide a partial answer asked in a paper of Li, Liao, Velani and Zorin (Adv. Math., 2023). A natural generalization to non-autonomous setting is also obtained. - oai:arXiv.org:2512.07686v1 - math.DS - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Junjie Huang, Bing Li, Bo Wang, Na Yuan - - - Decidability of equations and first-order theory in Seifert 3-manifold groups - https://arxiv.org/abs/2512.07690 - arXiv:2512.07690v1 Announce Type: new -Abstract: In [arXiv:1405.6274, Question 5.2 & Question 5.3] Aschenbrenner, Friedl and Wilton ask: (1) Is the equation problem solvable for the fundamental group of any $3$-manifold? and (2) Is the first-order theory of the fundamental group of any $3$-manifold decidable? In this paper we answer both of these questions by proving that Hilbert's tenth problem over the integers can be encoded in equations over any non-virtually abelian fundamental group of any Seifert fibered 3-manifold whose orbifold has non-negative Euler characteristic. We use this to show that the equation problem (and hence also the first-order theory) is undecidable in this infinite family of $3$-manifold groups and then apply it to classify the Seifert 3-manifold groups with decidable equation problems and decidable first-order theories, in the case that the orbifold has non-negative Euler characteristic. In contrast, we show that for this class of Seifert 3-manifold groups the single equation problem is decidable. For every Seifert 3-manifold group $G$ where the orbifold has negative Euler characteristic we show that either $G$ has decidable equation problem or $G$ has a finite index subgroup of index $2$ that has decidable equation problem. These negative Euler characteristic results follow from work of Liang on central extensions of hyperbolic groups. We also discuss why Liang's results do not suffice to deal with all the negative Euler characteristic cases. We show how to construct several other infinite families of $3$-manifold groups with undecidable equation problem (and hence also undecidable first-order theory) including examples that are not Seifert manifold groups and examples that are not virtually nilpotent. In addition, we observe that there are numerous other infinite families for which the first-order theory is undecidable such as fundamental groups of manifolds modeled on 3-dimensional Sol geometry. - oai:arXiv.org:2512.07690v1 - math.GR - math.GT - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Robert D. Gray, Alex Levine - - - Enhancing Channel Estimation for OTFS systems using Sparse Bayesian Learning with Adaptive Threshold - https://arxiv.org/abs/2512.07704 - arXiv:2512.07704v1 Announce Type: new -Abstract: Orthogonal time frequency space (OTFS) modulation is a two-dimensional modulation scheme designed in the delay-Doppler (DD) domain, exhibiting superior performance over orthogonal frequency division multiplexing (OFDM) modulation in environments with high Doppler frequency shifts. We investigated the channel estimation in the DD domain of OTFS systems, modeling it as a sparse signal recovery problem. Subsequently, within the existing sparse Bayesian learning framework, we proposed an adaptive Bayesian threshold-based active denoising mechanism. Combined with inverse-free sparse Bayesian learning, this effectively addresses the pseudo-peak issue in low signal-to-noise ratio (SNR) scenarios while maintaining low complexity. The simulation results demonstrate that this algorithm outperforms existing channel estimation algorithms in terms of anti-noise performance and complexity. - oai:arXiv.org:2512.07704v1 - cs.IT - math.IT - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Tengfei Qi, Yifei Yang, Xiong Deng, Zhinan Sun, Ziqiang Gao, Xihua Zou, Wei Pan, Lianshan Yan - - - The topology of local quaternionic toric actions - https://arxiv.org/abs/2512.07707 - arXiv:2512.07707v1 Announce Type: new -Abstract: In this paper we examine the topology of manifolds equipped with a local quaternionic toric action modeled on the regular representation of the quaternionic torus $Q^n=(S^3)^n$. Building on our previous work, where the toric, differential and tetraplectic foundations were established, we show that the global topology of such manifolds is determined by the orbit space and its characteristic data. We construct Leray--Serre and Atiyah--Hirzebruch spectral sequences for the orbit projection, yielding explicit descriptions of the cohomology and $K$-theory of manifolds equipped with local quaternionic toric actions. In dimension four, we develop a quaternionic analogue of the Meyer signature formula and we briefly outline an $L$-theoretic interpretation of the resulting signature invariants. These results extend the methods of the classical (complex) toric topology to the quaternionic setting. - oai:arXiv.org:2512.07707v1 - math.GT - math.AT - math.DG - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Panagiotis Batakidis, Ioannis Gkeneralis - - - $\sigma$-Porosity of Certain Ideals - https://arxiv.org/abs/2512.07711 - arXiv:2512.07711v1 Announce Type: new -Abstract: We investigate the $\sigma$-porosity of certain known ideals of subsets of natural numbers. Porosity is a notion of smallness in metric spaces that is stronger than nowhere density. Analogously, $\sigma$-porosity is a strengthening of meagerness. In this paper, we verify which ideals are $\sigma$-porous. - oai:arXiv.org:2512.07711v1 - math.LO - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Pawe{\l} Klinga, Andrzej Nowik, Anna W\k{a}sik - - - Stieltjes differential equations with bounded-variation derivators and application to thermal stress in solar panels - https://arxiv.org/abs/2512.07717 - arXiv:2512.07717v1 Announce Type: new -Abstract: In this work we extend the theory of Stieltjes systems beyond the monotone case, establishing new chain rules, generalized versions of the Fundamental Theorem of Calculus, compactness tools for Peano-type results, and a $g$-exponential for explicit linear solutions. Continuity notions relative to vector-valued derivators further allow us to study everywhere differentiable solutions. As an application, we model thermal stress effects on solar panels and battery health, highlighting the practical value of non-monotone derivators. - oai:arXiv.org:2512.07717v1 - math.CA - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Lamiae Maia, F. Adri\'an F. Tojo - - - Groupoid graded rings and their categories of graded modules - https://arxiv.org/abs/2512.07722 - arXiv:2512.07722v1 Announce Type: new -Abstract: Let $G$ be a groupoid acting on a set $X$ and let $R$ be a $G$-graded ring with graded local units. We study the main properties of the category $gr-(R,G,X)$ of $X$-graded $R$-modules and adjoint functors between categories of this kind. We characterize the latter in terms of tensor-like and hom-like functors. As an application we obtain a characterization of equivalences between such categories in the spirit of Morita theory. Then we introduce restriction and induction functors between categories of type $gr-(R,G,X)$ and show that many functors between such categories can be realized naturally as a restriction or induction functor. This includes the forgetful functor, the functor associating a $G$ graded $R$-module with the $H$-graded module formed by the sum of the homogeneous components of degree in subgroupoid $H$, and the one associating it with the collapsing of homogeneous components in cosets modulo $H$ for $H$ a wide subgrupoid. We characterize when a restriction or induction functor is an equivalence of categories. Finally, we prove that $gr-(R,G,X)$ is always equivalent to the category of modules over a ring with local units and, generalizing a result of Menini and N\u{a}st\u{a}sescu, we characterize when $gr-(R,G,X)$ is equivalent to the category of modules over a unital ring. - oai:arXiv.org:2512.07722v1 - math.RA - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Caio Antony, \'Angel del R\'io - - - Symmetric weak multicategories - https://arxiv.org/abs/2512.07732 - arXiv:2512.07732v1 Announce Type: new -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:2512.07732v1 - math.CT - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Volodymyr Lyubashenko - - - Index and nullity of minimal surface doublings, I - https://arxiv.org/abs/2512.07734 - arXiv:2512.07734v1 Announce Type: new -Abstract: We prove that for any large enough $m \in\mathbb{N}$, the genus $\gamma=m+1$ equator-poles minimal surface doubling of the equatorial two-sphere $\Sigma^0 = \mathbb{S}^2_{\mathrm{eq}}$ in the round three-sphere $\mathbb{S}^3$, which has two catenoidal bridges at the poles and $m$ bridges equidistributed along the equatorial circle $\mathscr{C}$ of $\Sigma^0 $ and was discovered in earlier work of Kapouleas, has index $2\gamma+5=2m+7$ and nullity $6$, and so it has no exceptional Jacobi fields and is $C^1$-isolated. - oai:arXiv.org:2512.07734v1 - math.DG - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Nikolaos Kapouleas, Jiahua Zou - - - Time-asymptotic behavior of the Boltzmann equation with random inputs in whole space and its stochastic Galerkin approximation - https://arxiv.org/abs/2512.07735 - arXiv:2512.07735v1 Announce Type: new -Abstract: We consider the Boltzmann equation with random uncertainties arising from the initial data and collision kernel in the {\it whole space}, along with their stochastic Galerkin (SG) approximations. By employing Green's function method, we show that, the higher-order derivatives of the solution with respect to the random variable exhibit polynomial decay over time. These results are then applied to analyze the SG method for the SG system and to demonstrate the polynomial decay of the numerical error over time. - oai:arXiv.org:2512.07735v1 - math.NA - cs.NA - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Shi Jin, Qi Shao, Haitao Wang - - - Bounded oscillation operators on BMO spaces - https://arxiv.org/abs/2512.07736 - arXiv:2512.07736v1 Announce Type: new -Abstract: Bounded Oscillation (BO) operators were recently introduced in the author's paper [13], where it was proved that many operators in harmonic analysis (Calder\'on-Zygmund operators, Carleson type operators, martingale transforms, Littlewood-Paley square functions, maximal operators, etc) are $BO$ operators. $BO$ operators are defined on abstract measure spaces equipped with a basis of abstract balls. The abstract balls in their definition owe four basic properties of classical balls in $\mathbb{R}^n$, which are crucial in the study of singular operators on $\mathbb{R}^n$. Among various properties studied in these papers it was proved that $BO$ operators allow pointwise sparse domination, establishing the $A_2$-conjecture for those operators. In the present paper we study boundedness properties of $BO$ operators on $BMO$ spaces. In particular, we prove that general $BO$ operators boundedly map $L^\infty$ into $BMO$, and under a logarithmic localization condition those map $BMO$ into itself. We obtain these properties as corollaries of new local type bounds, involving oscillations of functions over the balls. We apply the results in the $BMO$ estimations of Calder\'on-Zygmund operators, martingale transforms, Carleson type operators, as well as in the unconditional basis properties of general wavelet type systems in atomic Hardy spaces $H^1$. - oai:arXiv.org:2512.07736v1 - math.CA - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - 10.1007/s00209-025-03901-9 - Mathematische Zeitschrift, Volume 312, article number 12, (2026) - Grigori A. Karagulyan - - - Quantitative indistinguishability and sparse and dense clusters in factor of IID percolations - https://arxiv.org/abs/2512.07740 - arXiv:2512.07740v1 Announce Type: new -Abstract: Chifan-Ioana (2010) implies that, for any factor of IID percolation on any nonamenable Cayley graph $G$, there is a countable set of (strong) indistinguishability classes for non-hyperfinite clusters. We introduce quantitative strengthenings, called (qI) and (qSI): for $\eta$-non-hyperfinite clusters, there are at most $M(G,\eta)<\infty$ (strong) indistinguishability classes, for any FIID percolation. - We first show that (qI) and (qSI) for any $G$ are equivalent to the ``sparse implies thin'' property (SiT): any FIID percolation with $\eta$-non-hyperfinite clusters has density at least $c(G,\eta)>0$. Also, (SiT) is independent of the finite generating set of a group. We prove, using entropy inequalities, that (SiT) holds for free groups, even for weak FIIDs. On the other hand, recent work of Jard\'on-S\'anchez, Mellick, Poulin, and Wr\'obel implies that (SiT) fails for weak FIIDs on non-exact, i.e., not property (A) groups. - Furthermore, (SiT) implies that the Bernoulli graphing over any non-hyperfinite FIID cluster is strongly ergodic, and that indistinguishability for non-hyperfinite FIID clusters is equivalent to strong indistinguishability. These results follow from the work of Chifan-Ioana for every nonamenable Cayley graph, but with non-probabilistic proofs. - We also prove, again using entropy inequalities, this time for all nonamenable Cayley graphs, that any FIID percolation with high enough expected degree must have a density close to 1, and there must be a single indistinguishability class of such clusters. On Kazhdan groups, there must be a single such cluster. - Our results have finite counterparts: in any large girth $d$-regular graph sequence, any FIID subgraph of average degree at least $2+\delta$ must have density at least $c(d,\delta)>0$. In the uniform random d-regular graph $G_{n,d}$, this holds for every subgraph of average degree at least $2+\delta$. - oai:arXiv.org:2512.07740v1 - math.PR - math.CO - math.DS - math.GR - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Endre Cs\'oka, P\'eter Mester, G\'abor Pete - - - Bifurcation from the Kurth solution in galactic dynamics - https://arxiv.org/abs/2512.07746 - arXiv:2512.07746v1 Announce Type: new -Abstract: It will be shown that there exists an infinite-dimensional continuum ${\cal C}$ of weak static solutions of the Vlasov-Poisson system that bifurcates from the Kurth solution. Each $f_\ast\in {\cal C}$ has the charge density $\rho_{f_\ast}=\rho_{{\rm Kurth}}$, and (like the Kurth solution itself) each $f_\ast$ is surrounded by time-periodic weak solutions. - oai:arXiv.org:2512.07746v1 - math.AP - math-ph - math.MP - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Markus Kunze, Rafael Ortega - - - Exact supported co-degree bounds for Hamilton cycles - https://arxiv.org/abs/2512.07751 - arXiv:2512.07751v1 Announce Type: new -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:2512.07751v1 - math.CO - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Shoham Letzter, Arjun Ranganathan - - - Enumeration of maps with the Dumitriu-Edelman model - https://arxiv.org/abs/2512.07753 - arXiv:2512.07753v1 Announce Type: new -Abstract: We give an expansion in $1/N$ and $\beta$ of the cumulants of power sums of the particles of the $\beta$-ensemble. This new expansion is obtained using the tridiagonal model of Dumitriu and Edelman. The coefficients of the expansion are expressed in terms of suitably labelled maps introduced by Bouttier, Fusy, and Guitter. Our expansion is of a different nature than the one obtained by LaCroix in is study of the $b$-conjecture of Goulden and Jackson, and involves only orientable maps. We are able to relate bijectively the first two orders of our expansion to the one of LaCroix using a novel many-to-one mapping that relates suitably labelled planar maps with two minima and maps on the projective plane. - oai:arXiv.org:2512.07753v1 - math.CO - math.PR - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Thomas Buc-d'Alch\'e - - - Charge functions for high dimensional partitions - https://arxiv.org/abs/2512.07758 - arXiv:2512.07758v1 Announce Type: new -Abstract: To construct a BPS algebra with representations furnished by n-dimensional partitions, the first step is to construct the eigenvalue of the Cartan operators acting on them. The generating function of the eigenvalues are called the charge function. It has an important property that for each partition, the poles of the function correspond to the projection of the boxes which can be added to or removed from the partition legally. The charge functions of lower dimensional partitions, i.e., Young diagrams for 2D, plane partitions for 3D and solid partitions for 4D, are already given in the literature. In this paper, we propose an expression of the charge function for arbitrary odd dimensional partitions and have it proved for 5D case. Some explicit numerical tests for 7D and 9D case are also conducted to confirm our formula. - oai:arXiv.org:2512.07758v1 - math-ph - hep-th - math.MP - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Shang Xiang, Hao Feng, Keyou Zhuo, Tian-Shun Chen, Kilar Zhang - - - Normal closure of finite subgroups of $\mathrm{Aut}(F_n)$ and $\mathrm{Out}(F_n)$ - https://arxiv.org/abs/2512.07759 - arXiv:2512.07759v1 Announce Type: new -Abstract: For $n\geq 3$, let $G$ be a nontrivial finite subgroup of $\mathrm{Aut}(F_n)$ with $|G|$ not a power of $2$. We prove that the normal closure $N(G)$ is $\mathrm{SAut}(F_n)$ if $G\subset\mathrm{SAut}(F_n)$ and $N(G)$ is $\mathrm{Aut}(F_n)$ otherwise. When $|G|$ is a power of $2$, we have a partial theorem. Similarly, let $G'$ be a nontrivial finite subgroup of $\mathrm{Out}(F_n)$ with $|G'|$ not a power of $2$. Then the normal closure $N(G')$ is $\mathrm{SOut}(F_n)$ if $G'\subset\mathrm{SOut}(F_n)$ and $N(G')$ is $\mathrm{Out}(F_n)$ otherwise. When $|G'|$ is a power of $2$, we have a partial theorem as well. - oai:arXiv.org:2512.07759v1 - math.GR - math.GT - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Jiayi Shen - - - Skein-valued mirror curves for toric CY3 strips - https://arxiv.org/abs/2512.07762 - arXiv:2512.07762v1 Announce Type: new -Abstract: For a smooth semi-projective toric Calabi-Yau 3-fold containing no compact surface, we show the count of all-genus holomorphic curves with boundary on a single Aganagic-Vafa brane is annihilated by a skein-valued quantization of the mirror curve, and that this determines the count. We give explicit expressions for the equation and its solution. - oai:arXiv.org:2512.07762v1 - math.SG - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Mingyuan Hu, Vivek Shende - - - Bethe equations for the critical three-state Potts spin chain with toroidal boun dary conditions - https://arxiv.org/abs/2512.07763 - arXiv:2512.07763v1 Announce Type: new -Abstract: In this paper, we consider the parameterization of the spectra of the three-state critical Potts quantum chain with integrable twisted boundary conditions in terms of Bethe ansatz type equations. The Bethe equations are found by investigating the structure of the eigenvalues of the respective twisted transfer matrices, and with the help of certain identities satisfied by the product of transfer matrix operators. We have studied the completeness of the spectrum in terms of the Bethe roots for small lattice sizes and have computed the eigenstate momenta. We found that the spins of the low-lying excitations can have fractional values in accordance with predictions of the underlying conformal field theory. We argue that our framework can be used to build integrable Hamiltonians whose spectra are determined by mixing different toroidal boundary conditions. - oai:arXiv.org:2512.07763v1 - math-ph - math.MP - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - M. J. Martins - - - Selection mechanisms in front invasion - https://arxiv.org/abs/2512.07764 - arXiv:2512.07764v1 Announce Type: new -Abstract: We review progress on questions related to front propagation into unstable states and point out open problems in the area. We strive to highlight different theoretical perspectives and challenges while also addressing more practical questions with examples and guides to computational methods. Throughout we take a dynamical systems point of view that focuses on the ability of invasion processes to act as a selection mechanism in complex systems. - oai:arXiv.org:2512.07764v1 - math.AP - math.DS - nlin.PS - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Montie Avery, Matt Holzer, Arnd Scheel - - - Large deviations principle for the cubic NLS equation with slowly decaying data - https://arxiv.org/abs/2512.07773 - arXiv:2512.07773v1 Announce Type: new -Abstract: In this note, we prove a sharp large derivation principle (LDP) for the cubic nonlinear Schr\"odinger equation with Gaussian random initial data in Fourier Lebesgue spaces. As a consequence, we improve the exponential decay condition in [M.A. Garrido, R. Grande, K.M. Kurianski, G. Staffilani. Commun. Pure Appl. Math. 76 (2023), 4087--4136] to $\ell^1$ decay. - oai:arXiv.org:2512.07773v1 - math.AP - math.PR - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Rui Liang, Yuzhao Wang - - - The local homological structure of generalized splines - https://arxiv.org/abs/2512.07789 - arXiv:2512.07789v1 Announce Type: new -Abstract: Generalized splines are a simultaneous generalization of GKM theory -- which studies equivariant cohomology -- and classical splines, which provide piecewise approximations of functions. Generalized splines can also be understood via schemes, with the interpolation constraints -- or so-called GKM-condition -- encoded by gluing along certain closed subschemes. This view provides a local-global principle, with the local pictures retaining the generalized spline structure. Consequently, the behavior of generalized splines over local rings controls certain global phenomena, such as projectivity and often freeness. - We introduce an interface between the homological study of local rings and the combinatorial study of generalized splines. We identify precisely how the generalized spline structure coordinates with the existing homological local ring machinery. This is accomplished by two exact sequences that provide a regulatory structure on the local cohomology of a generalized spline module. As an application, we use this to prove that for any edge-labeled graph $G$ with principal ideal labels, and any Cohen-Macaulay ring $R$ of Krull dimension 2 at each maximal ideal, the module of splines $R_G$ is free, provided it has finite projective dimension. As a special case, this implies every generalized spline module over $k[x,y]$ with principal edge labels is free. - oai:arXiv.org:2512.07789v1 - math.AC - math.CO - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Kyle Stoltz - - - Nahm sum identities for Cartan matrices of type $D_k$ - https://arxiv.org/abs/2512.07790 - arXiv:2512.07790v1 Announce Type: new -Abstract: Around 2007, Warnaar proved four identities related to Nahm sums associated with twice the inverse of the Cartan matrix of type $D_k$. Three of these had been conjectured by Flohr, Grabow, and Koehn, while special cases of two of the identities were first conjectured in 1993 by Kedem, Klassen, McCoy, and Melzer. Warnaar's proof relies on a multi-sum identity from Andrews' proof of the Andrews-Gordon identities. We give a new proof of all four identities using the theory of Bailey pairs. Furthermore, we establish a parametric generalization of two of the identities and provide two distinct proofs of this generalization. - oai:arXiv.org:2512.07790v1 - math.CO - math.NT - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Liuquan Wang, Shangwen Wang - - - How many coin tosses would you need until you get $n$ Heads or $m$ Tails? - https://arxiv.org/abs/2512.07803 - arXiv:2512.07803v1 Announce Type: new -Abstract: We harness both human ingenuity and the power of symbolic computation to study the number of coin tosses until reaching $n$ Heads or $m$ Tails. We also talk about the closely related problem of reaching $n$ Heads and $m$ Tails. This paper is accompanied by a Maple package that enables fast computation of expectations, variances, and higher moments of these quantities. - oai:arXiv.org:2512.07803v1 - math.PR - math.CO - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - Svante Janson, Lucy Martinez, Doron Zeilberger - - - Universality of AMP via Tree Pairings - https://arxiv.org/abs/2512.07816 - arXiv:2512.07816v1 Announce Type: new -Abstract: We prove universality for Approximate Message Passing (AMP) with polynomial nonlinearities applied to symmetric sub-Gaussian matrices $A\in\mathbb R^{N\times N}$. Our approach is combinatorial: we represent AMP iterates as sums over trees and define a Wick pairing algebra that counts the number of valid row-wise pairings of edges. The number of such pairings coincides with the trees contribution to the state evolution formulas. This algebra works for non-Gaussian entries. For polynomial nonlinearities of degree at most $D$, we show that the moments of AMP iterates match their state evolution predictions for $t \lesssim \frac{\log N}{D\log D}$ iterations. The proof controls all "excess" trees via explicit enumeration bounds, showing non "Wick-paired" contributions vanish in the large-$N$ limit. The same framework should apply, with some modifications, to spiked AMP and tensor AMP models. - oai:arXiv.org:2512.07816v1 - math.PR - Tue, 09 Dec 2025 00:00:00 -0500 - new - http://creativecommons.org/licenses/by/4.0/ - David Kogan - - - Two-spinon effects on the thermal Tonks-Girardeau gas - https://arxiv.org/abs/2410.20929 - arXiv:2410.20929v4 Announce Type: cross -Abstract: We study the effects of the two-spinon excitations on the field-field correlator of the Tonks-Girardeau gas. While these excitations have been previously examined in the ground state of the system, their role at finite temperatures remains unexplored. Here, we extend the analysis to the one-dimensional interacting Bose gas at thermal equilibrium, focusing on the one-body correlation function of the infinitely repulsive Lieb-Liniger model. We demonstrate that two-spinon excitations, characterized by two holes within the rapidity distribution, constitute the dominant contribution to the field-field correlator at low temperatures. Furthermore, we analytically show that incorporating additional particle-hole excitations diminishes their contribution, highlighting the efficacy of the two-spinon framework in capturing the essential physics of the system. Numerical evaluations of both the Fredholm determinant and the spectral sum stemming from the two-spinon program, with the addition of particle-hole excitations, reveal convergence at low temperatures. - oai:arXiv.org:2410.20929v4 - cond-mat.quant-gas - cond-mat.stat-mech - math-ph - math.MP - nlin.SI - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Felipe Taha Sant'Ana, Hui Liu - - - Formal Integration of Derived Foliations - https://arxiv.org/abs/2502.05257 - arXiv:2502.05257v2 Announce Type: cross -Abstract: Frobenius' theorem in differential geometry asserts that every involutive subbundle of the tangent bundle of a manifold $M$ integrates to a decomposition of $M$ into smooth leaves. We prove an infinitesimal analogue of this result for locally coherent qcqs schemes $X$ over coherent rings. More precisely, we integrate partition Lie algebroids on $X$ to formal moduli stacks $X \rightarrow S$ where $S$ is the formal leaf space and the fibres of $X \rightarrow S$ are the formal leaves. We deduce that deformations of $X$-families of algebro-geometric objects are controlled by partition Lie algebroids on $X$. Combining our integration equivalence with a result of Fu, we deduce that To\"{e}n-Vezzosi's infinitesimal derived foliations (under suitable finiteness hypotheses) are formally integrable. - oai:arXiv.org:2502.05257v2 - math.AG - math.AT - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Lukas Brantner, Kirill Magidson, Joost Nuiten - - - Investigating the effect of adaptive optimal control function in epidemic dynamics: predictions and strategy evolution based on SIR/V game theoretic framework - https://arxiv.org/abs/2512.06021 - arXiv:2512.06021v1 Announce Type: cross -Abstract: In this paper, we consider an adaptive optimal control problem for an SIR/V epidemic model with human behavioral effects.We develop a model where effective management of infectious diseases are monitored by the means of non pharmaceutical interventions.This study develops an adaptive optimal control function within an SIR/V framework embedding a non cooperative game theoretic mechanism to capture the dynamic interplay between individual vaccination behavior and population level transmission. We derive analytical expression for the optimal control trajectory under resource constrain and heterogeneous susceptibility and we validate our model using numerical simulations,calibrated with the real world epidemic parameters. We find that for the adaptive optimal policy for a generally known SIR/V model depending on the game theoretic epidemic state leads to substantial reduction in expenses compared to non adaptive policies. Moreover, our results demonstrate that, adaptive strategies significantly outperform the static policies by achieving lower peak infections and faster epidemic extinctions while evolutionary game dynamics identify critical behavioral thresholds that drive strategy evolution and inform timely policy adaptation - oai:arXiv.org:2512.06021v1 - physics.soc-ph - math.DS - q-bio.PE - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Nuruzzaman Rahat, Abid Hossain, Muntasir Alam - - - Entropic Regularization in the Deep Linear Network - https://arxiv.org/abs/2512.06137 - arXiv:2512.06137v1 Announce Type: cross -Abstract: We study regularization for the deep linear network (DLN) using the entropy formula introduced in arXiv:2509.09088. The equilibria and gradient flow of the free energy on the Riemannian manifold of end-to-end maps of the DLN are characterized for energies that depend symmetrically on the singular values of the end-to-end matrix. - The only equilibria are minimizers and the set of minimizers is an orbit of the orthogonal group. In contrast with random matrix theory there is no singular value repulsion. The corresponding gradient flow reduces to a one-dimensional ordinary differential equation whose solution gives explicit relaxation rates toward the minimizers. We also study the concavity of the entropy in the chamber of singular values. The entropy is shown to be strictly concave in the Euclidean geometry on the chamber but not in the Riemannian geometry defined by the DLN metric. - oai:arXiv.org:2512.06137v1 - cs.NE - math.DS - math.PR - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Alan Chen, Tejas Kotwal, Govind Menon - - - A fast algorithm for the Hecke representation of the braid group, and applications to the computation of the HOMFLY-PT polynomial and the search for interesting braids - https://arxiv.org/abs/2512.06142 - arXiv:2512.06142v1 Announce Type: cross -Abstract: Knot theory is an active field of mathematics, in which combinatorial and computational methods play an important role. One side of computational knot theory, that has gained interest in recent years, both for complexity analysis and practical algorithms, is quantum topology and the computation of topological invariants issued from the theory. - In this article, we leverage the rigidity brought by the representation-theoretic origins of the quantum invariants for algorithmic purposes. We do so by exploiting braids and the algebraic properties of the braid group to describe, analyze, and implement a fast algorithm to compute the Hecke representation of the braid group. We apply this construction to design a parameterized algorithm to compute the HOMFLY-PT polynomial of knots, and demonstrate its interest experimentally. Finally, we combine our fast Hecke representation algorithm with Garside theory, to implement a reservoir sampling search and find non-trivial braids with trivial Hecke representations with coefficients in $\mathbb{Z}/p\mathbb{Z}$. We find several such braids, in particular proving that the Hecke representation of $B_5$ with $\mathbb{Z}/2\mathbb{Z}$ coefficients is non-faithful, a previously unknown fact. - oai:arXiv.org:2512.06142v1 - cs.CG - math.GT - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Cl\'ement Maria, Hoel Queffelec - - - gp2Scale: A Class of Compactly-Supported Non-Stationary Kernels and Distributed Computing for Exact Gaussian Processes on 10 Million Data Points - https://arxiv.org/abs/2512.06143 - arXiv:2512.06143v1 Announce Type: cross -Abstract: Despite a large corpus of recent work on scaling up Gaussian processes, a stubborn trade-off between computational speed, prediction and uncertainty quantification accuracy, and customizability persists. This is because the vast majority of existing methodologies exploit various levels of approximations that lower accuracy and limit the flexibility of kernel and noise-model designs -- an unacceptable drawback at a time when expressive non-stationary kernels are on the rise in many fields. Here, we propose a methodology we term \emph{gp2Scale} that scales exact Gaussian processes to more than 10 million data points without relying on inducing points, kernel interpolation, or neighborhood-based approximations, and instead leveraging the existing capabilities of a GP: its kernel design. Highly flexible, compactly supported, and non-stationary kernels lead to the identification of naturally occurring sparse structure in the covariance matrix, which is then exploited for the calculations of the linear system solution and the log-determinant for training. We demonstrate our method's functionality on several real-world datasets and compare it with state-of-the-art approximation algorithms. Although we show superior approximation performance in many cases, the method's real power lies in its agnosticism toward arbitrary GP customizations -- core kernel design, noise, and mean functions -- and the type of input space, making it optimally suited for modern Gaussian process applications. - oai:arXiv.org:2512.06143v1 - cs.LG - math.PR - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Marcus M. Noack, Mark D. Risser, Hengrui Luo, Vardaan Tekriwal, Ronald J. Pandolfi - - - An abstraction for solving multi-domain problems using finite element methods - https://arxiv.org/abs/2512.06146 - arXiv:2512.06146v1 Announce Type: cross -Abstract: We introduce a new abstraction for the representation and solution of multi-domain problems using finite element methods. This is an advance over previous work in that it achieves a single higher-level abstraction that represents multi-domain problems in the mixed variational problem formalism. We implemented our new abstraction in UFL and Firedrake, and validated our implementations solving a quad-triangle mixed-cell-type problem, a hex-quad mixed-cell-type problem, and a fluid-structure interaction benchmark problem. - oai:arXiv.org:2512.06146v1 - cs.MS - cs.NA - math.NA - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Koki Sagiyama, Lawrence Mitchell, David A. Ham - - - Learning Invariant Graph Representations Through Redundant Information - https://arxiv.org/abs/2512.06154 - arXiv:2512.06154v1 Announce Type: cross -Abstract: Learning invariant graph representations for out-of-distribution (OOD) generalization remains challenging because the learned representations often retain spurious components. To address this challenge, this work introduces a new tool from information theory called Partial Information Decomposition (PID) that goes beyond classical information-theoretic measures. We identify limitations in existing approaches for invariant representation learning that solely rely on classical information-theoretic measures, motivating the need to precisely focus on redundant information about the target $Y$ shared between spurious subgraphs $G_s$ and invariant subgraphs $G_c$ obtained via PID. Next, we propose a new multi-level optimization framework that we call -- Redundancy-guided Invariant Graph learning (RIG) -- that maximizes redundant information while isolating spurious and causal subgraphs, enabling OOD generalization under diverse distribution shifts. Our approach relies on alternating between estimating a lower bound of redundant information (which itself requires an optimization) and maximizing it along with additional objectives. Experiments on both synthetic and real-world graph datasets demonstrate the generalization capabilities of our proposed RIG framework. - oai:arXiv.org:2512.06154v1 - cs.LG - cs.AI - cs.IT - math.IT - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Barproda Halder, Pasan Dissanayake, Sanghamitra Dutta - - - Strategic Experimentation with Private Payoffs - https://arxiv.org/abs/2512.06180 - arXiv:2512.06180v1 Announce Type: cross -Abstract: We study a strategic experimentation game with exponential bandits, in which experiment outcomes are private. The equilibrium amount of experimentation is always higher than in the benchmark case where experiment outcomes are publicly observed. In addition, for pure equilibria, the equilibrium amount of experimentation is at least socially optimal, and possibly higher. We provide a tight bound on the degree of over-experimentation. The analysis rests on a new form of encouragement effect, according to which a player may hide the absence of a success to encourage future experimentation by the other player, which incentivizes current experimentation. - oai:arXiv.org:2512.06180v1 - cs.GT - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - J\'er\^ome Renault, Eilon Solan, Nicolas Vieille - - - On the hardness of recognizing graphs of small mim-width and its variants - https://arxiv.org/abs/2512.06186 - arXiv:2512.06186v1 Announce Type: cross -Abstract: The mim-width of a graph is a powerful structural parameter that, when bounded by a constant, allows several hard problems to be polynomial-time solvable - with a recent meta-theorem encompassing a large class of problems [SODA2023]. Since its introduction, several variants such as sim-width and omim-width were developed, along with a linear version of these parameters. It was recently shown that mim-width and all these variants all paraNP-hard, a consequence of the NP-hardness of distinguishing between graphs of linear mim-width at most 1211 and graphs of sim-width at least 1216 [ICALP2025]. The complexity of recognizing graphs of small width, particularly those close to $1$, remained open, despite their especially attractive algorithmic applications. - In this work, we show that the width recognition problems remain NP-hard even on small widths. Specifically, after introducing the novel parameter Omim-width sandwiched between omim-width and mim-width, we show that: (1) deciding whether a graph has sim-width = 1, omim-width = 1, or Omin-width = 1 is NP-hard, and the same is true for their linear variants; (2) the problems of deciding whether mim-width $\leq$ 2 or linear mim-width $\leq$ 2 are both NP-hard. Interestingly, our reductions are relatively simple and are from the Unrooted Quartet Consistency problem, which is of great interest in computational biology but is not commonly used (if ever) in the theory of algorithms. - oai:arXiv.org:2512.06186v1 - cs.DM - cs.CC - math.CO - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Max Dupr\'e la Tour, Manuel Lafond, Ndiam\'e Ndiaye - - - Average-reward reinforcement learning in semi-Markov decision processes via relative value iteration - https://arxiv.org/abs/2512.06218 - arXiv:2512.06218v1 Announce Type: cross -Abstract: This paper applies the authors' recent results on asynchronous stochastic approximation (SA) in the Borkar-Meyn framework to reinforcement learning in average-reward semi-Markov decision processes (SMDPs). We establish the convergence of an asynchronous SA analogue of Schweitzer's classical relative value iteration algorithm, RVI Q-learning, for finite-space, weakly communicating SMDPs. In particular, we show that the algorithm converges almost surely to a compact, connected subset of solutions to the average-reward optimality equation, with convergence to a unique, sample path-dependent solution under additional stepsize and asynchrony conditions. Moreover, to make full use of the SA framework, we introduce new monotonicity conditions for estimating the optimal reward rate in RVI Q-learning. These conditions substantially expand the previously considered algorithmic framework and are addressed through novel arguments in the stability and convergence analysis of RVI Q-learning. - oai:arXiv.org:2512.06218v1 - cs.LG - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Huizhen Yu, Yi Wan, Richard S. Sutton - - - Highly robust logical qubit encoding in an ensemble of V-symmetrical qutrits - https://arxiv.org/abs/2512.06219 - arXiv:2512.06219v1 Announce Type: cross -Abstract: We propose using even and odd Sch\"odinger cat states formed from coherent states of U(3) of an ensemble of qutrits with a symmetrical V-configuration (a qubit-disguised qutrit) to encode a logical qubit. These carefully engineered logical qubit states are parameter independent stationary states of the effective master equation governing the evolution of the ensemble and, consequently, constitute dark states and are invulnerable to dissipation and correlated collective dephasing. In particular, the logical qubit states are immune to single qutrit decay (the analogous of single photon loss process for qutrits) and simultaneous decay and driving of two qutrits (the analogous two-photon loss and driving processes for qutrits). In addition, we show how to implement the single-qubit quantum NOT gate and the Hadamard gate followed by either the phase gate or the phase and $Z$ gates. We study analytically the case of two qutrits and conclude that the logical qubit states exhibit parity-sensitive inhomogeneous broadening and local correlated dephasing: the even logical state is completely immune to these processes, while odd one is vulnerable. Nevertheless, in the presence of these interactions one can also define another odd state with mixed permutation symmetry that is immune to both inhomogeneous broadening and local correlated dephasing. We suggest that these results can be extrapolated to an arbitrary number of qutrits. The effective master equation is deduced from a physical system composed of two parametrically coupled cavities with one of them interacting dispersively with an ensemble of three-level atoms (the qutrits). In principle this physical system can be implemented by means of two coplanar waveguide resonators, a SQUID parametrically coupling them, and a cloud of alkali atoms close to one of the resonators. - oai:arXiv.org:2512.06219v1 - quant-ph - math-ph - math.MP - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Luis Octavio Casta\~nos-Cervantes, Manuel Calixto, Julio Guerrero - - - Beamspace Dimensionality Reduction for Massive MU-MIMO: Geometric Insights and Information-Theoretic Limits - https://arxiv.org/abs/2512.06234 - arXiv:2512.06234v1 Announce Type: cross -Abstract: Beamspace dimensionality reduction, a classical tool in array processing, has been shown in recent work to significantly reduce computational complexity and training overhead for adaptive reception in massive multiuser (MU) MIMO. For sparse multipath propagation and uniformly spaced antenna arrays, beamspace transformation, or application of a spatial FFT, concentrates the energy of each user into a small number of spatial frequency bins. Empirical evaluations demonstrate the efficacy of linear Minimum Mean Squared Error (LMMSE) detection performed in parallel using a beamspace window of small, fixed size for each user, even as the number of antennas and users scale up, while being robust to moderate variations in the relative powers of the users. In this paper, we develop a fundamental geometric understanding of this ``unreasonable effectiveness'' in a regime in which zero-forcing solutions do not exist. For simplified channel models, we show that, when we enforce a suitable separation in spatial frequency between users, the interference power falling into a desired user's beamspace window of size $W$ concentrates into a number of dominant eigenmodes smaller than $W$, with the desired user having relatively small projection onto these modes. Thus, linear suppression of dominant interference modes can be accomplished with small noise enhancement. We show that similar observations apply for MIMO-OFDM over wideband multipath channels synthesized from measured 28 GHz data. We propose, and evaluate via information-theoretic benchmarks, per-subcarrier reduced dimension beamspace LMMSE in this setting. - oai:arXiv.org:2512.06234v1 - eess.SP - cs.IT - math.IT - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Canan Cebeci, Oveys Delafrooz Noroozi, Upamanyu Madhow - - - Auto-exploration for online reinforcement learning - https://arxiv.org/abs/2512.06244 - arXiv:2512.06244v1 Announce Type: cross -Abstract: The exploration-exploitation dilemma in reinforcement learning (RL) is a fundamental challenge to efficient RL algorithms. Existing algorithms for finite state and action discounted RL problems address this by assuming sufficient exploration over both state and action spaces. However, this yields non-implementable algorithms and sub-optimal performance. To resolve these limitations, we introduce a new class of methods with auto-exploration, or methods that automatically explore both state and action spaces in a parameter-free way, i.e.,~without a priori knowledge of problem-dependent parameters. We present two variants: one for the tabular setting and one for linear function approximation. Under algorithm-independent assumptions on the existence of an exploring optimal policy, both methods attain $O(\epsilon^{-2})$ sample complexity to solve to $\epsilon$ error. Crucially, these complexities are novel since they are void of algorithm-dependent parameters seen in prior works, which may be arbitrarily large. The methods are also simple to implement because they are parameter-free and do not directly estimate the unknown parameters. These feats are achieved by new algorithmic innovations for RL, including a dynamic mixing time, a discounted state distribution for sampling, a simple robust gradient estimator, and a recent advantage gap function to certify convergence. - oai:arXiv.org:2512.06244v1 - cs.LG - cs.AI - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Caleb Ju, Guanghui Lan - - - Distributionally Robust Kalman Filter - https://arxiv.org/abs/2512.06286 - arXiv:2512.06286v1 Announce Type: 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:2512.06286v1 - eess.SY - cs.SY - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Minhyuk Jang, Astghik Hakobyan, Insoon Yang - - - Theoretical Compression Bounds for Wide Multilayer Perceptrons - https://arxiv.org/abs/2512.06288 - arXiv:2512.06288v1 Announce Type: cross -Abstract: Pruning and quantization techniques have been broadly successful in reducing the number of parameters needed for large neural networks, yet theoretical justification for their empirical success falls short. We consider a randomized greedy compression algorithm for pruning and quantization post-training and use it to rigorously show the existence of pruned/quantized subnetworks of multilayer perceptrons (MLPs) with competitive performance. We further extend our results to structured pruning of MLPs and convolutional neural networks (CNNs), thus providing a unified analysis of pruning in wide networks. Our results are free of data assumptions, and showcase a tradeoff between compressibility and network width. The algorithm we consider bears some similarities with Optimal Brain Damage (OBD) and can be viewed as a post-training randomized version of it. The theoretical results we derive bridge the gap between theory and application for pruning/quantization, and provide a justification for the empirical success of compression in wide multilayer perceptrons. - oai:arXiv.org:2512.06288v1 - cs.LG - math.ST - stat.TH - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Houssam El Cheairi, David Gamarnik, Rahul Mazumder - - - Interpretable Neural Approximation of Stochastic Reaction Dynamics with Guaranteed Reliability - https://arxiv.org/abs/2512.06294 - arXiv:2512.06294v1 Announce Type: cross -Abstract: Stochastic Reaction Networks (SRNs) are a fundamental modeling framework for systems ranging from chemical kinetics and epidemiology to ecological and synthetic biological processes. A central computational challenge is the estimation of expected outputs across initial conditions and times, a task that is rarely solvable analytically and becomes computationally prohibitive with current methods such as Finite State Projection or the Stochastic Simulation Algorithm. Existing deep learning approaches offer empirical scalability, but provide neither interpretability nor reliability guarantees, limiting their use in scientific analysis and in applications where model outputs inform real-world decisions. Here we introduce DeepSKA, a neural framework that jointly achieves interpretability, guaranteed reliability, and substantial computational gains. DeepSKA yields mathematically transparent representations that generalise across states, times, and output functions, and it integrates this structure with a small number of stochastic simulations to produce unbiased, provably convergent, and dramatically lower-variance estimates than classical Monte Carlo. We demonstrate these capabilities across nine SRNs, including nonlinear and non-mass-action models with up to ten species, where DeepSKA delivers accurate predictions and orders-of-magnitude efficiency improvements. This interpretable and reliable neural framework offers a principled foundation for developing analogous methods for other Markovian systems, including stochastic differential equations. - oai:arXiv.org:2512.06294v1 - q-bio.MN - cs.LG - math.PR - q-bio.QM - stat.ML - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Quentin Badolle, Arthur Theuer, Zhou Fang, Ankit Gupta, Mustafa Khammash - - - Integrable construction of a two-dimensional lattice model with anisotropic Hubbard couplings - https://arxiv.org/abs/2512.06310 - arXiv:2512.06310v1 Announce Type: cross -Abstract: By defining a graded global R-operator $\mathbb{R}_{ab}^{(2D,2S)}$ that couples free-fermion structures and incorporates anisotropic Hubbard interactions while satisfying the Yang--Baxter equation, we construct a strictly solvable two-dimensional lattice model. We then build the layer-to-layer transfer matrix through a bidirectional-monodromy construction and prove the model's integrability via the associated global RTT relations. Using the nested algebraic Bethe ansatz, we obtain the exact eigenvalues of the transfer matrix and derive the corresponding first- and second-level Bethe equations. Finally, by taking the logarithmic derivative of the transfer matrix at the regular point, we recover explicitly a local Hamiltonian that features anisotropic hopping, an on-site Hubbard interaction, and orbital-coupling contributions. - oai:arXiv.org:2512.06310v1 - nlin.SI - math-ph - math.MP - quant-ph - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Ze Tao, Fujun Liu - - - Control-Oriented System Identification: Classical, Learning, and Physics-Informed Approaches - https://arxiv.org/abs/2512.06315 - arXiv:2512.06315v1 Announce Type: cross -Abstract: We survey classical, machine learning, and data-driven system identification approaches to learn control-relevant and physics-informed models of dynamical systems. Recently, machine learning approaches have enabled system identification from noisy, high-dimensional, and complex data. However, their utility is limited by their ability to provide provable guarantees on control-relevant properties. Meanwhile, control theory has identified several properties that are useful in analysis and control synthesis, such as dissipativity, monotonicity, energy conservation, and symmetry-preserving structures. We posit that merging system identification with such control-relevant or physics-informed properties can provide useful inductive bias, enhance explainability, enable control synthesis with provable guarantees, and improve sample complexity. We formulate system identification as an optimization problem where control-relevant properties can be enforced through direct parameterization (constraining the model structure to satisfy a desired property by construction), soft constraints (encouraging control-relevant properties through regularization or penalty terms), and hard constraints (imposing control-relevant properties as constraints in the optimization problem). Through this lens, we survey methods to learn physics-informed and control-relevant models spanning classical linear and nonlinear system identification, machine learning approaches, and direct identification through data-driven and behavioral representations. We also provide several expository examples that are accompanied by code and brief tutorials on a public Github repository. We also describe challenging directions for future research, including identification in networked, switched, and time-varying systems, experiment design, and bridging the gaps between data-driven, learning-based, and control-oriented approaches. - oai:arXiv.org:2512.06315v1 - eess.SY - cs.SY - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - S. Sivaranjani, Yuanyuan Shi, Nikolay Atanasov, Thai Duong, Jie Feng, Tim Martin, Yuezhu Xu, Vijay Gupta, Frank Allg\"ower - - - Interpretive Efficiency: Information-Geometric Foundations of Data Usefulness - https://arxiv.org/abs/2512.06341 - arXiv:2512.06341v1 Announce Type: cross -Abstract: Interpretability is central to trustworthy machine learning, yet existing metrics rarely quantify how effectively data support an interpretive representation. We propose Interpretive Efficiency, a normalized, task-aware functional that measures the fraction of task-relevant information transmitted through an interpretive channel. The definition is grounded in five axioms ensuring boundedness, Blackwell-style monotonicity, data-processing stability, admissible invariance, and asymptotic consistency. We relate the functional to mutual information and derive a local Fisher-geometric expansion, then establish asymptotic and finite-sample estimation guarantees using standard empirical-process tools. Experiments on controlled image and signal tasks demonstrate that the measure recovers theoretical orderings, exposes representational redundancy masked by accuracy, and correlates with robustness, making it a practical, theory-backed diagnostic for representation design. - oai:arXiv.org:2512.06341v1 - cs.LG - cs.IR - cs.IT - math.IT - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Ronald Katende - - - KyFrog: A High-Security LWE-Based KEM Inspired by ML-KEM - https://arxiv.org/abs/2512.06411 - arXiv:2512.06411v1 Announce Type: cross -Abstract: KyFrog is a conservative Learning-with-Errors (LWE) key-encapsulation mechanism designed to explore an alternative operating point compared to schemes with relatively small public keys and ciphertexts. KyFrog uses a larger dimension ($n = 1024$) and a small prime modulus $q = 1103$, together with narrow error distributions with standard deviations $\sigma_s = \sigma_e = 1.4$, to target approximately $2^{325}$ classical and quantum security against state-of-the-art lattice attacks under standard cost models, as estimated using the Lattice Estimator. The price paid for this security margin is an extremely large KEM ciphertext (about 0.5 MiB), while public and secret keys remain in the same ballpark as ML-KEM. We describe the design rationale, parameter search methodology, and implementation details of KyFrog, and we compare its asymptotic security and concrete parameter sizes with the ML-KEM standard. All code and data for this work are released as free and open-source software, with the full C++23 implementation and experimental scripts available at: https://github.com/victormeloasm/kyfrog - oai:arXiv.org:2512.06411v1 - cs.CR - math.RA - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Victor Duarte Melo, Willian J. Buchanan - - - Characteristic Bending in Incompressible Flows - https://arxiv.org/abs/2512.06455 - arXiv:2512.06455v1 Announce Type: cross -Abstract: We present the Characteristic Bending (CB) method, a general framework for advecting quantities under incompressible velocity fields. The method builds on standard semi-Lagrangian advection by interpreting the backward-in-time characteristic reconstruction as the construction of a reference map, a diffeomorphism between the current and initial geometries of the advected space. From this viewpoint, the CB method applies a volume-preserving projection to the map, systematically removing spurious compressible errors arising from time integration, interpolation, or from velocity fields that are only approximately divergence-free. This projection bends the characteristics toward the divergence-free space, preserving mass and geometric features of the advected fields, even in the presence of significant error. We demonstrate the method in both two and three dimensions using benchmark problems and for multiphase flows governed by the incompressible Navier-Stokes equations. The results show that the CB method serves as a drop-in replacement for traditional semi-Lagrangian schemes and as an augmentation of reference map formulations, offering improved robustness and accuracy in incompressible flow simulations. - oai:arXiv.org:2512.06455v1 - physics.flu-dyn - cs.NA - math.NA - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Matthew Blomquist, St\'ephane Gaudreault, Maxime Theillard - - - Non-Equiprobable Signaling for Wireless Channels Subject to Mobility and Delay Spread - https://arxiv.org/abs/2512.06494 - arXiv:2512.06494v1 Announce Type: cross -Abstract: This letter describes how to improve performance of OFDM systems by combining non-equiprobable signaling with low density parity check (LDPC) coding. We partition a standard QAM constellation into annular subconstellations of equal size, and we implement non-equiprobable signaling through a shaping code which selects subconstellations with large average energy less frequently than subconstellations with small average energy. In equiprobable signaling, the LDPC code selects a signal point from the inner subconstellation. In non-equiprobable signaling this inner signal point has a representative in each subconstellation and the shaping code selects the representative for transmission. It is possible to use standard QAM constellations to achieve any desired fractional bit rate with this method of shaping the energy distribution of the transmitted signal. We describe how to combine coding and shaping by integrating shaping into the calculation of log-likelihood ratios (LLRs) necessary for decoding LDPC codes. We present simulation results for non-equiprobable transmission at $1.5$ bits/symbol on a representative Veh-A channel showing gains of $4$ dB at a bit error rate (BER) of $10^{-3}$. As the transmission rate increases, the gains from non-equiprobable signaling diminish, but we show through simulation that they are still significant for $16$-QAM. - oai:arXiv.org:2512.06494v1 - eess.SP - cs.IT - math.IT - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Sandesh Rao Mattu, Nishant Mehrotra, Robert Calderbank - - - String Diagrams for Closed Symmetric Monoidal Categories - https://arxiv.org/abs/2512.06499 - arXiv:2512.06499v1 Announce Type: cross -Abstract: We introduce a graphical language for closed symmetric monoidal categories based on an extension of string diagrams with special bracket wires representing internal homs. These bracket wires make the structure of the internal hom functor explicit, allowing standard morphism wires to interact with them through a well-defined set of graphical rules. - We establish the soundness and completeness of the diagrammatic calculus, and illustrate its expressiveness through examples drawn from category theory, logic and programming language semantics. - oai:arXiv.org:2512.06499v1 - cs.LO - math.CT - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Callum Reader, Alessandro Di Giorgio - - - Hierarchical Clustering With Confidence - https://arxiv.org/abs/2512.06522 - arXiv:2512.06522v1 Announce Type: cross -Abstract: Agglomerative hierarchical clustering is one of the most widely used approaches for exploring how observations in a dataset relate to each other. However, its greedy nature makes it highly sensitive to small perturbations in the data, often producing different clustering results and making it difficult to separate genuine structure from spurious patterns. In this paper, we show how randomizing hierarchical clustering can be useful not just for measuring stability but also for designing valid hypothesis testing procedures based on the clustering results. - We propose a simple randomization scheme together with a method for constructing a valid p-value at each node of the hierarchical clustering dendrogram that quantifies evidence against performing the greedy merge. Our test controls the Type I error rate, works with any hierarchical linkage without case-specific derivations, and simulations show it is substantially more powerful than existing selective inference approaches. To demonstrate the practical utility of our p-values, we develop an adaptive $\alpha$-spending procedure that estimates the number of clusters, with a probabilistic guarantee on overestimation. Experiments on simulated and real data show that this estimate yields powerful clustering and can be used, for example, to assess clustering stability across multiple runs of the randomized algorithm. - oai:arXiv.org:2512.06522v1 - stat.ME - math.ST - stat.ML - stat.TH - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Di Wu, Jacob Bien, Snigdha Panigrahi - - - A result from the thesis of the french astronomer Alexandre V\'eronnet: critical latitudes - https://arxiv.org/abs/2512.06543 - arXiv:2512.06543v1 Announce Type: cross -Abstract: We are interested in a result found in the thesis of the astronomer Alexandre V\'eronnet (1876-1951) : "Precession of a fluid ring rotating along a parallel axis. Zone of maximum crustal compression at 35$^\circ$. A cause of earthquakes". In 1912, Alexandre V\'eronnet hypothesizes that the Earth's rotation influences the occurrence of earthquakes in the 35th parallel zone. Has this hypothesis been taken up by other authors, geophysicists, seismologists, etc.? Has it been confirmed or refuted? What is the literature on this subject? Our aim is not to draw a conclusion on this hypothesis but to examine the dissemination of a scientific result. - oai:arXiv.org:2512.06543v1 - physics.hist-ph - math.HO - physics.geo-ph - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Herv\'e Le Ferrand - - - The Two-Sheeted Topology of Extended Kerr-Type Spacetimes and a Parity-of-Crossings Property for Ring-Traversing Geodesics - https://arxiv.org/abs/2512.06549 - arXiv:2512.06549v1 Announce Type: cross -Abstract: We revisit the global structure of the extended Kerr spacetime and of a broader class of Kerr-type spacetimes possessing ring singularities. By working with the elementary analytic extension (the union of the interior and exterior regions glued across the disk), we show that excising the ring singularity yields a domain that can be realised as a branched double cover of an exterior Kerr region. The branch locus is the ring itself, and the associated deck transformation defines a non-trivial $\mathbb{Z}_2$-action that exchanges the two sheets ($r>0$ and $r<0$) of the spacetime. - We give a covering-space characterisation of this double-sheeted structure and show that admissible geodesics which cross the ring singularity implement the non-trivial deck transformation. In particular, we prove a parity-of-crossings property: any admissible geodesic that traverses an even number of ring singularities returns to its original sheet, while an odd number of traversals terminates on the opposite sheet. - Generalising to $N$ disjoint ring singularities, we prove that the fundamental group of the excised manifold is the free group $F_N$ generated by simple loops around each ring, and we classify the associated double covers. Identifying the physically distinguished cover where every ring induces a sheet exchange, we extend the parity-of-crossings theorem to the multi-ring setting. We then formally extend these results to the maximal analytic extension (the infinite Carter--Penrose chain), proving that the sheet-exchange mechanism applies globally to this infinite structure. - Finally, applying the Novikov self-consistency principle to this topological framework, we demonstrate that the requirement of global consistency restricts admissible histories to discrete sectors labelled by ring-crossing parities. - oai:arXiv.org:2512.06549v1 - gr-qc - hep-th - math-ph - math.MP - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Sabbir A. Rahman - - - Learning Reachability of Energy Storage Arbitrage - https://arxiv.org/abs/2512.06600 - arXiv:2512.06600v1 Announce Type: cross -Abstract: Power systems face increasing weather-driven variability and, therefore, increasingly rely on flexible but energy-limited storage resources. Energy storage can buffer this variability, but its value depends on intertemporal decisions under uncertain prices. Without accounting for the future reliability value of stored energy, batteries may act myopically, discharging too early or failing to preserve reserves during critical hours. This paper introduces a stopping-time reward that, together with a state-of-charge (SoC) range target penalty, aligns arbitrage incentives with system reliability by rewarding storage that maintains sufficient SoC before critical hours. We formulate the problem as an online optimization with a chance-constrained terminal SoC and embed it in an end-to-end (E2E) learning framework, jointly training the price predictor and control policy. The proposed design enhances reachability of target SoC ranges, improves profit under volatile conditions, and reduces its standard deviation. - oai:arXiv.org:2512.06600v1 - eess.SY - cs.SY - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Tom\'as Tapia, Agustin Castellano, Enrique Mallada, Yury Dvorkin - - - Geometry-Induced Vacuum Polarization and Mode Shifts in Maxwell-Klein-Gordon Theory - https://arxiv.org/abs/2512.06605 - arXiv:2512.06605v1 Announce Type: cross -Abstract: Geometric confinement is known to modify single-particle dynamics through effective potentials, yet its imprint on the interacting quantum vacuum remains largely unexplored. In this work, we investigate the Maxwell--Klein--Gordon system constrained to curved surfaces and demonstrate that the geometric potential $\Sigma_{\mathrm{geom}}(\mathbf{r})$ acts as a local renormalization environment. We show that extrinsic curvature modifies the scalar loop spectrum, entering the vacuum polarization as a position-dependent mass correction $M^2(\mathbf{r}) \to m^2 + \Sigma_{\mathrm{geom}}(\mathbf{r})$. This induces a finite, gauge-invariant ``geometry-induced running'' of the electromagnetic response. In the long-wavelength regime ($|{\bf Q}|R \ll 1$), we derive a closed-form expression for the relative frequency shift $\Delta\omega/\omega$, governed by the overlap between the electric energy density and the geometric potential. Applying this formalism to Gaussian bumps, cylindrical shells, and tori, we identify distinct spectral signatures that distinguish these quantum loop corrections from classical geometric optics. Our results suggest that spatial curvature can serve as a tunable knob for ``vacuum engineering,'' offering measurable shifts in high-$Q$ cavities and plasmonic systems. - oai:arXiv.org:2512.06605v1 - physics.optics - gr-qc - math-ph - math.MP - quant-ph - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Li Wang, Jun Wang, Yong-Long Wang - - - Half-explicit Runge-Kutta integrators for variational multiscale turbulence modeling: Toward higher-order accuracy in space and time - https://arxiv.org/abs/2512.06626 - arXiv:2512.06626v1 Announce Type: cross -Abstract: The residual-based variational multiscale (VMS) formulation has achieved remarkable success in large-eddy simulation of turbulent flows. However, its temporal discretization has largely remained limited to second-order implicit schemes. The present work aims at advancing this direction through the introduction of Runge-Kutta (RK) schemes within the VMS framework in a mathematically consistent manner. Guided by the Rothe method, the half-explicit RK scheme is employed as its accuracy is theoretically guaranteed for index-2 differential-algebraic equations. Owing to the explicit treatment of the nonlinear term, the resulting spatial problem exhibits a structure analogous to that of the Darcy equation. Following the philosophy of the VMS analysis, a subgrid-scale model is derived without invoking linearization based on perturbation series and related assumptions. The analysis further reveals that the parameter in the subgrid model is independent of the spatial mesh size. Fourier analysis demonstrates that the Rothe method, compared with the conventional vertical method of lines, provides improved dissipation and dispersion properties and exhibits a larger stability region for convection-dominated regimes. In the Taylor-Green vortex benchmark, the proposed schemes demonstrate superior performance as a large-eddy simulation model, achieving higher fidelity in predicting the kinetic energy evolution, energy spectra, and vortex structures than the conventional VMS formulation. Simulations of the open cavity flow further show that the proposed schemes can accurately capture the periodic limit cycle caused by the supercritical Hopf bifurcation, confirming its effectiveness and fidelity for highly sensitive flow instability problems. - oai:arXiv.org:2512.06626v1 - physics.flu-dyn - cs.NA - math.NA - physics.comp-ph - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Yujie Sun, Chi Ding, Ju Liu - - - FlatFormer: A Flat Transformer Knowledge Tracing Model Based on Cognitive Bias Injection - https://arxiv.org/abs/2512.06629 - arXiv:2512.06629v1 Announce Type: cross -Abstract: Knowledge Tracing (KT) models face a critical ``Performance-Complexity Trap'': capturing complex cognitive dynamics like learning sessions and memory decay typically requires deep hierarchical architectures, which incur prohibitive computational costs for real-time deployment. To resolve this, we propose FlatFormer, a streamlined architecture based on the novel design paradigm of ``Information Injection over Structural Stacking.'' Unlike parameter-heavy hierarchical models, FlatFormer leverages a standard flat Transformer augmented with two lightweight injection mechanisms: (i) a hybrid input encoding strategy combining learnable session identifiers with fixed sinusoidal step embeddings; and (ii) a pre-computed power-law bias integrated directly into attention logits to explicitly model the forgetting curve. Extensive experiments on four large-scale datasets (e.g., EdNet, Junyi) show that FlatFormer achieves state-of-the-art performance. For example, on the EdNet dataset, compared to the strongest hierarchical baseline (HiTSKT), its absolute AUC increased by 8.3%, while using less than 15% of parameters, and inference speed was about three times faster. These results validate that high cognitive fidelity does not necessitate architectural complexity. - oai:arXiv.org:2512.06629v1 - cs.AI - cs.IT - math.IT - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Xiao-li Xia, Hou-biao Li - - - Varied Branches of Nondegenerate Vector Solitons - https://arxiv.org/abs/2512.06667 - arXiv:2512.06667v1 Announce Type: cross -Abstract: Our study on nondegenerate dark-bright-bright solitons in a three-component Manakov model with repulsive interactions reveals the existence of diverse branches of nondegenerate vector solitons. For fixed bright component particle numbers and a given soliton velocity, the nondegenerate dark-bright-bright solitons exhibit four distinct branches with different density profiles and phase distributions, comprising two positive mass branches and two negative mass branches. The energy-velocity dispersion relation of each pair of positive- and one negative-mass branches form a closed loop, resulting in two mutually independent loops for the soliton's overall dispersion. All soliton branches share a common maximal velocity, which is determined by the larger bright soliton particle number. Linear stability analysis shows that all these branches are stable against weak perturbations. Extending to an $N$-component Manakov system, the nondegenerate solitons have $2^{N-1}$ distinct branches, of which $2^{N-2}$ branches solitons is positive mass and $2^{N-2}$ branches solitons is negative mass. Each pair of positive- and negative-mass branches form a closed dispersion relation loop, so that the vector solitons have $2^{N-2}$ disjoint loops. These results uncover the rich branches and interesting dispersion relations of nondegenerate vector solitons in multi-component models. - oai:arXiv.org:2512.06667v1 - nlin.PS - math-ph - math.MP - nlin.SI - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Yu-Hao Wang, Liang Duan, Yan-Hong Qin, Li-Chen Zhao - - - Interplay between Standard Quantum Detailed Balance and Thermodynamically Consistent Entropy Production - https://arxiv.org/abs/2512.06707 - arXiv:2512.06707v1 Announce Type: cross -Abstract: We demonstrate that if a quantum Markovian semigroup satisfies the standard quantum detailed balance condition, its generator admits a special representation that yields a vanishing entropy production rate. Conversely, if the generator admits a special representation adhering to the condition of thermodynamic consistency and leading to a vanishing entropy production rate, then the corresponding quantum Markovian semigroup must satisfy the standard quantum detailed balance condition. In this context, we adopt the definition of entropy production rate that is motivated by the physics literature and standard for thermodynamically consistent Lindbladians. - oai:arXiv.org:2512.06707v1 - quant-ph - cond-mat.stat-mech - math-ph - math.MP - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Xin-Hai Tong, Kohei Yoshimura, Tan Van Vu, Naruo Ohga - - - Optimal experimental design with k-space data: application to inverse hemodynamics - https://arxiv.org/abs/2512.06712 - arXiv:2512.06712v1 Announce Type: cross -Abstract: Subject-specific cardiovascular models rely on parameter estimation using measurements such as 4D Flow MRI data. However, acquiring high-resolution, high-fidelity functional flow data is costly and taxing for the patient. As a result, there is growing interest in using highly undersampled MRI data to reduce acquisition time and thus the cost, while maximizing the information gain from the data. Examples of such recent work include inverse problems to estimate boundary conditions of aortic blood flow from highly undersampled k-space data. The undersampled data is selected based on a predefined sampling mask which can significantly influences the performance and the quality of the solution of the inverse problem. While there are many established sampling patterns to collect undersampled data, it remains unclear how to select the best sampling pattern for a given set of inference parameters. In this paper we propose an Optimal Experimental Design (OED) framework for MRI measurements in k-space, aiming to find optimal masks for estimating specific parameters directly from k-space. As OED is typically applied to sensor placement problems in spatial locations, this is, to our knowledge, the first time the technique is used in this context. We demonstrate that the masks optimized by employing OED consistently outperform conventional sampling patterns in terms of parameter estimation accuracy and variance, facilitating a speed-up of 10x of the acquisition time while maintaining accuracy. - oai:arXiv.org:2512.06712v1 - physics.med-ph - cs.NA - math.NA - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Miriam L\"ocke, Ahmed Attia, Dariusz Uc\'inski, Crist\'obal Bertoglio - - - Symmetry-Based Formation Control on Cycle Graphs Using Dihedral Point Groups - https://arxiv.org/abs/2512.06733 - arXiv:2512.06733v1 Announce Type: 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:2512.06733v1 - eess.SY - cs.SY - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Zamir Martinez, Daniel Zelazo - - - Small-Gain Nash: Certified Contraction to Nash Equilibria in Differentiable Games - https://arxiv.org/abs/2512.06791 - arXiv:2512.06791v1 Announce Type: cross -Abstract: Classical convergence guarantees for gradient-based learning in games require the pseudo-gradient to be (strongly) monotone in Euclidean geometry as shown by rosen(1965), a condition that often fails even in simple games with strong cross-player couplings. We introduce Small-Gain Nash (SGN), a block small-gain condition in a custom block-weighted geometry. SGN converts local curvature and cross-player Lipschitz coupling bounds into a tractable certificate of contraction. It constructs a weighted block metric in which the pseudo-gradient becomes strongly monotone on any region where these bounds hold, even when it is non-monotone in the Euclidean sense. The continuous flow is exponentially contracting in this designed geometry, and projected Euler and RK4 discretizations converge under explicit step-size bounds derived from the SGN margin and a local Lipschitz constant. Our analysis reveals a certified ``timescale band'', a non-asymptotic, metric-based certificate that plays a TTUR-like role: rather than forcing asymptotic timescale separation via vanishing, unequal step sizes, SGN identifies a finite band of relative metric weights for which a single-step-size dynamics is provably contractive. We validate the framework on quadratic games where Euclidean monotonicity analysis fails to predict convergence, but SGN successfully certifies it, and extend the construction to mirror/Fisher geometries for entropy-regularized policy gradient in Markov games. The result is an offline certification pipeline that estimates curvature, coupling, and Lipschitz parameters on compact regions, optimizes block weights to enlarge the SGN margin, and returns a structural, computable convergence certificate consisting of a metric, contraction rate, and safe step-sizes for non-monotone games. - oai:arXiv.org:2512.06791v1 - cs.LG - cs.GT - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Vedansh Sharma - - - Free energy dissipation and a decomposition of general jump diffusions on $\mathbb{R}^n$ without detailed balance - https://arxiv.org/abs/2512.06839 - arXiv:2512.06839v1 Announce Type: cross -Abstract: We analyze the thermodynamic structure of jump diffusions combining Brownian and Poisson noise, a class of stochastic dynamics relevant to nonequilibrium statistical physics. For such nonlocal dynamics, the free energy admits a full dissipation formula that decomposes into entropy production and housekeeping heat. A central result is a decomposition of the generator into symmetric and anti-symmetric parts with respect to the invariant measure $\rho_{ss}$. The symmetric sector corresponds to a reversible dynamics and yields a nonlocal Fisher information governing free-energy decay, whereas the anti-symmetric sector generates a canonical conservative flow that produces circulation but no dissipation. Several numerical examples demonstrate how this decomposition clarifies the structure of nonequilibrium stationary states in jump-driven systems. - oai:arXiv.org:2512.06839v1 - cond-mat.stat-mech - math.PR - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Shuyuan Fan, Qi Zhang - - - Bridging Abstraction-Based Hierarchical Control and Moment Matching: A Conceptual Unification - https://arxiv.org/abs/2512.06875 - arXiv:2512.06875v1 Announce Type: cross -Abstract: In this paper, we establish a relation between approximate-simulation-based hierarchical control (ASHC) and moment matching techniques, and build a conceptual bridge between these two frameworks. To this end, we study the two key requirements of the ASHC technique, namely the bounded output discrepancy and the $M$-relation, through the lens of moment matching. We show that, in the linear time-invariant case, both requirements can be interpreted in the moment matching perspective through certain system interconnection structures. Building this conceptual bridge provides a foundation for cross-pollination of ideas between these two frameworks. - oai:arXiv.org:2512.06875v1 - eess.SY - cs.SY - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Zirui Niu, Mohammad Fahim Shakib, Giordano Scarciotti - - - A first-order formulation of f(R) gravity in spherical symmetry - https://arxiv.org/abs/2512.06908 - arXiv:2512.06908v1 Announce Type: cross -Abstract: We develop a first-order formulation of the field equations in f(R) gravity governing the global evolution of a (possibly massive) scalar field under spherical symmetry. Our formulation allows us to pose the characteristic initial value problem and to establish several properties of solutions. More precisely, we work in generalized Bondi-Sachs coordinates and prescribe initial data on an asymptotically Euclidean, future light cone with vertex at the center of symmetry, and we identify the precise regularity conditions required at the center. Following and extending Christodoulou's approach to the Einstein-massless scalar-field system, we recast the f(R) field equations as an integro-differential system of two coupled, first-order, nonlocal, nonlinear hyperbolic equations, whose principal unknowns are the scalar field and the spacetime scalar curvature. In deriving this reduced two-equation system, we identify the regularity conditions at the center of symmetry and impose natural assumptions on the scalar-field potential and on the function f(R) governing the gravitational Lagrangian density. As an application, we prove the monotonicity of the Hawking mass in this setting and formally analyze the singular limit in which the integrand f(R) of the action approaches R, corresponding to the Einstein-Hilbert action. Hence, the formulation isolates the essential evolution and constraint content on the future domain of dependence of two null hypersurfaces and is designed to facilitate subsequent advances in geometric analysis and robust numerical simulations of spherical collapse in modified gravity. - oai:arXiv.org:2512.06908v1 - gr-qc - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Philippe G. LeFloch, Filipe C. Mena - - - Angular Momentum Penrose Inequality - https://arxiv.org/abs/2512.06918 - arXiv:2512.06918v1 Announce Type: cross -Abstract: We prove the Angular Momentum Penrose Inequality for axisymmetric vacuum initial data satisfying the dominant energy condition. This inequality establishes a sharp lower bound on the ADM mass in terms of both the horizon area and the Komar angular momentum of a black hole, with equality achieved precisely by the Kerr solution. The proof combines four main ingredients: solving an axisymmetric Jang equation where twist enters as a lower-order perturbation, establishing conformal factor bounds via a divergence identity, proving angular momentum conservation along level sets using de Rham cohomology, and applying the proven Dain-Reiris area-angular momentum inequality for sub-extremality. The monotonicity of a combined area-angular momentum functional along the Agostiniani-Mazzieri-Oronzio flow yields the result. This provides the first geometric inequality incorporating both horizon area and angular momentum, with implications for cosmic censorship, black hole thermodynamics, and gravitational wave observations of spinning black holes. - oai:arXiv.org:2512.06918v1 - gr-qc - math.FA - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Da Xu - - - Optimal Transport of a Free Quantum Particle and its Shape Space Interpretation - https://arxiv.org/abs/2512.06940 - arXiv:2512.06940v1 Announce Type: cross -Abstract: A solution of the free Schr\"odinger equation is investigated by means of Optimal transport. The curve of probability measures $\mu_t$ this solution defines is shown to be an absolutely continuous curve in the Wasserstein space $W_2(\mathbb{R}^3)$. The optimal transport map from $\mu_t$ to $\mu_s$, the cost for this transport (i.e. the Wasserstein distance) and the value of the Fisher information along $\mu_t$ are being calculated. It is finally shown that this solution of the free Schr\"odinger equation can naturally be interpreted as a curve in so-called Shape space, which forgets any positioning in space but only describes properties of shapes. In Shape space, $\mu_t$ continues to be a shortest path geodesic. - oai:arXiv.org:2512.06940v1 - quant-ph - math-ph - math.FA - math.MP - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Bernadette Lessel - - - $L_\infty$-algebraic extensions of non-Lorentzian kinematical Lie algebras, gravities, and brane couplings - https://arxiv.org/abs/2512.06942 - arXiv:2512.06942v1 Announce Type: cross -Abstract: The Newtonian limit of Newton-Cartan gravity relies crucially on the Lie-algebraic central extension to the Galilean algebra, namely the Bargmann algebra. Lie-algebraic central extensions naturally generalise to $L_\infty$-algebraic central extensions, which in turn classify branes in superstring theory via the brane bouquet. This paper classifies all $L_\infty$-algebraic central extensions of all kinematical Lie algebras that do not depend on the spatial rotation generators as well as all iterated central extensions thereof (for codimensions $\le3$). The Bargmann central extension of the Galilean algebra then appears as merely one term in a sequence of $L_\infty$-algebraic central extensions in each degree; a similar situation obtains for the Newton-Hooke algebra and the static algebra, but not for the Carrollian algebra nor those kinematical Lie algebras that are not Wigner-\.In\"on\"u deformations of a simple algebra. - The sequence of $L_\infty$-algebraic central extensions in each degree then corresponds to a tower of $p$-form fields. After imposing conventional constraints, the zero-form field provides absolute time, and the higher-form fields are certain wedge products of the field strengths of the one-form (Bargmann) gravitational field. These then provide natural $(p-1)$-brane couplings to the corresponding non-Lorentzian gravities, which are found to produce velocity-dependent gravitational effects in the presence of torsion. The $L_\infty$-algebraic cocycles also provide Wess-Zumino-Witten terms for the $(p-1)$-brane action, which require the introduction of doubled spatial coordinates that are reminiscent of double field theory, but which (in some cases at least, and given appropriate kinetic terms) do not result in doubled physics. - oai:arXiv.org:2512.06942v1 - hep-th - gr-qc - math-ph - math.MP - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Hyungrok Kim - - - Resource-Bounded Type Theory: Compositional Cost Analysis via Graded Modalities - https://arxiv.org/abs/2512.06952 - arXiv:2512.06952v1 Announce Type: cross -Abstract: We present a compositional framework for certifying resource bounds in typed programs. Terms are typed with synthesized bounds drawn from an abstract resource lattice, enabling uniform treatment of time, memory, gas, and domain-specific costs. - We introduce a graded feasibility modality with co-unit and monotonicity laws. Our main result is a syntactic cost soundness theorem for the recursion-free simply-typed fragment: if a closed term has synthesized bound b under a given budget, its operational cost is bounded by b. We provide a syntactic term model in the topos of presheaves over the lattice -- where resource bounds index a cost-stratified family of definable values -- with cost extraction as a natural transformation. We prove canonical forms via reification and establish initiality of the syntactic model: it embeds uniquely into all resource-bounded models. - A case study demonstrates compositional reasoning for binary search using Lean's native recursion with separate bound proofs. - oai:arXiv.org:2512.06952v1 - cs.LO - cs.CE - math.LO - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Mirco A. Mannucci, Corey Thuro - - - Statistical analysis of Inverse Entropy-regularized Reinforcement Learning - https://arxiv.org/abs/2512.06956 - arXiv:2512.06956v1 Announce Type: cross -Abstract: Inverse reinforcement learning aims to infer the reward function that explains expert behavior observed through trajectories of state--action pairs. A long-standing difficulty in classical IRL is the non-uniqueness of the recovered reward: many reward functions can induce the same optimal policy, rendering the inverse problem ill-posed. In this paper, we develop a statistical framework for Inverse Entropy-regularized Reinforcement Learning that resolves this ambiguity by combining entropy regularization with a least-squares reconstruction of the reward from the soft Bellman residual. This combination yields a unique and well-defined so-called least-squares reward consistent with the expert policy. We model the expert demonstrations as a Markov chain with the invariant distribution defined by an unknown expert policy $\pi^\star$ and estimate the policy by a penalized maximum-likelihood procedure over a class of conditional distributions on the action space. We establish high-probability bounds for the excess Kullback--Leibler divergence between the estimated policy and the expert policy, accounting for statistical complexity through covering numbers of the policy class. These results lead to non-asymptotic minimax optimal convergence rates for the least-squares reward function, revealing the interplay between smoothing (entropy regularization), model complexity, and sample size. Our analysis bridges the gap between behavior cloning, inverse reinforcement learning, and modern statistical learning theory. - oai:arXiv.org:2512.06956v1 - stat.ML - cs.LG - math.ST - stat.TH - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Denis Belomestny, Alexey Naumov, Sergey Samsonov - - - Extending Action Logic with Omega Iteration - https://arxiv.org/abs/2512.06985 - arXiv:2512.06985v1 Announce Type: cross -Abstract: We present a proof system that extends action logic by omega iteration, which is viewed as infinitary multiplicative conjunction. We prove cut admissibility and establish complexity bounds for the provability predicate. - oai:arXiv.org:2512.06985v1 - cs.LO - math.LO - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Tikhon Pshenitsyn - - - Accurate Models of NVIDIA Tensor Cores - https://arxiv.org/abs/2512.07004 - arXiv:2512.07004v1 Announce Type: cross -Abstract: Matrix multiplication is a fundamental operation in for both training of neural networks and inference. To accelerate matrix multiplication, Graphical Processing Units (GPUs) provide it implemented in hardware. Due to the increased throughput over the software-based matrix multiplication, the multipliers are increasingly used outside of AI, to accelerate various applications in scientific computing. However, matrix multipliers targeted at AI are at present not compliant with IEEE 754 floating-point arithmetic behaviour, with different vendors offering different numerical features. This leads to non-reproducible results across different generations of GPU architectures, at the matrix multiply-accumulate instruction level. To study numerical characteristics of matrix multipliers-such as rounding behaviour, accumulator width, normalization points, extra carry bits, and others-test vectors are typically constructed. Yet, these vectors may or may not distinguish between different hardware models, and due to limited hardware availability, their reliability across many different platforms remains largely untested. We present software models for emulating the inner product behavior of low- and mixed-precision matrix multipliers in the V100, A100, H100 and B200 data center GPUs in most supported input formats of interest to mixed-precision algorithm developers: 8-, 16-, and 19-bit floating point. - oai:arXiv.org:2512.07004v1 - cs.MS - cs.AR - cs.NA - math.NA - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Faizan A. Khattak, Mantas Mikaitis - - - Learning Paths to Multi-Sector Equilibrium: Belief Dynamics Under Uncertain Returns to Scale - https://arxiv.org/abs/2512.07013 - arXiv:2512.07013v1 Announce Type: cross -Abstract: This paper explores the dynamics of learning in a multi-sector general equilibrium model where firms operate under incomplete information about their production returns to scale. Firms iteratively update their beliefs using maximum a-posteriori estimation, derived from observed production outcomes, to refine their knowledge of their returns to scale. The implications of these learning dynamics for market equilibrium and the conditions under which firms can effectively learn their true returns to scale are the key objects of this study. Our results shed light on how idiosyncratic shocks influence the learning process and demonstrate that input decisions encode all pertinent information for belief updates. Additionally, we show that a long-memory (path-dependent) learning which keeps track of all past estimations ends up having a worse performance than a short-memory (path-independent) approach. - oai:arXiv.org:2512.07013v1 - cs.GT - econ.TH - math.OC - math.PR - math.ST - stat.TH - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Stefano Nasini, Rabia Nessah, Bertrand Wigniolle - - - Symmetry, Invariant Manifolds and Flow Reversals in Active Nematic Turbulence - https://arxiv.org/abs/2512.07047 - arXiv:2512.07047v1 Announce Type: cross -Abstract: We investigate how symmetry, exact coherent structures (ECSs), and their invariant manifolds organize spontaneous flow reversals in a 2D active nematic confined to a periodic channel. In minimal flow units commensurate with the intrinsic active vortex scale, we use equivariant bifurcation theory to trace the origin of dynamically relevant ECSs via a sequence of symmetry-constrained local and global bifurcations. At low activity level, we identify relative periodic orbits, created via a sequence of SNIPER, homoclinic and heteroclinic bifurcations, whose invariant manifolds provide robust heteroclinic pathways between left- and right-flowing nearly uniaxial states. These result in several symmetry-dictated reversal mechanisms in the preturbulent regime, with and without vortex-lattice intermediate states. In the active turbulent regime, this ECS skeleton persists and organizes chaotic attractors exhibiting persistent two-way reversals. By classifying ECSs through their symmetry signatures, we relate a small set of ECSs embedded in turbulence back to the preturbulent branches, and show that typical turbulent trajectories repeatedly shadow these ECSs and their unstable manifolds, resulting in near-heteroclinic transitions between opposite-flow states. Our results establish that channel confined active nematic turbulence is organized by a low-dimensional, symmetry-governed network of invariant solutions and their manifolds, and identify dynamical mechanisms that could be exploited to design, promote, or suppress flow reversals in active matter microfluidic devices. - oai:arXiv.org:2512.07047v1 - cond-mat.soft - math.DS - nlin.CD - physics.flu-dyn - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Angel Naranjo, Rumayel Pallock, Caleb Wagner, Piyush Grover - - - Beam search decoder for quantum LDPC codes - https://arxiv.org/abs/2512.07057 - arXiv:2512.07057v1 Announce Type: cross -Abstract: We propose a decoder for quantum low density parity check (LDPC) codes based on a beam search heuristic guided by belief propagation (BP). Our beam search decoder applies to all quantum LDPC codes and achieves different speed-accuracy tradeoffs by tuning its parameters such as the beam width. We perform numerical simulations under circuit level noise for the $[[144, 12, 12]]$ bivariate bicycle (BB) code at noise rate $p=10^{-3}$ to estimate the logical error rate and the 99.9 percentile runtime and we compare with the BP-OSD decoder which has been the default quantum LDPC decoder for the past six years. A variant of our beam search decoder with a beam width of 64 achieves a $17\times$ reduction in logical error rate. With a beam width of 8, we reach the same logical error rate as BP-OSD with a $26.2\times$ reduction in the 99.9 percentile runtime. We identify the beam search decoder with beam width of 32 as a promising candidate for trapped ion architectures because it achieves a $5.6\times$ reduction in logical error rate with a 99.9 percentile runtime per syndrome extraction round below 1ms at $p=5 \times10^{-4}$. Remarkably, this is achieved in software on a single core, without any parallelization or specialized hardware (FPGA, ASIC), suggesting one might only need three 32-core CPUs to decode a trapped ion quantum computer with 1000 logical qubits. - oai:arXiv.org:2512.07057v1 - quant-ph - cs.IT - math.IT - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Min Ye, Dave Wecker, Nicolas Delfosse - - - Asymptotic theory and statistical inference for the samples problems with heavy-tailed data using the functional empirical process - https://arxiv.org/abs/2512.07088 - arXiv:2512.07088v1 Announce Type: cross -Abstract: This paper introduces the Trimmed Functional Empirical Process (TFEP) as a robust framework for statistical inference when dealing with heavy-tailed or skewed distributions, where classical moments such as the mean or variance may be infinite or undefined. Standard approaches including the classical Functional Empirical Process (FEP), break down under such conditions, especially for distributions like Pareto, Cauchy, low degree of freedom Student-t, due to their reliance on finite-variance assumptions to guarantee asymptotic convergence. The TFEP approach addresses these limitations by trimming a controlled proportion of extreme order statistics, thereby stabilizing the empirical process and restoring asymptotic Gaussian behavior. We establish the weak convergence of the TFEP under mild regularity conditions and derive new asymptotic distributions for one-sample and twosample problems. These theoretical developments lead to robust confidence intervals for truncated means, variances, and their differences or ratios. The efficiency and reliability of the TFEP are supported by extensive Monte Carlo experiments and an empirical application to Senegalese income data. In all scenarios, the TFEP provides accurate inference where both Gaussian-based methods and the classical FEP break down. The methodology thus offers a powerful and flexible tool for statistical analysis in heavy-tailed and non-standard environments. - oai:arXiv.org:2512.07088v1 - stat.ME - math.PR - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by-sa/4.0/ - Abdoulaye Camara, Saliou Diouf, Moumouni Diallo, Gane Samb Lo - - - Structure-conditioned input-to-state stability for layer-by-layer molecular computations in parallel chemical reaction networks - https://arxiv.org/abs/2512.07116 - arXiv:2512.07116v1 Announce Type: cross -Abstract: Molecular computation in chemical reaction networks (CRNs) now constitutes a foundational framework for designing programmable biological systems. However, prevailing design methodologies primarily treat parallelism of chemical reactions as a liability, consequently motivating researchers to redirect research focus toward leveraging parallelism to implement layer-by-layer computations of composite functions in coupled mass-action systems (MASs). MASs exhibiting this property are termed composable. Present composability verification for MASs mainly depends on input-to-state stability (ISS) conditions, with structural characteristics of networks remaining underexplored. This paper investigates the structural conditions under which two MASs are composable. By leveraging ISS-Lyapunov functions, we identify a class of CRN architectures, whose reduced systems have zero deficiency, that guarantee composability with other networks. We also extend our conclusions to encompass some CRN architectures possessing nonzero deficiency. Some examples are presented to demonstrate the validity of our theoretical results. Finally, we employ our methods to devise an algorithm for constructing MASs capable of executing specified molecular computations. - oai:arXiv.org:2512.07116v1 - q-bio.MN - math.DS - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Renlei Jiang, Chuanhou Gao, Denis Dochain - - - Beyond real: Investigating the role of complex numbers in self-testing - https://arxiv.org/abs/2512.07160 - arXiv:2512.07160v1 Announce Type: cross -Abstract: We investigate complex self-testing, a generalization of standard self-testing that accounts for quantum strategies whose statistics is indistinguishable from their complex conjugate's. We show that many structural results from standard self-testing extend to the complex setting, including lifting of common assumptions. Our main result is an operator-algebraic characterization: complex self-testing is equivalent to uniqueness of the real parts of higher moments, leading to a basis-independent formulation in terms of real C* algebras. This leads to a classification of non-local strategies, and a tight boundary where standard self-testing do not apply and complex self-testing is necessary. We further construct a strategy involving quaternions, establishing the first standard self-test for genuinely complex strategy. Our work clarifies the structure of complex self-testing and highlights the subtle role of complex numbers in bipartite Bell non-locality. - oai:arXiv.org:2512.07160v1 - quant-ph - math.OA - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Ranyiliu Chen, Laura Man\v{c}inska, Jurij Vol\v{c}i\v{c} - - - Phase Space Modeling of Extended Sources Based on Wigner Distribution and Hamiltonian Optics - https://arxiv.org/abs/2512.07161 - arXiv:2512.07161v1 Announce Type: cross -Abstract: Precise modeling of extended sources is a central challenge in modern optical engineering, laser physics, and computational lithography. Unlike ideal point sources or completely incoherent thermal radiation sources, real-world light sources -- such as high-power laser diode arrays, superluminescent diodes (SLD), extreme ultraviolet (EUV) lithography sources, and beams transmitted through atmospheric turbulence -- typically exhibit partial spatial coherence. - Traditional geometric optics based on ray tracing ignores diffraction and interference effects; while classical wave optics is accurate, the computational cost of handling four-dimensional correlation functions for partially coherent fields is enormous. To balance computational efficiency and physical accuracy, phase space optics provides a unified theoretical framework. By introducing the Wigner distribution function (WDF), we can map the light field into a joint space-time-spatial frequency domain $(\bm{r}, \bm{p})$. This description not only retains all the information of wave optics (including interference terms) but also naturally transitions to the ray description of Hamiltonian optics in the short-wavelength limit, governed by Liouville's theorem of phase space volume conservation. - This report aims to establish optimal modeling methods based on phase space and Hamiltonian optics for different types of extended sources such as partially coherent light, fully coherent light, and quasi-homogeneous light. The report will derive in detail the mathematical models for each source type and provide strict criteria for the applicability of geometric optics models using mathematical tools such as the Moyal expansion and generalized Fresnel number. - oai:arXiv.org:2512.07161v1 - physics.optics - math-ph - math.MP - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Rongqi Shang, Donglin Ma - - - Non-Hermitian Bose-Hubbard-like quantum models - https://arxiv.org/abs/2512.07250 - arXiv:2512.07250v1 Announce Type: cross -Abstract: Among all of the non-Hermitian large-tridiagonal-matrix quantum Hamiltonians we choose a subclass with the structure resembling the ``benchmark'' realistic Bose-Hubbard model. We demonstrate that this choice can be declared user-friendly in the sense that the underlying singular values can be specified via a ``Hermitized'' Schr\"{o}dinger-like equation. In particular, the related ``Hermitized'' Green's functions is shown given the two alternative compact and numerically efficient matrix continued fraction forms. - oai:arXiv.org:2512.07250v1 - quant-ph - cs.NA - math.NA - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - 10.1088/1742-6596/3152/1/012023 - J. Phys.: Conf. Ser. 3152 (2025) 012023 - Miloslav Znojil - - - Symmetries in Sorting - https://arxiv.org/abs/2512.07349 - arXiv:2512.07349v1 Announce Type: cross -Abstract: Sorting algorithms are fundamental to computer science, and their correctness criteria are well understood as rearranging elements of a list according to a specified total order on the underlying set of elements. As mathematical functions, they are functions on lists that perform combinatorial operations on the representation of the input list. In this paper, we study sorting algorithms conceptually as abstract sorting functions. - There is a canonical surjection from the free monoid on a set (lists of elements) to the free commutative monoid on the same set (multisets of elements). We show that sorting functions determine a section (right inverse) to this surjection satisfying two axioms, that do not presuppose a total order on the underlying set. Then, we establish an equivalence between (decidable) total orders on the underlying set and correct sorting functions. - The first part of the paper develops concepts from universal algebra from the point of view of functorial signatures, and gives constructions of free monoids and free commutative monoids in (univalent) type theory. Using these constructions, the second part of the paper develops the axiomatisation of sorting functions. The paper uses informal mathematical language, and comes with an accompanying formalisation in Cubical Agda. - oai:arXiv.org:2512.07349v1 - cs.LO - math.LO - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by-sa/4.0/ - Vikraman Choudhury, Wind Wong - - - Two-dimensional nonlinear Schr\"odinger equations with potential and dispersion given by arbitrary functions: Reductions and exact solutions - https://arxiv.org/abs/2512.07382 - arXiv:2512.07382v1 Announce Type: cross -Abstract: The paper deals with nonlinear Schr\"odinger equations of the general form, depending on time and two spatial variables, the potential and dispersion of which are specified by one or two arbitrary functions. The equations under consideration naturally generalize a number of related nonlinear partial differential equations that occur in various areas of theoretical physics, including nonlinear optics, superconductivity, and plasma physics. Two- and one-dimensional reductions are described, which lead the studied nonlinear Schr\"odinger equations to simpler equations of lower dimension or ordinary differential equations (or systems of ordinary differential equations). Using methods of generalized and functional separation of variables, a number of new exact solutions of two-dimensional nonlinear Schr\"odinger equations of the general form are found, which are expressed in quadratures or elementary functions. To analyze the equations under consideration, both Cartesian and polar coordinate systems are utilized. Special attention is paid to finding solutions with radial symmetry. The exact solutions obtained in this work can be used as test problems intended to assess the accuracy of numerical and approximate analytical methods for solving complex nonlinear PDEs of mathematical physics. - oai:arXiv.org:2512.07382v1 - nlin.SI - math-ph - math.AP - math.MP - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Andrei D. Polyanin - - - From sparse recovery to plug-and-play priors, understanding trade-offs for stable recovery with generalized projected gradient descent - https://arxiv.org/abs/2512.07397 - arXiv:2512.07397v1 Announce Type: cross -Abstract: We consider the problem of recovering an unknown low-dimensional vector from noisy, underdetermined observations. We focus on the Generalized Projected Gradient Descent (GPGD) framework, which unifies traditional sparse recovery methods and modern approaches using learned deep projective priors. We extend previous convergence results to robustness to model and projection errors. We use these theoretical results to explore ways to better control stability and robustness constants. To reduce recovery errors due to measurement noise, we consider generalized back-projection strategies to adapt GPGD to structured noise, such as sparse outliers. To improve the stability of GPGD, we propose a normalized idempotent regularization for the learning of deep projective priors. We provide numerical experiments in the context of sparse recovery and image inverse problems, highlighting the trade-offs between identifiability and stability that can be achieved with such methods. - oai:arXiv.org:2512.07397v1 - eess.IV - cs.NE - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Ali Joundi (IMB), Yann Traonmilin (IMB), Jean-Fran\c{c}ois Aujol (UB, IMB) - - - Social welfare optimisation in well-mixed and structured populations - https://arxiv.org/abs/2512.07453 - arXiv:2512.07453v1 Announce Type: cross -Abstract: Research on promoting cooperation among autonomous, self-regarding agents has often focused on the bi-objective optimisation problem: minimising the total incentive cost while maximising the frequency of cooperation. However, the optimal value of social welfare under such constraints remains largely unexplored. In this work, we hypothesise that achieving maximal social welfare is not guaranteed at the minimal incentive cost required to drive agents to a desired cooperative state. To address this gap, we adopt to a single-objective approach focused on maximising social welfare, building upon foundational evolutionary game theory models that examined cost efficiency in finite populations, in both well-mixed and structured population settings. Our analytical model and agent-based simulations show how different interference strategies, including rewarding local versus global behavioural patterns, affect social welfare and dynamics of cooperation. Our results reveal a significant gap in the per-individual incentive cost between optimising for pure cost efficiency or cooperation frequency and optimising for maximal social welfare. Overall, our findings indicate that incentive design, policy, and benchmarking in multi-agent systems and human societies should prioritise welfare-centric objectives over proxy targets of cost or cooperation frequency. - oai:arXiv.org:2512.07453v1 - physics.soc-ph - cs.AI - cs.MA - math.OC - nlin.AO - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Van An Nguyen, Vuong Khang Huynh, Ho Nam Duong, Huu Loi Bui, Hai Anh Ha, Quang Dung Le, Le Quoc Dung Ngo, Tan Dat Nguyen, Ngoc Ngu Nguyen, Hoai Thuong Nguyen, Zhao Song, Le Hong Trang, The Anh Han - - - Understanding LLM Agent Behaviours via Game Theory: Strategy Recognition, Biases and Multi-Agent Dynamics - https://arxiv.org/abs/2512.07462 - arXiv:2512.07462v1 Announce Type: cross -Abstract: As Large Language Models (LLMs) increasingly operate as autonomous decision-makers in interactive and multi-agent systems and human societies, understanding their strategic behaviour has profound implications for safety, coordination, and the design of AI-driven social and economic infrastructures. Assessing such behaviour requires methods that capture not only what LLMs output, but the underlying intentions that guide their decisions. In this work, we extend the FAIRGAME framework to systematically evaluate LLM behaviour in repeated social dilemmas through two complementary advances: a payoff-scaled Prisoners Dilemma isolating sensitivity to incentive magnitude, and an integrated multi-agent Public Goods Game with dynamic payoffs and multi-agent histories. These environments reveal consistent behavioural signatures across models and languages, including incentive-sensitive cooperation, cross-linguistic divergence and end-game alignment toward defection. To interpret these patterns, we train traditional supervised classification models on canonical repeated-game strategies and apply them to FAIRGAME trajectories, showing that LLMs exhibit systematic, model- and language-dependent behavioural intentions, with linguistic framing at times exerting effects as strong as architectural differences. Together, these findings provide a unified methodological foundation for auditing LLMs as strategic agents and reveal systematic cooperation biases with direct implications for AI governance, collective decision-making, and the design of safe multi-agent systems. - oai:arXiv.org:2512.07462v1 - cs.MA - cs.AI - cs.GT - cs.LG - math.DS - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Trung-Kiet Huynh, Duy-Minh Dao-Sy, Thanh-Bang Cao, Phong-Hao Le, Hong-Dan Nguyen, Phu-Quy Nguyen-Lam, Minh-Luan Nguyen-Vo, Hong-Phat Pham, Phu-Hoa Pham, Thien-Kim Than, Chi-Nguyen Tran, Huy Tran, Gia-Thoai Tran-Le, Alessio Buscemi, Le Hong Trang, The Anh Han - - - On the Role of the Canonical Transformation in the Single-Channel Kondo Model - https://arxiv.org/abs/2512.07465 - arXiv:2512.07465v1 Announce Type: cross -Abstract: This pedagogical work presents the significant role that canonical transformation plays in the interpretation of the Abelian bosonized single-channel SU(2) Kondo model, emphasizing its effect on the scaling dimension $\Delta$. The transformation shifts the longitudinal exchange coupling and modifies the scaling dimension of the spin-flip vertex $\tau_{\pm} e^{\pm i\beta \phi}$. Rather than fixing $\Delta$ to the fermionic value $\tfrac{1}{2}$, we keep $\alpha$ explicit, which allows us to identify how different choices lead to marginal or relevant regimes through $(1-\Delta(\alpha))J_\perp$. This approach offers a direct way to trace the scaling behavior from the bosonized Hamiltonian and shows how the RG flow connects to the definition of the Kondo temperature, where the resistance diverges, without switching to other methods. - oai:arXiv.org:2512.07465v1 - cond-mat.str-el - math-ph - math.MP - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Zehra \"Ozcan - - - On the emergence of preferred structures in quantum theory - https://arxiv.org/abs/2512.07468 - arXiv:2512.07468v1 Announce Type: cross -Abstract: We assess the possibilities offered by Hilbert space fundamentalism, an attitude towards quantum physics according to which all physical structures (e.g. subsystems, locality, spacetime, preferred observables) should emerge from minimal quantum ingredients (typically a Hilbert space, Hamiltonian, and state). As a case study, we first mainly focus on the specific question of whether the Hamiltonian can uniquely determine a tensor product structure, a crucial challenge in the growing field of quantum mereology. The present paper reviews, clarifies, and critically examines two apparently conflicting theorems by Cotler et al. and Stoica. We resolve the tension, show how the former has been widely misinterpreted and why the latter is correct only in some weaker version. We then propose a correct mathematical way to address the general problem of preferred structures in quantum theory, relative to the characterization of emergent objects by unitary-invariant properties. Finally, we apply this formalism in the particular case we started with, and show that a Hamiltonian and a state are enough structure to uniquely select a preferred tensor product structure. - oai:arXiv.org:2512.07468v1 - quant-ph - hep-th - math-ph - math.MP - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Antoine Soulas, Guilherme Franzmann, Andrea Di Biagio - - - An Analysis of Decision Problems for Relational Pattern Languages under Various Constraints - https://arxiv.org/abs/2512.07476 - arXiv:2512.07476v1 Announce Type: cross -Abstract: Patterns are words with terminals and variables. The language of a pattern is the set of words obtained by uniformly substituting all variables with words that contain only terminals. In their original definition, patterns only allow for multiple distinct occurrences of some variables to be related by the equality relation, represented by using the same variable multiple times. In an extended notion, called relational patterns and relational pattern languages, variables may be related by arbitrary other relations. We extend the ongoing investigation of the main decision problems for patterns (namely, the membership problem, the inclusion problem, and the equivalence problem) to relational pattern languages under a wide range of individual relations. It is shown show that - even for many much simpler or less restrictive relations - the complexity and (un)decidability characteristics of these problems do not change compared to the classical case where variables are related only by equality. - oai:arXiv.org:2512.07476v1 - cs.FL - cs.CC - math.CO - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Klaus Jansen, Dirk Nowotka, Lis Pirotton, Corinna Wambsganz, Max Wiedenh\"oft - - - The equation of Binet in classical and relativistic orbital mechanics - https://arxiv.org/abs/2512.07485 - arXiv:2512.07485v1 Announce Type: cross -Abstract: Binet's equation provides a direct way to obtain the geometric shape of orbits in a central force field. It is well known that in Newtonian gravitation Binet's equation leads to all the conic curves as solutions for an inverse-square force. In this work, we show how Binet's equation arises from the horizontal and vertical infinitesimal displacements of a body in free fall and in inertial motion. This derivation uses elementary concepts of infinitesimal calculus. Second, we derive the relativistic version of Binet's equation for the Schwarzschild-(anti-)de Sitter metric. This derivation, which is novel, directly relates the coordinates involved in Binet's equation without the need to introduce potentials or the use of Killing vectors. Finally, we tackle some controversies related to the role of the cosmological constant in the trajectory of photons in a Schwarzschild-(anti-)de Sitter or even in Reissner-Nordstr\"om-(anti-)de Sitter spacetimes. - oai:arXiv.org:2512.07485v1 - gr-qc - math-ph - math.MP - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jose Luis Alvarez-Perez - - - Efficient Low-Tubal-Rank Tensor Estimation via Alternating Preconditioned Gradient Descent - https://arxiv.org/abs/2512.07490 - arXiv:2512.07490v1 Announce Type: cross -Abstract: The problem of low-tubal-rank tensor estimation is a fundamental task with wide applications across high-dimensional signal processing, machine learning, and image science. Traditional approaches tackle such a problem by performing tensor singular value decomposition, which is computationally expensive and becomes infeasible for large-scale tensors. Recent approaches address this issue by factorizing the tensor into two smaller factor tensors and solving the resulting problem using gradient descent. However, this kind of approach requires an accurate estimate of the tensor rank, and when the rank is overestimated, the convergence of gradient descent and its variants slows down significantly or even diverges. To address this problem, we propose an Alternating Preconditioned Gradient Descent (APGD) algorithm, which accelerates convergence in the over-parameterized setting by adding a preconditioning term to the original gradient and updating these two factors alternately. Based on certain geometric assumptions on the objective function, we establish linear convergence guarantees for more general low-tubal-rank tensor estimation problems. Then we further analyze the specific cases of low-tubal-rank tensor factorization and low-tubal-rank tensor recovery. Our theoretical results show that APGD achieves linear convergence even under over-parameterization, and the convergence rate is independent of the tensor condition number. Extensive simulations on synthetic data are carried out to validate our theoretical assertions. - oai:arXiv.org:2512.07490v1 - cs.LG - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Zhiyu Liu, Zhi Han, Yandong Tang, Jun Fan, Yao Wang - - - Control of Discrete-Time Linear Systems with Charge-Balanced Inputs - https://arxiv.org/abs/2512.07506 - arXiv:2512.07506v1 Announce Type: cross -Abstract: Electrical brain stimulation relies on externally applied currents to modulate neural activity, but safety constraints require each stimulation cycle to be charge-balanced, enforcing a zero net injected charge. However, how such charge-balanced stimulation works remains poorly understood. This paper investigates the ability of charge-balanced inputs to steer state trajectories in discrete-time linear systems. Motivated by both open-loop and adaptive neurostimulation protocols, we study two practically relevant input structures: periodic (repetitive) charge-balanced inputs and non-repetitive charge-balanced inputs. For each case, we derive novel reachability and controllability conditions. The theoretical results are further validated through numerical demonstrations of minimum-energy control input design. - oai:arXiv.org:2512.07506v1 - eess.SY - cs.SY - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Yuzhen Qin, Zonglin Liu, Marcel van Gerven - - - On the structure of increasing profits in a 1D general diffusion market with interest rates - https://arxiv.org/abs/2512.07555 - arXiv:2512.07555v1 Announce Type: cross -Abstract: In this paper, we investigate a financial market model consisting of a risky asset, modeled as a general diffusion parameterized by a scale function and a speed measure, and a bank account process with a constant interest rate. This flexible class of financial market models allows for features such as reflecting boundaries, skewness effects, sticky points, and slowdowns on fractal sets. For this market model, we study the structure of a strong form of arbitrage opportunity called increasing profits. Our main contributions are threefold. First, we characterize the existence of increasing profits in terms of an auxiliary deterministic signed measure $\nu$ and a canonical trading strategy $\theta$, both of which depend only on the deterministic parametric characteristics of our model, namely the scale function, the speed measure, and the interest rate. More precisely, we show that an increasing profit exists if and only if $\nu$ is nontrivial, and that this is equivalent to $\theta$ itself generating an increasing profit. Second, we provide a precise characterization of the entire set of increasing profits in terms of $\nu$ and $\theta$, and moreover characterize the value processes associated with increasing profits. Finally, we establish novel connections between no-arbitrage theory and the general theory of stochastic processes. Specifically, we relate the failure of the representation property for general diffusions to the existence of certain types of increasing profits whose value processes are dominated by the quadratic variation measure of a space-transformed version of the asset price process. - oai:arXiv.org:2512.07555v1 - q-fin.MF - math.PR - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Alexis Anagnostakis, David Criens, Mikhail Urusov - - - Context-Adaptive Color Optimization for Web Accessibility: Balancing Perceptual Fidelity and Functional Requirements - https://arxiv.org/abs/2512.07623 - arXiv:2512.07623v1 Announce Type: cross -Abstract: We extend our OKLCH-based accessibility optimization with context-adaptive constraint strategies that achieve near-universal success rates across diverse use cases. Our original strict algorithm reached 66-77% success by prioritizing minimal perceptual change ($\Delta E \leq 5.0$), optimizing for enterprise contexts where brand fidelity is paramount. However, this one-size-fits-all approach fails to serve the broader ecosystem of web developers who need accessible solutions even when strict perceptual constraints cannot be satisfied. We introduce recursive optimization (Mode~1) that compounds small adjustments across iterations, achieving 93.68% success on all color pairs and 100% success on reasonable pairs (contrast ratio $\rho > 2.0$), representing a +27.23 percentage point improvement. A relaxed fallback mode (Mode~2) handles pathological edge cases, reaching 98.73% overall success. Evaluation on 10,000 realistic web color pairs demonstrates that context-aware constraint relaxation, combined with absolute hue preservation, enables practical accessibility compliance while maintaining brand color identity. The median perceptual change remains zero across all modes (most pairs already comply), while the 90th percentile reaches $\Delta E_{2000} = 15.55$ in Mode~1 -- perceptually acceptable when hue invariance preserves the essential character of the original color. The approach is deployed in CM-Colors v0.5.0 (800+ monthly downloads), providing developers with explicit control over the accessibility-fidelity trade-off appropriate to their context. - oai:arXiv.org:2512.07623v1 - cs.HC - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Lalitha A R - - - The Agent Capability Problem: Predicting Solvability Through Information-Theoretic Bounds - https://arxiv.org/abs/2512.07631 - arXiv:2512.07631v1 Announce Type: cross -Abstract: When should an autonomous agent commit resources to a task? We introduce the Agent Capability Problem (ACP), a framework for predicting whether an agent can solve a problem under resource constraints. Rather than relying on empirical heuristics, ACP frames problem-solving as information acquisition: an agent requires $\Itotal$ bits to identify a solution and gains $\Istep$ bits per action at cost $\Cstep$, yielding an effective cost $\Ceff = (\Itotal/\Istep), \Cstep$ that predicts resource requirements before search. We prove that $\Ceff$ lower-bounds expected cost and provide tight probabilistic upper bounds. Experimental validation shows that ACP predictions closely track actual agent performance, consistently bounding search effort while improving efficiency over greedy and random strategies. The framework generalizes across LLM-based and agentic workflows, linking principles from active learning, Bayesian optimization, and reinforcement learning through a unified information-theoretic lens. \ - oai:arXiv.org:2512.07631v1 - cs.AI - cs.CC - cs.IT - cs.LG - math.IT - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Shahar Lutati - - - Black Hole Scattering and Integrability: A Hyperboloidal Approach - https://arxiv.org/abs/2512.07641 - arXiv:2512.07641v1 Announce Type: cross -Abstract: Integrability structures are known to play a key role in one-dimensional scattering. In the Schwarzschild gravitational context, the analysis emphasizing the role of the so-called Darboux covariance and its intimate connection with KdV conserved quantities was recently introduced by Lenzi & Sopuerta. In a second stage, together with Jaramillo, this led in particular to the identification of the structural role of the "KdV-Virasoro-Schwarzian derivative" triangle in this problem. Such a gravitational scattering description dwells naturally on a Cauchy foliation of the spacetime. In the following, we first review--for the Schwarzschild background--this problem in a hyperboloidal foliation scheme, where the infinitesimal time generator of the dynamics is a non-selfadjoint operator. Then, we explore the underlying integrability features through a Lax-pair formulation. Specifically, the main results presented here are i) the explicit proposal of a weak Lax-pair, valid under suitable conditions involving fields at null infinity, with ii) the construction of the associated infinite sequence of isospectral flows. From a broader perspective, the very form of the non-selfadjoint infinitesimal time operator, which neatly separates into two components corresponding to bulk and boundary structures, paves the way for the description of the gravitational dynamics in terms of a "semi-direct action" of bulk degrees of freedom onto boundary degrees of freedom. This is akin to the "wave-mean flow" approach for black hole strong-gravity dynamics recently proposed in this line of research. - oai:arXiv.org:2512.07641v1 - gr-qc - math-ph - math.MP - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Corentin Vitel - - - Hirota-tau and Heun-function framework for Dirac vacuum polarization and quantum stabilization of kinks - https://arxiv.org/abs/2512.07658 - arXiv:2512.07658v1 Announce Type: cross -Abstract: We investigate a modified affine Toda model coupled to matter (ATM) which includes a scalar self-interacting potential and demonstrate that its first-order integro-differential structure, preserving a deformed Noether-topological current correspondence, provides a consistent framework for fermion-soliton interactions. In this formulation, the fermion-soliton energy is proportional to the soliton's topological charge. We show that fermionic back-reaction and the self-interacting scalar critically shape the fermion-kink energy, the in-gap bound-state spectrum, and the fermionic vacuum-polarization energy, yielding well-defined stability minima of the total energy as functions of the fermion and scalar masses and coupling parameters. A key result is that the Heun-equation formalism is necessary to construct nonzero-energy bound and scattering states: unlike the tau-function method, which captures only the zero mode, the Heun approach encodes the full scattering data through local solution matching conditions. These results refine the spectral analysis of deformed integrable models. The stability of soliton-fermion configurations has direct implications for topologically protected states in quantum information and condensed-matter systems. - oai:arXiv.org:2512.07658v1 - hep-th - math-ph - math.MP - nlin.SI - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Harold Blas - - - Loop Corrected Supercharges from Holomorphic Anomalies - https://arxiv.org/abs/2512.07771 - arXiv:2512.07771v1 Announce Type: cross -Abstract: We describe the loop corrections to supercharges in supersymmetric quantum field theories using the holomorphic twist formalism. We begin by reviewing the relation between supercharge corrections and the "twice-generalized" Konishi anomaly, which corrects the semi-chiral ring. In the holomorphic twist, these corrections appear as BRST anomalies and are computed using the higher operations of an underlying $L_\infty$ conformal algebra. We then apply this formalism to obtain the complete one-loop corrections to the supercharge of four-dimensional Lagrangian supersymmetric gauge theories, including $\mathcal{N}=4$ SYM, where it admits a remarkably compact expression in terms of superfields. - oai:arXiv.org:2512.07771v1 - hep-th - math-ph - math.MP - math.QA - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Kasia Budzik, Justin Kulp - - - VaR at Its Extremes: Impossibilities and Conditions for One-Sided Random Variables - https://arxiv.org/abs/2512.07787 - arXiv:2512.07787v1 Announce Type: 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:2512.07787v1 - q-fin.RM - math.PR - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - Nawaf Mohammed - - - Optimal Auction Design under Costly Learning - https://arxiv.org/abs/2512.07798 - arXiv:2512.07798v1 Announce Type: cross -Abstract: We study optimal auction design in an independent private values environment where bidders can endogenously -- but at a cost -- improve information about their own valuations. The optimal mechanism is two-stage: at stage-1 bidders register an information acquisition plan and pay a transfer; at stage-2 they bid, and allocation and payments are determined. We show that the revenue-optimal stage-2 rule is the Vickrey--Clarke--Groves (VCG) mechanism, while stage-1 transfers implement the optimal screening of types and absorb information rents consistent with incentive compatibility and participation. By committing to VCG ex post, the pre-auction information game becomes a potential game, so equilibrium information choices maximize expected welfare; the stage-1 fee schedule then transfers an optimal amount of payoff without conditioning on unverifiable cost scales. The design is robust to asymmetric primitives and accommodates a wide range of information technologies, providing a simple implementation that unifies efficiency and optimal revenue in environments with endogenous information acquisition. - oai:arXiv.org:2512.07798v1 - econ.TH - cs.GT - cs.IT - math.IT - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Kemal Ozbek - - - Caustics in the spherically symmetric Einstein-dust system - https://arxiv.org/abs/2512.07812 - arXiv:2512.07812v1 Announce Type: cross -Abstract: Caustics-envelopes formed by the trajectories of fluid particles-arise in proposed dynamical extensions for shell-crossing singularities occurring in the Einstein-dust system. In this study, a local existence result is established, describing the dynamics in a neighbourhood of such caustics. Specifically, we obtain spherically symmetric spacetimes $(M,g_{\mu\nu})$ containing a caustic $\mathcal{C}$, which, in the quotient $M/SO(3)$, is a timelike curve forming a singular boundary between a 2-dust region and a vacuum region. The spacetimes are constructed from solutions to a PDE problem posed with a spacelike direction of evolution. Curvature invariants and energy densities diverge as the caustic is approached. Consequently the metric has limited regularity $g\in C^{1,1/2}$ and is shown to satisfy Einstein's equation weakly. On the complement of the caustic, the metric is smooth and satisfies Einstein's equation classically. A (degenerate) coordinate system is identified in which the dynamical variables are smooth with extension to the caustic. Finally, a novel family of static, spherically symmetric spacetimes is identified, complementing the local construction above. Each spacetime contains an eternal annular 2-dust region bounded by a pair of caustics. - oai:arXiv.org:2512.07812v1 - gr-qc - math-ph - math.AP - math.DG - math.MP - Tue, 09 Dec 2025 00:00:00 -0500 - cross - http://creativecommons.org/licenses/by/4.0/ - David Bick - - - Left symmetric algebras from DNA insertion - https://arxiv.org/abs/1605.03837 - arXiv:1605.03837v3 Announce Type: replace -Abstract: DNA recombination is a fundamental biological process that encodes genetic information for organism development and function. In this study, we construct the left symmetric algebras arising from the operation of DNA insertion. We define a new operation of insertion by modifying the simplified insertion $$x\Rightarrow y:=f(\mid x\mid,\ \mid y \mid)\sum\limits_{i=0}^{q} y_{1}y_{2}\cdots y_{i} x y_{i+1}\cdots y_{q},$$ where $x = x_{1}x_{2}\cdots x_{p}$, $y = y_{1}y_{2}\cdots y_{q}$, and $\mid x\mid, \mid y\mid$ denote the lengths of $x$ and $y$, respectively. We prove that the algebra $\mathbb{F}(R)$ (over a field $\mathbb{F}$ of characteristic $0$, with $R$ being an infinite free semigroup generated by DNA nucleotides $\{A, G, C, T\}$) forms a left symmetric algebra if and only if the function $f$ satisfies the condition $$f(m, n) f(m+n, p)=f(n, p) f(m, n+p)= f(m, p) f(n, m+p),$$ where $m, n, p\in \mathbb{N}$. A key example of such a function is $f(m, n)=\exp\{g(m, n)\}$, where $g(m, n)=k\cdot mn,$ and $k$ is a fixed positive number, which effectively models length-dependent DNA insertion dynamics. This work enriches the theory of non-associative algebras and provides a mathematical framework for quantitative analysis of DNA recombination processes. - oai:arXiv.org:1605.03837v3 - math.RA - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Chen Yuan, Zhixiang Wu, Jing Wang - - - Algebra extensions and derived-discrete algebras - https://arxiv.org/abs/1904.07168 - arXiv:1904.07168v2 Announce Type: replace -Abstract: Let $\phi\colon A\rightarrow B$ be an algebra extension. We prove that if $\phi$ is split, the derived-discreteness of $A$ implies the derived-discreteness of $B$; if $\phi$ is separable and the right $A$-module $B$ is projective, the converse holds. We prove an analogous statement for piecewise hereditary algebras. - oai:arXiv.org:1904.07168v2 - math.RT - math.RA - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jie Li - - - Tautological algebra of the moduli stack of semistable bundles of rank 2 on a general curve - https://arxiv.org/abs/2002.00568 - arXiv:2002.00568v4 Announce Type: replace -Abstract: Our aim is to determine the tautological algebra generated by the cohomology classes of the Brill-Noether loci in the rational cohomology of the moduli stack $\mathcal{U}_C(n,d)$ of semistable bundles of rank $n$ and degree $d$. We show that for a general smooth projective curve $C$ of genus $g\geq 2$, $d=2g-2$, the tautological algebra of $ \mathcal{U}_C(2,2g-2)$ (resp. the moduli stack $\mathcal{SU}_C(2,\mathcal{L})$ of semistable bundles of rank $2$ and determinant $\mathcal{L}$ with $\deg(\mathcal{L})=2g-2$) is generated by the divisor classes (resp. the class of the Theta divisor $\Theta$). This is previously known in rank one situation, called the (classical) Porteous formula. - oai:arXiv.org:2002.00568v4 - math.AG - math.KT - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - 10.1080/00927872.2025.2578210 - Communications in Algebra, 21 Nov, 2025 - Chandranandan Gangopadhyay, Jaya NN Iyer, Arijit Mukherjee - - - Derived Representation Type and Field Extensions - https://arxiv.org/abs/2003.08589 - arXiv:2003.08589v2 Announce Type: replace -Abstract: Let $A$ be a finite-dimensional algebra over a field $k$. We define $A$ to be $\mathbf{C}$-dichotomic if it has the dichotomy property of the representation type on complexes of projective $A$-modules. $\mathbf{C}$-dichotomy implies the dichotomy properties of representation type on the levels of homotopy category and derived category. If $k$ admits a finite separable field extension $K/k$ such that $K$ is algebraically closed, the real number field for example, we prove that $A$ is $\mathbf{C}$-dichotomic. As a consequence, the second derived Brauer-Thrall type theorem holds for $A$, i.e., $A$ is either derived discrete or strongly derived unbounded. - oai:arXiv.org:2003.08589v2 - math.RT - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jie Li, Chao Zhang - - - The derived-discrete algebras over the real numbers - https://arxiv.org/abs/2010.03787 - arXiv:2010.03787v2 Announce Type: replace -Abstract: We classify derived-discrete algebras over the real numbers up to Morita equivalence, using the classification of complex derived-discrete algebras in [{\sc D. Vossieck}, {\em The algebras with discrete derived category}, J. Algebra {\bf 243} (2001), 168--176]. To this end, we investigate the quiver presentation of the complexified algebra of a real algebra given by a modulated quiver and an admissible ideal. - oai:arXiv.org:2010.03787v2 - math.RT - math.RA - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jie Li - - - Piecewise hereditary algebras under field extensions - https://arxiv.org/abs/2010.03789 - arXiv:2010.03789v2 Announce Type: replace -Abstract: Let $A$ be a finite-dimensional $k$-algebra and $K/k$ be a finite separable field extension. We prove that $A$ is derived equivalent to a hereditary algebra if and only if so is $A\otimes_kK$. - oai:arXiv.org:2010.03789v2 - math.RT - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jie Li - - - Up-down ordered Chinese restaurant processes with two-sided immigration, emigration and diffusion limits - https://arxiv.org/abs/2012.15758 - arXiv:2012.15758v2 Announce Type: replace -Abstract: We establish scaling limit theorems for the up-down ordered Chinese restaurant processes (oCRPs) of Rogers and Winkel as processes in a space of interval partitions. As previously conjectured, the limits are self-similar diffusions previously constructed directly in the continuum. We extend the oCRP model and the results to a three-parameter family ${\rm oCRP}^{(\alpha)}(\theta_1,\theta_2)$, $\alpha\in(0,1)$, $\theta_1,\theta_2\ge 0$. We use the scaling limit approach to extend existing stationarity results to the full three-parameter family, identifying an extended family of Poisson--Dirichlet interval partitions. Their ranked sequence of interval lengths has Poisson--Dirichlet distribution with parameters $\alpha\in(0,1)$ and $\theta:=\theta_1+\theta_2-\alpha\ge-\alpha$, including for the first time the usual range of $\theta>-\alpha$ rather than being restricted to $\theta\ge 0$. This has applications to Fleming--Viot processes, nested interval partition evolutions and tree-valued Markov processes, notably relying on the extended parameter range. - oai:arXiv.org:2012.15758v2 - math.PR - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Quan Shi, Matthias Winkel - - - A computable version of Hall's Harem Theorem and Geometric von Neumann Conjecture - https://arxiv.org/abs/2105.06304 - arXiv:2105.06304v4 Announce Type: replace -Abstract: We prove a computable version of the Hall Harem Theorem where the matching realizes a unary function with controlled sizes of cycles. We apply it to non-amenable computable coarse spaces. As a result, we obtain a computable version of the geometric von Neumann conjecture. - oai:arXiv.org:2105.06304v4 - math.LO - math.CO - math.GR - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Karol Duda - - - Scale-invariant Monte Carlo and multilevel Monte Carlo estimation of mean and variance: An application to simulation of linear elastic bone tissue - https://arxiv.org/abs/2106.13723 - arXiv:2106.13723v4 Announce Type: replace -Abstract: We propose novel scale-invariant error estimators for the Monte Carlo and multilevel Monte Carlo estimation of mean and variance. For any linear transformation of the distribution of the quantity of interest, the computation cost across fidelity levels is optimized using a normalized error estimate, which is not only fully dimensionless but also remains robust to variation in characteristics of the distribution. We demonstrate the effectiveness of the algorithms through application to a mechanical simulation of linear elastic bone tissue, where material uncertainty incorporating both heterogeneity and random anisotropy is considered in the constitutive law. - oai:arXiv.org:2106.13723v4 - math.NA - cs.CE - cs.NA - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Sharana Kumar Shivanand, Bojana Rosi\'c - - - Martingale solution, invariant measure and ergodicity for stochastic convective Brinkman-Forchheimer equations on general domains in $\mathbb{R}^d$ - https://arxiv.org/abs/2109.05510 - arXiv:2109.05510v2 Announce Type: replace -Abstract: The convective Brinkman-Forchheimer equations (CBFEs) \[ \frac{\partial \boldsymbol{X}}{\partial t} - \mu \Delta\boldsymbol{X} + (\boldsymbol{X}\cdot\nabla)\boldsymbol{X} + \alpha\boldsymbol{X} + \beta|\boldsymbol{X}|^{r-1}\boldsymbol{X} + \nabla p = \mathbf{F}, \qquad \nabla\cdot\boldsymbol{X}=0, \] with parameters $\mu,\alpha,\beta>0$ and $r\in[1,\infty)$ describe incompressible fluid motion in saturated porous media. In the stochastic setting, for $d=2,3$ and $r\in[3,\infty)$ (with $2\beta\mu\geq 1$ when $r=3$), strong pathwise solutions on general domains are already known, hence weak martingale solutions exist as well. In the same parameter regime, invariant probability measures on bounded domains have also been obtained. The present work complements and significantly extends these results. More precisely, on general domains in $\mathbb{R}^d$ (bounded or unbounded), for all $d\in\{2,3\}$, we prove the existence of a weak martingale solution to the stochastic CBFEs for every exponent $r\in[1,\infty)$, which includes the regimes where no strong solution theory is available. For $d=2$, $r\in[1,\infty)$, and for $d=3$, $r\in[3,\infty)$, we further show that the martingale solutions satisfy the energy equality (It\^o's formula) and possess $\mathbb{H}$-valued continuous trajectories almost surely. In this regularity regime (excluding $2\beta\mu < 1$ when $r=3$), we establish pathwise uniqueness and thereby, via the Yamada-Watanabe argument, obtain the existence of strong solutions and uniqueness in law, thereby recovering, in particular, the known results. Finally, for $d=2$, $r\in[1,\infty)$, and for $d=3$, $r\in[3,\infty)$ (with $2\beta\mu\geq 1$ when $r=3$), we prove the existence of an invariant probability measure for the associated Markov semigroup, while for $d=2,3$ with $r\in[3,\infty)$ (and with $2\beta\mu\geq 1$ for $r=3$), we show that at most one invariant measure can exist. - oai:arXiv.org:2109.05510v2 - math.PR - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Kush Kinra, Fernanda Cipriano, Manil T. Mohan - - - Sparse bounds for maximal triangle and bilinear spherical averaging operators - https://arxiv.org/abs/2110.08928 - arXiv:2110.08928v3 Announce Type: replace -Abstract: We show that the method in recent work of Roncal, Shrivastava, and Shuin can be adapted to show that certain $L^p$-improving bounds in the interior of the boundedness region for the bilinear spherical or triangle averaging operator imply sparse bounds for the corresponding lacunary maximal operator, and that $L^p$-improving bounds in the interior of the boundedness region for the corresponding single-scale maximal operators imply sparse bounds for the correpsonding full maximal operators. More generally we show that the framework applies for bilinear convolutions with compactly supported finite Borel measures that satisfy appropriate $L^p$-improving and continuity estimates. This shows that the method used by Roncal, Shrivastava, and Shuin can be adapted to obtain sparse bounds for a general class of bilinear operators that are not of product type, for a certain range of $L^p$ exponents. - oai:arXiv.org:2110.08928v3 - math.CA - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Eyvindur Ari Palsson, Sean R. Sovine - - - Local uniqueness of multi-peak positive solutions to a class of fractional Kirchhoff equations - https://arxiv.org/abs/2203.07468 - arXiv:2203.07468v2 Announce Type: replace -Abstract: This paper has two main purposes. In the first part, combining the nondegeneracy of the ground state with the Lyapunov--Schmidt reduction method, we prove the existence of multi-peak positive solutions to the singularly perturbed problem \[\Big(\varepsilon^{2s}a+\varepsilon^{4s-N} b\int_{\mathbb{R}^{N}}|(-\Delta)^{\frac{s}{2}}u|^2\,dx\Big)(-\Delta)^s u+V(x)u=u^p\quad \text{in }\mathbb{R}^{N},\] for all sufficiently small $\varepsilon> 0$, under the assumptions $2s<N<4s$, $1<p<2^*_s-1$, and some mild conditions on the potential $V$. The main difficulty comes from the interplay between the nonlocal operator $(-\Delta)^s$ and the nonlocal Kirchhoff term, which makes the corresponding limiting problem a coupled system of partial differential equations rather than a single fractional Kirchhoff equation. In the second part, under additional assumptions on $V$, we establish the local uniqueness of positive multi-peak solutions by means of a local Pohoz\v{a}ev identity. - oai:arXiv.org:2203.07468v2 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Zhipeng Yang - - - On the non-archimedean Monge-Amp\`ere equation in mixed characteristic - https://arxiv.org/abs/2203.12282 - arXiv:2203.12282v3 Announce Type: replace -Abstract: Let X be a smooth projective variety over a complete discretely valued field of mixed characteristic. We solve non-archimedean Monge-Amp\`ere equations on X assuming resolution and embedded resolution of singularities. We follow the variational approach of Boucksom, Favre, and Jonsson proving the continuity of the plurisubharmonic envelope of a continuous metric on an ample line bundle on X. We replace the use of multiplier ideals in equicharacteristic zero by the use of perturbation friendly test ideals introduced by Bhatt, Ma, Patakfalvi, Schwede, Tucker, Waldron, and Witaszek building upon previous constructions by Hacon, Lamarche, and Schwede. - oai:arXiv.org:2203.12282v3 - math.AG - math.NT - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - 10.1017/nmj.2025.8 - Nagoya Math. J. 259 (2025), 548-561 - Yanbo Fang, Walter Gubler, Klaus K\"unnemann - - - Generators and splitting fields of certain elliptic K3 surfaces - https://arxiv.org/abs/2206.05372 - arXiv:2206.05372v3 Announce Type: replace -Abstract: Let $k \subset {\mathbb C}$ be a number field and ${\mathcal E}$ be an elliptic curve defined over $k(t)$, the rational function field of the projective line ${\mathbb P}^1_k$, is isomorphic to the generic fiber of an elliptic surface $\pi:= \Sc_\Ee \rightarrow {\mathbb P}^1_k$. For any subfield ${\mathcal K}\subseteq {\mathbb C}$ of $k$, the set ${\mathcal E}({\mathcal K}(t))$ of ${\mathcal K}(t)$-rational points of ${\mathcal E}$ is known to be a finitely generated abelian group. The splitting field of ${\mathcal E}$ defined over $k(t)$ is the smallest finite extension ${\mathcal K} \subset {\mathbb C}$ of $k$ such that ${\mathcal E} ({\mathbb C} (t)) \iso {\mathcal E} ({\mathcal K}(t))$. In this paper, we consider the elliptic $K3$ surfaces defined over $k={\mathbb Q}$ with the generic fiber given by the Weierstrass equation ${\mathcal E}_n: \displaystyle y^2=x^3 + t^n + 1/t^n$, $1\leq n\leq 6$, and determine the splitting field ${\mathcal K}_n$, and find an explicit set of independent generators for ${\mathcal E}_n ({\mathcal K_n}(t))$ for $1\leq n \leq 6$. - oai:arXiv.org:2206.05372v3 - math.NT - math.AG - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Sajad Salami, Arman Shamsi Zargar - - - On the study of cellular automata on modulo-recurrent words - https://arxiv.org/abs/2211.14216 - arXiv:2211.14216v5 Announce Type: replace -Abstract: In this paper, we study a class of cellular automata (CA) called stable cellular automata (SCA) that preserve stability by reflection, modulo-recurrent, and richness. After applying these automata to Sturmian words, we determine some of their combinatorial properties. Next, we calculate the classical and palindromic complexity functions of these words. Finally, we demonstrate that these words are $2$-balanced and establish their abelian complexity function. - oai:arXiv.org:2211.14216v5 - math.CO - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Moussa Barro, K. Ernest Bognini, Boucar\'e Kient\'ega - - - Kummer surfaces and quadratic line complexes in characteristic two - https://arxiv.org/abs/2301.01450 - arXiv:2301.01450v3 Announce Type: replace -Abstract: In this paper, we study the classical theory of quadratic line complexes and Kummer surfaces. A quadratic line complex is the intersection of the Grassmannian $G(2,4)$ and a quadric hypersurface in ${\bf P}^5$, and a Kummer surface is the quotient of the Jacobian of a curve of genus 2 by the inversion. F. Klein discovered a relationship between a quadratic line complex and a curve of genus 2, its Jacobian and the associated Kummer surface. This theory holds in any characteristic not equal to two. However the situation in characteristic two is entirely different. The purpose of this paper is to give an analogue in characteristic 2 of this classical theory. - oai:arXiv.org:2301.01450v3 - math.AG - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by-sa/4.0/ - Toshiyuki Katsura, Shigeyuki Kondo - - - Disconnected Common Graphs via Supersaturation - https://arxiv.org/abs/2303.09296 - arXiv:2303.09296v3 Announce Type: replace -Abstract: A graph $H$ is said to be common if the number of monochromatic labelled copies of $H$ in a $2$-colouring of the edges of a large complete graph is asymptotically minimized by a random colouring. It is well known that the disjoint union of two common graphs may be uncommon; e.g., $K_2$ and $K_3$ are common, but their disjoint union is not. We investigate the commonality of disjoint unions of multiple copies of $K_3$ and $K_2$. As a consequence of our results, we obtain an example of a pair of uncommon graphs whose disjoint union is common. Our approach is to reduce the problem of showing that certain disconnected graphs are common to a constrained optimization problem in which the constraints are derived from supersaturation bounds related to Razborov's Triangle Density Theorem. We also improve bounds on the Ramsey multiplicity constant of a triangle with a pendant edge and the disjoint union of $K_3$ and $K_2$. - oai:arXiv.org:2303.09296v3 - math.CO - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Jae-baek Lee, Jonathan A. Noel - - - Complete non-ambiguous trees and associated permutations: new enumerative results - https://arxiv.org/abs/2303.15756 - arXiv:2303.15756v3 Announce Type: replace -Abstract: We study a link between complete non-ambiguous trees (CNATs) and permutations exhibited by Daniel Chen and Sebastian Ohlig in recent work. In this, they associate a certain permutation to the leaves of a CNAT, and show that the number of $n$-permutations that are associated with exactly one CNAT is $2^{n-2}$. We connect this to work by the first author and co-authors linking complete non-ambiguous trees and the acyclic orientation number of the associated permutation graph. This allows us to prove a number of conjectures by Chen and Ohlig on the number of $n$-permutations that are associated with exactly $k$ CNATs for various $k > 1$, via various bijective correspondences between such permutations. We also exhibit a new bijection between $(n-1)$-permutations and CNATs whose permutation is the decreasing permutation $n(n-1)\cdots1$. This bijection maps the left-to-right minima of the permutation to dots on the top row of the corresponding CNAT, and descents of the permutation to empty rows of the CNAT. - oai:arXiv.org:2303.15756v3 - math.CO - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Thomas Selig, Haoyue Zhu - - - Stochastic wave equation with additive fractional noise: solvability and global H\"older continuity - https://arxiv.org/abs/2305.02425 - arXiv:2305.02425v2 Announce Type: replace -Abstract: We determine the range of Hurst parameters that provide the necessary and sufficient conditions for the solvability, in $L^2(\Omega)$, of the stochastic wave equation: $ \frac{\partial^2 }{\partial t^2}u(t,x) =\Delta u(t,x)+\dot{W}(t,x)$, where $\{ W(t,x),\ t\geq 0, x\in \mathbb{R}^d\} $ is a fractional Brownian field with temporal Hurst parameter $H_0\in[\tfrac12,1]$ and spatial Hurst parameters $H_i\in(0,1)$ for $i=1,\cdots,d$. {In particular, the solvability condition exhibits a phase transition at $H_0 = 1$.} We also obtain the sharp growth rate and the sharp H\"older continuity of the solution on the real line in the case $H_0=1/2$. - oai:arXiv.org:2305.02425v2 - math.PR - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Shuhui Liu, Yaozhong Hu, Xiong Wang - - - Intermediate geodesic growth in virtually nilpotent groups - https://arxiv.org/abs/2306.10381 - arXiv:2306.10381v3 Announce Type: replace -Abstract: We give a criterion on pairs $(G,S)$ - where $G$ is a virtually $s$-step nilpotent group and $S$ is a finite generating set - saying whether the geodesic growth is exponential or strictly sub-exponential. Whenever $s=1,2$, this goes further and we prove the geodesic growth is either exponential or polynomial. For $s\ge 3$ however, intermediate growth is possible. We provide an example of virtually $3$-step nilpotent group for which $\gamma_{\mathrm{geod}}(n) \asymp \exp\!\big(n^{3/5}\cdot \log(n)\big)$. This is the first known example of group with intermediate geodesic growth. Along the way, we prove results on the geometry of virtually nilpotent groups, including asymptotics with error terms for their volume growth. - oai:arXiv.org:2306.10381v3 - math.GR - math.MG - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - 10.4171/ggd/857 - Groups, Geometry and Dynamics, 2025 - Corentin Bodart - - - On well-posedness of a mildly dissipative family of active scalar equations in borderline Sobolev spaces - https://arxiv.org/abs/2309.05844 - arXiv:2309.05844v2 Announce Type: replace -Abstract: This paper considers a family of active scalar equations which modify the generalized surface quasi-geostrophic (gSQG) equations through its constitutive law and a dissipative perturbation. These modifications are characteristically mild in the sense that they are logarithmic. The problem of well posedness, in the sense of Hadamard, is then studied in a borderline setting of regularity in analogy to the scaling-critical spaces of the gSQG equations. A novelty of the system considered is the nuanced form of smoothing provided by the proposed mild form of dissipation, which is able to support global well-posedness at the Euler endpoint, but in a setting where the inviscid counterpart is known to be ill-posed. A novelty of the analysis lies in the simultaneous treatment of modifications in the constitutive law, dissipative mechanism, and functional setting, which the existing literature has typically treated separately. A putatively sharp relation is identified between each of the distinct system-modifiers that is consistent with previous studies that considered these modifications in isolation. This unified perspective is afforded by the introduction of a linear model equation, referred to as the protean system, that successfully incorporates the more delicate commutator structure collectively possessed by the gSQG family and upon which each facet of well-posedness can effectively be reduced to its study. - oai:arXiv.org:2309.05844v2 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Anuj Kumar, Vincent R. Martinez - - - Higman-Thompson groups and profinite properties of right-angled Coxeter groups - https://arxiv.org/abs/2309.06213 - arXiv:2309.06213v2 Announce Type: replace -Abstract: We prove that every right-angled Coxeter group (RACG) is profinitely rigid amongst all Coxeter groups. On the other hand we exhibit RACGs which have infinite profinite genus amongst all finitely generated residually finite groups. We also establish profinite rigidity results for graph products of finite groups. Along the way we prove that the Higman-Thompson groups $V_{n}$ are generated by $4$ involutions, generalising a classical result of Higman for Thompson's group $V$. - oai:arXiv.org:2309.06213v2 - math.GR - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Samuel M. Corson, Sam Hughes, Philip M\"oller, Olga Varghese - - - A common approach to singular perturbation and homogenization I: Quasilinear ODE systems - https://arxiv.org/abs/2309.15611 - arXiv:2309.15611v4 Announce Type: replace -Abstract: We consider periodic homogenization of boundary value problems for quasilinear second-order ODE systems in divergence form of the type $a(x,x/\varepsilon,u(x),u'(x))'= f(x,x/\varepsilon,u(x),u'(x))$ for $x \in [0,1]$. For small $\varepsilon>0$ we show existence of weak solutions $u=u_\varepsilon$ as well as their local uniqueness for $\|u-u_0\|_\infty \approx 0$, where $u_0$ is a given non-degenerate solution to the homogenized boundary value problem, and we describe the rate of convergence to zero for $\varepsilon \to 0$ of the homogenization error $\|u_\varepsilon-u_0\|_\infty$. In particular, we show that this rate depends on the smoothness of the maps $a(\cdot,y,u,u')$ and $f(\cdot,y,u,u')$. - Our assumptions are, roughly speaking, as follows: The maps $a,f:[0,1]\times\mathbb{R}\times\mathbb{R}^n\times\mathbb{R}^n\to\mathbb{R}^n$ are continuous, the maps $a(x,y,\cdot,\cdot)$ and $f(x,y,\cdot,\cdot)$ are $C^1$-smooth, the maps $a(x,\cdot,u,u')$ and $f(x,\cdot,u,u')$ are 1-periodic, and the maps $a(x,y,u,\cdot)$ are strongly monotone and Lipschitz continuous uniformly with respect to $x$, $y$ and bounded $u$. No global solution uniqueness is supposed. Because $x$ is one-dimensional, no correctors and no cell problems are needed. But, because the problem is nonlinear, we have to care about commutability of homogenization and linearization. - The main tool of the proofs is an abstract result of implicit function theorem type which in the past has been applied to singularly perturbed nonlinear ODEs and elliptic and parabolic PDEs and, hence, which permits a common approach to existence and local uniqueness results for singularly perturbed problems and and for homogenization problems. - oai:arXiv.org:2309.15611v4 - math.CA - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Nikolai N. Nefedov, Lutz Recke - - - Linear and nonlinear instability of vortex columns - https://arxiv.org/abs/2310.20674 - arXiv:2310.20674v3 Announce Type: replace -Abstract: We consider vortex column solutions $v = V(r) e_\theta + W(r) e_z$ to the $3$D Euler equations. We give a mathematically rigorous construction of the countable family of unstable modes discovered by Liebovich and Stewartson (J. Fluid Mech. 126, 1983) via formal asymptotic analysis. The unstable modes exhibit $O(1)$ growth rates and concentrate on a ring $r= r_0$ asymptotically as the azimuthal and axial wavenumbers $n, \alpha \to \infty$ with a fixed ratio. We construct these so-called ring modes with an inner-outer gluing procedure. Finally, we prove that each linear instability implies nonlinear instability for vortex columns. In particular, our analysis yields nonlinear instability for the Batchelor trailing line vortex $V(r) :=\frac{q}{r} (1-\mathrm{e}^{-r^2})$ and $W(r) :=\mathrm{e}^{-r^2}$ when $0<q <\log 2 / \sqrt{1-\log 2} \approx 1.251$. - oai:arXiv.org:2310.20674v3 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Dallas Albritton, Wojciech O\.za\'nski - - - Generalized Fr\'{e}chet means with random minimizing domains and its strong consistency - https://arxiv.org/abs/2311.10958 - arXiv:2311.10958v2 Announce Type: replace -Abstract: This paper introduces a novel extension of Fr\'{e}chet means, called \textit{generalized Fr\'{e}chet means} as a comprehensive framework for characterizing features in probability distributions in general topological spaces. The generalized Fr\'{e}chet means are defined as minimizers of a suitably defined cost function. The framework encompasses various extensions of Fr\'{e}chet means in the literature. The most distinctive difference of the new framework from the previous works is that we allow the domain of minimization of the empirical means be random and different from that of the population means. This expands the applicability of the Fr\'{e}chet mean framework to diverse statistical scenarios, including dimension reduction for manifold-valued data. - oai:arXiv.org:2311.10958v2 - math.ST - stat.TH - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Jaesung Park, Sungkyu Jung - - - Uniqueness of critical points of the second Neumann eigenfunctions on triangles - https://arxiv.org/abs/2311.12659 - arXiv:2311.12659v2 Announce Type: replace -Abstract: This paper investigates the second Neumann eigenfunction $u$ of a planar triangle $T$. In a recent paper by Judge and Mondal [Ann. Math., 2022], it was shown that $u$ has no critical points in the interior of $T$. In this paper, we show that $u$ has at most one non-vertex critical point and that $u$ is monotone in a certain direction in $T$. More precisely, when $T$ is not equilateral, we show that $u$ vanishes at some vertex if and only if $T$ is superequilateral, and that $u$ has a non-vertex critical point if and only if $T$ is acute and not superequilateral. These results confirm both the original theorem and Conjecture 13.6 of Judge and Mondal [Ann. Math., 2020]. We also resolve the objective of Polymath 7 (research thread 1), namely, that the extrema of $u$ are attained only at the endpoints of the longest side. In addition, we settle a conjecture of Siudeja [Proc. Amer. Math. Soc., 2016] on the ordering of mixed Dirichlet--Neumann Laplacian eigenvalues for triangles. Our proofs combine the continuity method, eigenvalue inequalities, the maximum principle, and the moving plane method. - oai:arXiv.org:2311.12659v2 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Hongbin Chen, Changfeng Gui, Ruofei Yao - - - RIS-Assisted Generalized Receive Quadrature Spatial Modulation with Extension to Multicast Communications - https://arxiv.org/abs/2311.18542 - arXiv:2311.18542v2 Announce Type: replace -Abstract: This paper proposes a novel reconfigurable intelligent surface (RIS)-assisted generalized receive quadrature spatial modulation (RIS-GRQSM) scheme to enhance the spectral efficiency (SE) of RIS-aided \textit{quadrature} spatial modulation (QSM) systems. By leveraging the principle of \textit{generalized} spatial modulation (GSM), multiple receive antennas are independently activated for \textit{both} the in-phase and quadrature components of spatial symbols. To fully exploit the potential of RIS, we formulate a max-min optimization problem to adjust the phase shifts of all RIS elements, thereby maximizing the effective signal-to-noise ratios (SNRs) at the activated antennas. Using Lagrange duality, the original high-dimensional non-convex problem is reduced to a tractable problem with a smaller number of real variables, and a closed-form suboptimal solution is also proposed, which achieves near-optimal performance with a sufficiently large RIS. At the receiver, a low-complexity non-coherent energy-based greedy detector (GD) is introduced for efficient symbol detection. We further extend the RIS-GRQSM framework to a multicast communication system, where all users receive identical information with equal SNR levels, and provide a detailed performance analysis of both systems. In particular, we derive the average bit error probability (ABEP) for the proposed RIS-GRQSM and multicast systems under optimal and suboptimal optimization strategies. Numerical results show that RIS-GRQSM significantly improves the SE and error rate performance compared with benchmark schemes, while the multicast extension achieves performance close to benchmark methods at substantially lower complexity. - oai:arXiv.org:2311.18542v2 - cs.IT - eess.SP - math.IT - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Mohamad H. Dinan, Khatereh Nadali, Mark F. Flanagan - - - Roots of polynomials under repeated differentiation and repeated applications of fractional differential operators - https://arxiv.org/abs/2312.14883 - arXiv:2312.14883v3 Announce Type: replace -Abstract: We start with a random polynomial $P^{N}(z)$ of degree $N$ with independent coefficients. We then consider a new polynomial $P_{t}^{N}$ obtained by $\lceil Nt\rceil$ applications of a fractional differential operator of the form $z^{a} (d/dz)^{b},$ where $a$ and $b$ are real numbers. When $b>0,$ we compute the limiting root distribution $\mu_{t}$ of $P_{t}^{N}$ as $N\rightarrow\infty.$ We show that $\mu_{t}$ is the push-forward of the limiting root distribution of $P^{N}$ under a transport map $T_{t}$. The map $T_{t}$ is defined by flowing along the characteristic curves of a PDE satisfied by the log potential of $\mu_{t}.$ - In the special case of repeated differentiation, our results may be interpreted as saying that the roots evolve radially \textit{with constant speed} until they hit the origin, at which point, they cease to exist. For general $a$ and $b,$ the transport map $T_{t}$ has a free probability interpretation as multiplication of an $R$-diagonal operator by an $R$-diagonal \textquotedblleft transport operator.\textquotedblright As an application, we obtain a push-forward characterization of the free self-convolution semigroup $\oplus$ of radial measures on $\mathbb{C}$. - We also consider the case $b<0,$ which includes the case of repeated integration. More complicated behavior of the roots can occur in this case. - oai:arXiv.org:2312.14883v3 - math.PR - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Brian C. Hall, Ching-Wei Ho, Jonas Jalowy, Zakhar Kabluchko - - - Geometric universal Jones invariant from configurations on ovals in the disc - https://arxiv.org/abs/2401.17245 - arXiv:2401.17245v3 Announce Type: replace -Abstract: We construct geometrically a universal Jones invariant as a limit of invariants given by graded intersections in configuration spaces. For any fixed level $\mathscr N$, we define a new knot invariant, called ``$\mathscr N^{th}$ Unified Jones invariant'' globalising topologically all coloured Jones polynomials at levels less than $\mathscr N$. It is defined via the intersection points between {Lagrangian submanifolds} supported on arcs and ovals in the disc. The geometry of these Lagrangians is novel: previous topological models involved immersed submanifolds rather than embedded ones. We do this by defining a new local system that refines the Lawrence representation, and depends of the distribution of multiplicities of points in the configuration space on the ovals. - On the algebraic side, Habiro's famous invariant for knots \cite{H3} is a universal invariant globalising the family of coloured Jones polynomials. He conjectured that this universal invariant recovers also the ADO invariant divided by the Alexander polynomials, which was proved by Willetts \cite{W} in a version of Habiro's ring (\cite{H2}). The universal Jones invariant that we construct belongs to a different ring that comes with a map to Habiro's ring \cite{H2}. - We prove that our invariant recovers this version of Habiro's invariant. The difference is that our invariant is given as a limit of new knot invariants, the $\mathscr N^{th}$ unified Jones invariants. These invariants in turn provide a geometrical understanding of sets of all coloured Jones polynomials of bounded colour, collecting more information as we increase the colour. - oai:arXiv.org:2401.17245v3 - math.GT - math.AT - math.RT - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Cristina Ana-Maria Anghel - - - Colorings of $k$-sets with low discrepancy on small sets - https://arxiv.org/abs/2402.05286 - arXiv:2402.05286v3 Announce Type: replace -Abstract: For $0<\delta\leq 1$, let $R_k(m;\delta)$ denote the smallest $N$ such that every coloring of $k$-element subsets by two colors yields an $m$-element set $M$ with relative discrepancy $\delta$, which means that one color class has at least $(\frac{1+\delta}2){m\choose k}$ elements. The number $R_k(m;\delta)$ may be viewed as an extension of the usual $k$-hypergraph Ramsey number because $R_k(m)=R_k(m,1)$. Our main result is the following theorem. - %\begin{theorem} For some constants $c,k_0$, and $\eps>0$, and for all $k\geq k_0$, $c\log k\leq n\leq k/11$, \[ R_k(k+n);2^{-\eps n})\geq \tw_{\lfloor k/n\rfloor}(2). \] %\end{theorem} - In particular, for $n=\lceil c\log k\rceil$, we get a tower of height $\delta k/\log k$ and relative discrepancy polynomial in~$k$. - oai:arXiv.org:2402.05286v3 - math.CO - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Pavel Pudl\'ak, Vojt\v{e}ch R\"odl - - - Smooth Structures on $M\times\mathbb{S}^k$ - https://arxiv.org/abs/2402.18914 - arXiv:2402.18914v2 Announce Type: replace -Abstract: This paper explores various differentiable structures on the product manifold $M \times \mathbb{S}^k$, where $M$ is either a 4-dimensional closed, oriented, smooth manifold or a simply connected 5-dimensional closed, smooth manifold. We identify the possible stable homotopy types of $M$ and use it to calculate the concordance inertia group and the concordance structure set of $M\times\mathbb{S}^k$ for $1\leq k\leq 10$. These calculations enable us to further classify all manifolds that are homeomorphic to $\mathbb{C}P^2\times\mathbb{S}^k$, up to diffeomorphism, for each $4\leq k\leq 6$. - oai:arXiv.org:2402.18914v2 - math.AT - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Samik Basu, Ramesh Kasilingam, Ankur Sarkar - - - Applications of $\mathrm{C}^*$-classification - https://arxiv.org/abs/2403.07993 - arXiv:2403.07993v2 Announce Type: replace -Abstract: We provide some background on the category of classifiable $\mathrm{C}^*$-algebras, whose objects are infinite-dimensional, simple, separable, unital $\mathrm{C}^*$-algebras that have finite nuclear dimension and satisfy the universal coefficient theorem, and describe some applications of the classification of objects in, and morphisms into, this category. - oai:arXiv.org:2403.07993v2 - math.OA - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - 10.4064/bc130-2 - Banach Center Publications 130 (2026), 29-57 - Bhishan Jacelon - - - Central motives on parahoric flag varieties - https://arxiv.org/abs/2403.11007 - arXiv:2403.11007v2 Announce Type: replace -Abstract: We construct a refinement of Gaitsgory's central functor for integral motivic sheaves, and show it preserves stratified Tate motives. Towards this end, we develop a reformulation of unipotent motivic nearby cycles, which also works over higher-dimensional bases. We moreover introduce Wakimoto motives and use them to show that our motivic central functor is t-exact. A decategorification of these functors yields a new approach to generic Hecke algebras for general parahorics. - oai:arXiv.org:2403.11007v2 - math.AG - math.NT - math.RT - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Robert Cass, Thibaud van den Hove, Jakob Scholbach - - - Robust pointwise second order necessary conditions for singular stochastic optimal control with model uncertainty - https://arxiv.org/abs/2403.15703 - arXiv:2403.15703v3 Announce Type: replace -Abstract: We study the singular stochastic optimal control problem with model uncertainty, where the necessary conditions determined by the corresponding maximum principle are trivial. Robust integral form and pointwise second order necessary optimality conditions under certain compactness conditions are derived. Both the drift and diffusion terms are control dependent but the control region are assumed to be convex. The convex variational method is employed, because linear structure is essential in deriving the weak limit of uncertainty measures. Other main technical ingredients in obtaining the integral type conditions are compact analysis and minimax theorem, while for the pointwise ones it is Clark-Ocone formula and Lebesgue differentiation type theorem. Besides, a compendious example is given to illustrate the motivation and effectiveness of the results. - oai:arXiv.org:2403.15703v3 - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - 10.1007/s00245-025-10297-9 - Volume 92, article number 66, (2025)https://link.springer.com/article/10.1007/s00245-025-10297-9 - Guangdong Jing - - - Properties for transposition solutions to operator-valued BSEEs, and applications to robust second order necessary conditions for controlled SEEs - https://arxiv.org/abs/2403.15710 - arXiv:2403.15710v2 Announce Type: replace -Abstract: This article is concerned with the second order necessary conditions for the stochastic optimal control problem of stochastic evolution equation with model uncertainty when the traditional Pontryagin-type maximum principle holds trivially and do not provide any information depicting the optimal control. The diffusion term of the state equation is allowed to be control dependent with convex control constraints. Transposition method is adopted to deal with the adjoint operator-valued backward stochastic evolution equations, especially the correction terms. Besides, weak convergence arguments are performed to obtain the optimal uncertainty measure, among which the regularities of the state processes, variational processes, and adjoint processes (in the transposition sense) are carefully characterized. Malliavin calculus is applied to pave the way for Lebesgue differentiation theorem to deduce the pointwise robust optimality conditions. - oai:arXiv.org:2403.15710v2 - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - 10.1016/j.jmaa.2025.129445 - Journal of Mathematical Analysis and Applications. Volume 549, Issue 1, 1 September 2025, 129445 - Guangdong Jing - - - Theoretical Guarantees for the Subspace-Constrained Tyler's Estimator - https://arxiv.org/abs/2403.18658 - arXiv:2403.18658v3 Announce Type: replace -Abstract: This work analyzes the subspace-constrained Tyler's estimator (STE), a method designed to recover a low-dimensional subspace from a dataset that may be heavily corrupted by outliers. The STE has previously been shown to be competitive for fundamental computer vision problems. We assume a weak inlier-outlier model and allow the inlier fraction to fall below the threshold at which robust subspace recovery becomes computationally hard. We show that, in this setting, if the initialization of STE satisfies a certain condition, then STE-which is computationally efficient-can effectively recover the underlying subspace. Furthermore, we establish approximate recovery guarantees for STE in the presence of noisy inliers. Finally, under the asymptotic generalized haystack model, we demonstrate that STE initialized with Tyler's M-estimator (TME) recovers the subspace even when the inlier fraction is too small for TME to succeed on its own. - oai:arXiv.org:2403.18658v3 - math.ST - stat.ML - stat.TH - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Gilad Lerman, Teng Zhang - - - Hypertree shrinking avoiding low degree vertices - https://arxiv.org/abs/2405.02049 - arXiv:2405.02049v2 Announce Type: replace -Abstract: The shrinking operation converts a hypergraph into a graph by choosing, from each hyperedge, two endvertices of a corresponding graph edge. A hypertree is a hypergraph which can be shrunk to a tree on the same vertex set. Klimo\v{s}ov\'{a} and Thomass\'{e} [J. Combin. Theory Ser. B 156 (2022), 250--293] proved (as a tool to obtain their main result on edge-decompositions of graphs into paths of equal length) that any rank $3$ hypertree $T$ can be shrunk to a tree where the degree of each vertex is at least $1/100$ times its degree in $T$. We prove a stronger and a more general bound, replacing the constant $1/100$ with $1/2k$ when the rank is $k$. In place of entropy compression (used by Klimo\v{s}ov\'{a} and Thomass\'{e}), we use a hypergraph orientation lemma combined with a characterisation of edge-coloured graphs admitting rainbow spanning trees. - oai:arXiv.org:2405.02049v2 - math.CO - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Karol\'ina Hylasov\'a, Tom\'a\v{s} Kaiser - - - A topological model for the HOMFLY-PT polynomial - https://arxiv.org/abs/2405.03679 - arXiv:2405.03679v2 Announce Type: replace -Abstract: We give the first known topological model for the HOMFLY-PT polynomial constructed directly from link diagrams. More precisely, we prove that this invariant is given by graded intersections between explicit Lagrangian submanifolds in a fixed configuration space on a Heegaard surface for the link exterior. The submanifolds are supported on a collection of arcs and ovals on the Heegaard surface. We also obtain two topological models for the Jones polynomial via a Heegaard surface associated to a link diagram. This opens up new avenues for constructing categorifications for the Jones and the HOMFLY-PT polynomials of a geometric nature. - oai:arXiv.org:2405.03679v2 - math.GT - math.AT - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Cristina Ana-Maria Anghel, Christine Ruey Shan Lee - - - Similarity of Matrices over Dedekind Rings - https://arxiv.org/abs/2405.08501 - arXiv:2405.08501v4 Announce Type: replace -Abstract: We extend Latimer and MacDuffee's theorem to a general commutative domain and apply this result to study similarity of matrices over integral rings of number fields. We also conjecture similarity over discrete valuation rings can be descent by a finite covering and verify this conjecture for $2\times2$ matrices and separable characteristic polynomials. - oai:arXiv.org:2405.08501v4 - math.NT - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Ziyang Zhu - - - Special potentials for relativistic Laplacians I: Fractional Rollnik-class - https://arxiv.org/abs/2405.08805 - arXiv:2405.08805v2 Announce Type: replace -Abstract: We propose a counterpart of the classical Rollnik-class of potentials for fractional and massive relativistic Laplacians, and describe this space in terms of appropriate Riesz potentials. These definitions rely on precise resolvent estimates. We show that Coulomb-type potentials are elements of fractional Rollnik-class up to but not including the critical singularity of the Hardy potential. For the operators with fractional exponent $\alpha = 1$ there exists no fractional Rollnik potential, however, in low dimensions we make sense of these classes as limiting cases by using $\Gamma$-convergence. In a second part of the paper we derive detailed results on the self-adjointness and spectral properties of relativistic Schr\"odinger operators obtained under perturbations by fractional Rollnik potentials. We also define an extended fractional Rollnik-class which is the maximal space for the Hilbert-Schmidt property of the related Birman-Schwinger operators. - oai:arXiv.org:2405.08805v2 - math.FA + 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 - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - 10.1016/j.jfa.2025.111282 - Journal of Functional Analysis, 290.6, March 2026, 111282 - Giacomo Ascione, Atsuhide Ishida, J\'ozsef L\H{o}rinczi - - - A Unified Framework for Sponge-Layer Relaxation Methods and Damping Operators for Conservation Laws: Application to the Piston Problem of Gas Dynamics - https://arxiv.org/abs/2405.11588 - arXiv:2405.11588v2 Announce Type: replace -Abstract: This work addresses the imposition of outflow boundary conditions for one-dimensional conservation laws. While a highly accurate numerical solution can be obtained in the interior of the domain, boundary discretization can lead to unphysical reflections. We investigate and implement some classes of relaxation methods and far-field operators to deal with this problem without significantly increasing the size of the computational domain. We formulate these methods within a framework that allows to reveal relationships among them, and to propose novel extensions. In particular, we introduce a simple and robust relaxation method with a matrix-valued weight function that selectively absorbs outgoing waves. As a challenging model problem, we consider the Lagrangian formulation of the Euler equations for a polytropic gas with inflow boundary conditions determined by an oscillating piston. - oai:arXiv.org:2405.11588v2 - math.NA - cs.NA - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Carlos Mu\~noz-Moncayo - - - Small Prime $k$th Power Residues and Nonresidues in Arithmetic Progressions - https://arxiv.org/abs/2405.13159 - arXiv:2405.13159v2 Announce Type: replace -Abstract: Let $p$ be a large odd prime, let $x=\log p)(\log\log p)^{3+\varepsilon}$ and let $q\ll\log\log p$ be an integer, where $\varepsilon>0$ is a small number. This note proves the existence of small prime quadratic residues and small prime quadratic nonresidues in the arithmetic progression $a+qm\ll x$, with relatively prime $1\leq a<q$, unconditionally. The same results are generalized to small prime $k$th power residues and nonresidues, where $k\mid p-1$ and $k\ll\log\log p$. - oai:arXiv.org:2405.13159v2 - math.GM - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - N. A. Carella - - - Moduli of elliptic surfaces of Kodaira dimension one fibered over rational curves - https://arxiv.org/abs/2407.05539 - arXiv:2407.05539v2 Announce Type: replace -Abstract: In this article, we construct an infinite sequence of irreducible components of Koll\'{a}r--Shepherd-Barron (KSB-) moduli spaces of surfaces of arbitrarily large volumes, and describe the boundary of each component completely. Moreover, we describe the stable reduction steps in finding the KSB-limits in an explicit combinatorial way. Our main approach is to study the moduli spaces of elliptic surfaces with Kodaira dimension one, fibered over rational curves, using the techniques of wall-crossing for KSBA moduli and twisted stable maps. - oai:arXiv.org:2407.05539v2 - math.AG - Tue, 09 Dec 2025 00:00:00 -0500 - replace + Wed, 10 Dec 2025 00:00:00 -0500 + cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Dori Bejleri, Josiah Foster, Andres Fernandez Herrero, Giovanni Inchiostro, Svetlana Makarova, Junyan Zhao + Zachary P. Bradshaw, Margarite L. LaBorde, Dillon Montero - Anchored symplectic embeddings - https://arxiv.org/abs/2407.08512 - arXiv:2407.08512v2 Announce Type: replace -Abstract: Given two four-dimensional symplectic manifolds, together with knots in their boundaries, we define an ``anchored symplectic embedding'' to be a symplectic embedding, together with a two-dimensional symplectic cobordism between the knots (in the four-dimensional cobordism determined by the embedding). We use techniques from embedded contact homology to determine quantitative critera for when anchored symplectic embeddings exist, for many examples of toric domains. In particular we find examples where ordinarily symplectic embeddings exist, but they cannot be upgraded to anchored symplectic embeddings unless one enlarges the target domain. - oai:arXiv.org:2407.08512v2 - math.SG - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Michael Hutchings, Agniva Roy, Morgan Weiler, Yuan Yao + 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 + cross + http://creativecommons.org/licenses/by/4.0/ + Shi Jin, Nana Liu - Filtering the linearization of the category of surjections - https://arxiv.org/abs/2407.11627 - arXiv:2407.11627v5 Announce Type: replace -Abstract: A filtration of the morphisms of the $k$-linearization $k \mathbf{FS}$ of the category $\mathbf{FS}$ of finite sets and surjections is constructed using a natural $k \mathbf{FI}^{op}$-module structure induced by restriction, where $\mathbf{FI}$ is the category of finite sets and injections. In particular, this yields the `primitive' subcategory $ k \mathbf{FS}^0 \subset k \mathbf{FS}$ that is of independent interest; for example, the category of $k \mathbf{FS}^0$-modules is closely related to the category of $k \mathbf{FA}$-modules, where $\mathbf{FA}$ is the category of finite sets and all maps. - Working over a field of characteristic zero, the subquotients of this filtration are identified as bimodules over $k \mathbf{FB}$, where $\mathbf{FB}$ is the category of finite sets and bijections, also exhibiting and exploiting additional structure. In particular, this describes the underlying $k \mathbf{FB}$-bimodule of $k \mathbf{FS}^0$. - oai:arXiv.org:2407.11627v5 - math.RT - Tue, 09 Dec 2025 00:00:00 -0500 - replace + 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/ - 10.46298/cm.16066 - Communications in Mathematics, Volume 34 (2026), Issue 1 - Geoffrey Powell + Tatiana Yavorskaya (Steklov Mathematical Institute of Russian Academy of Science), Elena Popova (Steklov Mathematical Institute of Russian Academy of Science) - Dynamics on invariant tori emerging through forced symmetry breaking in phase oscillator networks - https://arxiv.org/abs/2408.02119 - arXiv:2408.02119v2 Announce Type: replace -Abstract: We consider synchrony patterns in coupled phase oscillator networks that correspond to invariant tori. For specific nongeneric coupling, these tori are equilibria relative to a continuous symmetry action. We analyze how the invariant tori deform under forced symmetry breaking as more general network interaction terms are introduced. We first show in general that perturbed tori that are relative equilibria can be computed using a parametrization method; this yields an asymptotic expansion of an embedding of the perturbed torus, as well as the local dynamics on the torus. We then apply this result to a coupled oscillator network, and we numerically study the dynamics on the persisting tori in the network by looking for bifurcations of their periodic orbits in a boundary-value-problem setup. This way we find new bifurcating stable synchrony patterns that can be the building blocks of larger global structures such as heteroclinic cycles. - oai:arXiv.org:2408.02119v2 + 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 - nlin.AO - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Christian Bick, Jos\'e Mujica, Bob Rink + 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 - Admissible operators for sun-dual semigroups - https://arxiv.org/abs/2408.02150 - arXiv:2408.02150v3 Announce Type: replace -Abstract: We extend classical duality results by Weiss on admissible operators to settings where the dual semigroup lacks strong continuity. This is possible using the sun-dual framework, which is not immediate from the duality of the input and output maps. This extension enables the testing of admissibility for a broader range of examples, in particular for state space of continuous functions or $L^1$. - oai:arXiv.org:2408.02150v3 - math.FA - Tue, 09 Dec 2025 00:00:00 -0500 - replace + 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 + cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - 10.1007/s00498-025-00430-y - Mathematics of Control, Signals, and Systems (2025) - Sahiba Arora, Felix L. Schwenninger + Robert Lefringhausen, Theodor Springer, Sandra Hirche - Splitting methods based on the nonzero diagonal pattern for computing matrix functions - https://arxiv.org/abs/2408.04128 - arXiv:2408.04128v2 Announce Type: replace -Abstract: We consider the task of approximating a matrix function $f(A)$, where $A$ is a matrix in which only a relatively small number of (not necessarily consecutive) sub- and superdiagonals contain nonzero entries. Approximating $f$ by a low-degree polynomial $p$ allows us to obtain sparse approximations to $f(A)$, which one can efficiently work with (while, in general, $f(A)$ is a dense matrix, even when $A$ is sparse). Our approach is based on carefully inspecting the locations where nonzeros can occur in $p(A)$, and identifying the entries in $A$ that influence them. In particular, we illustrate how this approach can be used for efficiently approximating the trace of $f(A)$ and identify how this approach is related to established (stochastic) probing methods for trace estimation. Another application area in which our approach works particularly well is the computation of functions of Toeplitz matrices. Here, studying the sparsity pattern of $p(A)$ allows us to reduce the computation of the whole matrix polynomial to that of a single small-scale submatrix, yielding an algorithm that scales exceptionally well to large problem sizes. - oai:arXiv.org:2408.04128v2 - math.NA - cs.NA - Tue, 09 Dec 2025 00:00:00 -0500 - replace + 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 + math-ph + math.MP + physics.class-ph + Wed, 10 Dec 2025 00:00:00 -0500 + cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Majed Hamadi, Nezam Mahdavi-Amiri, Marcel Schweitzer + \'Angel E. Reyna-Cruz, Julio C. Guti\'errez-Vega - Fredholm Neural Networks - https://arxiv.org/abs/2408.09484 - arXiv:2408.09484v5 Announce Type: replace -Abstract: Within the family of explainable machine-learning, we present Fredholm neural networks (Fredholm NNs): deep neural networks (DNNs) architectures motivated by fixed-point iteration schemes for the solution of linear and nonlinear Fredholm integral equations (FIEs) of the second kind. We also show how the proposed framework can be used for the solution of inverse problems. Applications of FIEs include the solution of ordinary, as well as partial differential equations (ODEs, PDEs) and many more. We first prove that Fredholm NNs provide accurate solutions. We then provide insight into the values of the hyperparameters and trainable/explainable weights and biases of the DNN, by directly connecting their values to the underlying mathematical theory. For our illustrations, we use Fredholm NNs to solve both linear and nonlinear problems, including elliptic PDEs and boundary value problems. We show that the proposed scheme achieves significant numerical approximation accuracy across both the domain and boundary. The proposed methodology provides insight into the connection between neural networks and classical numerical methods, and we posit that it can have applications in fields such as Uncertainty Quantification (UQ) and explainable artificial intelligence (XAI). Thus, we believe that it will trigger further advances in the intersection between scientific machine learning and numerical analysis. - oai:arXiv.org:2408.09484v5 - math.NA + 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.DS - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - 10.1137/24M1686991 - SIAM Journal on Scientific Computing, Vol. 47, Iss. 4, 2025 - Kyriakos Georgiou, Constantinos Siettos, Athanasios N. Yannacopoulos - - - On the loss of orthogonality in low-synchronization variants of reorthogonalized block classical Gram-Schmidt - https://arxiv.org/abs/2408.10109 - arXiv:2408.10109v3 Announce Type: replace -Abstract: Interest in communication-avoiding orthogonalization schemes for high-performance computing has been growing recently. This manuscript addresses open questions about the numerical stability of various block classical Gram-Schmidt variants that have been proposed in the past few years. An abstract framework is employed, the flexibility of which allows for new rigorous bounds on the loss of orthogonality in these variants. We first analyze a generalization of (reorthogonalized) block classical Gram-Schmidt and show that a "strong" intrablock orthogonalization routine is only needed for the very first block in order to maintain orthogonality on the level of the unit roundoff. In particular, this ``strong" first step does not have to be a reorthogonalized QR itself and subsequent steps can use less stable QR variants, thus keeping the overall communication costs low. - Then, using this variant, which has four synchronization points per block column, we remove the synchronization points one at a time and analyze how each alteration affects the stability of the resulting method. Our analysis shows that the variant requiring only one synchronization per block column cannot be guaranteed to be stable in practice, as stability begins to degrade with the first reduction of synchronization points. - Our analysis of block methods also provides new theoretical results for the single-column case. In particular, it is proven that DCGS2 from [Bielich, D. et al. Par. Comput. 112 (2022)] and CGS-2 from [\'{S}wirydowicz, K. et al, Num. Lin. Alg. Appl. 28 (2021)] are as stable as Householder QR. Numerical examples from the BlockStab toolbox are included throughout, to help compare variants and illustrate the effects of different choices of intraorthogonalization subroutines. - oai:arXiv.org:2408.10109v3 math.NA - cs.NA - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Erin Carson, Kathryn Lund, Yuxin Ma, Eda Oktay - - - Lifting Brauer indecomposability of a Scott module - https://arxiv.org/abs/2409.00403 - arXiv:2409.00403v3 Announce Type: replace -Abstract: It is proven that if a finite group $G$ has a normal subgroup $H$ with $p'$-index (where $p$ is a prime) and $G/H$ is solvable, then for a $p$-subgroup $P$ of $H$, if the Scott $kH$-module with vertex $P$ is Brauer indecomposable, then so is the Scott $kG$-module with vertex $P$, where $k$ is a field of characteristic $p>0$. This has several applications. - oai:arXiv.org:2409.00403v3 - math.RT - math.GR - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Shigeo Koshitani, \.Ipek Tuvay - - - Hyper-bishops, Hyper-rooks, and Hyper-queens: Percentage of Safe Squares on Higher Dimensional Chess Boards - https://arxiv.org/abs/2409.04423 - arXiv:2409.04423v4 Announce Type: replace -Abstract: The $n$ queens problem considers the maximum number of safe squares on an $n \times n$ chess board when placing $n$ queens; the answer is only known for small $n$. Miller, Sheng and Turek considered instead $n$ randomly placed rooks, proving the proportion of safe squares converges to $1/e^2$. We generalize and solve when randomly placing $n$ hyper-rooks and $n^{k-1}$ line-rooks on a $k$-dimensional board, using combinatorial and probabilistic methods, with the proportion of safe squares converging to $1/e^k$. We prove that the proportion of safe squares on an $n \times n$ board with bishops in 2 dimensions converges to $2/e^2$. This problem is significantly more interesting and difficult; while a rook attacks the same number of squares wherever it's placed, this is not so for bishops. We expand to the $k$-dimensional chessboard, defining line-bishops to attack along $2$-dimensional diagonals and hyper-bishops to attack in the $k-1$ dimensional subspace defined by its diagonals in the $k-2$ dimensional subspace. We then combine the movement of rooks and bishops to consider the movement of queens in 2 dimensions, as well as line-queens and hyper-queens in $k$ dimensions. - oai:arXiv.org:2409.04423v4 - math.CO math.PR - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Caroline Cashman, Joseph Cooper, Raul Marquez, Steven J. Miller, Jenna Shuffelton - - - Failure of Esakia's theorem in the monadic setting - https://arxiv.org/abs/2409.05607 - arXiv:2409.05607v2 Announce Type: replace -Abstract: Esakia's theorem states that Grzegorczyk's logic is the greatest modal companion of intuitionistic propositional calculus. We prove that already the one-variable fragment of intuitionistic predicate calculus does not have a greatest modal companion, yielding that Esakia's theorem fails in the monadic setting. - oai:arXiv.org:2409.05607v2 - math.LO - Tue, 09 Dec 2025 00:00:00 -0500 - replace + math.ST + stat.TH + Wed, 10 Dec 2025 00:00:00 -0500 + cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Guram Bezhanishvili, Luca Carai + Jinyuan Chang, Chenguang Duan, Yuling Jiao, Ruoxuan Li, Jerry Zhijian Yang, Cheng Yuan - The abundance and SYZ conjectures in families of hyperkahler manifolds - https://arxiv.org/abs/2409.09142 - arXiv:2409.09142v3 Announce Type: replace -Abstract: Let $L$ be a holomorphic line bundle on a hyperkahler manifold $M$, with $c_1(L)$ nef and not big. SYZ conjecture predicts that $L$ is semiample. We prove that this is true, assuming that $(M,L)$ has a deformation $(M',L')$ with $L'$ semiample. We introduce a version of the Teichmuller space that parametrizes pairs $(M,L)$ up to isotopy. We prove a version of the global Torelli theorem for such Teichmuller spaces and use it to deduce the deformation invariance of semiampleness. - oai:arXiv.org:2409.09142v3 - math.AG - math.DG - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by-sa/4.0/ - \'Epijournal de G\'eom\'etrie Alg\'ebrique, Volume 9 (2025), Article no. 26 - Andrey Soldatenkov, Misha Verbitsky + 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 + gr-qc + hep-th + math-ph + math.MP + Wed, 10 Dec 2025 00:00:00 -0500 + cross + http://creativecommons.org/licenses/by/4.0/ + A. Agung, U. Sambiri, G. Hikmawan, F. P. Zen - A degenerate version of Brion's formula - https://arxiv.org/abs/2409.09544 - arXiv:2409.09544v3 Announce Type: replace -Abstract: Let $\mathfrak{p} \subset V$ be a polytope and $\xi \in V_{\mathbb{C}}^*$. We obtain an expression for $I(\mathfrak{p}; \alpha) := \int_{\mathfrak{p}} e^{\langle \alpha, x \rangle} dx$ as a sum of meromorphic functions in $\alpha \in V^*_{\mathbb{C}}$ parametrized by the faces $\mathfrak{f}$ of $\mathfrak{p}$ on which $\langle \xi, x \rangle$ is constant. Each term only depends on the local geometry of $\mathfrak{p}$ near $\mathfrak{f}$ (and on $\xi$) and is holomorphic at $\alpha = \xi$. When $\langle \xi, \cdot \rangle$ is only constant on the vertices of $\mathfrak{p}$ our formula reduces to Brion's formula. - Suppose $\mathfrak{p}$ is a rational polytope with respect to a lattice $\Lambda$. We obtain an expression for $S(\mathfrak{p}; \alpha) := \sum_{\lambda \in \mathfrak{p} \cap \Lambda} e^{\langle \alpha, \lambda \rangle}$ as a sum of meromorphic functions parametrized by the faces $\mathfrak{f}$ on which $e^{\langle \xi, x \rangle} = 1$ on a finite index sublattice of $\text{lin}(\mathfrak{f}) \cap \Lambda$. Each term only depends on the local geometry of $\mathfrak{p}$ near $\mathfrak{f}$ (and on $\xi$ and $\Lambda$) and is holomorphic at $\alpha = \xi$. When $e^{\langle \xi, \cdot \rangle} \neq 1$ at any non-zero lattice point on a line through the origin parallel to an edge of $\mathfrak{p}$, our formula reduces to Brion's formula, and when $\xi = 0$, it reduces to the Ehrhart quasi-polynomial. - Our formulas are particularly useful for understanding how $I(\mathfrak{p}(h); \xi)$ and $S(\mathfrak{p}(h); \xi)$ vary in a family of polytopes $\mathfrak{p}(h)$ with the same normal fan. When considering dilates of a fixed polytope, our formulas may be viewed as polytopal analogues of Laplace's method and the method of stationary phase. Such expressions naturally show up in analysis on symmetric spaces and affine buildings. - oai:arXiv.org:2409.09544v3 - math.CO - Tue, 09 Dec 2025 00:00:00 -0500 - replace + 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/ - Carsten Peterson + Kyriakos Lotidis, Panayotis Mertikopoulos, Nicholas Bambos, Jose Blanchet - Bounds and Hardness Results for Conflict-free Choosability - https://arxiv.org/abs/2409.12672 - arXiv:2409.12672v3 Announce Type: replace -Abstract: A '(partial) conflict-free coloring' of a hypergraph $\mathcal{H}$ is an assignment of colors to (a subset of) the vertex set of $\mathcal{H}$ such that every hyperedge in $\mathcal{H}$ has a vertex whose color is distinct from every other vertex in that hyperedge. The minimum number of colors required for such a coloring is known as the '(partial) conflict-free chromatic number' of $\mathcal{H}$. It is easy to see that the conflict-free chromatic number of a hypergraph is at most its partial conflict-free chromatic number plus one. Conflict-free coloring has also been studied on the open/closed neighborhood hypergraphs of a given graph under the name open/closed neighborhood conflict-free coloring. In this paper, we study partial and full list variants of conflict-free coloring where, for every vertex $v$, we are given a list of admissible colors $L_v$ such that $v$ is allowed to be colored only from $L_v$. - Bhyravarapu, Kalyanasundaram, and Mathew [Journal of Graph Theory, 2021] showed that the closed-neighborhood conflict-free chromatic number of any graph $G$ with maximum degree $\Delta$ is at most $O(\ln^2 \Delta)$. In this paper, we extend the $O(\ln^2 \Delta)$ upper bound to the partial list variant of the closed-neighborhood conflict-free chromatic number. Further, we establish computational complexity results concerning the list open/closed-neighborhood conflict-free chromatic numbers. - oai:arXiv.org:2409.12672v3 - math.CO - cs.DM - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Shiwali Gupta, Rogers Mathew + 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 - Note on a Coin Tossing Problem Posed by Daniel Litt - https://arxiv.org/abs/2409.13087 - arXiv:2409.13087v3 Announce Type: replace -Abstract: We present an analysis of a coin-tossing problem posed by Daniel Litt which has generated some popular interest. We demonstrate a recursive identity which leads to relatively simple formulas for the excess number of wins for one player over the other together with its increments as the number of coin tosses increases. Formulas and recursive algorithms are provided to calculate the number of sequences with any given point-score difference. - oai:arXiv.org:2409.13087v3 + 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 - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Bruce Levin + Wed, 10 Dec 2025 00:00:00 -0500 + cross + http://creativecommons.org/licenses/by/4.0/ + Alastair Kay, Christino Tamon - Von Neumann Orbit Equivalence - https://arxiv.org/abs/2409.15535 - arXiv:2409.15535v3 Announce Type: replace -Abstract: We generalize the notion of orbit equivalence to the non-commutative setting by introducing a new equivalence relation on groups, which we call von Neumann orbit equivalence (vNOE). We prove the stability of this equivalence relation under taking free products and graph products of groups. To achieve this, we introduce von Neumann orbit equivalence of tracial von Neumann algebras, show that two countable discrete groups $\Gamma$ and $\Lambda$ are vNOE if and only if the corresponding group von Neumann algebras $L\Gamma$ and $L\Lambda$ are vNOE, and that vNOE of tracial von Neumann algebras is stable under taking free products and graph products of tracial von Neumann algebras. - oai:arXiv.org:2409.15535v3 - math.OA - math.GR - Tue, 09 Dec 2025 00:00:00 -0500 - replace + 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 + math.ST + stat.CO + stat.TH + Wed, 10 Dec 2025 00:00:00 -0500 + cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Ishan Ishan, Aoran Wu + Fangzheng Xie, Hsin-Hsiung Huang - Moment problems related to intrinsic characterizations of the moment functionals - https://arxiv.org/abs/2410.09751 - arXiv:2410.09751v2 Announce Type: replace -Abstract: In this paper, we consider linear functionals defined on an unital commutative real algebra A and establish characterizations for moment functionals on compact sets of characters that depend only on the given functional. For example, we obtain a characterization of a moment functional on a product of symmetric intervals, in which we do not assume that the functional is positive semidefinite but positive on a semiring of A, and a characterization of a moment functional that is a solution to the moment problem on a product of arbitrary intervals. We also prove a Positivstellensatz for an archimedean cone, which is neither a quadratic module nor a semiring. - oai:arXiv.org:2410.09751v2 - math.FA - Tue, 09 Dec 2025 00:00:00 -0500 - replace + 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 + cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Dragu Atanasiu + H{\aa}vard Bakke Bjerkevik, Nello Blaser, Lars M. Salbu - Near-Pilotless Single Carrier Communications Using Matrix Decomposition - https://arxiv.org/abs/2410.10403 - arXiv:2410.10403v2 Announce Type: replace -Abstract: Single Input-Multiple Output (SIMO) systems are key enablers of high data rates in the next generation wireless communications. However in SIMO systems, channel estimation and equalization are challenging particularly in the presence of rapidly changing channels. The high pilot overhead required for channel estimation can reduce the system throughput for large antenna configuration. In this paper, we provide an iterative matrix decomposition algorithm for near-pilotless or blind decoding of SIMO signals, in a single carrier system with frequency domain equalization. This novel approach replaces the standard equalization and estimates both the transmitted data and the channel without the knowledge of any prior distributions, by making use of only one pilot. Our simulations demonstrate improved performance, in terms of error rates, compared to the more widely used pilot-based Maximal Ratio Combining (MRC) method. - oai:arXiv.org:2410.10403v2 + 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 - eess.SP math.IT - Tue, 09 Dec 2025 00:00:00 -0500 - replace + Wed, 10 Dec 2025 00:00:00 -0500 + cross http://creativecommons.org/licenses/by/4.0/ - K Sai Praneeth, P Aswathylakshmi, Radhakrishna Ganti + Kyle Yates, Antsa Pierrottet, Abdullah Al Mamun, Ryann Cartor, Mashrur Chowdhury, Shuhong Gao - A bijective proof of Andrews' refinement of the Alladi-Schur theorem - https://arxiv.org/abs/2410.15630 - arXiv:2410.15630v3 Announce Type: replace -Abstract: This paper gives a bijective proof of Andrews' refinement of the Alladi-Schur theorem. Moreover, it demonstrates that the bijective framework introduced here can be used to reproduce and provide a bijective account of Andrews' recursive relations for the Alladi-Schur polynomials. - oai:arXiv.org:2410.15630v3 - math.NT - math.CO - Tue, 09 Dec 2025 00:00:00 -0500 - replace + 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 + stat.ME + math.ST + stat.CO + stat.ML + stat.TH + Wed, 10 Dec 2025 00:00:00 -0500 + cross http://creativecommons.org/licenses/by/4.0/ - Yazan Alamoudi + Fatih K{\i}z{\i}laslan, Valeria Vitelli - The grad-div conforming virtual element method for the quad-div problem in three dimensions - https://arxiv.org/abs/2410.18375 - arXiv:2410.18375v2 Announce Type: replace -Abstract: We propose a new stable variational formulation for the quad-div problem in three dimensions and prove its well-posedness. Using this weak form, we develop and analyze the $\boldsymbol{H}(\operatorname{grad-div})$-conforming virtual element method of arbitrary approximation orders on polyhedral meshes. Three families of $\boldsymbol{H}(\operatorname{grad-div})$-conforming virtual elements are constructed based on the structure of a de Rham sub-complex with enhanced smoothness, resulting in an exact discrete virtual element complex. In the lowest-order case, the simplest element has only one degree of freedom at each vertex and face, respectively. We rigorously prove the interpolation error estimates, the stability of discrete bilinear forms, the well-posedness of discrete formulation and the optimal error estimates. Some numerical examples are shown to verify the theoretical results. - oai:arXiv.org:2410.18375v2 - math.NA - cs.NA - Tue, 09 Dec 2025 00:00:00 -0500 - replace + 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/ - Xiaojing Dong, Yibing Han, Yunqing Huang + Xiuyuan Cheng, Yao Xie, Linglingzhi Zhu, Yunqin Zhu - A Power Method for Computing Singular Value Decomposition - https://arxiv.org/abs/2410.23999 - arXiv:2410.23999v4 Announce Type: replace -Abstract: The singular value decomposition (SVD) allows to write a matrix as a product of a left singular vectors matrix, a nonnegative singular values diagonal matrix and a right singular vectors matrix. Among the applications of the SVD are the principal component analysis, the low-rank matrix approximation and the solving of a linear system of equations. The methods used for computing this decomposition allow to get the complete or partial result. For very large size matrix, the probabilistic methods allow to get partial result by using less computational load. A power method is proposed in this paper for computing all or the $k$ first largest SVD subspaces for a real-valued matrix. The $k$ first right singular vectors of this method are the $k$ columns of a neural network encoder weight matrix. The accuracy of this iterative search method depends on the behavior of the singular values and the settings of the gradient search optimizer used. A R package implementing the proposed method is available at https://cran.r-project.org/web/packages/psvd/index.html. - oai:arXiv.org:2410.23999v4 - math.NA - cs.NA - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Doulaye Dembele + 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 - On codes induced from Hadamard matrices - https://arxiv.org/abs/2410.24027 - arXiv:2410.24027v3 Announce Type: replace -Abstract: Unit derived schemes applied to Hadamard matrices are used to construct and analyse linear block and convolutional codes. Codes are constructed to prescribed types, lengths and rates and multiple series of self-dual, dual-containing, linear complementary dual and quantum error-correcting of both linear block {\em and} convolutional codes are derived. - oai:arXiv.org:2410.24027v3 - cs.IT - math.IT - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/publicdomain/zero/1.0/ - Ted Hurley + 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 + cross + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Jan Albert, Yamato Honda, Justin Kaidi, Yunqin Zheng - Gaskets of $O(2)$ loop-decorated random planar maps - https://arxiv.org/abs/2411.05541 - arXiv:2411.05541v2 Announce Type: replace -Abstract: We prove that for $n = 2$ the gaskets of critical rigid $O(n)$ loop-decorated random planar maps are $3/2$-stable maps. The case $n = 2$ thus corresponds to the critical case in random planar maps. The proof relies on the Wiener-Hopf factorisation for random walks. Our techniques also provide a characterisation of weight sequences of critical $O(2)$ loop-decorated maps. - oai:arXiv.org:2411.05541v2 + 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 + stat.ME math.PR + math.ST + stat.AP + stat.TH + Wed, 10 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 + + + 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 + cross + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Deepak Gupta, Himanshu Pandey, Ratikanta Behera + + + 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 - Tue, 09 Dec 2025 00:00:00 -0500 - replace + physics.optics + Wed, 10 Dec 2025 00:00:00 -0500 + cross http://creativecommons.org/licenses/by/4.0/ - Emmanuel Kammerer + Neil Beri, John Palastro, Qian Qian, Kyle Miller, Brandon Russell, Alexander Thomas - Zero-sum Dynkin games under common and independent Poisson constraints - https://arxiv.org/abs/2411.07134 - arXiv:2411.07134v2 Announce Type: replace -Abstract: Zero-sum Dynkin games under Poisson constraints, where players can only stop at the event times of a Poisson process, have been studied widely in the recent literature. The constraint can be modelled in two ways: either both players share the same Poisson process (the common constraint) or each player has their own Poisson process (the independent constraint). In a Markovian framework, where payoffs are functions of an underlying diffusion, we establish necessary and sufficient conditions for the equivalence of the game's solution--comprising the value function and optimal stopping sets--under the common and independent constraints. Specifically, if the stopping sets of the maximiser and minimiser in the game under the common constraint are disjoint, then the solution to the game is the same under both the common and the independent constraint. However, the fact that the stopping sets are disjoint in the game under the independent constraint is not sufficient to guarantee that the solution of the game under the independent constraint is also the solution under the common constraint. To demonstrate the broad applicability of our results, we solve infinite-horizon Dynkin games satisfying the assumptions of our main theorems, using backward stochastic differential equation (BSDE) techniques. This requires extending standard BSDE results from the finite-horizon setting to the infinite-horizon case, allowing for unbounded solutions. - oai:arXiv.org:2411.07134v2 + 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 + cs.LG math.OC - math.PR - Tue, 09 Dec 2025 00:00:00 -0500 - replace + stat.ML + Wed, 10 Dec 2025 00:00:00 -0500 + cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - David Hobson, Gechun Liang, Edward Wang + Wang Chen, Ziyan Luo, Shuangyue Wang - Further Results on the Majority Roman Domination in graphs - https://arxiv.org/abs/2411.07266 - arXiv:2411.07266v2 Announce Type: replace -Abstract: Let $G=(V,E)$ be a simple graph of order $n$. A Majority Roman Dominating Function (MRDF) on a graph G is a function $f: V\rightarrow\{-1, +1, 2\}$ if the sum of its function values over at least half the closed neighborhoods is at least one , this is , for at least half of the vertices $v\in V$, $f(N[v])\geq 1$. Moreover, every vertex u with $f(u)=-1$ is adjacent to at least one vertex $w$ with $f(w)=2$. The Majority Roman Domination number of a graph $G$, denoted by $\gamma_{MR}(G)$ , is the minimum value of $\sum_{v\in{V(G)}}f(v)$ over all Majority Roman Dominating Function $f$ of $G$. In this paper we study properties of the Majority Roman Domination in graphs and obtain lower and upper bounds the Majority Roman Domination number of some graphs. - oai:arXiv.org:2411.07266v2 - math.CO - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Azam Sadat Emadi, Iman Masoumi, Seyed Reza Musawi + 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 number of crossings and bouncings of a diffusion at a sticky threshold - https://arxiv.org/abs/2411.08846 - arXiv:2411.08846v2 Announce Type: replace -Abstract: In this paper, we study the asymptotic behavior of the number of crossings by a one-dimensional diffusion of a threshold where the process exhibits stickiness. We distinguish three types of crossings and show that to each type corresponds a distinct asymptotic regime for the respective number of crossings statistic. We introduce notions of bouncing as the symmetric counterparts to crossings and show that the corresponding number of bouncings statistics share the same asymptotic properties as their crossings counterparts. We first prove the results for sticky Brownian motion, then extend them to sticky-reflected Brownian motion (where only bouncing is possible) and to sticky diffusions. As an application, we propose consistent estimators for the stickiness parameter of sticky diffusions and sticky-reflected Brownian motion. - oai:arXiv.org:2411.08846v2 + 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 - Tue, 09 Dec 2025 00:00:00 -0500 - replace + Wed, 10 Dec 2025 00:00:00 -0500 + cross http://creativecommons.org/licenses/by/4.0/ - Alexis Anagnostakis, Sara Mazzonetto + Laurence Carassus, Mikl\'os R\'asonyi - Further Notes on Tightness - https://arxiv.org/abs/2411.12410 - arXiv:2411.12410v3 Announce Type: replace -Abstract: Tight and essentially tight modules generalize weakly injective modules. Essential tightness requires embeddings to be essential. This restriction makes the two notions totally different. In this note, we investigate cases when those two notions are the same. Moreover, we look at the cases when essentiallity is imposed only on one of the embeddings rather than both. This allows defining a special class of tight and essentially tight modules and a generalization of both. - oai:arXiv.org:2411.12410v3 - math.RA - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Nasief Khlaif, Mohammad Saleh + 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 + cross + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Gunjan Kumar, Yash Pote, Jonathan Scarlett - A block-acoustic preconditioner for the elastic Helmholtz equation - https://arxiv.org/abs/2411.15897 - arXiv:2411.15897v2 Announce Type: replace -Abstract: We present a novel block-preconditioner for the elastic Helmholtz equation, based on a reduction to acoustic Helmholtz equations. Both versions of the Helmholtz equations are challenging numerically. The elastic Helmholtz equation is larger, as a system of PDEs, and harder to solve due to its more complicated physics. It was recently suggested that the elastic Helmholtz equation can be reformulated as a generalized saddle-point system, opening the door to the current development. Utilizing the approximate commutativity of the underlying differential operators, we suggest a block-triangular preconditioner whose diagonal blocks are acoustic Helmholtz operators. Thus, we enable the solution of the elastic version using virtually any existing solver for the acoustic version as a black-box. We prove a sufficient condition for the convergence of our method, that sheds light on the long questioned role of the commutator in the convergence of approximate commutator preconditioners. We show scalability of our preconditioner with respect to the Poisson ratio and with respect to the grid size. We compare our approach, combined with multigrid solve of each block, to a recent monolithic multigrid method for the elastic Helmholtz equation. The block-acoustic multigrid achieves a lower computational cost for various heterogeneous media, and a significantly lower memory consumption, compared to the monolithic approach. It results in a fast solution method for wave propagation problems in challenging heterogeneous media in 2D and 3D. - oai:arXiv.org:2411.15897v2 - math.NA - cs.NA - Tue, 09 Dec 2025 00:00:00 -0500 - replace + 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 + 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/ - Rachel Yovel, Eran Treister + Sergii V. Siryk, Walter Rocchia - Infinitesimal $\mathcal{R}$-matrices for some families of Hopf algebras - https://arxiv.org/abs/2412.02350 - arXiv:2412.02350v2 Announce Type: replace -Abstract: Given a bialgebra $H$ such that the associated trivial topological bialgebra $H[[\hbar]]$ admits a quasitriangular structure $\tilde{\mathcal{R}}=\mathcal{R}(1\otimes 1+\hbar\chi+\mathcal{O}(\hbar^2))$, one gets a distinguished element $\chi \in H \otimes H$ which is an infinitesimal $\mathcal{R}$-matrix, according to the definition given in [1]. In this paper we classify infinitesimal $\mathcal{R}$-matrices for some families of well-known Hopf algebras, among which are the generalized Kac-Paljutkin Hopf algebras $H_{2n^2}$, the Radford Hopf algebras $H_{(r,n,q)}$, and the Hopf algebras $E(n)$. - oai:arXiv.org:2412.02350v2 - math.QA - math.RA - math.RT - Tue, 09 Dec 2025 00:00:00 -0500 - replace + 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/ - Lucrezia Bottegoni, Fabio Renda, Andrea Sciandra + Saptak Bhattacharya - A Variable Smoothing for Weakly Convex Composite Minimization with Manifold Constraint - https://arxiv.org/abs/2412.04225 - arXiv:2412.04225v3 Announce Type: replace -Abstract: In this paper, we address a manifold constrained nonsmooth optimization problem involving the composition of a weakly convex function and a smooth mapping. To find a stationary point of the target problem, we propose a variable smoothing-type algorithm by combining the ideas of (i) translating the constrained problem into a Euclidean optimization problem with a smooth parametrization of the constraint set; (ii) exploiting a sequence of smoothed surrogate functions, of the cost function, given with the Moreau envelope of a weakly convex function. The proposed algorithm produces a vector sequence by the gradient descent update of a smoothed surrogate function at each iteration. In a case where the proximity operator of the weakly convex function is available, the proposed algorithm does not require any iterative solver for subproblems therein. By leveraging tools in the variational analysis, we show the so-called {\em gradient consistency property}, which is a key ingredient for smoothing-type algorithms, of the smoothed surrogate function used in this paper. Based on the gradient consistency property, we also establish an asymptotic convergence analysis for the proposed algorithm together with convergence rate analysis. Numerical experiments demonstrate the efficacy of the proposed algorithm. - oai:arXiv.org:2412.04225v3 + 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 math.OC - Tue, 09 Dec 2025 00:00:00 -0500 - replace + Wed, 10 Dec 2025 00:00:00 -0500 + cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Keita Kume, Isao Yamada - - - Generalized Homogeneous Derivations on Graded Rings - https://arxiv.org/abs/2412.17187 - arXiv:2412.17187v4 Announce Type: replace -Abstract: We introduce a notion of generalized homogeneous derivations on graded rings as a natural extension of the homogeneous derivations defined by Kanunnikov. We then define gr-generalized derivations, which preserve the degrees of homogeneous components. Several significant results originally established for prime rings are extended to the setting of gr-prime rings, and we characterize conditions under which gr-semiprime rings contain nontrivial central graded ideals. In addition, we investigate the algebraic and module-theoretic structures of these maps, establish their functorial properties, and develop categorical frameworks that describe their derivation structures in both ring and module contexts. - oai:arXiv.org:2412.17187v4 - math.RA - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Yassine Ait Mohamed - - - Constructing locally flat surfaces in 4-manifolds - https://arxiv.org/abs/2412.18423 - arXiv:2412.18423v2 Announce Type: replace -Abstract: There are two main approaches to building locally flat embedded surfaces in 4-manifolds: direct methods which geometrically manipulate a given map of a surface, and more indirect methods using surgery theory. Both rely on Freedman-Quinn's disc embedding theorem. In this expository article, we give an introduction to these methods by sketching proofs of the following results: every primitive second homology class in a closed, simply connected 4-manifold is represented by a locally flat embedded torus (Lee-Wilczynski); and every Alexander polynomial one knot in $S^3$ is topologically slice (Freedman-Quinn). - oai:arXiv.org:2412.18423v2 - math.GT - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Arunima Ray - - - Dynamics, data and reconstruction - https://arxiv.org/abs/2412.19734 - arXiv:2412.19734v4 Announce Type: replace -Abstract: The goal of data-driven learning of dynamical systems is to interpret time series as a continuous observation of an underlying dynamical system. This task is not well-posed for a variety of reasons - such as multiple co-existing sub-systems, topologically inter-weaving of these sub-systems; and more importantly, the non-injectivity of the correspondence between dynamical systems and time series. We show how these ambiguities are circumvented if one considers dynamical systems and measurement maps collectively. Dynamical systems, observed dynamical systems, and time series data - each of these three collections have an extensive network of relations within them, which gives them the mathematical structure of a category. One of the new concepts proposed is a rigorous definition of time series data as a chain of measurement sequences with decreasing information content. This definition subsumes the familiar notions of sequences, time series and even subshifts. Using these notions it is shown that the entire process of converting an observed dynamical systems into a time series object is functorial, and passes through a number of phases each bearing its own categorical structure. This discovery sheds new light on the nature of reconstruction algorithms. Under mild conditions of consistency, reconstruction itself is shown to be functorial operation. This provides a new category theoretic perspective on the nature and limits of reconstruction. - oai:arXiv.org:2412.19734v4 - math.DS - math.CT - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Suddhasattwa Das, Tomoharu Suda + Zhijian Lai, Dong An, Jiang Hu, Zaiwen Wen - A Particle Algorithm for Mean-Field Variational Inference - https://arxiv.org/abs/2412.20385 - arXiv:2412.20385v3 Announce Type: replace -Abstract: Variational inference is a fast and scalable alternative to Markov chain Monte Carlo and has been widely applied to posterior inference tasks in statistics and machine learning. A traditional approach for implementing mean-field variational inference (MFVI) is coordinate ascent variational inference (CAVI), which relies crucially on parametric assumptions on complete conditionals. We introduce a novel particle-based algorithm for MFVI, named PArticle VI (PAVI), for nonparametric mean-field approximation. We obtain non-asymptotic error bounds for our algorithm. To our knowledge, this is the first end-to-end guarantee for particle-based MFVI. - oai:arXiv.org:2412.20385v3 - math.ST + 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 + cs.NA + math.FA + math.NA math.OC - stat.ML - stat.TH - Tue, 09 Dec 2025 00:00:00 -0500 - replace + Wed, 10 Dec 2025 00:00:00 -0500 + cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Qiang Du, Kaizheng Wang, Edith Zhang, Chenyang Zhong + Andreas Hauptmann, Ozan \"Oktem - Joint equidistributions of mesh patterns 123 and 321 with symmetric and minus-antipodal shadings - https://arxiv.org/abs/2501.00357 - arXiv:2501.00357v2 Announce Type: replace -Abstract: In this paper, we extend recent results by Lv and Kitaev by proving 20 (out of 22 possible) joint equidistributions of mesh patterns 123 and 321 with symmetric shadings, as well as all 36 joint equidistributions of these patterns with minus-antipodal shadings. Our results link several joint equidistributions of mesh patterns to various integer sequences, including unsigned Stirling numbers of the first kind, harmonic numbers, and the numbers of inversion sequences avoiding a certain vincular pattern studied by Lin and Yan. - oai:arXiv.org:2501.00357v2 - math.CO - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Shuzhen Lv, Philip B. Zhang + 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 - On termination of minimal model program for log canonical pairs on complex analytic spaces - https://arxiv.org/abs/2501.03531 - arXiv:2501.03531v2 Announce Type: replace -Abstract: We study the termination of minimal model programs for log canonical pairs in the complex analytic setting. By using the termination, we prove a relation between the minimal model theory for projective log canonical pairs and that for log canonical pairs in the complex analytic setting. The minimal model programs for algebraic stacks and analytic stacks are also discussed. - oai:arXiv.org:2501.03531v2 - math.AG - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Makoto Enokizono, Kenta Hashizume + 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 + cross + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Zhigang Jia, Duan Wang, Hengkai Wang, Yajun Xie, Meixiang Zhao, Xiaoyu Zhao - Network Oblivious Transfer via Noisy Channels: Limits and Capacities - https://arxiv.org/abs/2501.17021 - arXiv:2501.17021v3 Announce Type: replace -Abstract: In this paper, we aim to study the information-theoretical limits of oblivious transfer. This work also investigates the problem of oblivious transfer over a noisy multiple access channel involving two non-colluding senders and a single receiver. The channel model is characterized by correlations among the parties, with the parties assumed to be either honest-but-curious or, in the receiver's case, potentially malicious. At first, we study the information-theoretical limits of oblivious transfer between two parties and extend it to the multiple access channel model. We propose a multiparty protocol for honest-but-curious parties where the general multiple access channel is reduced to a certain correlation. In scenarios where the receiver is malicious, the protocol achieves an achievable rate region. - oai:arXiv.org:2501.17021v3 - cs.IT - cs.CR - math.IT - Tue, 09 Dec 2025 00:00:00 -0500 - replace + 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 + stat.ML + cs.LG + math.OC + Wed, 10 Dec 2025 00:00:00 -0500 + cross http://creativecommons.org/licenses/by/4.0/ - Hadi Aghaee, Bahareh Akhbari, Christian Deppe + Orit Davidovich, Shimrit Shtern, Segev Wasserkrug, Nimrod Megiddo - Improved semiclassical eigenvalue estimates for the Laplacian and the Landau Hamiltonian - https://arxiv.org/abs/2502.02388 - arXiv:2502.02388v2 Announce Type: replace -Abstract: The Berezin--Li--Yau and the Kr\"oger inequalities show that Riesz means of order $\geq 1$ of the eigenvalues of the Laplacian on a domain $\Omega$ of finite measure are bounded in terms of their semiclassical limit expressions. We show that these inequalities can be improved by a multiplicative factor that depends only on the dimension and the product $\sqrt\Lambda |\Omega|^{1/d}$, where $\Lambda$ is the eigenvalue cut-off parameter in the definition of the Riesz mean. The same holds when $|\Omega|^{1/d}$ is replaced by a generalized inradius of $\Omega$. Finally, we show similar inequalities in two dimensions in the presence of a constant magnetic field. - oai:arXiv.org:2502.02388v2 - math.SP + $\mathcal{PT}$-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 - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Rupert L. Frank, Simon Larson, Paul Pfeiffer + physics.optics + Wed, 10 Dec 2025 00:00:00 -0500 + cross + http://creativecommons.org/licenses/by/4.0/ + Cham Oumie, Wu-Ming Liu, Kashif Ammar Yasir - Sum-of-Squares Hierarchy for the Gromov Wasserstein Problem - https://arxiv.org/abs/2502.09102 - arXiv:2502.09102v3 Announce Type: replace -Abstract: The Gromov-Wasserstein (GW) problem is a variant of the classical optimal transport problem that allows one to compute meaningful transportation plans between incomparable spaces. At an intuitive level, it seeks plans that minimize the discrepancy between metric evaluations of pairs of points. The GW problem is typically cast as an instance of a non-convex quadratic program that is, unfortunately, intractable to solve. In this paper, we describe tractable semidefinite relaxations of the GW problem based on the Sum-of-Squares (SOS) hierarchy. We describe how the Putinar-type and the Schm\"udgen-type moment hierarchies can be simplified using marginal constraints, and we prove convergence rates for these hierarchies towards computing global optimal solutions to the GW problem. The proposed SOS hierarchies naturally induce a distance measure analogous to the distortion metrics, and we show that these are genuine distances in that they satisfy the triangle inequality. In particular, the proposed SOS hierarchies provide computationally tractable proxies of the GW distance and the associated distortion distances (over metric measure spaces) that are otherwise intractable to compute. - oai:arXiv.org:2502.09102v3 - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Hoang Anh Tran, Binh Tuan Nguyen, Yong Sheng Soh + 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 + math.DS + Wed, 10 Dec 2025 00:00:00 -0500 + cross + http://creativecommons.org/licenses/by/4.0/ + Alexander Bratus, Tatiana Yakushkina, Vladimir Posvyanski - Globular subdivisions are dihomotopy equivalences - https://arxiv.org/abs/2502.11773 - arXiv:2502.11773v3 Announce Type: replace -Abstract: We prove that any globular subdivision of multipointed $d$-spaces gives rise to a dihomotopy equivalence between the associated flows. As a straightforward application, the flows associated to two multipointed $d$-spaces related by a finite zigzag of globular subdivisions have isomorphic branching and merging homology theories and isomorphic underlying homotopy types. - oai:arXiv.org:2502.11773v3 - math.AT - math.CT - Tue, 09 Dec 2025 00:00:00 -0500 - replace + 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/ - Philippe Gaucher + Sergii V. Siryk, Walter Rocchia - High-dimensional long-range statistical mechanical models have random walk correlation functions - https://arxiv.org/abs/2502.12104 - arXiv:2502.12104v3 Announce Type: replace -Abstract: We consider long-range percolation, Ising model, and self-avoiding walk on $\mathbb{Z}^d$, with couplings decaying like $|x|^{-(d+\alpha)}$ where $0 < \alpha \le 2$, above the upper critical dimensions. In the spread-out setting where the lace expansion applies, we show that the two-point function for each of these models exactly coincides with a random walk two-point function, up to a constant prefactor. Using this, for $0<\alpha < 2$, we prove upper and lower bounds of the form $|x|^{-(d-\alpha)} \min\{ 1, (p_c - p)^{-2} |x|^{-2\alpha} \}$ for the two-point function near the critical point $p_c$. For $\alpha=2$, we obtain a similar upper bound with logarithmic corrections. We also give a simple proof of the convergence of the lace expansion, assuming diagrammatic estimates. - oai:arXiv.org:2502.12104v3 - math.PR + 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 math-ph math.MP - Tue, 09 Dec 2025 00:00:00 -0500 - replace + 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/ - Yucheng Liu + Sergii V. Siryk, Walter Rocchia - The applications of Bieri-Neumann-Strebel invariant on K\"ahler groups - https://arxiv.org/abs/2502.16031 - arXiv:2502.16031v2 Announce Type: replace -Abstract: We give several applications of the Bieri-Neumann-Strebel invariant on K\"ahler groups. Specifically, we provide simpler proof of the Napier-Ramachandran theorem on the HNN extension about K\"ahler groups and show that amenable K\"ahler groups have an empty complement of the BNS invariant. - oai:arXiv.org:2502.16031v2 - math.GT - Tue, 09 Dec 2025 00:00:00 -0500 - replace + 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/ - Yuan Liu + Sahar Pourandi, P. Christian van der Sande, Igor A. Ostanin, Thomas Weinhart - On Almost Strong Approximation in Reductive Algebraic Groups - https://arxiv.org/abs/2503.00696 - arXiv:2503.00696v4 Announce Type: replace -Abstract: We investigate a slight weakening of the classical property of strong approximation, which we call almost strong approximation, for connected reductive algebraic groups over global fields with respect to special sets of valuations. While nonsimply connected groups (in particular, all algebraic tori) always fail to have strong approximation -- and even almost strong approximation -- with respect to any finite set of valuations, we show that under appropriate assumptions they do have almost strong approximation with respect to certain infinite sets of valuations that can be characterized in terms of Dirichlet density and include tractable sets of valuations, i.e. those sets that contain all archimedean valuations and a generalized arithmetic progression minus a set of Dirichlet density zero. Almost strong approximation is likely to have a variety of applications, and as an example we use almost strong approximation in tori with respect to tractable sets to extend the essential part of the result of Radhika and Raghunathan on the congruence subgroup problem for inner forms of type $\textsf{A}_n$ to all absolutely almost simple simply connected groups. This version of the paper has been updated to reflect recent results of Y. Cao and Y. Wang (arXiv:2511.00824). - oai:arXiv.org:2503.00696v4 - math.AG - Tue, 09 Dec 2025 00:00:00 -0500 - replace + 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 + eess.SY + cs.LG + cs.SY + math.OC + Wed, 10 Dec 2025 00:00:00 -0500 + cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Andrei S. Rapinchuk, Wojciech Tralle + Jannik Graebner, Ryne Beeson - Parameter estimation in fluid flow models from undersampled frequency space data - https://arxiv.org/abs/2503.04092 - arXiv:2503.04092v2 Announce Type: replace -Abstract: 4D Flow MRI is the state of the art technique for measuring blood flow, and it provides valuable information for inverse problems in the cardiovascular system. However, 4D Flow MRI has a very long acquisition time, straining healthcare resources and inconveniencing patients. Due to this, usually only a part of the frequency space is acquired, where then further assumptions need to be made in order to obtain an image. - Inverse problems from 4D Flow MRI data have the potential to compute clinically relevant quantities without the need for invasive procedures, and/or expanding the set of biomarkers for a more accurate diagnosis. However, reconstructing MRI measurements with Compressed Sensing techniques introduces artifacts and inaccuracies, which can compromise the results of the inverse problems. Additionally, there is a high number of different sampling patterns available, and it is often unclear which of them is preferable. - Here, we present a parameter estimation problem directly using highly undersampled frequency space measurements. This problem is numerically solved by a Reduced-Order Unscented Kalman Filter (ROUKF). We show that this results in more accurate parameter estimation for boundary conditions in a synthetic aortic blood flow than using measurements reconstructed with Compressed Sensing. - We also compare different sampling patterns, demonstrating how the quality of the parameter estimation depends on the choice of the sampling pattern. The results show a considerably higher accuracy than an inverse problem using velocity measurements reconstructed via compressed sensing. Finally, we confirm these findings on real MRI data from a mechanical phantom. - oai:arXiv.org:2503.04092v2 - math.NA + 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 + eess.SP cs.NA - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Miriam L\"ocke, Pim van Ooij, Crist\'obal Bertoglio - - - Full subcomplexes of Bier spheres - https://arxiv.org/abs/2503.05385 - arXiv:2503.05385v2 Announce Type: replace -Abstract: Full subcomplexes of a simplicial complex encode essential structure for understanding the complex itself. For a simplicial complex $K$, possibly with a ghost vertex, the Bier sphere of $K$ is a simplicial sphere obtained as the deleted join of $K$ and its combinatorial Alexander dual. In this paper, we determine the homotopy types of all full subcomplexes of Bier spheres. As applications, we provide a formula for the bigraded Betti numbers of the Bier sphere of $K$ in terms of full subcomplexes of $K$, and we explicitly describe the cohomology of real toric manifolds associated with Bier spheres. - oai:arXiv.org:2503.05385v2 - math.CO - math.AT - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Suyoung Choi, Younghan Yoon, Seonghyeon Yu - - - Intermittent two-point dynamics at the transition to chaos for random circle endomorphisms - https://arxiv.org/abs/2503.08244 - arXiv:2503.08244v2 Announce Type: replace -Abstract: We establish the existence of intermittent two-point dynamics and infinite stationary measures for a class of random circle endomorphisms with zero Lyapunov exponent, as a dynamical characterisation of the transition from synchronisation (negative Lyapunov exponent) to chaos (positive Lyapunov exponent). - oai:arXiv.org:2503.08244v2 - math.DS - Tue, 09 Dec 2025 00:00:00 -0500 - replace + math.NA + Wed, 10 Dec 2025 00:00:00 -0500 + cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Vincent P. H. Goverse, Ale Jan Homburg, Jeroen S. W. Lamb - - - Measure transport via pseudo-cones - https://arxiv.org/abs/2503.10449 - arXiv:2503.10449v2 Announce Type: replace -Abstract: For the solution of the Gauss image problem for pseudo-cones, which can be considered as a measure transport problem for certain measures on the sphere, we give a new proof, using a special case of Kantorovich duality. - oai:arXiv.org:2503.10449v2 - math.MG - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Rolf Schneider + Oscar Romero, N\'estor Thome - Two identities involving Cohen-Ramanujan expansions - https://arxiv.org/abs/2503.12027 - arXiv:2503.12027v2 Announce Type: replace -Abstract: An arithmetical function $f$ is said to admit a \emph{Cohen-Ramanujan expansion} $f(n) := \sum\limits_{r}\widehat{f}(r)c_r^s(n)$, if the series on the right hand side converges for suitable complex numbers $\widehat{f}(r)$. Here $c_r^s(n)$ denotes the Cohen-Ramanujan sum defined by E. Cohen. We deduce here a Cohen-Ramanujan expansion for the Jordan totient function $J_k(n)$. Further, we give an an asymptotic formula for the sum $\sum\limits_{n \leq N} \frac{J_a(n)}{n^a} \frac{J_b(n+h)}{(n+h)^b}$ using the expansion we derive. - oai:arXiv.org:2503.12027v2 - math.NT - Tue, 09 Dec 2025 00:00:00 -0500 - replace + 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/ - Arya Chandran, K Vishnu Namboothiri + A. J. D. Farias Junior, A. Smirnov, Herondy F. Santana Mota, E. R. Bezerra de Mello - Linear-Quadratic Partially Observed Mean Field Stackelberg Stochastic Differential Game with Applications - https://arxiv.org/abs/2503.15803 - arXiv:2503.15803v2 Announce Type: replace -Abstract: This paper is concerned with a linear-quadratic partially observed mean field Stackelberg stochastic differential game, which contains a leader and a large number of followers. Specifically, the followers confront a large-population Nash game subsequent to the leader's initial announcement of his strategy. In turn, the leader optimizes his own cost functional, taking into account the anticipated reactions of the followers. The state equations of both the leader and the followers are general stochastic differential equations, where the drift terms contain both the state average term and the state expectation term. However, the followers' state average terms enter into the drift term of the leader's state equation and the state expectation term of the leader enters into the state equation of the follower, reflecting the mutual influence between the leader and the followers. By utilizing the techniques of state decomposition and backward separation principle, we deduce the open-loop adapted decentralized strategies and feedback decentralized strategies of this leader-followers system, and demonstrate that the decentralized strategies are the corresponding $\varepsilon$-Stackelberg-Nash equilibrium. Finally, we apply the theoretical result to a product planning problem with sticky prices. - oai:arXiv.org:2503.15803v2 - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/publicdomain/zero/1.0/ - Yu Si, Yueyang Zheng, Jingtao Shi - - - Weighted Heights and GIT Heights - https://arxiv.org/abs/2503.17068 - arXiv:2503.17068v2 Announce Type: replace -Abstract: We investigate the relationship between Geometric Invariant Theory (GIT) heights and weighted heights, with a focus on their interaction in weighted projective spaces and their application to binary forms. Building on the weighted height framework developed in previous papers, we relate it to Zhang's GIT height via the Veronese map. For a semistable cycle, we show that the GIT height decomposes into the logarithmic weighted height plus an Archimedean correction from the Chow metric. - oai:arXiv.org:2503.17068v2 - math.AG - math.NT - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Elira Shaska, Tony Shaska - - - Topological consequences of null-geodesic refocusing and applications to $Z^x$ manifolds - https://arxiv.org/abs/2503.23565 - arXiv:2503.23565v4 Announce Type: replace -Abstract: Let $(M,h)$ be a connected, complete Riemannian manifold, let $x\in M$ and $l>0$. Then $M$ is called a $Z^x$ manifold if all geodesics starting at $x$ return to $x$ and it is called a $Y^x_l$ manifold if every unit-speed geodesic starting at $x$ returns to $x$ at time $l$. It is unknown whether there are $Z^x$ manifolds that are not $Y^x_l$ manifolds for any $l>0$. By the B\'erard-Bergery theorem, any $Y^x_l$ manifold of dimension at least $2$ is compact with finite fundamental group. We prove the same result for $Z^x$ manifolds $M$ for which all unit-speed geodesics starting at $x$ return to $x$ in uniformly bounded time. We also prove that any $Z^x$ manifold $(M,h)$ with $h$ analytic is a $Y^x_l$ manifold for some $l>0$. We start by defining a class of globally hyperbolic spacetimes (called observer-refocusing) such that any $Z^x$ manifold is the Cauchy surface of some observer-refocusing spacetime. We then prove that under suitable conditions the Cauchy surfaces of observer-refocusing spacetimes are compact with finite fundamental group and show that analytic observer-refocusing spacetimes of dimension at least $3$ are strongly refocusing. We end by stating a contact-theoretic conjecture analogous to our results in Riemannian and Lorentzian geometry. - oai:arXiv.org:2503.23565v4 - math.DG + 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.GT + math.DG math.MP - math.SG - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Friedrich Bauermeister + Wed, 10 Dec 2025 00:00:00 -0500 + cross + http://creativecommons.org/licenses/by-sa/4.0/ + Ferhat Ta\c{s} - Orthogonal Polynomials with Complex Densities and Quantum Minimal Surfaces - https://arxiv.org/abs/2504.06197 - arXiv:2504.06197v2 Announce Type: replace -Abstract: We show that the discrete Painlev\'e-type equations arising from quantum minimal surfaces are equations for recurrence coefficients of orthogonal polynomials for indefinite hermitian products. As a consequence, we obtain an explicit formula for the initial conditions leading to positive solutions. - oai:arXiv.org:2504.06197v2 + 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 - Tue, 09 Dec 2025 00:00:00 -0500 - replace + math.OC + Wed, 10 Dec 2025 00:00:00 -0500 + cross http://creativecommons.org/licenses/by/4.0/ - 10.3842/SIGMA.2025.103 - SIGMA 21 (2025), 103, 13 pages - Giovanni Felder, Jens Hoppe + Pietro Fr\'e - Decoding the Ishango Bone: Unveiling Prehistoric Mathematical Art - https://arxiv.org/abs/2504.06412 - arXiv:2504.06412v3 Announce Type: replace -Abstract: The Ishango Bone, a prehistoric artifact dated to approximately 20,000 years ago and discovered near the Semliki River in what is now the Democratic Republic of Congo, has intrigued researchers for the past 75 years. The artifact displays sixteen groups of notches arranged in three columns. While its function remains debated, this study suggests that the first two columns consist exclusively of all prime or odd numbers between 9 and 21, with the exception of 15, which appears only in the third column as two grouped pairs. Five groupings totaling 30 could be identified, and their arrangement may follow a consistent pattern. Additional numerical relationships between all three columns can be interpreted to support all four basic arithmetic operations. It is hypothesized that the notches may have served as reference marker to lay out their values for storytelling or teaching in the form of mathematical art. This study aims to broaden perspectives on the Ishango Bone and its traditional interpretation as a simple tallying device, and to encourage a re-evaluation of the mathematical capabilities of prehistoric humans. - oai:arXiv.org:2504.06412v3 - math.HO - Tue, 09 Dec 2025 00:00:00 -0500 - replace + 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 + cross http://creativecommons.org/licenses/by/4.0/ - Jenny Baur + Daniel Egger, Jacob Vestal - Grothendieck-Springer resolutions and TQFTs - https://arxiv.org/abs/2504.10285 - arXiv:2504.10285v2 Announce Type: replace -Abstract: The Moore-Tachikawa conjecture is that each connected complex semisimple group $G$ determines a two-dimensional TQFT in a category of Hamiltonian symplectic varieties. While it would be worthwhile to prove this conjecture outright, our objectives are drastically different. We instead view the Moore--Tachikawa conjecture as a first step in systematically assigning new TQFTs to purely Lie-theoretic data. At the same time, one should expect these new TQFTs to bear a close relation to those conjectured by Moore and Tachikawa. Our manuscript aims to integrate these two points of view. - Let $\mathfrak{g}$ be the Lie algebra of $G$. Consider a conjugacy class $\mathcal{C}$ of parabolic subalgebras of $\mathfrak{g}$. This class determines partial Grothendieck--Springer resolutions $\mu_{\mathcal{C}}:\mathfrak{g}_{\mathcal{C}}\longrightarrow\mathfrak{g}^*=\mathfrak{g}$ and $\nu_{\mathcal{C}}:G_{\mathcal{C}}\longrightarrow G$. We construct a canonical symplectic groupoid $(T^*G)_{\mathcal{C}}\substack{\longrightarrow\\[-9pt] \longrightarrow}\mathfrak{g}_{\mathcal{C}}$ and quasi-symplectic groupoid $\mathrm{D}(G)_{\mathcal{C}}\substack{\longrightarrow\\[-9pt] \longrightarrow} G_{\mathcal{C}}$. By considering a Kostant slice $\mathrm{Kos}\subseteq\mathfrak{g}$ and Steinberg slice $\mathrm{Ste}\subseteq G$, we prove that the pairs $(((T^*G)_{\mathcal{C}})_{\text{reg}}\substack{\longrightarrow\\[-9pt] \longrightarrow}(\mathfrak{g}_{\mathcal{C}})_{\text{reg}},\mu_{\mathcal{C}}^{-1}(\mathrm{Kos}))$ and $((\mathrm{D}(G)_{\mathcal{C}})_{\text{reg}}\substack{\longrightarrow\\[-9pt] \longrightarrow}(G_{\mathcal{C}})_{\text{reg}},\nu_{\mathcal{C}}^{-1}(\mathrm{Ste}))$ determine new and explicit TQFTs in a $1$-shifted Weinstein symplectic category. We then show that certain symplectic varieties arising from our new TQFTs have canonical Lagrangian relations to the open Moore-Tachikawa varieties. - oai:arXiv.org:2504.10285v2 - math.SG + 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 - math.RT - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Peter Crooks, Maxence Mayrand + Derong Qiu - Set families: restricted distances via restricted intersections - https://arxiv.org/abs/2504.12296 - arXiv:2504.12296v3 Announce Type: replace -Abstract: Denote by $f_D(n)$ the maximum size of a set family $\mathcal{F}$ on $[n] \stackrel{\mbox{\normalfont\tiny def}}{=} \{1, \dots, n\}$ with distance set $D$. That is, $|A \bigtriangleup B| \in D$ holds for every pair of distinct sets $A, B \in \mathcal{F}$. Kleitman's celebrated discrete isodiametric inequality states that $f_D(n)$ is maximized at Hamming balls of radius $d/2$ when $D = \{1, \dots, d\}$. We study the generalization where $D$ is a set of arithmetic progression and determine $f_D(n)$ asymptotically for all homogeneous $D$. In the special case when $D$ is an interval, our result confirms a conjecture of Huang, Klurman, and Pohoata. Moreover, we demonstrate a dichotomy in the growth of $f_D(n)$, showing linear growth in $n$ when $D$ is a non-homogeneous arithmetic progression. Different from previous combinatorial and spectral approaches, we deduce our results by converting the restricted distance problems to restricted intersection problems. - Our proof ideas can be adapted to prove upper bounds on $t$-distance sets in Hamming cubes (also known as binary $t$-codes), which has been extensively studied by algebraic combinatorialists community, improving previous bounds from polynomial methods and optimization approaches. - oai:arXiv.org:2504.12296v3 - math.CO - cs.DM - Tue, 09 Dec 2025 00:00:00 -0500 + 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/ - Zichao Dong, Jun Gao, Hong Liu, Minghui Ouyang, Qiang Zhou + Laurent Bus\'e, Thomas Dedieu - Eigenvalue distribution in gaps of the essential spectrum of the Bochner-Schr\"odinger operator - https://arxiv.org/abs/2504.12928 - arXiv:2504.12928v2 Announce Type: replace -Abstract: The Bochner-Schr\"odinger operator $H_{p}=\frac 1p\Delta^{L^p}+V$ on high tensor powers $L^p$ of a Hermitian line bundle $L$ on a Riemannian manifold $X$ of bounded geometry is studied under the assumption of non-degeneracy of the curvature form of $L$. For large $p$, the spectrum of $H_p$ asymptotically coincides with the union of all local Landau levels of the operator at the points of $X$. Moreover, if the union of the local Landau levels over the complement of a compact subset of $X$ has a gap, then the spectrum of $H_{p}$ in the gap is discrete. The main result of the paper is the trace asymptotics formula associated with these eigenvalues. As a consequence, we get a Weyl type asymptotic formula for the eigenvalue counting function. - oai:arXiv.org:2504.12928v2 - math.SP - math-ph - math.DG - math.MP - Tue, 09 Dec 2025 00:00:00 -0500 + 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://arxiv.org/licenses/nonexclusive-distrib/1.0/ - 10.1134/S0001434625603739 - Mathematical Notes, 2025, Vol. 118, No. 2, pp. 309-320 - Yuri A. Kordyukov + http://creativecommons.org/licenses/by/4.0/ + Ulrich Bunke, Alexander Engel, Markus Land - Topological lax comma categories - https://arxiv.org/abs/2504.12965 - arXiv:2504.12965v2 Announce Type: replace -Abstract: This paper investigates the interplay between properties of a topological space $X$, in particular of its natural order, and properties of the lax comma category $\mathsf{Top} \Downarrow X$, where $\mathsf{Top}$ denotes the category of topologicalspaces and continuous maps. Namely, it is shown that, whenever $X$ is a topological $\bigwedge$-semilattice, the canonical forgetful functor $\mathsf{Top} \Downarrow X \to \mathsf{Top}$ is topological, preserves and reflects exponentials, and preserves effective descent morphisms. Moreover, under additional conditions on $X$, a characterisation of effective descent morphisms is obtained. - oai:arXiv.org:2504.12965v2 + 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 - math.GN - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - 10.1007/s11083-025-09714-z - Order 43, 3 (2026) - Maria Manuel Clementino, Dirk Hofmann, Rui Prezado + 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) - Sensing-Then-Beamforming: Robust Transmission Design for RIS-Empowered Integrated Sensing and Covert Communication - https://arxiv.org/abs/2504.13741 - arXiv:2504.13741v2 Announce Type: replace -Abstract: Traditional covert communication often relies on the knowledge of the warden's channel state information, which is inherently challenging to obtain due to the non-cooperative nature and potential mobility of the warden. The integration of sensing and communication technology provides a promising solution by enabling the legitimate transmitter to sense and track the warden, thereby enhancing transmission covertness. In this paper, we develop a framework for sensing-then-beamforming in reconfigurable intelligent surface (RIS)-empowered integrated sensing and covert communication (ISACC) systems, where the transmitter (Alice) estimates and tracks the mobile aerial warden's channel using sensing echo signals while simultaneously sending covert information to multiple legitimate users (Bobs) with the assistance of RIS, under the surveillance of the warden (Willie). Considering channel estimation errors, we formulate a robust non-convex optimization problem that jointly designs the communication beamformers, the sensing signal covariance matrix at Alice, and the phase shifts at the RIS to maximize the covert sum rate of Bobs while satisfying the constraints related to covert communication, sensing, transmitter power, and the unit modulus of the RIS elements. To solve this complex problem, we develop an efficient algorithm using alternating optimization, successive convex approximation, S-procedure, sequential rank-one constraint relaxation, and semidefinite relaxation techniques. Numerical results confirm the convergence of the proposed algorithm and demonstrate its effectiveness in tracking the warden's channel while ensuring robust covert transmission. Furthermore, the results highlight the advantages of using RIS to enhance the covert transmission rate compared to baseline schemes, and also illustrate the intricate trade-off between communication and sensing in ISACC systems. - oai:arXiv.org:2504.13741v2 - cs.IT - eess.SP - math.IT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + cs.LG + Wed, 10 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Xingyu Zhao, Min Li, Ming-Min Zhao, Shihao Yan, Min-Jian Zhao + Miroslav Dud\'ik, Robert E. Schapire, Matus Telgarsky - Time discretization in convected linearized thermo-visco-elastodynamics at large displacements - https://arxiv.org/abs/2504.14297 - arXiv:2504.14297v2 Announce Type: replace -Abstract: The fully-implicit time discretization (i.e. the backward Euler formula) is applied to compressible nonlinear dynamical models of thermo-viscoelastic solids in the Eulerian description, i.e. in the actual deforming configuration, formulated in terms of rates. The Kelvin-Voigt rheology or also, in the deviatoric part, the Jeffreys rheology (which covers creep or plasticity) are considered, using the additive Green-Naghdi decomposition of total strain into the elastic and the inelastic strains formulated in terms of (objective) rates exploiting the Zaremba-Jaumann time derivative. A linearized convective model at large displacements is considered, focusing on the case where the internal energy additively splits the (convex) mechanical and the thermal parts.A fully implicit time-discrete scheme is devised. Considering the multipolar 2nd-grade viscosity, the numerical stability and convergence towards weak solutions are proven by exploiting, in particular, the convexity of the kinetic energy when written in terms of linear momentum instead of velocity and by estimating the temperature gradient from the entropy-like inequality. - oai:arXiv.org:2504.14297v2 - math.NA - cs.NA - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Tom\'a\v{s} Roub\'i\v{c}ek + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Runbing Zheng, Minh Tang - Extremal divisors on moduli spaces of K3 surfaces - https://arxiv.org/abs/2504.16730 - arXiv:2504.16730v2 Announce Type: replace -Abstract: We establish criteria for when Noether--Lefschetz divisors generate an extremal ray in the cone of pseudoeffective divisors of an orthogonal modular variety. In particular, we exhibit many extremal rays of the cone of pseudoeffective divisors on any moduli space~$\mathcal{F}_{2d}$ of quasi-polarized K3 surfaces of degree $d$, as well as on any normal projective $\mathbb{Q}$-factorial compactification $\overline{\mathcal{F}}_{2d}$ of $\mathcal{F}_{2d}$ lying over the Baily--Borel compactification. - oai:arXiv.org:2504.16730v2 - math.AG - math.NT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Ignacio Barros, Laure Flapan, Riccardo Zuffetti + Tom Benhamou - Robust semi-implicit multilevel SDC methods for conservation laws - https://arxiv.org/abs/2504.18526 - arXiv:2504.18526v2 Announce Type: replace -Abstract: Semi-implicit multilevel spectral deferred correction (SI-MLSDC) methods provide a promising approach for high-order time integration for nonlinear evolution equations including conservation laws. However, existing methods lack robustness and often do not achieve the expected advantage over single-level SDC. This work adopts the novel SI time integrators from [48] for enhanced stability and extends the single-level SI-SDC method with a multilevel approach to increase computational efficiency. The favourable properties of the resulting SI-MLSDC method are shown by linear temporal stability analysis for a convection-diffusion problem. The robustness and efficiency of the fully discrete method involving a high-order discontinuous Galerkin SEM discretization are demonstrated through numerical experiments for the convection-diffusion, Burgers, Euler and Navier-Stokes equations. The method is shown to yield substantial reductions in fine-grid iterations compared to single-level SI-SDC across a broad range of test cases. Finally, current limitations of the SI-MLSDC framework are identified and discussed, providing guidance for future improvements. - oai:arXiv.org:2504.18526v2 - math.NA - cs.NA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Erik Pfister, J\"org Stiller + Are Austad, Sven Raum - Constrained Parameter Update Law for Adaptive Control - https://arxiv.org/abs/2504.19412 - arXiv:2504.19412v2 Announce Type: replace -Abstract: In this paper, a constrained parameter update law is derived in the context of adaptive control. The parameter update law is based on constrained optimization technique where a Lagrangian is formulated to incorporate the constraints on the parameters using inverse Barrier function. The constrained parameter update law is used to develop a adaptive tracking controller and the overall stability of the adaptive controller along with the constrained parameter update law is shown using Lyapunov analysis and development in stability of constrained primal-dual dynamics. The performance of the constrained parameter update law is tested in simulation for keeping the parameters within constraints and convergence to true parameters. - oai:arXiv.org:2504.19412v2 - math.OC - cs.SY - eess.SP - eess.SY - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace http://creativecommons.org/licenses/by-nc-nd/4.0/ - Ashwin P. Dani + Tom Benhamou, Sittinon Jirattikansakul - On the Schr\"odingerization method for linear non-unitary dynamics with optimal dependence on matrix queries - https://arxiv.org/abs/2505.00370 - arXiv:2505.00370v4 Announce Type: replace -Abstract: The Schr\"odingerization method converts linear partial and ordinary differential equations with non-unitary dynamics into systems of Schr\"odinger-type equations with unitary evolution. It does so via the so-called warped phase transformation that maps the original equation into a Schr\"odinger-type equation in one higher dimension \cite{Schrshort,JLY22SchrLong}. The original proposal used a particular initial function in the auxiliary space that did not achieve optimal scaling in precision. Here we show that, by choosing smoother initial functions in auxiliary space, Schr\"odingerization \textit{can} in fact achieve near optimal and even optimal scaling in matrix queries. We construct three necessary criteria that the initial auxiliary state must satisfy to achieve optimality. This paper presents detailed implementation of four smooth initializations for the Schr\"odingerization method: (a) the error function and related functions, (b) the cut-off function, (c) the higher-order polynomial interpolation, and (d) Fourier transform methods. Method (a) achieves optimality and methods (b), (c) and (d) can achieve near-optimality. A detailed analysis of key parameters affecting time complexity is conducted. - oai:arXiv.org:2505.00370v4 - math.NA - cs.NA - quant-ph - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Shi Jin, Nana Liu, Chuwen Ma, Yizhe Peng, Yue Yu + http://creativecommons.org/licenses/by/4.0/ + Hang Li, Derong Qiu - Asymptotic Property C for Certain Wreath-like Products of Groups - https://arxiv.org/abs/2505.01268 - arXiv:2505.01268v3 Announce Type: replace -Abstract: In this paper, we present generalizations of some results on the asymptotic property C for wreath products. Specifically, we prove that certain wreath-like products admit asymptotic property C, thus providing some new examples for further study. - oai:arXiv.org:2505.01268v3 - math.GR - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Han Liu + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Petter Br\"and\'en, Jonathan Leake - Decomposing conditional independence ideals with hidden variables - https://arxiv.org/abs/2505.02404 - arXiv:2505.02404v2 Announce Type: replace -Abstract: We study a family of determinantal ideals whose decompositions encode the structural zeros in conditional independence models with hidden variables. We provide explicit decompositions of these ideals and, for certain subclasses of models, we show that this is a decomposition into radical ideals by displaying Gr\"obner bases for the components. We identify conditions under which the components are prime, and establish formulas for the dimensions of these prime ideals. - Moreover, we show that the components in the decomposition can be grouped into equivalence classes defined by their combinatorial structure, and we derive a closed formula for the number of such classes. - oai:arXiv.org:2505.02404v2 - math.AC - math.CO - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Yulia Alexandr, Kristen Dawson, Hannah Friedman, Fatemeh Mohammadi, Pardis Semnani, Teresa Yu + 10.4153/S0008414X2400052X + Can. J. Math.-J. Can. Math. 77 (2025) 1686-1717 + Tom Benhamou, Gabriel Goldberg - On the Inoue-Bombieri construction - https://arxiv.org/abs/2505.03389 - arXiv:2505.03389v2 Announce Type: replace -Abstract: We study compact quotients of a Riemannian product $\mathbb{R}^q \times (N, g_N)$, where $(N, g_N)$ is a complete Riemannian manifold, by discrete subgroups $\Gamma$ of $\mathrm{Sim}(\mathbb{R}^q) \times \mathrm{Isom}(N)$. When $N$ is a symmetric space of non-compact type, this construction generalizes the well-known Inoue--Bombieri surfaces. We show that this setting is actually equivalent to that of the so-called LCP manifolds, and we establish a Bieberbach-type rigidity result in the case where $N$ is symmetric. In addition, we provide a classification of the manifolds $N$ and the groups $\Gamma$ when $N$ is a Hadamard manifold with strictly negative curvature. - oai:arXiv.org:2505.03389v2 - math.DG - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Brice Flamencourt, Abdelghani Zeghib + Ruiyu Han - On global rigidity of transversely holomorphic Anosov flows - https://arxiv.org/abs/2505.06572 - arXiv:2505.06572v2 Announce Type: replace -Abstract: In this paper, we study transversely holomorphic flows, i.e. those whose holonomy pseudo-group is given by biholomorphic maps. We prove that for Anosov flows on smooth compact manifolds, the strong unstable (respectively, stable) distribution is integrable to complex manifolds, on which the flow acts holomorphically. Furthermore, assuming its complex dimension to be one, it is uniquely integrable to complex affine one-dimensional manifolds, each moreover affinely diffeomorphic to $\mathbb C$, on which the flow acts affinely. In this case, the weak stable (respectively, unstable) foliation is transversely holomorphic, and even transversely projective if the flow is assumed to be topologically transitive. By combining these facts in low dimensions, our main result is as follows : if a transversely holomorphic Anosov flow on a smooth compact five-dimensional manifold is topologically transitive, then it is either $C^\infty$-orbit equivalent to the suspension of a hyperbolic automorphism of a complex torus, or, up to finite covers, $C^\infty$-orbit equivalent to the geodesic flow of a compact hyperbolic manifold. - oai:arXiv.org:2505.06572v2 - math.DS - math.DG - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Mounib Abouanass + Georg Oberdieck - The Piatetski-Shapiro prime number theorem - https://arxiv.org/abs/2505.10391 - arXiv:2505.10391v2 Announce Type: replace -Abstract: The Piatetski-Shapiro sequences are of the form $\mathcal{N}_{c} := (\lfloor n^{c} \rfloor)_{n=1}^\infty$, where $\lfloor \cdot \rfloor$ is the integer part. It is expected that there are infinitely many primes in a Piatetski-Shapiro sequence for $c \in (1,2)$. In this article, we prove there are infinitely many Piatetski-Shapiro prime numbers for $1 < c < 1.1612\dots$ with an asymptotic formula. As a key idea, we prove a new bound for related type $I$ sum. - oai:arXiv.org:2505.10391v2 - math.NT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math-ph + math.AP + math.MP + math.SP + Wed, 10 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - Lingyu Guo, Victor Zhenyu guo, Li Lu + Matteo Capoferri, Dmitri Vassiliev - Weak solutions to the parabolic $p$-Laplace equation in a moving domain under a Neumann type boundary condition - https://arxiv.org/abs/2505.12598 - arXiv:2505.12598v3 Announce Type: replace -Abstract: This paper studies the parabolic $p$-Laplace equation with $p>2$ in a moving domain under a Neumann type boundary condition corresponding to the total mass conservation. We establish the existence and uniqueness of a weak solution by the Galerkin method in evolving Bochner spaces and a monotonicity argument. The main difficulty is in characterizing the weak limit of the nonlinear gradient term, where we need to deal with a term which comes from the boundary condition and cannot be absorbed into a monotone operator. To overcome this difficulty, we prove a uniform-in-time Friedrichs type inequality on a moving domain with time-dependent basis functions and make use of it to get the strong convergence of approximate solutions. We also show that the time derivative exists in the $L^2$ sense when given data have a better regularity. - oai:arXiv.org:2505.12598v3 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.AG + Wed, 10 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Tatsu-Hiko Miura + Abhinandan - Spectral Theorem for Self-Adjoint Partial Integral Operators in Kaplansky-Hilbert Modules - https://arxiv.org/abs/2505.14837 - arXiv:2505.14837v3 Announce Type: replace -Abstract: In this paper, a spectral theorem is proved for self-adjoint cyclically compact partial integral operators in the space of functions with mixed norm, which is a Kaplansky--Hilbert module. The decomposition through eigenfunctions, integral representation using orthogonal projectors, and functional calculus are established. The results generalize Mercer theorem for positive definite kernels. The proofs rely on the gluing of projector-valued measures, presented in separate lemmas. An example illustrates all assertions of the theorem for a specific kernel and function. - oai:arXiv.org:2505.14837v3 - math.FA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - K. Kudaybergenov, A. Arziev, P. Orinbaev + Mar\'ia In\'es de Frutos-Fern\'andez, Daniel Macias Castillo, Daniel Mart\'inez Marqu\'es - Hilbert $*$-categories: Where limits in analysis and category theory meet - https://arxiv.org/abs/2505.17432 - arXiv:2505.17432v4 Announce Type: replace -Abstract: This article introduces Hilbert $*$-categories: an abstraction of categories with similar algebraic and analytic properties to the categories of real, complex, and quaternionic Hilbert spaces and bounded linear maps. Other examples include categories of Hilbert W*-modules and of unitary group-representations. Hilbert $*$-categories are "analytically" complete in two ways: every bounded increasing sequence of Hermitian endomorphisms has a supremum, and every suitably bounded orthogonal family of parallel morphisms is summable. These "analytic" completeness properties are not assumed outright; rather, they are derived, respectively, from two new universal constructions: codirected $\ell^2$-limits of contractions and $\ell^2$-products. In turn, these are built from directed colimits in the wide subcategory of isometries. - oai:arXiv.org:2505.17432v4 - math.CT - math.FA - math.OA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + cs.IT + cs.AI + cs.LG + math.IT + Wed, 10 Dec 2025 00:00:00 -0500 replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Matthew Di Meglio, Chris Heunen + http://creativecommons.org/licenses/by-nc-sa/4.0/ + Mehdi Letafati, Samad Ali, Matti Latva-aho - Universal geometrical link invariants - https://arxiv.org/abs/2505.18108 - arXiv:2505.18108v2 Announce Type: replace -Abstract: We construct geometrically two universal link invariants: universal ADO invariant and universal Jones invariant, as limits of invariants given by graded intersections in configuration spaces. More specifically, for a fixed level $\mathscr N$, we define new link invariants: ``$\mathscr N^{th}$ Unified Jones invariant'' and ``$\mathscr N^{th}$ Unified Alexander invariant''. They globalise topologically all coloured Jones polynomials for links with multi-colours bounded by $\mathscr N$ and all ADO polynomials with bounded colours. These invariants both come from the same weighted Lagrangian intersection supported on configurations on arcs and ovals in the disc. - The question of providing a universal non semi-simple link invariant, recovering all the ADO polynomials was an open problem. A parallel question about semi-simple invariants for the case of knots is the subject of Habiro's famous universal knot invariant \cite{H3}. Habiro's universal construction is well defined for knots and can be extended just for certain classes of links. Our universal Jones link invariant is defined for any link and recovers all coloured Jones polynomials, providing a new semi-simple universal link invariant. The first non semi-simple universal link invariant that we construct unifies all ADO invariants for links, answering the open problem about the globalisation of these invariants. - oai:arXiv.org:2505.18108v2 - math.GT - math.RT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace - http://creativecommons.org/licenses/by/4.0/ - Cristina Ana-Maria Anghel + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Yumiharu Nakano - On low regularity well-posedness of the binormal flow - https://arxiv.org/abs/2505.23284 - arXiv:2505.23284v2 Announce Type: replace -Abstract: We focus on a class of solutions of the binormal flow, model of the evolution of vortex filaments, that generate several corner singularities in finite time. This phenomenon has been studied earlier in the regular case, which in this context is in terms of the summability of the angles of the corners generated. Our goal here is to investigate the lower regularity case, using further the Hasimoto approach that allows to use the 1D cubic nonlinear Schr\"odinger to study the binormal flow. We first obtain a deterministic result by proving an existence result for general binormal flow solutions at low regularity. Then we obtain improved results on the above class of solutions by a suitable randomization of the curvature and torsion of the vortex filament. To do so, we prove a scattering result for a quasi-invariance measure associated with a suitable 1D cubic nonlinear Schr\"odinger equation that we consider of independent interest. An interesting feature of this result is that we are able to identify a limit measure, which is usually not possible when working on quasi-invariant Gaussian measures for Hamiltonian PDEs on bounded domains. - oai:arXiv.org:2505.23284v2 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Valeria Banica, Renato Luc\`a, Nikolay Tzvetkov, Luis Vega + 10.2140/gt.2025.29.4469 + Geom. Topol. 29 (2025) 4469-4476 + J. Jelisiejew, M. Kool, R. F. Schmiermann - An additive two-level parallel variant of the DMRG algorithm with coarse-space correction - https://arxiv.org/abs/2505.23429 - arXiv:2505.23429v2 Announce Type: replace -Abstract: The density matrix renormalization group (DMRG) algorithm is a popular alternating minimization scheme for solving high-dimensional optimization problems in the tensor train format. Classical DMRG, however, is based on sequential minimization, which raises challenges in its implementation on parallel computing architectures. To overcome this, we propose a novel additive two-level DMRG algorithm that combines independent, local minimization steps with a global update step using a subsequent coarse-space minimization. Our proposed algorithm, which is directly inspired by additive Schwarz methods from the domain decomposition literature, is particularly amenable to implementation on parallel, distributed architectures since both the local minimization steps and the construction of the coarse-space can be performed in parallel. Numerical experiments on strongly correlated molecular systems demonstrate that the method achieves competitive convergence rates while achieving significant parallel speedups. - oai:arXiv.org:2505.23429v2 + 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 - Tue, 09 Dec 2025 00:00:00 -0500 + math.PR + Wed, 10 Dec 2025 00:00:00 -0500 replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Laura Grigori, Muhammad Hassan + http://creativecommons.org/licenses/by/4.0/ + James Foster, Andra\v{z} Jelin\v{c}i\v{c} - Principal minors of Fourier matrices of square-free order - https://arxiv.org/abs/2505.24326 - arXiv:2505.24326v3 Announce Type: replace -Abstract: Chebotarev's theorem on roots of unity states that all minors of a Fourier matrix are non-zero if and only if the order of the matrix is prime. We establish cases in which all principal minors of Fourier matrices of square-free order are non-zero. In a subsequent paper we discuss the case of composites containing squares. - oai:arXiv.org:2505.24326v3 - math.FA - math.NT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Andrei Caragea, Dae Gwan Lee, Romanos Malikiosis, Goetz E. Pfander + http://creativecommons.org/licenses/by/4.0/ + Javier F. Pena, Juan C. Vera, Luis F. Zuluaga - Detecting non-uniform patterns on high-dimensional hyperspheres - https://arxiv.org/abs/2506.00444 - arXiv:2506.00444v2 Announce Type: replace -Abstract: We propose a new probabilistic characterization of the uniform distribution on the hypersphere in terms of the distribution of inner products, extending the ideas of \citep{cuesta2009projection,cuesta2007sharp} in a data-driven manner. Using this characterization, we define a new distance that quantifies the deviation of an arbitrary distribution from uniformity. - As an application, we construct a novel nonparametric test for the problem of testing uniformity, namely the task of determining whether a set of \(n\) i.i.d.\ random points on the \(p\)-dimensional hypersphere is approximately uniformly distributed. The proposed test is asymptotically a Brownian bridge and it can detect any alternative lying outside a ball of radius \(1/n\) with respect to the proposed distance, in both high and low-dimensional settings. - We then prove a matching lower bound with respect to this distance and study its behavior when restricted to parametric models. In particular, we show that the minimax detection thresholds with respect to this distance coincide with the usual minimax thresholds in two important families: (i) the class of Fisher--von Mises--Langevin (FvML) alternatives, and (ii) a class of low-rank uniform distributions. Thus, the proposed test is optimal in these models. We also derive the limiting distributions of the test under the corresponding local alternatives. - As a byproduct of our analysis, we determine the detection threshold in the high-dimensional regime for testing the intrinsic dimension of the uniform distribution on $\mathbb{S}^{p-1}$; that is, for testing whether the distribution is uniformly supported on $\mathbb{S}^{p-1}$ against the alternative that it is uniformly distributed on \[ \mathbb{S}^{p-1} \cap H, \] for some $k$-dimensional linear subspace $H \subset \mathbb{R}^p$. - oai:arXiv.org:2506.00444v2 - math.ST - stat.TH - Tue, 09 Dec 2025 00:00:00 -0500 + 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://creativecommons.org/publicdomain/zero/1.0/ - Tiefeng Jiang, Tuan Pham + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Tom Benhamou - On the number of divisors of Mersenne numbers - https://arxiv.org/abs/2506.04883 - arXiv:2506.04883v3 Announce Type: replace -Abstract: Denote $f(n):=\sum_{1\le k\le n} \tau(2^k-1)$, where $\tau$ is the number of divisors function. Motivated by a question of Paul Erd\H{o}s, we show that the sequence of ratios $f(2n)/f(n)$ is unbounded. We also present conditional results on the divergence of this sequence to infinity. Finally, we test numerically both the conjecture $f(2n)/f(n)\to\infty$ and our sufficient conditions for it to hold. - oai:arXiv.org:2506.04883v3 - math.NT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.CV + math.MP + Wed, 10 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Vjekoslav Kova\v{c}, Florian Luca + 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 - Failure of Bott vanishing for (co)adjoint partial flag varieties - https://arxiv.org/abs/2506.09811 - arXiv:2506.09811v2 Announce Type: replace -Abstract: Bott vanishing is a strong vanishing result for the cohomology of exterior powers of the cotangent bundle twisted by ample line bundles. Buch-Thomsen-Lauritzen-Mehta conjectured that partial flag varieties (which are not products of projective spaces) do not satisfy Bott vanishing, despite all their other nice properties. The cominuscule case is an easy application of the Borel-Weil-Bott theorem, following results of Snow. We show that the (co)adjoint partial flag varieties of all classical and exceptional Dynkin types also do not satisfy Bott vanishing, thus confirming the conjecture for this class of varieties. - oai:arXiv.org:2506.09811v2 - math.AG - math.RT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace - http://creativecommons.org/licenses/by/4.0/ - Pieter Belmans + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Pascal Auscher (LMO, FAMSI), Cyril Imbert (DMA), Lukas Niebel - A Branch-and-Cut Algorithm for the Optimal Design of Parking Lots with One-way and Two-way Lanes - https://arxiv.org/abs/2506.09961 - arXiv:2506.09961v2 Announce Type: replace -Abstract: We address the problem of maximizing the number of stalls in parking lots where vehicles park perpendicular to the driveways. Building on recent research on two-way driving lanes, we first formulate a mixed integer program to maximize the number of parking stalls using a flow-based approach. Parking lots are rasterized into a grid, and the proposed MIP model optimizes them in a generic manner, adapting to the grid resolution and stall size without requiring custom formulations. The constraints ensure the connectivity of parking stalls and driveways to the entrance/exit. This formulation is then extended to the case of one-way driving lanes. We then propose valid inequalities and a branch-and-cut algorithm for the one-way and two-way lane configurations. This approach eliminates flow variables, big-M type constraints, and improves solution times for medium-sized instances. The effectiveness of the suggested models is showcased on 325 parking lots from New York City. For instances in which the flow version could be solved in 15 minutes, the branch-and-cut algorithm improved the median runtimes by 87.43% for the one-way case and by 79.36% for the two-way case and resulted in better optimality gaps for the other instances, compared to the baseline flow-based formulation. Similar advantages were observed when run with a time budget of two hours. One-way configurations accommodated, on average, 18.63% more vehicles on average than their two-way counterparts across all instances. Modifications to the proposed formulations that consider the turning characteristics of vehicles and the presence of multiple entrances and exits are also examined. - oai:arXiv.org:2506.09961v2 - math.OC - cs.DM - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace - http://creativecommons.org/licenses/by/4.0/ - Helen Thomas, Tarun Rambha + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Fernando Argentieri, Livia Corsi - IG-PINNs: Interface-gated physics-informed neural networks for solving elliptic interface problems - https://arxiv.org/abs/2506.18332 - arXiv:2506.18332v2 Announce Type: replace -Abstract: In this work, we develop interface-gated physics-informed neural networks (IG-PINNs) to solve elliptic interface equations. In IG-PINNs, we use a fully connected neural network to capture the smooth behavior across the entire domain. In each subdomain separated by the interface, an interface-gated network is utilized to provide corrections at the interface. In the architectural design of the interface-gated network, we introduce a gating mechanism and a level-set function derived from the interface. This design enables the interface-gated network to effectively handle discontinuous jumps across the interface. Some numerical experiments have confirmed the effectiveness of the IG-PINNs, demonstrating higher accuracy compared with PINNs, interface PINNs (I-PINNs) and multi-domain PINNs (M-PINNs). - oai:arXiv.org:2506.18332v2 + 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 - Tue, 09 Dec 2025 00:00:00 -0500 + math.PR + Wed, 10 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - Jiachun Zheng, Yunqing Huang, Nianyu Yi - - - On Fico's Lemmata and the Homotopy Type of Certain Gyrations - https://arxiv.org/abs/2506.18893 - arXiv:2506.18893v2 Announce Type: replace -Abstract: We undertake to determine the homotopy type of gyrations of sphere products and of connected sums, thereby generalising results known in earlier literature as ''Fico's Lemmata'' which underpin gyrations in their original formulation from geometric topology. We provide applications arising from recasting these results into the modern homotopy theoretic setting. - oai:arXiv.org:2506.18893v2 - math.AT - math.GT - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Sebastian Chenery + B. Leimkuhler, A. Sharma, M. V. Tretyakov - Nonlinear Power Amplifier-Resilient Cell-Free Massive MIMO: A Joint Optimization Approach - https://arxiv.org/abs/2506.22094 - arXiv:2506.22094v2 Announce Type: replace -Abstract: This letter analyzes the effects of power amplifiers (PAs) on the downlink of cell-free massive MIMO systems. We model signal transmission incorporating nonlinear PA distortion and derive a unified spectral efficiency (SE) expression applicable to arbitrary precoding schemes. To combat PA-induced performance degradation, a joint optimization approach for user association and max-min power control is proposed. Furthermore, a low-complexity alternative is developed to approximate the joint optimization with reduced computational overhead. Simulations validate the analysis and demonstrate significant performance gains of the proposed approaches over conventional techniques. - oai:arXiv.org:2506.22094v2 - cs.IT - eess.SP - math.IT - Tue, 09 Dec 2025 00:00:00 -0500 + 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-nc-nd/4.0/ - Wei Jiang, Hans D. Schotten + http://creativecommons.org/licenses/by/4.0/ + Harbir Antil, Sean P. Carney, Hugo D\'iaz, Johannes O. Royset - Joint equidistributions of mesh patterns 123 and 132 with minus antipodal shadings - https://arxiv.org/abs/2506.23148 - arXiv:2506.23148v3 Announce Type: replace -Abstract: The study of joint equidistributions of mesh patterns 123 and 132 with the same symmetric shadings was recently initiated by Kitaev and Lv, where 75 of 80 potential joint equidistributions were proven. In this paper, we prove 112 out of 126 potential joint equidistributions of mesh patterns 123 and 132 with the same minus antipodal shadings. As a byproduct, we present 562 joint equidistribution results for non-symmetric and non-minus-antipodal shadings. To achieve this, we construct bijections, find recurrence relations, and obtain generating functions. Moreover, we demonstrate that the joint distributions of several pairs of mesh patterns are related to the unsigned Stirling numbers of the first kind. - oai:arXiv.org:2506.23148v3 - math.CO - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace - http://creativecommons.org/licenses/by/4.0/ - Shuzhen Lv, Philip B. Zhang + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Yann Issartel, Christophe Giraud, Nicolas Verzelen - Cauchy Data for 1D singular Schr\"odinger operators - https://arxiv.org/abs/2507.05772 - arXiv:2507.05772v2 Announce Type: replace -Abstract: We study semiclassical 1-D Schr\"odinger operators of the form $Pu = -h^2 u'' \,+\,x^\gamma W(x) u$ on a finite interval $[0,b]$ for $0 < \gamma \in \mathbb{R} \setminus \mathbb{Q}$. We show that that the WKB expansions of solution can be extended on $[h^{1-\epsilon},b]$, for any $\epsilon>0$. Using a different approximation near $0$ and a matching procedure, we obtain the Cauchy Data at $0$ of such WKB solutions. This allows us to derive singular Bohr-Sommerfeld rules. We also pay special attention to uniformity in $W$ for our expansions. - oai:arXiv.org:2507.05772v2 - math-ph - math.CA - math.MP + 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 - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Luc Hillairet, Jeremy L. Marzuola + http://creativecommons.org/licenses/by/4.0/ + Jean-Claude Cuenin - - Invariant Hilbert spaces of distribution vectors in Lie group representations - https://arxiv.org/abs/2507.05988 - arXiv:2507.05988v2 Announce Type: replace -Abstract: For every unitary irreducible representation of a Lie group we prove that the representation Hilbert space is the only nonzero invariant Hilbert space of distribution vectors. - oai:arXiv.org:2507.05988v2 - math.RT - math.FA - Tue, 09 Dec 2025 00:00:00 -0500 + + 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 + math.NT + Wed, 10 Dec 2025 00:00:00 -0500 replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Ingrid Beltita, Daniel Beltita + http://creativecommons.org/licenses/by/4.0/ + Mounir Hajli - Fredholm Neural Networks for forward and inverse problems in elliptic PDEs - https://arxiv.org/abs/2507.06038 - arXiv:2507.06038v3 Announce Type: replace -Abstract: Building on our previous work introducing Fredholm Neural Networks (Fredholm NNs/ FNNs) for solving integral equations, we extend the framework to tackle forward and inverse problems for linear and semi-linear elliptic partial differential equations. The proposed scheme consists of a deep neural network (DNN) which is designed to represent the iterative process of fixed-point iterations for the solution of elliptic PDEs using the boundary integral method within the framework of potential theory. The number of layers, weights, biases and hyperparameters are computed in an explainable manner based on the iterative scheme, and we therefore refer to this as the Potential Fredholm Neural Network (PFNN). We show that this approach ensures both accuracy and explainability, achieving small errors in the interior of the domain, and near machine-precision on the boundary. We provide a constructive proof for the consistency of the scheme and provide explicit error bounds for both the interior and boundary of the domain, reflected in the layers of the PFNN. These error bounds depend on the approximation of the boundary function and the integral discretization scheme, both of which directly correspond to components of the Fredholm NN architecture. In this way, we provide an explainable scheme that explicitly respects the boundary conditions. We assess the performance of the proposed scheme for the solution of both the forward and inverse problem for linear and semi-linear elliptic PDEs in two dimensions. - oai:arXiv.org:2507.06038v3 - math.NA - cs.LG - cs.NA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.AP + math-ph + math.MP + Wed, 10 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Kyriakos Georgiou, Constantinos Siettos, Athanasios N. Yannacopoulos + Roland Donninger, Birgit Sch\"orkhuber - Multiscale Approximation as a Bias-Reducing Strategy for Manifold-Valued Functions - https://arxiv.org/abs/2507.06707 - arXiv:2507.06707v2 Announce Type: replace -Abstract: We study the bias-variance tradeoff within a multiscale approximation framework. Our approach utilizes a given quasi-approximation operator that is repeatedly applied in an error-correction scheme over a hierarchical data structure. We introduce a new bias measure, the bias ratio, to quantitatively assess the improvements afforded by multiscale approximations and demonstrate that this strategy effectively reduces the bias component of the approximation error, thereby providing a more flexible and robust framework for addressing scattered-data approximation problems. Our findings exhibit consistent bias decay across various scenarios, including applications to manifold-valued functions. - oai:arXiv.org:2507.06707v2 - math.NA - cs.NA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.FA + Wed, 10 Dec 2025 00:00:00 -0500 replace - http://creativecommons.org/licenses/by/4.0/ - Asaf Abas, Nir Sharon + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Ignacio Vergara - Restricted graph Lie algebras in even characteristic - https://arxiv.org/abs/2507.07627 - arXiv:2507.07627v3 Announce Type: replace -Abstract: We investigate restricted Lie algebras arising as analogues of (twisted) right-angled Artin groups and right-angled Coxeter groups over fields of characteristic two. These algebras are defined via quadratic relations determined by decorated graphs. We compute their cohomology rings with trivial coefficients and uncover phenomena specific to characteristic two: unlike in zero/odd characteristics, where quadratically defined ordinary and restricted Lie algebras have equivalent cohomology theories, the characteristic two case exhibits dependence on the base field. In particular, we prove that the ground field being the prime field $\mathbb F_2$ characterizes when a Lie-theoretic analogue of the twisted Droms theorem holds. Generalizations of graph Lie algebras are also discussed. - oai:arXiv.org:2507.07627v3 - math.RA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace http://creativecommons.org/licenses/by/4.0/ - Simone Blumer + Bernhard Heim und Markus Neuhauser - Branching space of multipointed d-space - https://arxiv.org/abs/2507.08377 - arXiv:2507.08377v3 Announce Type: replace -Abstract: Using the notion of short directed path, we introduce the branching space of a multipointed $d$-space. We prove that for any q-cofibrant multipointed $d$-space, it is homeomorphic to the branching space of the q-cofibrant flow obtained by applying the categorization functor. As an application, we deduce a purely topological proof of the invariance of the branching space and of the branching homology of cellular multipointed $d$-spaces up to globular subdivision. By reversing the time direction, the same results are obtained for the merging space and the merging homology. - oai:arXiv.org:2507.08377v3 - math.AT - math.CT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Philippe Gaucher + V. N. Berestovskii, Yu. G. Nikonorov - Stochastic Approximation with Block Coordinate Optimal Stepsizes - https://arxiv.org/abs/2507.08963 - arXiv:2507.08963v2 Announce Type: replace -Abstract: We consider stochastic approximation with block-coordinate stepsizes and propose adaptive stepsize rules that aim to minimize the expected distance from the next iterate to an (unknown) target point. These stepsize rules employ online estimates of the second moment of the search direction along each block coordinate. The popular Adam algorithm can be interpreted as a variant with a specific estimator. By leveraging a simple conditional estimator, we derive a new method that obtains competitive performance against Adam but requires less memory and fewer hyper-parameters. We prove that this family of methods converges almost surely to a small neighborhood of the target point, and the radius of the neighborhood depends on the bias and variance of the second-moment estimator. Our analysis relies on a simple aiming condition that assumes neither convexity nor smoothness, thus has broad applicability. - oai:arXiv.org:2507.08963v2 - math.OC - cs.LG - stat.ML - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Tao Jiang, Lin Xiao + Harris Daniels, Jeremy Rouse - Ramsey numbers for sparse graphs versus path or cycle - https://arxiv.org/abs/2507.11835 - arXiv:2507.11835v3 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 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 $n=\Omega(k)$. The lower bounds $n=\Omega(k)$ are tight up to a constant factor. - oai:arXiv.org:2507.11835v3 - math.CO - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.DS + math.GT + Wed, 10 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Chunchao Fan, Qizhong Lin + David Aulicino, Aaron Calderon, Carlos Matheus, Nick Salter, Martin Schmoll - Link Bundles of Compact Toric Varieties of Real Dimension 8 - https://arxiv.org/abs/2507.12309 - arXiv:2507.12309v2 Announce Type: replace -Abstract: The main goal of this work is to determine the Betti numbers of the links of isolated singularities in a compact toric variety of real dimension 8, using the CW-structure of the links. Additionally, we construct the intersection spaces associated with these links. Using the duality of the Betti numbers of intersection spaces, we conclude that, similar to the case of toric varieties of real dimension 6, the Betti numbers of the links contain only one non-combinatorial invariant parameter. In the final section, we extend our discussion to arbitrary compact toric varieties and their associated link bundles. We show that for any given link $\mathcal{L}$, there exists a fiber bundle $\pi: \mathcal{L} \to X$ with fiber $S^{1}$, where the base space $X$ is a compact toric variety. Furthermore, using the Chern-Spanier exact sequences for sphere bundles, we show that for the fiber bundle $\pi:\mathcal{L}\longrightarrow X$, where $\dim_{\mathbb{R}}(X)=6$, the non-combinatorial invariant parameters appearing in the Betti numbers of $\mathcal{L}$ and $X$ are equal. In addition, we provide an algebraic description of the non-combinatorial invariant parameter of $X$ in terms of the cohomological Euler class of the fiber bundle. - oai:arXiv.org:2507.12309v2 - math.AT - Tue, 09 Dec 2025 00:00:00 -0500 + 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/ - Shahryar Ghaed Sharaf + Andrei Bud - Topology and Algebra of Bonded Knots and Braids - https://arxiv.org/abs/2507.15086 - arXiv:2507.15086v4 Announce Type: replace -Abstract: In this paper we present a detailed study of \emph{bonded knots} and their related structures, integrating recent developments into a single framework. Bonded knots are classical knots endowed with embedded bonding arcs modeling physical or chemical bonds. We consider bonded knots in three categories (long, standard, and tight) according to the type of bonds, and in two categories, topological vertex and rigid vertex, according to the allowed isotopy moves, and we define invariants for each category. We then develop the theory of \emph{bonded braids}, the algebraic counterpart of bonded knots. We define the {\it bonded braid monoid}, with its generators and relations, and formulate the analogues of the Alexander and Markov theorems for bonded braids, including an $L$-equivalence for bonded braids. Next, we introduce \emph{enhanced bonded knots and braids}, incorporating two types of bonds (attracting and repelling) corresponding to different interactions. We define the enhanced bonded braid group and show how the bonded braid monoid embeds into this group. Finally, we study \emph{bonded knotoids}, which are open knot diagrams with bonds, and their closure operations, and we define the \emph{bonded closure}. We introduce \emph{bonded braidoids} as the algebraic counterpart of bonded knotoids. These models capture the topology of open chains with inter and intra-chain bonds and suggest new invariants for classifying biological macromolecules. - oai:arXiv.org:2507.15086v4 - math.GT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace - http://creativecommons.org/licenses/by/4.0/ - 10.3390/math13203260 - Mathematics. 2025; 13(20):3260 - Ioannis Diamantis, Louis H. Kauffman, Sofia Lambropoulou + http://creativecommons.org/licenses/by-nc-sa/4.0/ + Guillermo Pineda-Villavicencio, Aholiab Tritama, Jie Wang, David Yost - Skew braces, near-rings, skew rings, dirings - https://arxiv.org/abs/2507.22182 - arXiv:2507.22182v2 Announce Type: replace -Abstract: We introduce a new point of view to present classical notions related to set-theoretic solutions of the Yang-Baxter equation: left skew braces, dirings, left skew rings. The idea is to replace the single multiplication on a left near-ring by two operations, one associative and the other left distributive. Two algebraic structures naturally appear: left skew rings and left weak rings, whose categories turn out to be canonically isomorphic. - oai:arXiv.org:2507.22182v2 - math.RA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Alberto Facchini + Pengfei Huang, Yichen Qin, Hao Sun - Invariants for isomorphism classes in the category $\bcalNT$ - https://arxiv.org/abs/2508.00084 - arXiv:2508.00084v2 Announce Type: replace -Abstract: The category $\bcalNT$ is a category of certain commutative graded algebras over a field. It was introduced in \cite{Lobos2} as a generalization of algebras generated by Jucys-Murphy elements in the many \textbf{End} algebras of the diagrammatic Soergel category of Elias and Williamson. In the first part of this article we define certain \emph{Invariants} for the isomorphism classes in $\bcalNT,$ following in the same spirit of \cite{Lobos3}, where a series of \emph{Isomorphism criteria} were found. At the end, we use our invariants to provide a new lower bound for the number of isomorphism classes, improving a similar result obtained in \cite{Lobos3}. - oai:arXiv.org:2508.00084v2 - math.AC - math.RT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Diego Lobos Maturana + http://creativecommons.org/licenses/by/4.0/ + Sebasti\'an Donoso, Andreas Koutsogiannis, Borys Kuca, Wenbo Sun, Konstantinos Tsinas - The Space of Dirac-Minimal Metrics is Connected in Dimensions 2 and 4 - https://arxiv.org/abs/2508.01420 - arXiv:2508.01420v2 Announce Type: replace -Abstract: Let $M$ be a closed connected spin manifold. Index theory provides a topological lower bound on the dimension of the kernel of the Dirac operator which depends on the choice of Riemannian metric. Riemannian metrics for which this bound is attained are called Dirac-minimal. We show that the space of Dirac-minimal metrics on $M$ is connected if $M$ is of dimension 2 or 4. - oai:arXiv.org:2508.01420v2 + 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 - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - 10.3842/SIGMA.2025.102 - SIGMA 21 (2025), 102, 18 pages - Bernd Ammann, Mattias Dahl + Bernardo Carvalho - Non-negative polynomials without hyperbolic certificates of non-negativity - https://arxiv.org/abs/2508.04027 - arXiv:2508.04027v2 Announce Type: replace -Abstract: In this paper we study the relationship between the set of all non-negative multivariate homogeneous polynomials and those, which we call hyperwrons, whose non-negativity can be deduced from an identity involving the Wronskians of hyperbolic polynomials. We give a sufficient condition on positive integers $m$ and $2y$ such that there are non-negative polynomials of degree $2y$ in $m$ variables that are not hyperwrons. Furthermore, we give an explicit example of a non-negative quartic form that is not a sum of hyperwrons. We partially extend our results to hyperzouts, which are polynomials whose non-negativity can be deduced from an identity involving the B\'ezoutians of hyperbolic polynomials. - oai:arXiv.org:2508.04027v2 - math.OC + 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 - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - H. L. Brian Ng, James Saunderson + Andrei Bud, Dawei Chen, Martin M\"oller - Inner models from extended logics and the Delta-operation - https://arxiv.org/abs/2508.07892 - arXiv:2508.07892v2 Announce Type: replace -Abstract: If $\mathcal{L}$ is an abstract logic (a.k.a. model theoretic logic), we can define the inner model $C(\mathcal{L})$ by replacing first order logic with $\mathcal{L}$ in G\"odel's definition of the inner model $L$ of constructible sets. Set theoretic properties of such inner models $C(\mathcal{L})$ have been investigated recently and a spectrum of new inner models is emerging between $L$ and $\mathrm{HOD}$. The topic of this paper is the effect on $C(\mathcal{L})$ of a slight modification of $\mathcal{L}$ i.e. how sensitive is $C(\mathcal{L})$ on the exact definition of $\mathcal{L}$? The $\Delta$-extension $\Delta(\mathcal{L})$ of a logic is generally considered a "mild" extension of $\mathcal{L}$. We give examples of logics $\mathcal{L}$ for which the inner model $C(\mathcal{L})$ is consistently strictly smaller than the inner model $C(\Delta(\mathcal{L}))$, and in one case we show this follows from the existence of $0^{\sharp}$. - oai:arXiv.org:2508.07892v2 - math.LO - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.PR + Wed, 10 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jouko V\"a\"an\"anen, Ur Ya'ar + Shiping Cao, Zhen-Qing Chen - The Multivariate Taylor Measure Function Space and a Generalization of Taylor's Theorem - https://arxiv.org/abs/2508.10662 - arXiv:2508.10662v2 Announce Type: replace -Abstract: Using the recently defined concept of Taylor measures, we propose a generalization of Taylor's theorem to measurable, non-analytic functions, that do not require differentiation. We study consequences of the generalization, including the definition and properties of a new space of functions, which will be called multivariate Taylor measure function space. The proposed generalization emerges as a unifying framework that includes many concepts from mathematics as special cases. - oai:arXiv.org:2508.10662v2 - math.FA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Athanasios Christou Micheas + Stephan Mescher, Maximilian Stegemeyer - Standard conjecture D and some conjectures around Weil's Riemann hypothesis - https://arxiv.org/abs/2508.13882 - arXiv:2508.13882v5 Announce Type: replace -Abstract: Let $X$ be a smooth projective variety defined on a finite field $\mathbb{F}_q$. On $X$ there is a special morphism $Fr_X$, which raises coordinates to exponent $q$: $t\mapsto t^q$. The two main results in this paper are: - Result 1: If Standard conjecture D holds (for algebraic cycles of dimension $=\dim (X)$) on $X\times X$, then all polarised endomorphisms on $X$ are semisimple. - Result 2: We provide heuristic arguments to show that Standard Conjecture D should imply both Dynamical degree comparison conjecture (a generalisation of both Weil's Riemann hypothesis and Tate's question on the absolute value of the eigenvalues of polarised endomorphisms), Norm comparison conjecture (allowing to bound the growth of the pullback of iterations of an endomorphism on cohomology groups in terms of that on algebraic cycles, in particularly implying the semisimplicity of polarised endomorphisms), and Conjecture $G_r$ (which together with Standard conjecture D imply the previous mentioned two conjectures), proposed in previous works by Fei Hu and the author. The heuristic argument relies on the possibility of defining the self-composition $Fr_X^s$ in a good way, where $s$ is an arbitrary rational number (allowed to be negative), and similarly for another object related to the Frobenius morphism. - oai:arXiv.org:2508.13882v5 + 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 - math.AG - math.SP - Tue, 09 Dec 2025 00:00:00 -0500 + cs.SY + eess.SY + math.OC + Wed, 10 Dec 2025 00:00:00 -0500 replace - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Tuyen Trung Truong + http://creativecommons.org/licenses/by/4.0/ + Wouter Jongeneel - Bekka's $(c)$-regularity condition and families of line singularities with constant L\^e numbers - https://arxiv.org/abs/2508.14545 - arXiv:2508.14545v2 Announce Type: replace -Abstract: We show that the natural stratifications arising from certain deformation families of line singularities with constant L\^e numbers satisfy Bekka's $(c)$-regularity condition. As a corollary, we obtain that these families are topologically equisingular. Similar results for families of isolated singularities were established by Abderrahmane. - oai:arXiv.org:2508.14545v2 - math.AG - Tue, 09 Dec 2025 00:00:00 -0500 + 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/ - Christophe Eyral, \"Oznur Turhan + Riccardo Cristoferi, Gabriele Fissore, Marco Morandotti - Branching space of precubical set - https://arxiv.org/abs/2508.14839 - arXiv:2508.14839v3 Announce Type: replace -Abstract: Using the notion of short natural directed path, we introduce the homotopy branching space of a precubical set. It is unique only up to homotopy equivalence. We prove that, for any precubical set, it is homotopy equivalent to the branching space of any q-realization, any m-realization and any h-realization of the precubical set as a flow. As an application, we deduce the invariance of the homotopy branching space and of the branching homology up to cubical subdivision. By reversing the time direction, the same results are obtained for the merging space and the merging homology of a precubical set. - oai:arXiv.org:2508.14839v3 - math.AT - math.CT - Tue, 09 Dec 2025 00:00:00 -0500 + 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/ - Philippe Gaucher + Tom Benhamou, Gabriel Goldberg - Involutive and minimal generating sets of Extended Special Linear group $ES{L_3}(\mathbb{Z})$, $ES{L_2}(\mathbb{Z})$ and formulas of roots in GL$_2$($\mathbb{F}_p$), GL$_2(\mathbb{Z})$ and SL$_3(\mathbb{Z})$ \, \, \, \RomanNumeralCaps{2} - https://arxiv.org/abs/2508.15399 - arXiv:2508.15399v3 Announce Type: replace -Abstract: In this research we continue our previous investigation of wreath product normal structure \cite{SkuESL}. We generalize the group of unimodular matrices \cite{Amit} and find its structure. For this goal we propose one extension of the special linear group. Groups generated by three involutions, two of which are permutable, have long been of interest in the theory of matrix groups \cite{Maz}, for instance such generating set was researched for $S{{L}_{2}}({{\mathbb{Z}+ i\mathbb{Z}}})$. But for size of matrix 3 on 3 this is imposable for some groups. We research this question for $ES{{L}_{3}}({{\mathbb{Z}}})$. An analytical formula of root in $SL(3, \mathbb{Z}$) is found, recursive formula for $n$-th power root in $SL(2, \mathbb{Z}$) is found too. - oai:arXiv.org:2508.15399v3 - math.GR - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.CO + Wed, 10 Dec 2025 00:00:00 -0500 replace - http://creativecommons.org/publicdomain/zero/1.0/ - R. V. Skuratovskii + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Honggang Zhao, Eminjan Sabir, Cheng-Kuan Lin - Transcendency of variants of Mills' constant - https://arxiv.org/abs/2508.16068 - arXiv:2508.16068v3 Announce Type: replace -Abstract: Let $\lfloor x\rfloor$ denote the integer part of $x$. For every sequence $(C_k)_{k\ge 1}$ of positive integers, we define $\xi(C_k)$ as the smallest real number $\xi>1$ such that $\lfloor \xi^{C_k} \rfloor$ is a prime number for every positive integer $k$. The number $\xi(3^k)$ is called Mills' constant. Recently, the author showed that $\xi(3^k)$ is irrational; however, the transcendency remains open. In this paper, we show that Mills' constant is transcendental under the Density Hypothesis of the Riemann zeta function. Furthermore, we obtain four classes of sequences $(C_k)_{k\ge 1}$ for which we can verify the arithmetic properties of $\xi(C_k)$. For simplicity, we give four representative examples belonging to each class: (A) $\xi(\lfloor b^k\rfloor)$ is irrational for every real number $b\ge 1+\sqrt{2}$; (B) $\xi((1+\sqrt{2})^k+(1-\sqrt{2})^k)$ is transcendental; (C) $\xi(r3^k-1)$ is transcendental for every integer $r\ge 4.003\times 10^{14}$; (D) $\xi(3^{k-\lfloor (\log k)^{1/2} \rfloor}2^{\lfloor (\log k)^{1/2}\rfloor})$ is transcendental. - oai:arXiv.org:2508.16068v3 - math.NT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + replace + http://creativecommons.org/licenses/by/4.0/ + Krist\'of B\'erczi, Tam\'as Kir\'aly, Yutaro Yamaguchi, Yu Yokoi + + + 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 + replace + http://creativecommons.org/licenses/by/4.0/ + Philippe Gagnon + + + 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 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Kota Saito + Aaron Chan, Osamu Iyama, Rene Marczinzik - A new class of regularized preconditioners for double saddle-point problems - https://arxiv.org/abs/2508.19469 - arXiv:2508.19469v2 Announce Type: replace -Abstract: The block structure of double saddle-point problems has prompted extensive research into efficient preconditioners. This paper introduces a novel class of three-by-three block preconditioners tailored for such systems from the time-dependent Maxwell equations or liquid crystal director modeling. The main motivation of this work is to highlight the limitations of recent preconditioners under high Reynolds numbers, as the original studies did not explore this scenario, and to demonstrate that our preconditioner outperforms the existing ones in such regimes. We thoroughly analyze the convergence and spectral properties of the proposed preocnditioner. We illustrate the efficiency of the proposed preconditioners, and verify the theoretical bounds. - oai:arXiv.org:2508.19469v2 - math.NA + 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 - Tue, 09 Dec 2025 00:00:00 -0500 + math.NA + Wed, 10 Dec 2025 00:00:00 -0500 replace - http://creativecommons.org/publicdomain/zero/1.0/ - Achraf Badahmane + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + A. Martina Neuman, Andres Felipe Lerma Pineda, Jason J. Bramburger, Simone Brugiapaglia - Superoptimal continued fractions - https://arxiv.org/abs/2508.19743 - arXiv:2508.19743v2 Announce Type: replace -Abstract: Motivated by the optimal continued fractions studied independently by Selenius and Bosma, we define and introduce algorithms producing superoptimal continued fraction expansions of irrationals. The convergents of these expansions simultaneously provide arbitrarily good rational approximations and converge arbitrarily quickly. - oai:arXiv.org:2508.19743v2 - math.NT - math.DS - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace - http://creativecommons.org/licenses/by/4.0/ - Slade Sanderson + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Guille Carri\'on Santiago, Ram\'on Flores, J\'er\^ome Scherer - Plenitudinous Urelements and the Definability of Cardinality - https://arxiv.org/abs/2508.20641 - arXiv:2508.20641v2 Announce Type: replace -Abstract: The Axiom of Plenitude asserts that every ordinal is equinumerous with a set of urelements, while its stronger form, Plenitude$^+$, extends it to all sets. We investigate these two axioms within ZF set theory with urelements. Assuming that cardinality is definable, Plenitude$^+$ together with the Collection Principle implies the Reflection Principle. If either cardinality is representable or Small Violations of Choice (SVC) holds, Plenitude$^+$ implies the Reflection Principle. In contrast, Plenitude is considerably weaker: SVC + Plenitude does not prove the Collection Principle, and SVC + Plenitude + Reflection Principle does not prove Plenitude$^+$. - oai:arXiv.org:2508.20641v2 - math.LO - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Bokai Yao + http://creativecommons.org/licenses/by/4.0/ + Andreas Cap - Scattering norm estimate near the threshold for the energy-subcritical NLS - https://arxiv.org/abs/2509.01505 - arXiv:2509.01505v2 Announce Type: replace -Abstract: We consider the focusing energy-subcritical Schr\"odinger equations. In earlier works by Holmer-Roudenko \cite{holmer}, Duyckaerts-Holmer-Roudenko \cite{duyckaerts2}, Akahori-Nawa \cite{akahori}, Fang-Xie-Cazenave \cite{fang}, Guevara \cite{guevara} and later by Dodson-Murphy \cite{dodson1,dodson2} and Arora-Dodson-Murphy \cite{arora}, they proved that scattering is the only dynamical behavior if the $H^1$ initial data satisfies $M(u_0)^{(1-s_c)/s_c}E(u_0)<M(Q)^{(1-s_c)/s_c}E(Q)$ and $\| u\|^{(1-s_c)/s_c}_{L^2}\| u\|_{\dot{H}^1}<\| Q\|^{(1-s_c)/s_c}_{L^2}\|Q\|_{\dot{H}^1}$, where $Q$ is the ground state. In this paper, we establish asymptotic estimates for the upper bound of the scattering norms as $M(u_0)^{(1-s_c)/s_c}E(u_0)$ approaches the threshold mass-energy threshold $M(Q)^{(1-s_c)/s_c}E(Q)$, which generalizes the work of Duyckaerts-Merle \cite{duyckaerts} on the energy-critical Schr\"odinger equation($s_c=1$). - oai:arXiv.org:2509.01505v2 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Zuyu Ma + Jonathan Leake, Kasper Lindberg, Shayan Oveis Gharan - Long memory score-driven models as approximations for rough Ornstein-Uhlenbeck processes - https://arxiv.org/abs/2509.09105 - arXiv:2509.09105v2 Announce Type: replace -Abstract: This paper investigates the continuous-time limit of score-driven models with long memory. By extending score-driven models to incorporate infinite-lag structures with coefficients exhibiting heavy-tailed decay, we establish their weak convergence, under appropriate scaling, to fractional Ornstein-Uhlenbeck processes with Hurst parameter $H < 1/2$. When score-driven models are used to characterize the dynamics of volatility, they serve as discrete-time approximations for rough volatility. We present several examples, including EGARCH($\infty$) whose limits give rise to a new class of rough volatility models. Building on this framework, we carry out numerical simulations and option pricing analyses, offering new tools for rough volatility modeling and simulation. - oai:arXiv.org:2509.09105v2 - math.PR - q-fin.MF - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Yinhao Wu, Ping He + 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 - Witt Groups and Bulk-Boundary Correspondence for Stabilizer States - https://arxiv.org/abs/2509.10418 - arXiv:2509.10418v2 Announce Type: replace -Abstract: We establish a bulk--boundary correspondence for translation-invariant stabilizer states in arbitrary spatial dimension, formulated in the framework of modules over Laurent polynomial rings. To each stabilizer state restricted to half-space geometry we associate a boundary operator module. Boundary operator modules provide examples of quasi-symplectic modules, which are objects of independent mathematical interest. In their study, we use ideas from algebraic L-theory in a setting involving non-projective modules and non-unimodular forms. Our results about quasi-symplectic modules in one spatial dimension allow us to resolve the conjecture that every stabilizer state in two dimensions is characterized by a corresponding abelian anyon model with gappable boundary. Our techniques are also applicable beyond two dimensions, such as in the study of fractons. - oai:arXiv.org:2509.10418v2 + 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 - cond-mat.str-el - math.AC math.MP - quant-ph - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - B{\l}a\.zej Ruba, Bowen Yang + Pierre Yves Gaudreau Lamarre - Brownian motion on the Fubini extension space and applications - https://arxiv.org/abs/2509.12096 - arXiv:2509.12096v2 Announce Type: replace -Abstract: We study a family of essentially pairwise independent Brownian motions indexed by a continuum of labels and show how the Fubini extension framework provides a rigorous way to represent such families as a single jointly measurable process. Within this framework, we address two main objectives: first, we show how a system of graphon stochastic differential equations can be reformulated as a single McKean-Vlasov type equation driven by a standard Brownian motion, which significantly facilitates its analysis. Second, we establish a Girsanov theorem for a continuum of essentially pairwise independent Brownian motions. - oai:arXiv.org:2509.12096v2 - math.PR - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Hamed Amini, Nina H. Amini, Sofiane Chalal, Gaoyue Guo + Remi A. Chou - Atoms meet symbols - https://arxiv.org/abs/2509.15831 - arXiv:2509.15831v3 Announce Type: replace -Abstract: This paper introduces a novel framework for constructing invariants in $G$-equivariant birational geometry by unifying two recent approaches: the theory of atoms recently developed by Katzarkov, Kontsevich, Pantev, and Yu, and the theory of modular symbols due to Kontsevich, Tschinkel, and Pestun. - We initiate the theory of Chen-Ruan atoms. Assuming the blowup formula for the quantum Chen-Ruan cohomology, we outline how to extend the theory of atoms to global quotient orbifolds and present some striking applications. - In addition, we develop a separate class of purely geometric invariants for $\mathbb{Z}/2$- and $\mathbb{Z}/3$-actions on surfaces and threefolds. - We provide many examples of non-$G$-linearizable $G$-actions on projective varieties treated with these new techniques. - oai:arXiv.org:2509.15831v3 - math.AG + 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 - math.SG - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - Leonardo F. Cavenaghi, Ludmil Katzarkov, Maxim Kontsevich + 10.1016/j.jmaa.2025.130324 + J. Math. Anal. Appl., Vol 557 (2), 2026 + Aritra Bhowmick, Jin-ichi Itoh, Sachchidanand Prasad - Calabi-Yau locally conformally K\"ahler manifolds - https://arxiv.org/abs/2509.18364 - arXiv:2509.18364v2 Announce Type: replace -Abstract: We study compact locally conformally K\"ahler (lcK) manifolds which are Calabi--Yau, in the sense that $c_1^{BC}(X)=0$. First of all, we prove that all the known lcK manifolds which are Calabi--Yau are Vaisman. Then we prove that an lcK Chern--Ricci flat metric that is Gauduchon is necessarily Vaisman. Finally, specializing to Calabi--Yau solvmanifolds with left-invariant complex structure, we prove that a left-invariant metric is lcK if and only if it is Vaisman. Therefore, they are finite quotients of the Kodaira manifold. - oai:arXiv.org:2509.18364v2 - math.DG - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Giuseppe Barbaro, Alexandra Otiman + Tom Benhamou, Gabriel Goldberg - Spectrality of Prime Size Tiles - https://arxiv.org/abs/2509.23752 - arXiv:2509.23752v5 Announce Type: replace -Abstract: We prove that if a tile in $\mathbb Z^d$ has prime size $p$, then it must be spectral. The proof is by contradiction, it is simply shown that the tiling complement of such a tile can not annihilate all $p$-subgroups. In addition, with a simple transformation we prove that any $p$ points in general linear positions in $\mathbb Z^d$ must be both tiling and spectral if $d\ge p-1$. - oai:arXiv.org:2509.23752v5 - math.CA - math.CO - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace - http://creativecommons.org/licenses/by/4.0/ - Weiqi Zhou + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Jes\'us Guillera - Note on a conjecture of S\'ark\"ozy on special sequences - https://arxiv.org/abs/2509.25025 - arXiv:2509.25025v2 Announce Type: replace -Abstract: Let $\alpha>1$ be an irrational number and $k\ge 2$ a positive integer. Let $f(x)$ be a polynomial with positive integer coefficients. Solving a 2001 problem of S\'ark\"ozy on special sequences, Hegyv\'ari proved in 2003 that there exists an infinite sequence $A$ with density $\frac{1}{k}-\frac{1}{k\alpha}$ such that $$ \big\{f(a_1)+\ldots+f(a_k): a_i\in A, 1\le i\le k\big\}\cap \big\{\lfloor n\alpha\rfloor: n\in \mathbb{N}\big\}=\emptyset. $$ Hegyv\'ari also proved that the density given by him is optimal for $k=2$. In this article, we show that the density $\frac{1}{k}-\frac{1}{k\alpha}$ given by Hegyv\'ari is actually optimal for all $k\ge 2$. - oai:arXiv.org:2509.25025v2 - math.NT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace http://creativecommons.org/licenses/by/4.0/ - Yuchen Ding, Huixi Li, Zihan Zhang + Yanjiao Zhu, Wanquan Liu, Xianchao Xiu, Jianqin Sun - Algorithm for constructing optimal explicit finite-difference formulas in the Hilbert space - https://arxiv.org/abs/2510.06643 - arXiv:2510.06643v3 Announce Type: replace -Abstract: This work presents problems of constructing finite-difference formulas in the Hilbert space, i.e., setting problems of constructing finite-difference formulas using functional methods. The work presents a functional statement of the problem of optimizing finite-difference formulas in the space $W_{2}^{\left(m,m-1\right)} \left(0,1\right)$. Here, representations of optimal coefficients of explicit finite-difference formulas of the Adams type on classes $W_{2}^{\left(m,m-1\right)} \left(0,1\right)$ for any $m\ge 3$ will be found. - oai:arXiv.org:2510.06643v3 - math.NA - cs.NA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Kh. M. Shadimetov, R. S. Karimov + 10.1016/j.ejc.2025.104304 + European Journal of Combinatorics, Vol. 133, Mar. 2026, P. 104304 + Teemu Lundstr\"om, Leonardo Saud Maia Leite - Marked Poincar\'e rigidity near hyperbolic metrics and injectivity of the Lichnerowicz Laplacian in dimension 3 - https://arxiv.org/abs/2510.11399 - arXiv:2510.11399v2 Announce Type: replace -Abstract: Let $M$ be a compact manifold without boundary equipped with a Riemannian metric $g$ of negative curvature. In this paper, we introduce the marked Poincar\'e determinant (MPD), a homothety invariant of $g$ depending on differentiable periodic data of its geodesic flow. The MPD associates to each free homotopy class of closed curves in $M$ a number which measures the unstable volume expansion of the geodesic flow along the associated closed geodesic. We prove a local MPD rigidity result in dimension 3: if $g$ is sufficiently close to a hyperbolic metric $g_0$ and both metrics have the same MPD, then they are homothetic. As a by-product of our proof, we show the Lichnerowicz Laplacian of $g_0$ is injective on the space of trace-free divergence-free symmetric 2-tensors, which, to our knowledge, is the first result of its kind in negative curvature. - oai:arXiv.org:2510.11399v2 + 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 - math.DS - math.SP - Tue, 09 Dec 2025 00:00:00 -0500 + gr-qc + math-ph + math.MG + math.MP + Wed, 10 Dec 2025 00:00:00 -0500 replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Karen Butt, Alena Erchenko, Tristan Humbert, Thibault Lefeuvre, Amie Wilkinson + http://creativecommons.org/licenses/by/4.0/ + Andrea Mondino, Clemens S\"amann - A 2-systolic inequality on non-rational compact K\"ahler surfaces with positive scalar curvature - https://arxiv.org/abs/2510.13353 - arXiv:2510.13353v2 Announce Type: replace -Abstract: In this note, we prove a 2-systolic inequality on non-rational compact positive scalar curvature K\"ahler surfaces admitting a nonconstant holomorphic map to a positive-genus compact Riemann surface. According to the classification of positive scalar curvature K\"ahler surfaces, any such surface must be a ruled surface fibred over a complex curve with positive genus. - oai:arXiv.org:2510.13353v2 - math.DG - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Zehao Sha + http://creativecommons.org/licenses/by/4.0/ + Li Lu, Lingyu Guo, Victor Z. Guo - On the prospects of interpolatory spline bases for accurate mass lumping strategies in isogeometric analysis - https://arxiv.org/abs/2510.13510 - arXiv:2510.13510v2 Announce Type: replace -Abstract: While interpolatory bases such as the Lagrange basis form the cornerstone of classical finite element methods, they have been replaced in the more general finite element setting of isogeometric analysis in favor of other desirable properties. Yet, interpolation is a key property for devising accurate mass lumping strategies that are ubiquitous in explicit dynamic analyses of structures. In this article, we explore the possibility of restoring interpolation for spline bases within isogeometric analysis for the purpose of mass lumping. Although reminiscent of the spectral element method, this technique comes with its lot of surprises and challenges, which are critically assessed. - oai:arXiv.org:2510.13510v2 - math.NA + 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 - Tue, 09 Dec 2025 00:00:00 -0500 + math.MG + math.NA + Wed, 10 Dec 2025 00:00:00 -0500 + replace + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Yueqi Cao, Anthea Monod + + + 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 replace http://creativecommons.org/licenses/by/4.0/ - Yannis Voet, Espen Sande + Hong-Jun Ge, Jack Koolen, Akihiro Munemasa - Numerical computation of the density of states of aperiodic multiscale Schr\"odinger operators - https://arxiv.org/abs/2510.15369 - arXiv:2510.15369v2 Announce Type: replace -Abstract: Computing the electronic structure of incommensurate materials is a central challenge in condensed matter physics, requiring efficient ways to approximate spectral quantities such as the density of states (DoS). In this paper, we numerically investigate two distinct approaches for approximating the DoS of incommensurate Hamiltonians for small values of the incommensurability parameters $\epsilon$ (e.g., small twist angle, or small lattice mismatch): the first employs a momentum-space decomposition, and the second exploits a semiclassical expansion with respect to $\epsilon$. In particular, we compare these two methods using a 1D toy model. We check their consistency by comparing the asymptotic expansion terms of the DoS, and it is shown that, for full DoS, the two methods exhibit good agreement in the small $\epsilon$ limit, while discrepancies arise for less small $\epsilon$, which indicates the importance of higher-order corrections in the semiclassical method for such regimes. We find these discrepancies to be caused by oscillations in the DoS at the semiclassical analogues of Van Hove singularities, which can be explained qualitatively, and quantitatively for $\epsilon$ small enough, by a semiclassical approach. - oai:arXiv.org:2510.15369v2 - math-ph - math.MP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Eric Canc\`es, Daniel Massatt, Long Meng, \'Etienne Polack, Xue Quan + Haoyang Hu, Viveck R. Cadambe - Braid Group Action on $D^b(\mathfrak{M}_{\eta})$ - https://arxiv.org/abs/2510.15396 - arXiv:2510.15396v3 Announce Type: replace -Abstract: We construct an action of the braid group on the bounded derived category of coherent sheaves on hypertoric varieties arising from hyperplane arrangements. Using wall-crossing equivalences associated to paths in the complexified complement of the hyperplane arrangement, we show that these equivalences under certain conditions yield a functor from the Deligne groupoid to the category of triangulated equivalences. This gives rise to a canonical representation of the fundamental group, which recovers the braid group, acting on \(D^b(\mathfrak{M}_{\eta})\). This is a summary of Brad Hannigan-Daley's PhD thesis. - oai:arXiv.org:2510.15396v3 + 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.RT - math.SG - Tue, 09 Dec 2025 00:00:00 -0500 + math.CV + Wed, 10 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Trishan Mondal + Abraham del Valle Rodr\'iguez - Some configuration results for area-minimizing cones - https://arxiv.org/abs/2510.17240 - arXiv:2510.17240v3 Announce Type: replace -Abstract: We discover some configuration results for area-minimizing cones. In particular, given any closed minimal submanifold in some Euclidean sphere, every cone over the minimal product of sufficiently many copies of the submanifold turns out to be area-minimizing. - oai:arXiv.org:2510.17240v3 - math.DG - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Yongsheng Zhang + Abraham del Valle Rodr\'iguez - Quasilinear Equations with Neumann Boundary Conditions - https://arxiv.org/abs/2510.17374 - arXiv:2510.17374v2 Announce Type: replace -Abstract: We prove a multiplicity result for non-constant weak solutions $u \in H^1(\Omega)$ for the quasilinear elliptic equation \[ \begin{cases} \displaystyle-\text{div}(A(x,u)\nabla u) + \frac{1}{2} D_sA(x,u)\nabla u \cdot \nabla u = g(x,u) - \lambda u & \text{in } \Omega \\ A(x,u)\nabla u \cdot \eta = 0 & \text{on } \partial \Omega \end{cases} \] where $\lambda \in \mathbb{R}$, $ \Omega$ is a bounded lipschitz domain, $ \eta $ is the outward normal to the boundary $ \partial \Omega $, and $g(x,u)$ is a Carath\'eodory function that satisfies a general subcritical (and superlinear) growth condition. We also prove that any weak solution is bounded under a stronger growth assumption. - oai:arXiv.org:2510.17374v2 + 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 math.AP - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Annamaria Canino, Simone Mauro + http://creativecommons.org/licenses/by/4.0/ + Jhe-Kuan Su - On the Capacity of Erasure-prone Quantum Storage with Erasure-prone Entanglement Assistance - https://arxiv.org/abs/2510.17781 - arXiv:2510.17781v2 Announce Type: replace -Abstract: A quantum message is encoded into $N$ storage nodes (quantum systems $Q_1\dots Q_N$) with assistance from $N_B$ maximally entangled bi-partite quantum systems $A_1B_1, \dots, A_{N_B}B_{N_B}$, that are prepared in advance such that $B_1\dots B_{N_B}$ are stored separately as entanglement assistance (EA) nodes, while $A_1\dots A_{N_B}$ are made available to the encoder. Both the storage nodes and EA nodes are erasure-prone. The quantum message must be recoverable given any $K$ of the $N$ storage nodes along with any $K_B$ of the $N_B$ EA nodes. The capacity for this setting is the maximum size of the quantum message, given that the size of each EA node is $\lambda_B$. All node sizes are relative to the size of a storage node, which is normalized to unity. The exact capacity is characterized as a function of $N,K,N_B,K_B, \lambda_B$ in all cases, with one exception. The capacity remains open for an intermediate range of $\lambda_B$ values when a strict majority of the $N$ storage nodes, and a strict non-zero minority of the $N_B$ EA nodes, are erased. As a key stepping stone, an analogous classical storage (with shared-randomness assistance) problem is introduced. A set of constraints is identified for the classical problem, such that classical linear code constructions translate to quantum storage codes, and the converse bounds for the two settings utilize similar insights. In particular, the capacity characterizations for the classical and quantum settings are shown to be identical in all cases where the capacity is settled. - oai:arXiv.org:2510.17781v2 - cs.IT - math.IT - quant-ph - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Hua Sun, Syed A. Jafar + Yanbo Zhang, Yaojun Chen - DualHash: A Stochastic Primal-Dual Algorithm with Theoretical Guarantee for Deep Hashing - https://arxiv.org/abs/2510.18218 - arXiv:2510.18218v2 Announce Type: replace -Abstract: Deep hashing converts high-dimensional feature vectors into compact binary codes, enabling efficient large-scale retrieval. A fundamental challenge in deep hashing stems from the discrete nature of quantization in generating the codes. W-type regularizations, such as $||z|-1|$, have been proven effective as they encourage variables toward binary values. However, existing methods often directly optimize these regularizations without convergence guarantees. While proximal gradient methods offer a promising solution, the coupling between W-type regularizers and neural network outputs results in composite forms that generally lack closed-form proximal solutions. In this paper, we present a stochastic primal-dual hashing algorithm, referred to as DualHash, that provides rigorous complexity bounds. Using Fenchel duality, we partially transform the nonconvex W-type regularization optimization into the dual space, which results in a proximal operator that admits closed-form solutions. We derive two algorithm instances: a momentum-accelerated version with $\mathcal{O}(\varepsilon^{-4})$ complexity and an improved $\mathcal{O}(\varepsilon^{-3})$ version using variance reduction. Experiments on three image retrieval databases demonstrate the superior performance of DualHash. - oai:arXiv.org:2510.18218v2 - math.OC - cs.CV - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace - http://creativecommons.org/licenses/by/4.0/ - Luxuan Li, Xiao Wang, Chunfeng Cui + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Andreas Bode - A proof of the Kim-Vu sandwich conjecture - https://arxiv.org/abs/2510.20765 - arXiv:2510.20765v2 Announce Type: replace -Abstract: In 2004, Kim and Vu conjectured that, when $d=\omega(\log n)$, the random $d$-regular graph $G_d(n)$ can be sandwiched with high probability between two random binomial graphs $G(n,p)$ with edge probabilities asymptotically equal to $\frac{d}{n}$. That is, there should exist $p_*=(1-o(1))\frac{d}{n}$, $p^*=(1+o(1))\frac{d}{n}$ and a coupling $(G_*,G,G^*)$ such that $G_*\sim G(n,p_*)$, $G\sim G_d(n)$, $G^*\sim G(n,p^*)$, and $\mathbb{P}(G_*\subset G\subset G^*)=1-o(1)$. Known as the sandwich conjecture, such a coupling is desirable as it would allow properties of the random regular graph to be inferred from those of the more easily studied binomial random graph. The conjecture was recently shown to be true when $d\gg\log^4n$ by Gao, Isaev and McKay. In this paper, we prove the sandwich conjecture in full. We do so by analysing a natural coupling procedure introduced in earlier work by Gao, Isaev and McKay, which had only previously been done when $d\gg n/\sqrt{\log n}$. - oai:arXiv.org:2510.20765v2 + 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 - Tue, 09 Dec 2025 00:00:00 -0500 + math.QA + Wed, 10 Dec 2025 00:00:00 -0500 replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Natalie Behague, Daniel Il'kovi\v{c}, Richard Montgomery + http://creativecommons.org/licenses/by-nc-nd/4.0/ + \'Alvaro Guti\'errez, \'Alvaro L. Mart\'inez, Micha{\l} Szwej, Mark Wildon - A Retraction-free Method for Nonsmooth Minimax Optimization over a Compact Manifold - https://arxiv.org/abs/2510.22065 - arXiv:2510.22065v2 Announce Type: replace -Abstract: We study the minimax problem $\min_{x\in M} \max_y f_r(x,y):=f(x,y)-h(y)$, where $M$ is a compact submanifold, $f$ is continuously differentiable in $(x, y)$, $h$ is a closed, weakly-convex (possibly non-smooth) function and we assume that the regularized coupling function $-f_r(x,\cdot)$ is either $\mu$-PL for some $\mu>0$ or concave ($\mu = 0$) for any fixed $x$ in the vicinity of $M$. To address the nonconvexity due to the manifold constraint, we use an exact penalty for the constraint $x \in M$, and enforcing a convex constraint $x\in X$ for some $X \supset M$, onto which projections can be computed efficiently. Building upon this new formulation for the manifold minimax problem in question, a single-loop smoothed manifold gradient descent-ascent (sm-MGDA) algorithm is proposed. Theoretically, any limit point of sm-MGDA sequence is a stationary point of the manifold minimax problem and sm-MGDA can generate an $O(\epsilon)$-stationary point of the original problem with $O(1/\epsilon^2)$ and $\tilde{O}(1/\epsilon^4)$ complexity for $\mu > 0$ and $\mu = 0$ scenarios, respectively. Moreover, for the $\mu = 0$ setting, through adopting Tikhonov regularization of the dual, one can improve the complexity to $O(1/\epsilon^3)$ at the expense of asymptotic stationarity. The key component, common in the analysis of all cases, is to connect $\epsilon$-stationary points between the penalized problem and the original problem by showing that the constraint $x \in X$ becomes inactive and the penalty term tends to $0$ along any convergent subsequence. To our knowledge, sm-MGDA is the first retraction-free algorithm for minimax problems over compact submanifolds, and this is a very desirable algorithmic property since through avoiding retractions, one can get away with matrix orthogonalization subroutines required for computing retractions to manifolds arising in practice, which are not GPU friendly. - oai:arXiv.org:2510.22065v2 - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Necdet Serhat Aybat, Jiang Hu, Zhanwang Deng + http://creativecommons.org/licenses/by/4.0/ + Alexander E. Litvak, Mathias Sonnleitner, Tomasz Szczepanski - Traslation surfaces in the Heisenberg Group - https://arxiv.org/abs/2510.23916 - arXiv:2510.23916v2 Announce Type: replace -Abstract: A translation surface in the Heisenberg group is constructed as the product of two planar curves. We classify a type of such surfaces with vanishing intrinsic curvature by analyzing the determinant of their Gauss map - oai:arXiv.org:2510.23916v2 - math.DG - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.CO + math.GR + math.MG + Wed, 10 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Christiam Figueroa + Victor Chepoi, Kolja Knauer - Variational problem and Hamiltonian formulation of the Lagrange-d'Alembert equations with nonlinear nonholonomic constraints - https://arxiv.org/abs/2510.24492 - arXiv:2510.24492v4 Announce Type: replace -Abstract: Any given system of ordinary differential equations in $n$-dimensional configuration space can be obtained from a peculiar variational problem with one local symmetry. The obtained action functional leads to the Hamiltonian formulation in $(4n+2)$-dimensional phase space. As concrete examples, we discuss the cases of Lagrange-d'Alembert equations with nonlinear nonholonomic constraints, as well as the equations of motion with dissipative (frictional) forces. - oai:arXiv.org:2510.24492v4 - math-ph - hep-th - math.MP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.CT + Wed, 10 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Alexei A. Deriglazov + Shai Keidar, Shaul Ragimov + + + 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 + replace + http://creativecommons.org/licenses/by/4.0/ + Dongho Lee - A Self Propelled Vortex Dipole Model on a Catenoid - https://arxiv.org/abs/2511.00923 - arXiv:2511.00923v2 Announce Type: replace -Abstract: We investigate vortex dipoles on surfaces of variable negative curvature, focusing on a catenoid of arbitrary throat radius as a concrete example. We construct the effective dynamical system including mutual and geometric self-interaction terms and show that the resulting Hamiltonian dynamics makes dipoles follow catenoid geodesics, in agreement with recent works, Gustafsson (J. Nonlinear Sci. 32, 62, 2022) and by Drivas, Glukhovskiy and Khesin (Int. Math. Res. Not. 2024, 14, 10880-10894). We utilize the symplectic structure to find a conserved momentum map J related to the U(1) symmetry along the azimuthal direction. We verify the conservation of both the Hamiltonian and this momentum for arbitrary throat radius. We then demonstrate direct and exchange scattering of classical vortices on the catenoid, and we contrast this with the collective rotational motion (with azimuthal drift) that arises for chiral pairs. Finally, we build a finite-dipole dynamical system on the catenoid and show that the self-propulsion terms emerge to leading order in the dipole size. This provides a concrete realization, on a curved minimal surface, of the intuitive statement that a finite dipole propels orthogonal to the dipole axis, with a speed modulated by curvature. - oai:arXiv.org:2511.00923v2 + 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 math-ph - cond-mat.quant-gas - hep-th math.MP - Tue, 09 Dec 2025 00:00:00 -0500 + quant-ph + Wed, 10 Dec 2025 00:00:00 -0500 replace - http://creativecommons.org/licenses/by/4.0/ - Khushi Banthia, Rickmoy Samanta + http://creativecommons.org/licenses/by-nc-nd/4.0/ + Antoine Soulas - Extremal effective curves and non-semiample line bundles on $\overline{\rm{M}}_{g,n}$ - https://arxiv.org/abs/2511.02019 - arXiv:2511.02019v2 Announce Type: replace -Abstract: We develop a new method for establishing the extremality in the closed cone of effective curves on the moduli space of curves and determine the extremality of many boundary $1$-strata. As a consequence, by using a general criterion for non-semiampleness which extends Keel's argument, we demonstrate that a substantial portion of the cone of nef divisors of $\overline{\mathrm{M}}_{g,n}$ is not semiample. As an application, we construct the first explicit example of a non-contractible extremal ray of the closed cone of effective curves on $\overline{\mathrm{M}}_{3,n}$. Our method relies on two main ingredients: (1) the construction of a new collection of nef divisors on $\overline{\mathrm{M}}_{g,n}$, and (2) the identification of a tractable inductive structure on the Picard group, arising from Knudsen's construction of $\overline{\mathrm{M}}_{g,n}$. - oai:arXiv.org:2511.02019v2 + 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 - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Daebeom Choi + Xiaodong Yi - Representations of loop groups as factorization module categories - https://arxiv.org/abs/2511.02916 - arXiv:2511.02916v2 Announce Type: replace -Abstract: We show that the (2-)category of categorical representations of the loop group embeds fully faithfully into the (2-)category of factorization module categories with respect to the affine Grassmannian. - oai:arXiv.org:2511.02916v2 - math.AG - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.CO + Wed, 10 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - Lin Chen, Yuchen Fu, Dennis Gaitsgory, David Yang + Josef F. Dorfmeister, Sebastian Walcher - DeepPAAC: A New Deep Galerkin Method for Principal-Agent Problems - https://arxiv.org/abs/2511.04309 - arXiv:2511.04309v2 Announce Type: replace -Abstract: We consider numerical resolution of principal-agent (PA) problems in continuous time. We formulate a generic PA model with continuous and lump payments and a multi-dimensional strategy of the agent. To tackle the resulting Hamilton-Jacobi-Bellman equation with an implicit Hamiltonian we develop a novel deep learning method: the Deep Principal-Agent Actor Critic (DeepPAAC) Actor-Critic algorithm. DeepPAAC is able to handle multi-dimensional states and controls, as well as constraints. We investigate the role of the neural network architecture, training designs, loss functions, etc. on the convergence of the solver, presenting five different case studies. - oai:arXiv.org:2511.04309v2 - math.NA - cs.LG - cs.NA - Tue, 09 Dec 2025 00:00:00 -0500 + 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://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Michael Ludkovski, Changgen Xie, Zimu Zhu + http://creativecommons.org/licenses/by-nc-nd/4.0/ + Wei Wu, Youzi He - Classification of fractional, singular Yamabe metrics on a twice punctured sphere I - https://arxiv.org/abs/2511.05225 - arXiv:2511.05225v2 Announce Type: replace -Abstract: The Delaunay metrics form a family of conformally flat, constant fractional Q-curvature metrics on a twice-punctured sphere. They are all (after a M\"obius transformation) rotationally symmetric and periodic, and admit several elegant variational descriptions. We prove that, when s is close to but less than 1, any complete, conformally flat constant Q-curvature metric on a twice-punctured sphere is a Delaunay metric. Along the way, we prove a sharp a priori bound for the conformal factor of these metrics, which may be of independent interest. - oai:arXiv.org:2511.05225v2 + 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 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 replace - http://creativecommons.org/licenses/by/4.0/ - Jo\~ao Henrique Andrade, Azahara DelaTorre, Jo\~ao Marcos do \`O, Jesse Ratzkin, Juncheng Wei + http://creativecommons.org/licenses/by-nc-sa/4.0/ + Murat Altunba\c{s}, Ay\c{s}e Karanl{\i}k Akp{\i}nar - A coupled finite element-virtual element method for thermomechanical analysis of electronic packaging structures - https://arxiv.org/abs/2511.09348 - arXiv:2511.09348v2 Announce Type: replace -Abstract: This study presents a finite element and virtual element (FE-VE) coupled method for thermomechanical analysis in electronic packaging structures. The approach partitions computational domains strategically, employing FEM for regular geometries to maximize computational efficiency and VEM for complex shapes to enhance geometric flexibility. Interface compatibility is maintained through coincident nodal correspondence, ensuring solution continuity across domain boundaries while reducing meshing complexity and computational overhead. Validation through electronic packaging applications demonstrates reasonable agreement with reference solutions and acceptable convergence characteristics across varying mesh densities. The method effectively captures thermal distributions and stress concentrations in multi-material systems, establishing a practical computational framework for electronic packaging analysis involving complex geometries. Source codes are available at https://github.com/yanpeng-gong/FeVeCoupled-ElectronicPackaging. - oai:arXiv.org:2511.09348v2 - math.NA - cs.CE - cs.NA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace - http://creativecommons.org/licenses/by/4.0/ - Yanpeng Gong, Sishuai Li, Yue Mei, Bingbing Xu, Fei Qin, Xiaoying Zhuang, Timon Rabczuk + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Chunchao Fan, Qizhong Lin - Bilinear forms with trace functions - https://arxiv.org/abs/2511.09459 - arXiv:2511.09459v2 Announce Type: replace -Abstract: We obtain non-trivial bounds for bilinear sums of trace functions below the P\'olya-Vinogradov range assuming only that the geometric monodromy group of the underlying ell-adic sheaf satisfies certain simple structural properties, in contrast to previous works which handled only special cases of Kloosterman and hypergeometric sheaves. Our approach builds on a general "soft" stratification theorem for sums of products of trace functions, based on an idea of Junyan Xu, combined with a new robust version of the Goursat-Kolchin-Ribet criterion. - oai:arXiv.org:2511.09459v2 - math.NT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - \'Etienne Fouvry, Emmanuel Kowalski, Philippe Michel, Will Sawin + Nicola Abatangelo, Elisa Affili, Matteo Cozzi - Explicit pulsating fronts and minimal speeds in periodic Fisher-KPP equations - https://arxiv.org/abs/2511.10104 - arXiv:2511.10104v2 Announce Type: replace -Abstract: We study a Fisher-KPP equation with spatially periodic diffusion and reaction terms. We identify a class of periodic media for which the equation admits an explicit, closed-form solution. Through a nonlinear change of variables, the problem is reduced to the homogeneous Fisher-KPP equation, allowing us to construct an exact pulsating traveling front that connects the positive periodic stationary state to 0. We also derive an explicit expression for the asymptotic spreading speed and establish new asymptotic and comparison results. Finally, combining our change of variables and eigenvalue transform with existing results on KPP fronts in periodic media, we extend Bramson-type logarithmic delay results to the case of heterogeneous periodic diffusion. - oai:arXiv.org:2511.10104v2 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.CO + Wed, 10 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Lionel Roques (BioSP) + Stefano Lia, Giovanni Longobardi, Corrado Zanella - Ground states of the defocusing NLSE with a point interaction - https://arxiv.org/abs/2511.12593 - arXiv:2511.12593v2 Announce Type: replace -Abstract: Suppose that either (i) $N = 2$, $\alpha \in \mathbb{R}$ and $p > 2$ or (ii) $N = 3$, $\alpha < 0$ and $2 < p < 3$. We prove that there exists an explicitly computable $\mu_0 = \mu_0 (N, \alpha, p) > 0$ such that if $0 < \mu < \mu_0$, then the following normalized semilinear elliptic problem with a point interaction admits ground states: \[ \begin{cases} - \Delta_\alpha u + \omega u + u |u|^{p - 2} = 0 &\text{in} ~ \mathbb{R}^N; \\ \|u\|_{\mathscr{L}^2}^2 = \mu, \end{cases} \] where $- \Delta_\alpha$ denotes the Laplacian of point interaction (centered at the origin) with inverse scattering length $- 2 (N - 1) \pi \alpha$ and we want to solve for $\omega \in \mathbb{R}$, $u \colon \mathbb{R}^N \to \mathbb{R}$. We remark that this kind of solutions does not exist in the framework of the defocusing NLSE without a point interaction. - oai:arXiv.org:2511.12593v2 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.NA + cs.GR + cs.NA + Wed, 10 Dec 2025 00:00:00 -0500 replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Gustavo de Paula Ramos + http://creativecommons.org/licenses/by-nc-nd/4.0/ + A. Canton, L. Fernandez-Jambrina, M. J. Vazquez-Gallo - Closed neighborhood complexes of graphs - https://arxiv.org/abs/2511.12608 - arXiv:2511.12608v2 Announce Type: replace -Abstract: The closed neighborhood complex $\mathcal{N}[G]$ of a simple graph $G$ is the simplicial complex whose simplices are finite sets of vertices contained in a closed neighborhood of a vertex in $G$. We reveal that the closed neighborhood complex has close connections with other concepts, including the independence complex of the canonical double covering and the independence complex of the neighborhood hypergraph. Furthermore, we show that the fundamental group of the closed neighborhood complex is isomorphic to Grigor'yan--Lin--Muranov--Yau's fundamental group of a graph introduced in the study of path homology. - oai:arXiv.org:2511.12608v2 - math.CO - math.AT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Takahiro Matsushita + Mark Hughes, Alexandra Kjuchukova, Maggie Miller - Gaussian rational numbers in Cantor sets in the complex plane - https://arxiv.org/abs/2511.16281 - arXiv:2511.16281v2 Announce Type: replace -Abstract: Given $\beta\in\mathbb{Z}[i]$ with $|\beta|>1$ and a finite set $D\subset\mathbb{Q}(i)$, let \[K_{\beta, D}=\left\{\sum_{j=1}^{\infty}\frac{d_j}{\beta^j}: d_j\in D, \forall j\geq 1\right\}.\] Let $\mathcal{S}$ be a finite set of non-associate prime elements in $\mathbb{Z}[i]$ not dividing $\beta$. We prove that if the Hausdorff dimension of $K_{\beta,D}$ is less than $1$, then there are only finitely many Gaussian rational numbers in $K_{\beta,D}$ whose denominators have all their prime factors in $\mathcal{S}$. - oai:arXiv.org:2511.16281v2 - math.NT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Yu-Feng Wu + Abolfazl Tarizadeh - A tower of complete moduli spaces of Calabi-Yau $n$-folds - https://arxiv.org/abs/2511.16562 - arXiv:2511.16562v3 Announce Type: replace -Abstract: We generalize to dimensions $n\ge3$ the compactified moduli stack of elliptic curves $\overline{M}_{1,1}=\mathbb{P}(4,6)$ and Brieskorn's family of $U\oplus~E_8$-polarized K3 surfaces over a $10$-dimensional weighted projective space. - oai:arXiv.org:2511.16562v3 - math.AG - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Valery Alexeev + Moeen Nehzati - Algebraic versions of $\mathbb{T}^2$ and of $\mathbb{P}^1\times\mathbb{P}^1$ and Hochschild cohomology - https://arxiv.org/abs/2511.18073 - arXiv:2511.18073v2 Announce Type: replace -Abstract: We examine the Hochschild cohomology for triangular algebras that capture some aspects of geometry and topology of the torus and of the quadric surface, and for deformations of these algebras. In particular, this shows that the cup product on the Hochschild cohomology of a triangular algebra does not generally follow the intuition coming from monomial algebras. Our examples also demonstrate that the Hochschild cohomology of a deformation of an algebra may not experience the dimension drop but still have a different cup product structure, and that the Hochschild cohomologies of deformations of two derived equivalent algebras may exhibit noticeably different behaviours. - oai:arXiv.org:2511.18073v2 - math.RA - math.KT - math.QA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + cs.IT + 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 replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Vladimir Dotsenko, Andrea Solotar + http://creativecommons.org/licenses/by/4.0/ + Iosif Lytras, Panayotis Mertikopoulos - Complex structures of the Gibbons-Hawking ansatz with infinite topological type - https://arxiv.org/abs/2511.18836 - arXiv:2511.18836v2 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:2511.18836v2 - math.DG - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.AG + Wed, 10 Dec 2025 00:00:00 -0500 replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Wenxin He, Bin Xu + http://creativecommons.org/licenses/by/4.0/ + Juanita Duque-Rosero, Christopher Keyes, Andrew Kobin, Manami Roy, Soumya Sankar, Yidi Wang - Information Physics of Intelligence: Unifying Logical Depth and Entropy under Thermodynamic Constraints - https://arxiv.org/abs/2511.19156 - arXiv:2511.19156v3 Announce Type: replace -Abstract: The rapid scaling of artificial intelligence models has revealed a fundamental tension between model capacity (storage) and inference efficiency (computation). While classical information theory focuses on transmission and storage limits, it lacks a unified physical framework to quantify the thermodynamic costs of generating information from compressed laws versus retrieving it from memory. In this paper, we propose a theoretical framework that treats information processing as an enabling mapping from ontological states to carrier states. We introduce a novel metric, Derivation Entropy, which quantifies the effective work required to compute a target state from a given logical depth. By analyzing the interplay between Shannon entropy (storage) and computational complexity (time/energy), we demonstrate the existence of a critical phase transition point. Below this threshold, memory retrieval is thermodynamically favorable; above it, generative computation becomes the optimal strategy. This "Energy-Time-Space" conservation law provides a physical explanation for the efficiency of generative models and offers a rigorous mathematical bound for designing next-generation, energy-efficient AI architectures. Our findings suggest that the minimization of Derivation Entropy is a governing principle for the evolution of both biological and artificial intelligence. - oai:arXiv.org:2511.19156v3 + 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 - cs.AI - cs.LO math.IT - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jianfeng Xu, Zeyan Li + Tong Zhang, Qianren Li, Shuai Wang, Wanli Ni, Jiliang Zhang, Rui Wang, Kai-Kit Wong, Chan-Byoung Chae - Low-lying eigenvalues in the semiclassical limit of a Schr{\"o}dinger operator with an inverse square potential, and non-asymptotic a-zeros of Kummer functions - https://arxiv.org/abs/2511.20025 - arXiv:2511.20025v2 Announce Type: replace -Abstract: We provide a precise description of the bottom of the spectrum in the semiclassical limit of a harmonic-type Schr{\"o}dinger operator with an inverse square potential. By exploiting the connection between the eigenfunctions of these operators and the Kummer and Whittaker functions, we derive accurate localization results for the non-asymptotic zeros of these functions with respect to their first parameter, uniformly with respect to the argument taken large and real. Moreover, our operators are linked to the magnetic Dirichlet Laplacian with a constant magnetic field, so that our results describe its spectrum. Our spectral analysis relies on a WKB-type approach. - oai:arXiv.org:2511.20025v2 - math.CA - math.SP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.FA + Wed, 10 Dec 2025 00:00:00 -0500 replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Roman Vanlaere (CEREMADE) + http://creativecommons.org/licenses/by/4.0/ + Fernanda M. Ba\^eta, Monika Ludwig - A Generalization of Zalcman's Lemma on Complex Lie Groups - https://arxiv.org/abs/2511.20536 - arXiv:2511.20536v2 Announce Type: replace -Abstract: Zalcman's Lemma makes significant applications in normal families, complex dynamics and related problems in complex analysis. In the present paper, we are devoted to generalizing the classical Zalcman's lemma to complex Lie groups by means of exponential mappings defined by holomorphic one-parameter subgroups. - oai:arXiv.org:2511.20536v2 - math.CV - math.GR - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Xianjing Dong, Yanda Lv - - - Distributions of bounded real sequences and Astorg-Boc Thaler's question - https://arxiv.org/abs/2511.21324 - arXiv:2511.21324v2 Announce Type: replace -Abstract: While studying the existence of wandering domains in complex dynamics, Astorg-Boc Thaler posed a question concerning the distribution of bounded real sequences: for $\alpha>1$ that has the Pisot property, is $\frac{\beta\ln\alpha}{\alpha-1}$ being rational necessary for the existence of an increasing sequence of integers $(n_k)_{k\geqslant 1}$ such that $(n_{k+1}-\alpha n_k-\beta\ln n_k)_{k\geqslant 1}$ converges to a cycle? - When $\alpha$ is an algebraic number, we answer Astorg-Boc Thaler's question in the affirmative: the condition $\theta$ being rational is necessary and sufficient for the convergence to a cycle. - Furthermore, let $P(x)\in\mathbb{Z}[x]$ be the minimal polynomial of $\alpha$. We prove that $P(1)\theta\in\mathbb{Z}$ is a necessary condition, while $\frac{P(1)\theta}{\gcd(P(1),P'(1))}\in\mathbb{Z}$ is a sufficient condition, for the convergence to a cycle of length 1. - As an application, we present explicit new examples of polynomial skew products in $\mathbb{C}^2$ with wandering domains. - oai:arXiv.org:2511.21324v2 - math.DS - Tue, 09 Dec 2025 00:00:00 -0500 - replace - http://creativecommons.org/licenses/by/4.0/ - Zhangchi Chen, Zihao Ye + Piotr Koszmider, Ma{\l}gorzata Rojek - Mean-square exponential stability of exact and numerical solutions for neutral stochastic delay differential equations with Markovian switching - https://arxiv.org/abs/2511.21620 - arXiv:2511.21620v3 Announce Type: replace -Abstract: This paper investigates the mean-square exponential stability of neutral stochastic differential delay equations (NSDDEs) with Markovian switching. The analysis addresses the complexities arising from the interaction between the neutral term, time-varying delays, and structural changes governed by a continuous-time Markov chain. We establish novel and practical criteria for the mean-square exponential stability of both the underlying system and its numerical approximations via the Euler-Maruyama method. Furthermore, we prove that the numerical scheme can reproduce the exponential decay rate of the true solution with arbitrary accuracy, provided the step size is sufficiently small. The theoretical results are supported by a numerical example that illustrates their effectiveness. - oai:arXiv.org:2511.21620v3 + 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 - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Jina Yang, Ky Quan Tran + Wei Liu, Jie Xu - Central limit theorems for random multiplicative functions over function fields - https://arxiv.org/abs/2511.22905 - arXiv:2511.22905v2 Announce Type: replace -Abstract: We provide a sufficient characterization for subsets $\mathcal{A}$ of the polynomial ring $\mathbb{F}_q[t]$ for which partial sums of Steinhaus random multiplicative functions approach a complex standard normal distribution. This extends recent work of Soundararajan and Xu to the function field setting. We apply this characterization to deduce central limit theorems in four cases: polynomials in short intervals, polynomials with few prime factors, shifted primes, and rough polynomials. In doing so, we also establish an explicit Hildebrand inequality for smooth polynomials in short intervals, a function field form of Shiu's theorem for multiplicative functions, and an explicit Chebyshev bound for rough polynomials in short intervals. - oai:arXiv.org:2511.22905v2 - math.NT - math.PR - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Declan Hoban, Jibran Iqbal Shah, Nadya-Catherine Ismail, William Verreault, Asif Zaman + http://creativecommons.org/licenses/by/4.0/ + Mirai Ikebuchi - Algebraic study on rooted products of graphs and multi-clique corona graphs - https://arxiv.org/abs/2511.22953 - arXiv:2511.22953v3 Announce Type: replace -Abstract: In this paper, we study rooted products of graphs from the perspective of combinatorial commutative algebra. For edge ideals, we introduce the 2-Cohen-Macaulayness with respect to a vertex and use it to investigate when edge ideals of rooted products of graphs are Cohen-Macaulay. Moreover, we completely determine when attaching a graph on at most six vertices to a given graph as rooted products, yields a Cohen-Macaulay edge ideal. Also, we define mulit-clique corona graphs as a generalization of clique-corona graphs and multi-whisker graphs. We prove that multi-clique corona graphs are vertex decomposable and hence sequentially Cohen-Macaulay. Also, we give formulas for the projective dimension and the Castelnuovo-Mumford regularity. - oai:arXiv.org:2511.22953v3 - math.AC + 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 - Tue, 09 Dec 2025 00:00:00 -0500 + cs.CC + cs.DS + Wed, 10 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Yuji Muta, Naoki Terai + Jonathan Leake, Shayan Oveis Gharan - On the nullspace of split graphs - https://arxiv.org/abs/2512.00190 - arXiv:2512.00190v2 Announce Type: replace -Abstract: We study the nullspace of the adjacency matrix of split graphs, whose vertex set can be partitioned into a clique and an independent set. We introduce the clique-kernel, a subspace that decides whether clique vertices lie in the support of a kernel eigenvector, and we prove that its dimension is at most one. This yields the formula $null(Sp) = null(R) + \dim(\mathrm{Cker}(Sp))$, which fully describes the nullity of a split graph in terms of the biadjacency submatrix $R$. We also analyze unbalanced split graphs through the concept of swing vertices and characterize the structure of their kernel supports. Furthermore, we study the behavior of the nullspace under Tyshkevich composition and derive a closed formula for the determinant. These results provide a unified algebraic framework for understanding when a split graph is singular and how its combinatorial structure determines its nullspace. - oai:arXiv.org:2512.00190v2 - math.CO - math.SP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + 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/ - Daniel A. Jaume, Victor N. Schv\"ollner, Cristian Panelo, Kevin Pereyra + Nicholas Gismondi, Alexandru F. Radu - The diophantine equation $(2^{k}-1)(b^{k}-1)=y^{q}$ - https://arxiv.org/abs/2512.00548 - arXiv:2512.00548v2 Announce Type: replace -Abstract: In this paper, we consider the exponential Diophantine equation \( (2^k-1)(b^k-1)=y^q \) with $k\ge 2$, odd integer $b$ and an odd prime exponent $q$ and obtain effective upper bounds for $q$ in terms of $b$. In particular, we show that $q\le \log_2(b+1)$ holds apart from a finite, explicitly determined set of exceptional pairs $(b,q)$ when $3\le b<10^6$. As an application, we prove that the related equation \( (2^k-1)(b^k-1)=x^n, \) has no positive integer solution $(k,x,n)$ for several specific odd values of $b$, including $b\in\{5,7,11,13,21,23,27,29\}$. - oai:arXiv.org:2512.00548v2 + 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 - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Chang Liu, Bo He + http://creativecommons.org/publicdomain/zero/1.0/ + Bo-Hae Im, Hansol Kim - The Linear Slicing Method for Equal Sums of Like Powers: Modular and Geometric Constraints - https://arxiv.org/abs/2512.00551 - arXiv:2512.00551v2 Announce Type: replace -Abstract: We study the Diophantine equation $a^k + b^k = c^k + d^k$ with integer variables and exponent $k>1$, under the linear constraint $(c+d) - (a+b) = h$. We analyze the geometry and arithmetic of these linear slices. On the central slice $h=0$, we prove strictly convex uniqueness: distinct unordered pairs with the same sum yield distinct power sums. For shifted slices $h\neq 0$, we establish a Modular Divisibility Obstruction (MDO): any solution requires $h$ to be divisible by a specific squarefree modulus $M_k = \prod_{p-1 \mid k-1} p$. This condition creates a strong divisibility filter; for example, if $k=13$, the obstruction eliminates $99.96\%$ of all possible shifts. We combine this arithmetic constraint with a geometric exclusion zone principle and a global overlap bound, showing that the slice size must satisfy $\min\{S, S+h\} \gg |h|$. Finally, we prove an asymptotic dominance bound $k \le \max\{S, S+h\} \log 2$, implying that for any fixed slice, solutions cannot exist for sufficiently large $k$. - oai:arXiv.org:2512.00551v2 - math.NT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace - http://creativecommons.org/licenses/by/4.0/ - Valery Asiryan + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Duc-Manh Nguyen - Finiteness of leaps of modules of integrable derivations of algebras of finite type - https://arxiv.org/abs/2512.00690 - arXiv:2512.00690v2 Announce Type: replace -Abstract: We prove the finiteness of leaps of modules of integrable derivations for algebras essentially of finite type and, more generally, for schemes essentially of finite type over an algebraically closed field of positive characteristic. This gives an affirmative answer to a question posed by L. N. Macarro. - oai:arXiv.org:2512.00690v2 + 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 math.AG - math.AC - Tue, 09 Dec 2025 00:00:00 -0500 + math.RT + Wed, 10 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - Takuya Miyamoto + 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 - A Dual-Mode Framework for Mean-Field Systems: Model-Based $H_2/H_\infty$ Control with Jump Diffusions and Model-Free Reinforcement Learning - https://arxiv.org/abs/2512.01000 - arXiv:2512.01000v2 Announce Type: replace -Abstract: Two methods for solving the robust control of mean-field systems are investigated in this paper. For the stochastic $H_2/H_\infty$ control problem of continuous-time mean-field stochastic differential equations with Poisson jumps over a finite horizon, the continuous and jump diffusion terms in the system depend not only on the state but also on the control input, external disturbance, and mean-field components. By employing the quasi-linear technique and the method of completing the square, a mean-field stochastic jump bounded real lemma for the system is derived. The feasibility of the stochastic $H_2/H_\infty$ control problem is demonstrated to be equivalent to the solvability of four sets of cross-coupled generalized differential Riccati equations. Based on this conclusion, a model-based numerical method is presented. Furthermore, this paper proposes a data-driven, model-free, off-policy reinforcement learning approach, which can be utilized to solve the $H_\infty$ control problem for the mean-field systems discussed herein. The findings establish a systematic framework for designing robust controllers for interacting particle systems. - oai:arXiv.org:2512.01000v2 - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Huimin Han, Shaolin Ji, Weihai Zhang + Naillin Guan, Yongle Hu - Contraction Mapping: Case Studies - https://arxiv.org/abs/2512.01050 - arXiv:2512.01050v2 Announce Type: replace -Abstract: While exploring dynamical systems, we often come across the principle of contraction mapping, or better known as the Banach fixed point theorem. It is an essential concept based on successive approximation, whose utility comes from two main guarantees: establishing existence and uniqueness of a solution, and establishing constructive proof. The intent of this manuscript is to break down two major proofs incorporating this in ordinary differential equations (ODEs), and make them a little more understandable step-by-step to an audience that presumably has adequate knowledge of modern calculus and real analysis. These are not original proofs, only original narration. - oai:arXiv.org:2512.01050v2 - math.DS - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace - http://creativecommons.org/publicdomain/zero/1.0/ - Shamanth Sreekanth + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Cheng Lin, Ge Xiong - Growth rates of sequences governed by the squarefree properties of its translates - https://arxiv.org/abs/2512.01087 - arXiv:2512.01087v2 Announce Type: replace -Abstract: We answer several questions of Erd\H{o}s regarding sequences of natural numbers $A$ whose translates $n+A$ intersect with the squarefree numbers in various specified ways. For instance, we show that if every translate only contains finitely many squarefree numbers, then $A$ has zero density, although the decay rate of this density can be arbitrarily slow. On the other hand, there exist sequences $A$ with optimal density $6/\pi^2$ for which infinitely many $n$ exist such that $n+a$ is squarefree for all $a \in A$ with $a < n$. In fact, infinitely many such $n$ exist for every exponentially increasing sequence, as long as the sequence avoids at least one residue class modulo $p^2$ for all primes $p$, a property we call admissible. If one instead requires infinitely many $n$ to exist such that $n+a$ is squarefree for all $a \in A$, then $A$ can have density arbitrarily close to, but not equal to, $6/\pi^2$. Finally, we prove bounds on the growth rate of sequences $A$ for which $a+a'$ is squarefree for all $a,a' \in A$, as well as bounds on the largest admissible subset of $\{1, 2, \ldots, N\}$. - oai:arXiv.org:2512.01087v2 - math.NT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Wouter van Doorn, Terence Tao + Yiyuan Wang - Periodicity and finite complexity in higher real $K$-theories - https://arxiv.org/abs/2512.01161 - arXiv:2512.01161v2 Announce Type: replace -Abstract: In this paper, we establish periodicity results for higher real $K$-theories at all heights and for all finite subgroups of the Morava stabilizer group at the prime 2. We further analyze the $RO(G)$-periodicity lattice of the height-$h$ Lubin--Tate theory, proving new $RO(G)$-graded periodicities and explicit finiteness results for the $RO(G)$-graded homotopy groups of $E_h$. Together, these results provide a foundation for both the structural and computational study of higher real $K$-theories. - oai:arXiv.org:2512.01161v2 - math.AT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Zhipeng Duan, Michael A. Hill, Guchuan Li, Yutao Liu, XiaoLin Danny Shi, Guozhen Wang, Zhouli Xu + Zeev Dvir - Towards a finite-slope universal Rankin-Selberg p-adic L-function - https://arxiv.org/abs/2512.01184 - arXiv:2512.01184v2 Announce Type: replace -Abstract: This article studies the finite--slope analogue of Loeffler's conjectural framework for Rankin--Selberg $p$-adic $L$-functions in universal deformation families. Starting from residual representations $\bar\rho_1,\bar\rho_2$ of tame level~$1$ satisfying Hypothesis~3.1 of~\cite{LoefflerUD}, we consider the half--ordinary Panchishkin family $(R,V,V^+)$ of Example~3.17 of loc.\ cit., where the first factor varies in the ordinary Hida deformation and the second factor in the unrestricted universal deformation space. - oai:arXiv.org:2512.01184v2 - math.NT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math-ph + math.MP + quant-ph + Wed, 10 Dec 2025 00:00:00 -0500 replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Haonan Gu + http://creativecommons.org/licenses/by/4.0/ + Stefan Teufel, Marius Wesle, Tom Wessel - Ergodicity and invariant measure approximation of the stochastic Cahn-Hilliard equation via an explicit fully discrete scheme - https://arxiv.org/abs/2512.01621 - arXiv:2512.01621v3 Announce Type: replace -Abstract: This paper investigates the stochastic Cahn-Hilliard equation (SCHE) driven by additive space-time white noise. We first refine the analytical ergodic theory by proving that the continuum equation admits a unique invariant measure in the more regular state space H_\alpha, extending the classical result of Da Prato and Debussche (1996) on the negative Sobolev space $\dot{H}^{-1}_\alpha$. To approximate long-time behaviour, we introduce an explicit fully discrete scheme that combines a finite-difference spatial discretization with a strongly tamed exponential Euler method in time. Uniform-in-time moment bounds in the $L^\infty$-norm are established for the numerical solution, and a uniform strong convergence estimate with an explicit rate is derived for the fully discrete approximation. Exploiting a mass-preserving minorization tailored to Neumann boundary conditions, we further show that the numerical scheme is geometrically ergodic and possesses a unique invariant measure, together with polynomial-order error bounds for approximating the exact invariant measure. Strong laws of large numbers are proved for both the continuous and discrete systems, ensuring almost-sure convergence of temporal averages to the corresponding ergodic limits. Numerical experiments corroborate the theoretical findings, including the long-time strong convergence and the accuracy of invariant measure approximation. Overall, the results provide a complete analytical and numerical framework for investigating the long-time statistical behaviour of the SCHE. - oai:arXiv.org:2512.01621v3 - math.NA - cs.NA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Nan Deng, Yibo Wang, Wanrong Cao + http://creativecommons.org/licenses/by/4.0/ + Krist\'of B\'erczi, Tam\'as Kir\'aly, Yutaro Yamaguchi, Yu Yokoi - Wetterich's Equation and its Boundary Conditions for Radon Measures on Locally Convex Spaces - https://arxiv.org/abs/2512.01742 - arXiv:2512.01742v2 Announce Type: replace -Abstract: Wetterich's equation and corresponding flows of effective average actions are used frequently in theoretical physics to study the properties of quantum field theories. Under appropriate conditions, Wetterich's equation also holds for Radon measures on locally convex spaces and the domain of the effective average action is the Lusin affine kernel of the measure. The resulting flow interpolates between the convex conjugate of the cumulant-generating function of the measure in question and its (generalised) Onsager-Machlup function. The underlying metric of the latter is induced by a family of measurable bilinear functionals that can be understood as bilinear versions of Lusin measurable linear functionals. - oai:arXiv.org:2512.01742v2 - math.FA - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.AG + math.AT + Wed, 10 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - Jobst Ziebell + Klaus Mattis, Swann Tubach - The chromatic number of finite projective spaces - https://arxiv.org/abs/2512.01760 - arXiv:2512.01760v2 Announce Type: replace -Abstract: The chromatic number of the finite projective space $\mathrm{PG}(n-1,q)$, denoted $\chi_q(n)$, is the minimum number of colors needed to color its points so that no line is monochromatic. We establish a recursive upper bound $\chi_q(n) \leq \chi_q(d) + \chi_q(n - d)$ for all $1 \leq d < n$ and use it to prove new upper bounds on $\chi_q(n)$ for all $q$. For $q = 2$, we further refine this recursion and prove that \[ \chi_2(n) \le \lfloor 2n/3 \rfloor + 1 \] for all $n \ge 2$, and that this bound is tight for all $n \le 7$. In particular, this recovers all previously known cases for $n \le 6$ and resolves the first open case $n = 7$. On the lower-bound side, using a connection with multicolor Ramsey numbers for triangles, we note that \[ \chi_2(n) \ge (1 - o(1))\,\frac{n}{\log n}. \] - We also consider $\chi_q(t;n)$, the minimum number of colors needed to color the points of $\mathrm{PG}(n-1,q)$ with no monochromatic $(t - 1)$-dimensional subspace, and establish an equivalence between $\chi_q(t;n)$ and the multicolor vector-space Ramsey numbers $R_q(t;k)$. Using this equivalence together with our upper bounds on $\chi_q(t;n)$, we improve, for every fixed $t$, the best known lower bounds on $R_q(t;k)$ from $\Omega_q(\log k)$ to $\Omega(k)$. - oai:arXiv.org:2512.01760v2 + 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 - Tue, 09 Dec 2025 00:00:00 -0500 + math.RA + Wed, 10 Dec 2025 00:00:00 -0500 replace - http://creativecommons.org/licenses/by/4.0/ - Anurag Bishnoi, Wouter Cames van Batenburg, Ananthakrishnan Ravi + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Yu Hin Au, Murray R. Bremner - Ground state solutions of $p$-Laplacian equations with nonnegative potentials on Lattice graphs - https://arxiv.org/abs/2512.02881 - arXiv:2512.02881v2 Announce Type: replace -Abstract: In this paper, we study the $p$-Laplacian equation - $$ - -\Delta_p u + V(x)|u|^{p-2}u = f(x,u) - $$ - on the lattice graph $\mathbb{Z}^N$ with nonnegative potentials, where $\Delta_p$ is the discrete $p$-Laplacian and $p\in(1,\infty)$. By employing the Nehari manifold method, we establish the existence of ground state solutions under suitable growth conditions on the nonlinearity $f(x,u)$, provided that the potential $V(x)$ is either periodic or bounded. Moreover, we prove that if $f$ is odd in $u$ and $p\geq2$, then the above equation admits infinitely many geometrically distinct solutions. Finally, we extend these results from $\mathbb{Z}^N$ to the more general setting of Cayley graphs. - oai:arXiv.org:2512.02881v2 - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Xinrong Zhao + Bhishan Jacelon - Equivalence of Synchronization States in the Hybrid Kuramoto Flow - https://arxiv.org/abs/2512.02986 - arXiv:2512.02986v2 Announce Type: replace -Abstract: We establish a unified synchronization framework for the all-to-all hybrid Kuramoto model that couples first- and second-order oscillators within a single dynamical system. Although the Kuramoto model has become one of the most widely used paradigms for describing synchronization phenomena-appearing in more than 100,000 scientific studies-the fundamental relationships among distinct synchronization states remain unresolved. In this work, we rigorously prove that full phase-locking, phase-locking, frequency synchronization, and order-parameter synchronization are equivalent for arbitrary hybrid ensembles. The proof combines dissipative energy methods, LaSalle-type compactness arguments, the Poincar{\'e}-Bendixson theorem, and Thieme's asymptotically autonomous theory to demonstrate that synchronization equivalence is topological, determined solely by the finite equilibrium structure of the all-to-all network. This result provides a complete mathematical characterization of synchronization in finite oscillator systems and clarifies its geometric invariance across first-, second-, and hybrid-order models. - oai:arXiv.org:2512.02986v2 - math.DS - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Ting-Yang Hsiao, Yun-Feng Lo, Chengbin Zhu + Tarek M. Elgindi - Strengthening Han's Fourier Entropy-Influence Inequality via an Information-Theoretic Proof - https://arxiv.org/abs/2512.03117 - arXiv:2512.03117v2 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:2512.03117v2 - cs.IT - math.IT - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace http://creativecommons.org/licenses/by/4.0/ - Peijie Li, Guangyue Han + Sidney A. Morris, Marcelo O. Ribeiro, Diego Marques - Parameter Optimization in Trajectory Planning via Differentiable Convex Programming - https://arxiv.org/abs/2512.03557 - arXiv:2512.03557v2 Announce Type: replace -Abstract: Sequential convex programming has been established as an effective framework for solving nonconvex trajectory planning problems. However, its performance is highly sensitive to problem parameters, including trajectory variables, algorithmic hyperparameters, and physical vehicle parameters. This paper introduces a differentiable sequential convex programming framework that integrates differentiable convex optimization with sequential convex programming to enable end-to-end parameter optimization. By deriving first-order sensitivity relations of second-order cone programming solutions with respect to problem data, exact gradients of trajectory performance metrics with respect to arbitrary parameters are obtained and propagated through iterations. The effectiveness of the proposed framework is validated through three representative applications: optimal terminal-time prediction for powered landing, trust-region penalty optimization in subproblems, and surface-to-mass ratio optimization for hypersonic gliding vehicles. Simulation results show that the proposed framework enables reliable gradient-based parameter learning and significantly improves numerical performance, convergence behavior, and design efficiency. These results indicate that the differentiable sequential convex programming framework provides a powerful and general tool for vehicle design, mission optimization, and hyperparameter selection in aerospace trajectory planning. - oai:arXiv.org:2512.03557v2 - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.CO + Wed, 10 Dec 2025 00:00:00 -0500 replace - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Ziqi Xu, Lin Cheng, Di Wu, Shengping Gong + http://creativecommons.org/licenses/by/4.0/ + Voalaza Mahavily Romuald, Benjamin Randrianirina - Homogenization of non-divergence form operators in i.i.d. random environments - https://arxiv.org/abs/2512.04410 - arXiv:2512.04410v2 Announce Type: replace -Abstract: We study random walks in a balanced, i.i.d. random environment in $\mathbb Z^d$ for $d\geq 3$. We establish improved convergence rates for the homogenization of the Dirichlet problem associated with the corresponding non-divergence form difference operators, surpassing the $O(R^{-1})$ rate, which is expected to be optimal for environments with a finite range of dependence. In particular, the improved rates are $O(R^{-3/2})$ when $d=3$, and $O(R^{-2}\log R)$ when $d\geq 4$. - oai:arXiv.org:2512.04410v2 - math.PR - math.AP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Xiaoqin Guo, Timo Sprekeler, Hung V. Tran + Geraldo Botelho, Ariel Mon\c{c}\~ao - Marton's Conjecture in Finite Fields of Odd Characteristic via a Polynomial Stability Lemma - https://arxiv.org/abs/2512.04433 - arXiv:2512.04433v2 Announce Type: replace -Abstract: We study small-doubling subsets of finite-dimensional vector spaces over finite fields of odd characteristic. Let $A \subset \mathbb{F}_p^n$ be non-empty with $|A+A| \le K|A|$. We prove that $A$ can be covered by at most $K^{O(1)}$ cosets of a subspace $H \le \mathbb{F}_p^n$ with $|H| \le K^{O(1)}|A|$, giving a polynomial Freiman--Ruzsa (PFR/Marton) theorem in $\mathbb{F}_p^n$ for odd primes $p$. The key input is a polynomial stability lemma which yields a dichotomy: either the $L^4$ Fourier mass of $1_A$ concentrates on a span of dimension $\operatorname{poly}(K)$, or in a quotient of codimension $\operatorname{poly}(K)$ the doubling constant decreases by at least $K^{-C}$. Iterating the latter alternative and combining it with standard covering arguments gives the polynomial-structured conclusion. Together with the characteristic-$2$ result of Green, Gowers, Manners, and Tao (2023), this completes the resolution of Marton's conjecture for all finite fields. Our proof provides an independent, direct Fourier-analytic approach with explicit spectral stability dichotomies. - oai:arXiv.org:2512.04433v2 - math.CO + 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 - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Mohammad Taha Kazemi Moghadam + Dante Bonolis - A solution to Banach conjecture - https://arxiv.org/abs/2512.04628 - arXiv:2512.04628v2 Announce Type: replace -Abstract: In this paper, we first prove that the origin-symmetric star body with ellipsoidal sections is an ellipsoid. Then we give a complete proof of Banach's isometric subspace problem in finite dimensions through the John ellipsoid. - oai:arXiv.org:2512.04628v2 - math.FA - math.MG - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.AT + Wed, 10 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Ning Zhang + Dongwoo Gang - Detect duality obstruction of calibrations in smooth category - https://arxiv.org/abs/2512.04789 - arXiv:2512.04789v2 Announce Type: replace -Abstract: This paper consists of three parts: (a) exhibit a new gluing result which can dramatically simplify extensions of calibration pairs; (b) observe that every Lawlor cone can support coflat calibrations singular only at the origin; (c) show that there exist many Lawlor cones which cannot support any smooth calibrations. As an application, we extend our previous work on detecting duality obstruction of calibrations in the smooth category. - oai:arXiv.org:2512.04789v2 - math.DG - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math-ph + math.MP + Wed, 10 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Yongsheng Zhang + Mark Sellke + + + 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 + replace + http://creativecommons.org/licenses/by/4.0/ + Kuiyue Liu, Shanshan Chen - A Nehari manifold method for nonvariational problems - https://arxiv.org/abs/2512.05055 - arXiv:2512.05055v2 Announce Type: replace -Abstract: The aim of this paper is to extend the Nehari manifold method from the variational setting to the nonvariational framework of fixed point equations. This is achieved by constructing a radial energy functional that generalizes the standard one from the variational case. Furthermore, the solutions obtained through our method are localized in conical annular sets, which leads to the existence of multiple solutions. The abstract results are illustrated by two representative applications. - oai:arXiv.org:2512.05055v2 + 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 - math.FA - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 replace http://creativecommons.org/licenses/by/4.0/ - Radu Precup, Andrei Stan + \'Angel Castro, Daniel Lear - Scarf complexes of connected and path ideals - https://arxiv.org/abs/2512.05376 - arXiv:2512.05376v2 Announce Type: replace -Abstract: The $t$-connected ideal of a graph $G$ is generated by all connected induced subgraphs of $G$ with $t$ vertices. When $t = 2$, this coincides with the usual edge ideal of the graph. Following the work of Faridi et al., we give a classification of the graphs whose $t$-connected ideals are minimally resolved by their Scarf complex. We also consider the $t$-path ideal of a graph $G$ which is the ideal generated by all paths of length $t$ in $G$. In this case, we are able to give a classification of the same type for paths of length $t = 4$. - oai:arXiv.org:2512.05376v2 - math.AC - math.CO - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.GT + Wed, 10 Dec 2025 00:00:00 -0500 replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Trung Chau, Richie Sheng, Tim Tribone, Deborah Wooton + Hao Liang, Yunhao Qiu, Yan Tan, Qinghai Zhang - The Optimal Approximation Factor in Density Estimation - https://arxiv.org/abs/1902.05876 - arXiv:1902.05876v4 Announce Type: replace-cross -Abstract: Consider the following problem: given two arbitrary densities $q_1,q_2$ and a sample-access to an unknown target density $p$, find which of the $q_i$'s is closer to $p$ in total variation. - A remarkable result due to Yatracos shows that this problem is tractable in the following sense: there exists an algorithm that uses $O(\epsilon^{-2})$ samples from $p$ and outputs~$q_i$ such that with high probability, $TV(q_i,p) \leq 3\cdot\mathsf{opt} + \epsilon$, where $\mathsf{opt}= \min\{TV(q_1,p),TV(q_2,p)\}$. Moreover, this result extends to any finite class of densities $\mathcal{Q}$: there exists an algorithm that outputs the best density in $\mathcal{Q}$ up to a multiplicative approximation factor of 3. - We complement and extend this result by showing that: (i) the factor 3 can not be improved if one restricts the algorithm to output a density from $\mathcal{Q}$, and (ii) if one allows the algorithm to output arbitrary densities (e.g.\ a mixture of densities from $\mathcal{Q}$), then the approximation factor can be reduced to 2, which is optimal. In particular this demonstrates an advantage of improper learning over proper in this setup. - We develop two approaches to achieve the optimal approximation factor of 2: an adaptive one and a static one. Both approaches are based on a geometric point of view of the problem and rely on estimating surrogate metrics to the total variation. Our sample complexity bounds exploit techniques from {\it Adaptive Data Analysis}. - oai:arXiv.org:1902.05876v4 - cs.LG - cs.CC + 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 + replace + http://creativecommons.org/licenses/by/4.0/ + Peijie Li, Guangyue Han + + + 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 + math.CO math.PR - stat.ML - Tue, 09 Dec 2025 00:00:00 -0500 - replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Olivier Bousquet, Daniel Kane, Shay Moran + Wed, 10 Dec 2025 00:00:00 -0500 + replace + http://creativecommons.org/licenses/by/4.0/ + Dawid Ignasiak, Lyuben Lichev - Cumulative Games: Who is the current player? - https://arxiv.org/abs/2005.06326 - arXiv:2005.06326v2 Announce Type: replace-cross -Abstract: Combinatorial Game Theory(CGT)is a branch of Game Theory that has developed largely independently of Economic Game Theory (EGT), and is concerned with deep mathematical properties of two-player zero-sum games recursively defined over various combinatorial structures. The aim of this work is to lay the foundations for bridging the conceptual and technical gaps between CGT and EGT, here interpreted as multiplayer Extensive Form Games, so that they can be treated within a unified framework. More specifically, we introduce a class of $n$-player, general-sum games, called {\sc Cumulative Games}, which can be analyzed using tools from both CGT and EGT. We show how two of the most fundamental definitions of CGT, the outcome function and the disjunctive sum operator, naturally extend to the class of {\sc Cumulative Games}. The outcome function allows for efficient equilibrium computation under certain restrictions, while the disjunctive sum operator lets us define a partial order over games according to the advantage that a given player has. Finally, we show that any Extensive Form Game can be written as a {\sc Cumulative Game}. - oai:arXiv.org:2005.06326v2 - cs.GT + 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 - Tue, 09 Dec 2025 00:00:00 -0500 - replace-cross + math.NT + Wed, 10 Dec 2025 00:00:00 -0500 + replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Urban Larsson, Reshef Meir, Yair Zick + Mohammad Taha Kazemi Moghadam - AR-sieve Bootstrap for High-dimensional Time Series - https://arxiv.org/abs/2112.00414 - arXiv:2112.00414v2 Announce Type: replace-cross -Abstract: This paper proposes a new AR-sieve bootstrap approach to high-dimensional time series. The major challenge of classical bootstrap methods on high-dimensional time series is two-fold: curse of dimensionality and temporal dependence. To address such a difficulty, we utilize factor modeling to reduce dimension and capture temporal dependence simultaneously. A factor-based bootstrap procedure is constructed, which performs an AR-sieve bootstrap on the extracted low-dimensional common factor time series and then recovers the bootstrap samples for the original data from the factor model. Asymptotic properties for bootstrap mean statistics and extreme eigenvalues are established. Various simulation studies further demonstrate the advantages of the new AR-sieve bootstrap in high-dimensional scenarios. An empirical application on particulate matter (PM) concentration data is studied, where bootstrap confidence intervals for mean vectors and autocovariance matrices are provided. - oai:arXiv.org:2112.00414v2 - stat.ME - math.ST - stat.TH - Tue, 09 Dec 2025 00:00:00 -0500 - replace-cross + 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 + replace http://creativecommons.org/licenses/by/4.0/ - Daning Bi, Han Lin Shang, Yanrong Yang, Huanjun Zhu + Kassie Archer, Aaron Geary, Robert P. Laudone - One-Shot Distributed Source Simulation: As Quantum as it Can Get - https://arxiv.org/abs/2301.04301 - arXiv:2301.04301v3 Announce Type: replace-cross -Abstract: Distributed source simulation is the task where two (or more) parties share some correlated randomness and use local operations and no communication to convert this into some target correlation. Wyner's seminal result showed that asymptotically the rate of uniform shared randomness needed for this task is given by a mutual information induced measure, now referred to as Wyner's common information. This asymptotic result was extended by Hayashi in the quantum setting to separable states, the largest class of states for which this task can be performed to vanishing error. In this work we characterize this task in a near-tight manner in the one-shot setting using the smooth entropy framework. We do this by introducing one-shot operational quantities and correlation measures that characterize them. We establish asymptotic equipartition properties for our correlation measures thereby recovering the previous vanishing-error asymptotic results. In doing so, we consider technical points in one-shot network information theory and provide methods for cardinality bounds in the smooth entropy calculus. We also introduce entangled state versions of the distributed source simulation task and determine bounds in this setting via quantum embezzling. This provides a strong characterization of this network task in the one-shot, quantum regime. - oai:arXiv.org:2301.04301v3 - quant-ph - cs.IT - math.IT - Tue, 09 Dec 2025 00:00:00 -0500 - replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - 10.1109/TIT.2025.3624812 - IEEE Transactions on Information Theory, vol. 71, no. 12, pp. 9251 - 9284, Oct 2025 - Ian George, Min-Hsiu Hsieh, Eric Chitambar - - - Static and Dynamic BART for Rank-Order Data - https://arxiv.org/abs/2308.10231 - arXiv:2308.10231v5 Announce Type: replace-cross -Abstract: Ranking lists are often provided at regular time intervals in a range of applications, including economics, sports, marketing, and politics. Most popular methods for rank-order data postulate a linear specification for the latent scores, which determine the observed ranks, and ignore the temporal dependence of the ranking lists. To address these issues, novel nonparametric static (ROBART) and autoregressive (ARROBART) models are developed, with latent scores defined as nonlinear Bayesian additive regression tree functions of covariates. To make inferences in the dynamic ARROBART model, closed-form filtering, predictive, and smoothing distributions for the latent time-varying scores are derived. These results are applied in a Gibbs sampler with data augmentation for posterior inference. The proposed methods are shown to outperform existing competitors in simulation studies, static data applications to electoral data, stated preferences for sushi and movies, and dynamic data applications to economic complexity rankings of countries and weekly pollster rankings of NCAA football teams. - oai:arXiv.org:2308.10231v5 - stat.ME - math.ST - stat.CO - stat.TH - Tue, 09 Dec 2025 00:00:00 -0500 - replace-cross + 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 + replace http://creativecommons.org/licenses/by-nc-nd/4.0/ - Matteo Iacopini, Eoghan O'Neill, Luca Rossini + Qingxiang Xu - Asymptotic implementation of multipartite quantum channels and other quantum instruments using local operations and classical communication - https://arxiv.org/abs/2310.05362 - arXiv:2310.05362v3 Announce Type: replace-cross -Abstract: We prove a necessary condition that a quantum channel on a multipartite system may be approximated arbitrarily closely using local operations and classical communication (LOCC). We then extend those arguments to obtain a condition that applies to all quantum instruments, which range from the most refined case, a generalized measurement, to the most coarse-grained, which is a quantum channel. We illustrate these results by a detailed analysis of a quantum instrument that is known not to be implementable by LOCC, but which can be arbitrarily closely approximated within that framework. As one outgrowth of this analysis, we find a quantum measurement that falls into the same category: it cannot be implemented exactly by LOCC, but can be approximated by LOCC arbitrarily closely. This measurement has an infinite number of outcomes, leaving open the question as to whether or not there exists a measurement within this same category but having only a finite number of outcomes. - oai:arXiv.org:2310.05362v3 - quant-ph - math-ph - math.MP - Tue, 09 Dec 2025 00:00:00 -0500 - replace-cross + 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 + math.OC + cs.LG + cs.RO + cs.SY + eess.SY + Wed, 10 Dec 2025 00:00:00 -0500 + replace http://creativecommons.org/licenses/by/4.0/ - Scott M. Cohen + Ajinkya Bhole, Mohammad Mahmoudi Filabadi, Guillaume Crevecoeur, Tom Lefebvre - Hidden Minima in Two-Layer ReLU Networks - https://arxiv.org/abs/2312.16819 - arXiv:2312.16819v3 Announce Type: replace-cross -Abstract: We consider the optimization problem arising from fitting two-layer ReLU networks with $d$ inputs under the square loss, where labels are generated by a target network. Two infinite families of spurious minima have recently been identified: one whose loss vanishes as $d \to \infty$, and another whose loss remains bounded away from zero. The latter are nevertheless avoided by vanilla SGD, and thus hidden, motivating the search for analytic properties distinguishing the two types. Perhaps surprisingly, the Hessian spectra of hidden and non-hidden minima agree up to terms of order $O(d^{-1/2})$, providing limited explanatory power. Consequently, our analysis of hidden minima proceeds instead via curves along which the loss is minimized or maximized. The main result is that arcs emanating from hidden minima differ, characteristically, by their structure and symmetry, precisely on account of the $O(d^{-1/2})$-eigenvalue terms absent from previous analyses. - oai:arXiv.org:2312.16819v3 - cs.LG + 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 - stat.ML - Tue, 09 Dec 2025 00:00:00 -0500 - replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Yossi Arjevani - - - Non-Abelian Self-Correcting Quantum Memory and Transversal Non-Clifford Gate beyond the $n^{1/3}$ Distance Barrier - https://arxiv.org/abs/2405.11719 - arXiv:2405.11719v5 Announce Type: replace-cross -Abstract: We construct a family of infinitely many new candidate non-Abelian self-correcting topological quantum memories in $D\geq 5+1$ spacetime dimensions without particle excitations using local commuting non-Pauli stabilizer lattice models and field theories of $\mathbb{Z}_2^3$ higher-form gauge fields with nontrivial topological action. We call such non-Pauli stabilizer models magic stabilizer codes. The family of topological orders have Abelian electric excitations and non-Abelian magnetic excitations that obey Ising-like fusion rules and non-Abelian braiding, including Borromean ring type braiding which is a signature of non-Abelian topological order, generalizing the dihedral group $\mathbb{D}_8$ gauge theory in (2+1)D. The simplest example includes a new non-Abelian self-correcting memory in (5+1)D with Abelian loop excitations and non-Abelian membrane excitations. We prove the self-correction property and the thermal stability, and devise a probabilistic local cellular-automaton decoder. We also construct fault-tolerant non-Clifford CCZ logical gate using constant depth circuit from higher cup products in the 5D non-Abelian code. The use of higher-cup products and non-Pauli stabilizers allows us to get an $O(n^{2/5})$ distance overcoming the $O(n^{1/3})$ distance barrier in conventional topological stabilizer codes, including the 3D color code and the 6D self-correcting color code. - oai:arXiv.org:2405.11719v5 - quant-ph - cond-mat.str-el - hep-th - math.QA - Tue, 09 Dec 2025 00:00:00 -0500 - replace-cross + Wed, 10 Dec 2025 00:00:00 -0500 + replace http://creativecommons.org/licenses/by-nc-nd/4.0/ - Po-Shen Hsin, Ryohei Kobayashi, Guanyu Zhu + Federico Della Croce, Quentin Schau - Kinodynamic Motion Planning for Collaborative Object Transportation by Multiple Mobile Manipulators - https://arxiv.org/abs/2409.14910 - arXiv:2409.14910v2 Announce Type: replace-cross -Abstract: This work proposes a kinodynamic motion planning technique for collaborative object transportation by multiple mobile manipulators in dynamic environments. A global path planner computes a linear piecewise path from start to goal. A novel algorithm detects the narrow regions between the static obstacles and aids in defining the obstacle-free region to enhance the feasibility of the global path. We then formulate a local online motion planning technique for trajectory generation that minimizes the control efforts in a receding horizon manner. It plans the trajectory for finite time horizons, considering the kinodynamic constraints and the static and dynamic obstacles. The planning technique jointly plans for the mobile bases and the arms to utilize the locomotion capability of the mobile base and the manipulation capability of the arm efficiently. We use a convex cone approach to avoid self-collision of the formation by modifying the mobile manipulators admissible state without imposing additional constraints. Numerical simulations and hardware experiments showcase the efficiency of the proposed approach. - oai:arXiv.org:2409.14910v2 - cs.RO - cs.MA - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 - replace-cross + 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 + replace http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - 10.1115/1.4069407 - J. Mechanisms Robotics. Dec 2025, 17(12) - Keshab Patra, Arpita Sinha, Anirban Guha + Yiru Wang, Bingqian Li, Yi Zhou, Zhiqiang Wei, Yu Ye, Yiqian Shi, Bin Xu - Compressing multivariate functions with tree tensor networks - https://arxiv.org/abs/2410.03572 - arXiv:2410.03572v2 Announce Type: replace-cross -Abstract: Tensor networks are a compressed format for multi-dimensional data. One-dimensional tensor networks -- often referred to as tensor trains (TT) or matrix product states (MPS) -- are increasingly being used as a numerical ansatz for continuum functions by ``quantizing'' the inputs into discrete binary digits. Here we demonstrate the power of more general tree tensor networks for this purpose. We provide direct constructions of a number of elementary functions as generic tree tensor networks and interpolative constructions for more complicated functions via a generalization of the tensor cross interpolation algorithm. For a range of multi-dimensional functions we show how more structured tree tensor networks offer a significantly more efficient ansatz than the commonly used tensor train. We demonstrate an application of our methods to solving multi-dimensional, non-linear Fredholm equations, providing a rigorous bound on the rank of the solution which, in turn, guarantees exponentially scaling accuracy with the size of the tree tensor network for certain problems. - oai:arXiv.org:2410.03572v2 - quant-ph - cs.NA - math.NA - physics.comp-ph - Tue, 09 Dec 2025 00:00:00 -0500 - replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Joseph Tindall, E. Miles Stoudenmire, Ryan Levy + 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 - Two waves of adaptation: speciation induced by dormancy in a model with changing environment - https://arxiv.org/abs/2410.10890 - arXiv:2410.10890v2 Announce Type: replace-cross -Abstract: We consider a population model in which the season alternates between winter and summer, and individuals can acquire mutations either that are advantageous in the summer and disadvantageous in the winter, or vice versa. Also, we assume that individuals in the population can either be active or dormant, and that individuals can move between these two states. Dormant individuals do not reproduce but do not experience selective pressures. We show that, under certain conditions, over time we see two waves of adaptation. Some individuals repeatedly acquire mutations that are beneficial in the summer, while others repeatedly acquire mutations that are beneficial in the winter. Individuals can survive the season during which they are less fit by entering a dormant state. This result demonstrates that, for populations in fluctuating environments, dormancy has the potential to induce speciation. - oai:arXiv.org:2410.10890v2 - q-bio.PE - math.PR - Tue, 09 Dec 2025 00:00:00 -0500 - replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Fernando Cordero, Adri\'an Gonz\'alez Casanova, Jason Schweinsberg + 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 + math.AG + math.CO + math.OC + Wed, 10 Dec 2025 00:00:00 -0500 + replace + http://creativecommons.org/licenses/by/4.0/ + Elisenda Feliu, Joan Ferrer, M\'at\'e L. Telek - Strong-field resummed heat kernels and effective actions: inhomogeneous fields - https://arxiv.org/abs/2410.11364 - arXiv:2410.11364v2 Announce Type: replace-cross -Abstract: We study the strong-field limit of a theory involving a quantum scalar field coupled to a vector background, which can be either an electromagnetic field or a non-gauge field coupled through the first derivative term. Our approach consists in obtaining resummed expressions for the associated heat kernels, from which we derive the corresponding resummed effective actions. These results allow us to discuss the effect of pair creation. Finally, we conjecture that resummations for more general theories should be possible. - oai:arXiv.org:2410.11364v2 - hep-th - math-ph - math.MP - quant-ph - Tue, 09 Dec 2025 00:00:00 -0500 - replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - S. A. Franchino-Vi\~nas, C. Garc\'ia-P\'erez, F. D. Mazzitelli, S. Pla, V. Vitagliano, U. Wainstein-Haimovichi + 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 + replace + http://creativecommons.org/licenses/by/4.0/ + Sam Adriaensen - Extendibility of Brauer states - https://arxiv.org/abs/2411.04597 - arXiv:2411.04597v2 Announce Type: replace-cross -Abstract: We investigate the extendibility problem for Brauer states, focusing on the symmetric two-sided extendibility and the de Finetti extendibility. By employing the representation theory of the unitary and orthogonal groups, we provide a general recipe for determining the set of $(n,m)$-extendible and $n$-de Finetti-extendible Brauer states. From the concrete form of the commutant of the diagonal action of the orthogonal group, we explicitly determine the set of parameters for which the Brauer states are $(1,2)$-, $(1,3)$- and $(2,2)$-extendible in any dimension $d$ and find that Brauer states extend with a non-trivial trade-off in $n$ and $m$. Using the same recipe we also provide an estimate of the set of $(1,m)$-extendible Brauer states for any $m$ and dimension $d$. Finally, using the branching rules from $\mathrm{U}(d)$ to $\mathrm{O}(d)$, we obtain the set of $n$-de Finetti-extendible Brauer states in any dimension, and also analytically describe the $n\to\infty$ limiting shape which turns out not to be a polygon for odd dimensions. - oai:arXiv.org:2411.04597v2 - quant-ph - math-ph - math.MP - Tue, 09 Dec 2025 00:00:00 -0500 - replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Adrian Solymos, D\'avid Jakab, Zolt\'an Zimbor\'as + 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 + replace + http://creativecommons.org/licenses/by/4.0/ + Amandip Sangha + + + 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 + replace + http://creativecommons.org/licenses/by/4.0/ + Shoham Letzter, Arjun Ranganathan - Information geometry of bosonic Gaussian thermal states - https://arxiv.org/abs/2411.18268 - arXiv:2411.18268v2 Announce Type: replace-cross -Abstract: Bosonic Gaussian thermal states form a fundamental class of states in quantum information science. This paper explores the information geometry of these states, focusing on characterizing the distance between two nearby states and the geometry induced by a parameterization in terms of their mean vectors and Hamiltonian matrices. In particular, for the family of bosonic Gaussian thermal states, we derive expressions for their Fisher-Bures, Kubo-Mori, and $\alpha$-$z$ information matrices with respect to their mean vectors and Hamiltonian matrices. An important application of our formulas consists of fundamental limits on how well one can estimate these parameters. We additionally establish formulas for the derivatives and the symmetric logarithmic derivatives of bosonic Gaussian thermal states. The former could have applications in gradient descent algorithms for quantum machine learning when using bosonic Gaussian thermal states as an ansatz, and the latter in formulating optimal strategies for single parameter estimation of bosonic Gaussian thermal states. Finally, the expressions for the aforementioned information matrices could have additional applications in natural gradient descent algorithms when using bosonic Gaussian thermal states as an ansatz. - oai:arXiv.org:2411.18268v2 + 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 - cs.IT + cond-mat.str-el hep-th math-ph - math.IT math.MP - Tue, 09 Dec 2025 00:00:00 -0500 - replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Zixin Huang, Mark M. Wilde - - - Dynamically optimal portfolios for monotone mean--variance preferences - https://arxiv.org/abs/2503.08272 - arXiv:2503.08272v2 Announce Type: replace-cross -Abstract: Monotone mean-variance (MMV) utility is the minimal modification of the classical Markowitz utility that respects rational ordering of investment opportunities. This paper provides, for the first time, a complete characterization of optimal dynamic portfolio choice for the MMV utility in asset price models with independent returns. The task is performed under minimal assumptions, weaker than the existence of an equivalent martingale measure and with no restrictions on the moments of asset returns. We interpret the maximal MMV utility in terms of the monotone Sharpe ratio (MSR) and show that the global squared MSR arises as the nominal yield from continuously compounding at the rate equal to the maximal local squared MSR. The paper gives simple necessary and sufficient conditions for mean-variance (MV) efficient portfolios to be MMV efficient. Several illustrative examples contrasting the MV and MMV criteria are provided. - oai:arXiv.org:2503.08272v2 - q-fin.PM - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 + math.PR + Wed, 10 Dec 2025 00:00:00 -0500 replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Ale\v{s} \v{C}ern\'y, Johannes Ruf, Martin Schweizer + 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 - Using Wavelet Decomposition to Determine the Dimension of Structures from Projected Images - https://arxiv.org/abs/2503.23202 - arXiv:2503.23202v2 Announce Type: replace-cross -Abstract: Mesoscale structures can often be described as fractional dimensional across a wide range of scales. We consider a $\gamma$ dimensional measure embedded in an $N$ dimensional space and discuss how to determine its dimension, both in $N$ dimensions and projected into $D$ dimensions. - It is a highly non-trivial problem to decode the original geometry from lower dimensional projection of a high-dimensional measure. The projections are space-feeling, the popular box-counting techniques do not apply, and the Fourier methods are contaminated by aliasing effects. In the present paper we demonstrate that under the "Copernican hypothesis'' that we are not observing objects from a special direction, projection in a wavelet basis is remarkably simple: the wavelet power spectrum of a projected $\gamma$ dimensional measure is $P_j \propto 2^{-j\gamma}$. This holds regardless of the embedded dimension, $N$, and the projected dimension, $D$. This approach could have potentially broad applications in data sciences where a typically sparse matrix encodes lower dimensional information embedded in an extremely high dimensional field and often measured in projection to a low dimensional space. - Here, we apply this method to JWST and Chandra observations of the nearby supernova Cas A. We find that the emissions can be represented by projections of mesoscale substructures with fractal dimensions varying from $\gamma = 1.7$ for the warm CO layer observed by JWST, up to $\gamma = 2.5$ for the hot X-ray emitting gas layer in the supernova remnant. The resulting power law indicates that the emission is coming from a fractal dimensional mesoscale structure likely produced by magneto-hydrodynamical instabilities in the expanding supernova shell. - oai:arXiv.org:2503.23202v2 - astro-ph.HE - astro-ph.GA - math.AP - physics.data-an - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.CO + Wed, 10 Dec 2025 00:00:00 -0500 replace-cross http://creativecommons.org/licenses/by/4.0/ - Svitlana Mayboroda, David N Spergel + Niloufar Fuladi, Alfredo Hubard, Arnaud de Mesmay - Entanglement recycling in two-step port-based teleportation - https://arxiv.org/abs/2504.00710 - arXiv:2504.00710v3 Announce Type: replace-cross -Abstract: A protocol involving the repetitive (twofold, to be precise) application of PBT protocol to the same resource is studied. The quantities characterizing the resulting protocol, so-called \textit{two-step PBT}, namely \textit{enatnglement fidelity} and \textit{success probability} are provided for two scenarios, relying on application of pretty-good measurement, i.e. deterministic and probabilistic PBT with non-EPR resource. This results show that two-step PBT is an accurate protocol, provided the resource is sufficiently large. In particular, the deterministic two-step PBT obtains fidelity that is remarkably close to the optimal MPBT fidelity for teleportation of two quantum states. Additionally, the \textit{recycling fidelity}, i.e. the quantity characterizing the degradation of the resource state is calculated for repetitive application of probabilistic protocol, for both EPR and optimized resource, showing that entanglement recycling with two-step PBT is possible in the former case as well. - oai:arXiv.org:2504.00710v3 - quant-ph - math-ph - math.MP - Tue, 09 Dec 2025 00:00:00 -0500 + 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/4.0/ - Piotr Kopszak, Dmitry Grinko, Adam Burchardt, Maris Ozols, Micha{\l} Studzi\'nski, Marek Mozrzymas + http://creativecommons.org/licenses/by-nc-sa/4.0/ + Philip Candelas, Xenia de la Ossa, Pyry Kuusela - Certifying Stability of Reinforcement Learning Policies using Generalized Lyapunov Functions - https://arxiv.org/abs/2505.10947 - arXiv:2505.10947v3 Announce Type: replace-cross -Abstract: Establishing stability certificates for closed-loop systems under reinforcement learning (RL) policies is essential to move beyond empirical performance and offer guarantees of system behavior. Classical Lyapunov methods require a strict stepwise decrease in the Lyapunov function but such certificates are difficult to construct for learned policies. The RL value function is a natural candidate but it is not well understood how it can be adapted for this purpose. To gain intuition, we first study the linear quadratic regulator (LQR) problem and make two key observations. First, a Lyapunov function can be obtained from the value function of an LQR policy by augmenting it with a residual term related to the system dynamics and stage cost. Second, the classical Lyapunov decrease requirement can be relaxed to a generalized Lyapunov condition requiring only decrease on average over multiple time steps. Using this intuition, we consider the nonlinear setting and formulate an approach to learn generalized Lyapunov functions by augmenting RL value functions with neural network residual terms. Our approach successfully certifies the stability of RL policies trained on Gymnasium and DeepMind Control benchmarks. We also extend our method to jointly train neural controllers and stability certificates using a multi-step Lyapunov loss, resulting in larger certified inner approximations of the region of attraction compared to the classical Lyapunov approach. Overall, our formulation enables stability certification for a broad class of systems with learned policies by making certificates easier to construct, thereby bridging classical control theory and modern learning-based methods. - oai:arXiv.org:2505.10947v3 - cs.LG - cs.RO - cs.SY - eess.SY - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + cs.IT + math.IT + nlin.AO + stat.ML + Wed, 10 Dec 2025 00:00:00 -0500 replace-cross http://creativecommons.org/licenses/by/4.0/ - Kehan Long, Jorge Cort\'es, Nikolay Atanasov + 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 - Stochastic Orthogonal Regularization for deep projective priors - https://arxiv.org/abs/2505.13078 - arXiv:2505.13078v3 Announce Type: replace-cross -Abstract: Many crucial tasks of image processing and computer vision are formulated as inverse problems. Thus, it is of great importance to design fast and robust algorithms to solve these problems. In this paper, we focus on generalized projected gradient descent (GPGD) algorithms where generalized projections are realized with learned neural networks and provide state-of-the-art results for imaging inverse problems. Indeed, neural networks allow for projections onto unknown low-dimensional sets that model complex data, such as images. We call these projections deep projective priors. In generic settings, when the orthogonal projection onto a lowdimensional model set is used, it has been shown, under a restricted isometry assumption, that the corresponding orthogonal PGD converges with a linear rate, yielding near-optimal convergence (within the class of GPGD methods) in the classical case of sparse recovery. However, for deep projective priors trained with classical mean squared error losses, there is little guarantee that the hypotheses for linear convergence are satisfied. In this paper, we propose a stochastic orthogonal regularization of the training loss for deep projective priors. This regularization is motivated by our theoretical results: a sufficiently good approximation of the orthogonal projection guarantees linear stable recovery with performance close to orthogonal PGD. We show experimentally, using two different deep projective priors (based on autoencoders and on denoising networks), that our stochastic orthogonal regularization yields projections that improve convergence speed and robustness of GPGD in challenging inverse problem settings, in accordance with our theoretical findings. - oai:arXiv.org:2505.13078v3 - eess.IV - cs.NE + 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 - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 replace-cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Ali Joundi (UB), Yann Traonmilin (UB), Alasdair Newson (ISIR) + Huizhen Yu, Yi Wan, Richard S. Sutton - Learning where to learn: Training data distribution optimization for scientific machine learning - https://arxiv.org/abs/2505.21626 - arXiv:2505.21626v3 Announce Type: replace-cross -Abstract: In scientific machine learning, models are routinely deployed with parameter values or boundary conditions far from those used in training. This paper studies the learning-where-to-learn problem of designing a training data distribution that minimizes average prediction error across a family of deployment regimes. A theoretical analysis shows how the training distribution shapes deployment accuracy. This motivates two adaptive algorithms based on bilevel or alternating optimization in the space of probability measures. Discretized implementations using parametric distribution classes or nonparametric particle-based gradient flows deliver optimized training distributions that outperform nonadaptive designs. Once trained, the resulting models exhibit improved sample complexity and robustness to distribution shift. This framework unlocks the potential of principled data acquisition for learning functions and solution operators of partial differential equations. - oai:arXiv.org:2505.21626v3 - cs.LG + 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 - stat.ML - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 replace-cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Nicolas Guerra, Nicholas H. Nelsen, Yunan Yang + Artemi Makarow, Christian Kirches - Fast prediction of plasma instabilities with sparse-grid-accelerated optimized dynamic mode decomposition - https://arxiv.org/abs/2507.03245 - arXiv:2507.03245v2 Announce Type: replace-cross -Abstract: Parametric data-driven reduced-order models (ROMs) that embed dependencies in a large number of input parameters are crucial for enabling many-query tasks in large-scale problems. These tasks, including design optimization, control, and uncertainty quantification, are essential for developing digital twins in real-world applications. However, standard grid-based data generation methods are computationally prohibitive due to the curse of dimensionality. This paper investigates efficient training of parametric data-driven ROMs using sparse grid interpolation with (L)-Leja points, specifically targeting scenarios with higher-dimensional input parameter spaces. (L)-Leja points are nested and exhibit slow growth, resulting in sparse grids with low cardinality in low-to-medium dimensional settings, making them ideal for large-scale, computationally expensive problems. Focusing on gyrokinetic simulations of plasma micro-instabilities in fusion experiments as a representative real-world application, we construct parametric ROMs for the full 5D gyrokinetic distribution function via optimized dynamic mode decomposition (optDMD) and sparse grids based on (L)-Leja points. We perform detailed experiments in two scenarios: First, the Cyclone Base Case benchmark assesses optDMD ROM prediction capabilities beyond training time horizons and across variations in the binormal wave number. Second, for a real-world electron-temperature-gradient-driven micro-instability simulation with six input parameters, we demonstrate that a predictive parametric optDMD ROM that is up to three orders of magnitude cheaper to evaluate can be constructed using only 28 high-fidelity gyrokinetic simulations, enabled by the use of sparse grids. In the broader context of fusion research, these results demonstrate the potential of sparse grid-based parametric ROMs to enable otherwise intractable many-query tasks. - oai:arXiv.org:2507.03245v2 - physics.comp-ph - cs.CE - cs.NA - math.NA - physics.plasm-ph - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math-ph + math.MP + Wed, 10 Dec 2025 00:00:00 -0500 replace-cross http://creativecommons.org/licenses/by/4.0/ - Kevin Gill, Ionut-Gabriel Farcas, Silke Glas, Benjamin J. Faber + 10.1007/s13324-025-01113-2 + Anal.Math.Phys. 15, 113 (2025) + Elena Apresyan, Gor Sarkissian - Analysis of the Chaotic Itinerancy Phenomenon using Entropy and Clustering - https://arxiv.org/abs/2507.22643 - arXiv:2507.22643v4 Announce Type: replace-cross -Abstract: We introduce a new methodology for the analysis of the phenomenon of chaotic itinerancy in a dynamical system using the notion of entropy and a clustering algorithm. We determine systems likely to experience chaotic itinerancy by means of local Shannon entropy and local permutation entropy. In such systems, we find quasi-stable states (attractor ruins) and chaotic transition states using a density-based clustering algorithm. Our approach then focuses on examining the chaotic itinerancy dynamics through the characterization of residence times within these states and chaotic transitions between them with the help of some statistical tests. We demonstrate the effectiveness of these methods on the system of globally coupled logistic maps (GCM), a well-known model exhibiting chaotic itinerancy. In particular, we conduct comprehensive computations for a large number of parameters in the GCM system and algorithmically identify itinerant dynamics observed previously by Kaneko in numerical simulations as coherent and intermittent phases. - oai:arXiv.org:2507.22643v4 - nlin.CD - math.DS - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace-cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - 10.1103/bcwd-nx7r - Nikodem Mierski, Pawe{\l} Pilarczyk + Marta Dell'Atti, Thomas Kecker - How to simulate L\'evy flights in a steep potential: An explicit splitting numerical scheme - https://arxiv.org/abs/2508.07339 - arXiv:2508.07339v3 Announce Type: replace-cross -Abstract: We propose an effective explicit numerical scheme for simulating solutions of stochastic differential equations with confining superlinear drift terms, driven by multiplicative heavy-tailed L\'evy noise. The scheme is designed to prevent explosion and accurately capture all finite moments of the solutions. - In the purely Gaussian case, it correctly reproduces moments of sub-Gaussian tails of the solutions. - This method is particularly well-suited for approximating statistical moments and other probabilistic characteristics of L\'evy flights in steep potential landscapes. - oai:arXiv.org:2508.07339v3 - physics.comp-ph + 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 math.PR - Tue, 09 Dec 2025 00:00:00 -0500 + physics.chem-ph + Wed, 10 Dec 2025 00:00:00 -0500 replace-cross http://creativecommons.org/licenses/by/4.0/ - Ilya Pavlyukevich, Olga Aryasova, Alexei Chechkin, Oleksii Kulyk + 10.1103/p3yc-kmt1 + Phys. Rev. E 112, 034116, 2025 + Suvam Pal, Leonardo Dagdug, Dibakar Ghosh, Denis Boyer, Arnab Pal - Multi-head Transformers Provably Learn Symbolic Multi-step Reasoning via Gradient Descent - https://arxiv.org/abs/2508.08222 - arXiv:2508.08222v2 Announce Type: replace-cross -Abstract: Transformers have demonstrated remarkable capabilities in multi-step reasoning tasks. However, understandings of the underlying mechanisms by which they acquire these abilities through training remain limited, particularly from a theoretical standpoint. This work investigates how transformers learn to solve symbolic multi-step reasoning problems through chain-of-thought processes, focusing on path-finding in trees. We analyze two intertwined tasks: a backward reasoning task, where the model outputs a path from a goal node to the root, and a more complex forward reasoning task, where the model implements two-stage reasoning by first identifying the goal-to-root path and then reversing it to produce the root-to-goal path. Our theoretical analysis, grounded in the dynamics of gradient descent, shows that trained one-layer transformers can provably solve both tasks with generalization guarantees to unseen trees. In particular, our multi-phase training dynamics for forward reasoning elucidate how different attention heads learn to specialize and coordinate autonomously to solve the two subtasks in a single autoregressive path. These results provide a mechanistic explanation of how trained transformers can implement sequential algorithmic procedures. Moreover, they offer insights into the emergence of reasoning abilities, suggesting that when tasks are structured to take intermediate chain-of-thought steps, even shallow multi-head transformers can effectively solve problems that would otherwise require deeper architectures. - oai:arXiv.org:2508.08222v2 - cs.LG - cs.AI - cs.IT - math.IT - math.OC - stat.ML - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace-cross - http://creativecommons.org/licenses/by/4.0/ - Tong Yang, Yu Huang, Yingbin Liang, Yuejie Chi + http://creativecommons.org/publicdomain/zero/1.0/ + Nikhil Kodali, Kartick Ramakrishnan, Phani Motamarri - Extended parameter shift rules with minimal derivative variance for parameterized quantum circuits - https://arxiv.org/abs/2508.08802 - arXiv:2508.08802v2 Announce Type: replace-cross -Abstract: Parameter shift rules (PSRs) are useful methods for computing arbitrary-order derivatives of the cost function in parameterized quantum circuits. The basic idea of PSRs is to evaluate the cost function at different parameter shifts, then use specific coefficients to combine them linearly to obtain the exact derivatives. In this work, we propose an extended parameter shift rule (EPSR) which generalizes a broad range of existing PSRs and has the following two advantages. First, EPSR offers an infinite number of possible parameter shifts, allowing the selection of the optimal parameter shifts to minimize the final derivative variance and thereby obtaining the more accurate derivative estimates with limited quantum resources. Second, EPSR extends the scope of the PSRs in the sense that EPSR can handle arbitrary Hermitian operator $H$ in gate $U(x) = \exp (iHx)$ in the parameterized quantum circuits, while existing PSRs are valid only for simple Hermitian generators $H$ such as simple Pauli words. Additionally, we show that the widely used ``general PSR'', introduced by Wierichs et al. (2022), is a special case of our EPSR, and we prove that it yields globally optimal shifts for minimizing the derivative variance under the weighted-shot scheme. Finally, through numerical simulations, we demonstrate the effectiveness of EPSR and show that the usage of the optimal parameter shifts indeed leads to more accurate derivative estimates. - oai:arXiv.org:2508.08802v2 + 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 quant-ph - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 + 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/ - 10.1103/f57b-q28w - Zhijian Lai, Jiang Hu, Dong An, Zaiwen Wen + Eric R. Anschuetz - Effective permeability conditions for diffusive transport through impermeable membranes with gaps - https://arxiv.org/abs/2508.10694 - arXiv:2508.10694v4 Announce Type: replace-cross -Abstract: Membranes regulate transport in a wide variety of industrial and biological applications. The microscale geometry of the membrane can significantly affect overall transport through the membrane, but the precise nature of this multiscale coupling is not well characterised in general. Motivated by the application of transport across a bacterial membrane, in this paper we use formal multiscale analysis to derive explicit effective coupling conditions for macroscale transport across a two-dimensional impermeable membrane with periodically spaced gaps, and validate these with numerical simulations. We derive analytic expressions for effective macroscale quantities associated with the membrane, such as the permeability, in terms of the microscale geometry. Our results generalise the classic constitutive membrane coupling conditions to a wider range of membrane geometries and time-varying scenarios. Specifically, we demonstrate that if the exterior concentration varies in time, for membranes with long channels, the transport gains a memory property where the coupling conditions depend on the system history. By applying our effective conditions in the context of small molecule transport through gaps in bacterial membranes called porins, we predict that bacterial membrane permeability is primarily dominated by the thickness of the membrane. Furthermore, we predict how alterations to membrane microstructure, for example via changes to porin expression, might affect overall transport, including when external concentrations vary in time. These results will apply to a broad range of physical applications with similar membrane structures, from medical and industrial filtration to carbon capture. - oai:arXiv.org:2508.10694v4 - cond-mat.soft - math.AP - math.DS - physics.bio-ph - Tue, 09 Dec 2025 00:00:00 -0500 + $f(R,\mathcal{G})$-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.MP + Wed, 10 Dec 2025 00:00:00 -0500 replace-cross http://creativecommons.org/licenses/by/4.0/ - Molly Brennan, Edwina F. Yeo, Philip Pearce, Mohit P. Dalwadi + 10.1007/s10714-025-03489-9 + Gen. Rel. Gravit. 57, 153 (2025) + Nikolaos Dimakis, Alex Giacomini, Genly Leon, Andronikos Paliathanasis, Ekaterina Pozdeeva, Sergey Vernov - Jointly Computation- and Communication-Efficient Distributed Learning - https://arxiv.org/abs/2508.15509 - arXiv:2508.15509v2 Announce Type: replace-cross -Abstract: We address distributed learning problems over undirected networks. Specifically, we focus on designing a novel ADMM-based algorithm that is jointly computation- and communication-efficient. Our design guarantees computational efficiency by allowing agents to use stochastic gradients during local training. Moreover, communication efficiency is achieved as follows: i) the agents perform multiple training epochs between communication rounds, and ii) compressed transmissions are used. We prove exact linear convergence of the algorithm in the strongly convex setting. We corroborate our theoretical results by numerical comparisons with state of the art techniques on a classification task. - oai:arXiv.org:2508.15509v2 - cs.LG - cs.SY - eess.SY - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 + 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/ - Xiaoxing Ren, Nicola Bastianello, Karl H. Johansson, Thomas Parisini + David Viennot - Conditionally adaptive augmented Lagrangian method for physics-informed learning of forward and inverse problems - https://arxiv.org/abs/2508.15695 - arXiv:2508.15695v2 Announce Type: replace-cross -Abstract: We present several key advances to the Physics and Equality Constrained Artificial Neural Networks (PECANN) framework, substantially improving its capacity to solve challenging partial differential equations (PDEs). Our enhancements broaden the framework's applicability and improve efficiency. First, we generalize the Augmented Lagrangian Method (ALM) to support multiple, independent penalty parameters for enforcing heterogeneous constraints. Second, we introduce a constraint aggregation technique to address inefficiencies associated with point-wise enforcement. Third, we incorporate a single Fourier feature mapping to capture highly oscillatory solutions with multi-scale features, where alternative methods often require multiple mappings or costlier architectures. Fourth, a novel time-windowing strategy enables seamless long-time evolution without relying on discrete time models. Fifth, and critically, we propose a conditionally adaptive penalty update (CAPU) strategy for ALM that accelerates the growth of Lagrange multipliers for constraints with larger violations, while enabling coordinated updates of multiple penalty parameters. CAPU accelerates the growth of Lagrange multipliers for selectively challenging constraints, enhancing constraint enforcement during training. We demonstrate the effectiveness of PECANN-CAPU across diverse problems, including the transonic rarefaction problem, reversible scalar advection by a vortex, high-wavenumber Helmholtz and Poisson's equations, and inverse heat source identification. The framework achieves competitive accuracy across all cases when compared with established methods and recent approaches based on Kolmogorov-Arnold networks. Collectively, these advances improve the robustness, computational efficiency, and applicability of PECANN to demanding problems in scientific computing. - oai:arXiv.org:2508.15695v2 + 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 cs.LG math.OC - physics.comp-ph - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 replace-cross - http://creativecommons.org/licenses/by/4.0/ - Qifeng Hu, Shamsulhaq Basir, Inanc Senocak + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Jianhao Ma, Geyu Liang, Salar Fattahi - Computation of Feasible Assume-Guarantee Contracts: A Resilience-based Approach - https://arxiv.org/abs/2509.01832 - arXiv:2509.01832v2 Announce Type: replace-cross -Abstract: We propose a resilience-based framework for computing feasible assume-guarantee contracts that ensure the satisfaction of temporal specifications in interconnected discrete-time systems. Interconnection effects are modeled as structured disturbances. We use a resilience metric, the maximum disturbance under which local specifications hold, to refine assumptions and guarantees across subsystems iteratively. We first demonstrate correctness and monotone refinement of guarantees for two subsystems. Then, we extend our approach to general networks of L subsystems using weighted combinations of interconnection effects. We instantiate the framework on linear systems by meeting finite-horizon safety, exact-time reachability, and finite-horizon reachability specifications, and on nonlinear systems by fulfilling general finite-horizon specifications. Our approach is demonstrated through numerical linear examples and a nonlinear DC microgrid case study, showcasing the impact of our framework on verifying temporal logic specifications with compositional reasoning. - oai:arXiv.org:2509.01832v2 - eess.SY - cs.LO - cs.SY - math.DS - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + cs.LG + cs.IT + math.IT + Wed, 10 Dec 2025 00:00:00 -0500 replace-cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Negar Monir, Youssef Ait Si, Ratnangshu Das, Pushpak Jagtap, Adnane Saoud, Sadegh Soudjani + Alexander Semenenko, Ivan Butakov, Alexey Frolov, Ivan Oseledets - Staying on the Manifold: Geometry-Aware Noise Injection - https://arxiv.org/abs/2509.20201 - arXiv:2509.20201v2 Announce Type: replace-cross -Abstract: It has been shown that perturbing the input during training implicitly regularises the gradient of the learnt function, leading to smoother models and enhancing generalisation. However, previous research mostly considered the addition of ambient noise in the input space, without considering the underlying structure of the data. In this work, we propose several strategies of adding geometry-aware input noise that accounts for the lower dimensional manifold the input space inhabits. We start by projecting ambient Gaussian noise onto the tangent space of the manifold. In a second step, the noise sample is mapped on the manifold via the associated geodesic curve. We also consider Brownian motion noise, which moves in random steps along the manifold. We show that geometry-aware noise leads to improved generalisation and robustness to hyperparameter selection on highly curved manifolds, while performing at least as well as training without noise on simpler manifolds. Our proposed framework extends to data manifolds approximated by generative models and we observe similar trends on the MNIST digits dataset. - oai:arXiv.org:2509.20201v2 + 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.DG - stat.ML - Tue, 09 Dec 2025 00:00:00 -0500 + math.FA + Wed, 10 Dec 2025 00:00:00 -0500 replace-cross http://creativecommons.org/licenses/by/4.0/ - Albert Kj{\o}ller Jacobsen, Johanna Marie Gegenfurtner, Georgios Arvanitidis + Transactions on Machine Learning Research, November 2025 + Anand Ganesh, Babhrubahan Bose, Anand Rajagopalan - Closed-form $\ell_r$ norm scaling with data for overparameterized linear regression and diagonal linear networks under $\ell_p$ bias - https://arxiv.org/abs/2509.21181 - arXiv:2509.21181v3 Announce Type: replace-cross -Abstract: For overparameterized linear regression with isotropic Gaussian design and minimum-$\ell_p$ interpolator $p\in(1,2]$, we give a unified, high-probability characterization for the scaling of the family of parameter norms $ \\{ \lVert \widehat{w_p} \rVert_r \\}_{r \in [1,p]} $ with sample size. - We solve this basic, but unresolved question through a simple dual-ray analysis, which reveals a competition between a signal *spike* and a *bulk* of null coordinates in $X^\top Y$, yielding closed-form predictions for (i) a data-dependent transition $n_\star$ (the "elbow"), and (ii) a universal threshold $r_\star=2(p-1)$ that separates $\lVert \widehat{w_p} \rVert_r$'s which plateau from those that continue to grow with an explicit exponent. - This unified solution resolves the scaling of *all* $\ell_r$ norms within the family $r\in [1,p]$ under $\ell_p$-biased interpolation, and explains in one picture which norms saturate and which increase as $n$ grows. - We then study diagonal linear networks (DLNs) trained by gradient descent. By calibrating the initialization scale $\alpha$ to an effective $p_{\mathrm{eff}}(\alpha)$ via the DLN separable potential, we show empirically that DLNs inherit the same elbow/threshold laws, providing a predictive bridge between explicit and implicit bias. - Given that many generalization proxies depend on $\lVert \widehat {w_p} \rVert_r$, our results suggest that their predictive power will depend sensitively on which $l_r$ norm is used. - oai:arXiv.org:2509.21181v3 - cs.LG + 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.ML stat.TH - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 replace-cross - http://creativecommons.org/licenses/by/4.0/ - Shuofeng Zhang, Ard Louis + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Mario Beraha, Jesper M{\o}ller - Structural and Compositional Complexities of Hierarchical Self-Assembly: a Hypergraph Approach - https://arxiv.org/abs/2509.26449 - arXiv:2509.26449v2 Announce Type: replace-cross -Abstract: Programmable self-assembly enables the construction of complex molecular, supramolecular, and crystalline architectures from well-designed building blocks. We introduce a hypergraph-based formalism, Blocks & Bonds (B&B), that generalizes classical chemical graph theory by incorporating directed and multicolored interactions, internal symmetries, and hierarchical organization. Within this framework, we develop the Structure Code (SC), a compact and versatile language for describing self-assembled architectures. We define a Kolmogorov-style Structural Complexity as the total information content of SC, obtained through its tokenization and Shannon information assignment. Complementing this encoding-based measure, we introduce a much simpler quantity, the Compositional Complexity, which depends only on the number and cumulative usage of block and bond types in the construction set. A central result of this work is a strong empirical correlation between the token-based Structural Complexity and the Compositional Complexity across all examined systems. Owing to this agreement, the Compositional Complexity emerges as the most practical and broadly applicable measure: it is easy to compute, requires no explicit encoding, and yet closely tracks the actual information content of structurally diverse architectures. Applications to molecular systems (ethylene glycol, glucose), DNA-origami lattices, and crystalline assemblies show that B\&B hypergraphs provide a unified, scalable, and information-efficient representation of structural organization, naturally capturing symmetry, modularity, and stereochemistry. This framework establishes a quantitative foundation for complexity-aware classification and inverse design of programmable matter. - oai:arXiv.org:2509.26449v2 - cond-mat.soft - cond-mat.mes-hall - math-ph - math.MP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Alexei V. Tkachenko + http://creativecommons.org/licenses/by-nc-nd/4.0/ + Kostya Druzhkov - A Conceptual Introduction To Signature Change Through a Natural Extension of Kaluza-Klein Theory - https://arxiv.org/abs/2510.02492 - arXiv:2510.02492v2 Announce Type: replace-cross -Abstract: We propose an extension of basic Kaluza-Klein theory in which the higher-dimensional Lorentzian manifold develops a Cauchy horizon rather than remaining globally hyperbolic as in the conventional framework. In this setting, the $U(1)$-generating Killing field, assumed to exist in Kaluza-Klein theory, undergoes a transition in its causal character, from spacelike in the globally hyperbolic region to timelike in an acausal extension through a horizon. This yields a (lower-dimensional) quotient manifold whose metric changes signature from Lorentzian to Riemannian. In this way, one observes a singular, signature changing transition emerging rather naturally from the projection of a globally smooth, even analytic, Lorentzian geometry ``up in the bundle''. This reveals a ``signature change without signature change'' scenario -- a phrasing inspired by John Wheeler -- and extends the usual Kaluza-Klein framework in a conceptually natural direction. - oai:arXiv.org:2510.02492v2 - gr-qc + 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-ph - math.MP - Tue, 09 Dec 2025 00:00:00 -0500 + math.IT + math.LO + Wed, 10 Dec 2025 00:00:00 -0500 replace-cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - 10.1103/tlqr-v678 - Vincent Moncrief, Nathalie E. Rieger + Fabrizio Canfora, Marco Cedeno - Model Monitoring: A General Framework with an Application to Non-life Insurance Pricing - https://arxiv.org/abs/2510.04556 - arXiv:2510.04556v2 Announce Type: replace-cross -Abstract: Maintaining the predictive performance of pricing models is challenging when insurance portfolios and data-generating mechanisms evolve over time. Focusing on non-life insurance, we adopt the concept-drift terminology from machine learning and distinguish virtual drift from real concept drift in an actuarial setting. Methodologically, we (i) formalize deviance loss and Murphy's score decomposition to assess global and local auto-calibration; (ii) study the Gini score as a rank-based performance measure, derive its asymptotic distribution, and develop a consistent bootstrap estimator of its asymptotic variance; and (iii) combine these results into a statistically grounded, model-agnostic monitoring framework that integrates a Gini-based ranking drift test with global and local auto-calibration tests. An application to a modified motor insurance portfolio with controlled concept-drift scenarios illustrates how the framework guides decisions on refitting or recalibrating pricing models. - oai:arXiv.org:2510.04556v2 + 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 - q-fin.ST - stat.AP stat.TH - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 replace-cross - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Alexej Brauer, Paul Menzel, Mario V. W\"uthrich + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Bogdan Butyrin, Artemy Rubtsov, Alexey Naumov, Vladimir Ulyanov, Sergey Samsonov - Space-time resonances in the spatiotemporal spectrum of nonlinear dispersive waves - https://arxiv.org/abs/2510.19828 - arXiv:2510.19828v2 Announce Type: replace-cross -Abstract: In weakly nonlinear dispersive wave systems, long-time dynamics are typically governed by time resonances, where wave phases evolve coherently due to exact frequency matching. Recent advances in spatio-temporal spectrum measurements, however, reveal prominent features that go beyond the predictions of time resonance theory. In this work, we develop a theoretical framework to interpret these signatures by identifying and characterizing an alternative mechanism: space resonances. These arise when wave packets share the same group velocity and remain co-located, leading to long-lived interactions. We further show that gauge-breaking terms in the Hamiltonian give rise to space resonances supported on negative frequencies. By combining sea-surface elevation data, numerical simulations, and analytical theory, we derive the leading-order spatio-temporal spectrum for weakly interacting water waves, providing a unified explanation for its observed features. - oai:arXiv.org:2510.19828v2 - nlin.PS + 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 + hep-th math-ph math.MP - nlin.CD - physics.flu-dyn - Tue, 09 Dec 2025 00:00:00 -0500 + nlin.SI + Wed, 10 Dec 2025 00:00:00 -0500 replace-cross http://creativecommons.org/licenses/by/4.0/ - Michal Shavit, Fabio Pusateri, Zhou Zhang, Yulin Pan, Davide Maestrini, Miguel Onorato, Jalal Shatah + Michael Lashkevich, Amir Nesturov - Simulating Clifford Circuits with Gaussian Elimination - https://arxiv.org/abs/2511.06127 - arXiv:2511.06127v2 Announce Type: replace-cross -Abstract: Quantum circuits are considered more powerful than classical circuits and require exponential resources to simulate classically. Clifford circuits are a special class of quantum circuits that can be simulated in polynomial time but still show important quantum effects such as entanglement. In this work, we present an algorithm that simulates Clifford circuits by performing Gaussian elimination on a modified adjacency matrix derived from the circuit structure. Our work builds on an ZX-calculus tensor network representation of Clifford circuits that reduces to quantum graph states. We give a concise formula of amplitudes of graph states based on the LDL decomposition of matrices over GF(2), and use it to get efficient algorithms for strong and weak simulation of Clifford circuits using tree-decomposition-based fast LDL algorithm. The complexity of our algorithm matches the state of art for weak graph state simulation and improves the state of art for strong graph state simulation by taking advantage of Strassen-like fast matrix multiplication. Our algorithm is also efficient when computing many amplitudes or samples of a Clifford circuit. Further, our amplitudes formula provides a new characterization of locally Clifford equivalent graph states as well as an efficient protocol to learn graph states with low-rank adjacency matrices. - oai:arXiv.org:2511.06127v2 + 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 +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 + hep-th + math-ph + math.MP quant-ph - cs.NA - math.NA - Tue, 09 Dec 2025 00:00:00 -0500 - replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Yuchen Pang, Edgar Solomonik - - - High-Performance Variance-Covariance Matrix Construction Using an Uncentered Gram Formulation - https://arxiv.org/abs/2511.08223 - arXiv:2511.08223v2 Announce Type: replace-cross -Abstract: Reichel (2025) defined the bariance as a pairwise-difference measure that can be rewritten in linear time using only scalar sums. We extend this idea to the covariance matrix by showing that the standard matrix expression involving the uncentered Gram matrix and a correction term is algebraically identical to the pairwise-difference definition while avoiding explicit centering. The computation then reduces to one outer product of dimension p-by-p and a single subtraction. Benchmarks in Python show clear runtime gains, especially when BLAS optimizations are absent. Optionally faster Gram-matrix routines such as RXTX (Rybin et al., 2025) further reduce overall cost. - oai:arXiv.org:2511.08223v2 - stat.CO - cs.LG - cs.NA - math.NA - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 replace-cross - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Felix Reichel + http://creativecommons.org/licenses/by/4.0/ + A. J. D. Farias Junior, Andrea Erdas, Herondy F. Santana Mota - Discrete Contact Angles and Electric Field Singularity in Electrowetting: A Multi-Scale Complex Potential Analysis - https://arxiv.org/abs/2511.11556 - arXiv:2511.11556v2 Announce Type: replace-cross -Abstract: This study constructed a multi-scale theoretical framework to resolve the electric field singularity at the Triple Contact Point in electrowetting. Utilizing conformal transformation and complex analysis, we established the structure for both the global potential and local field solutions, complementing the analysis with numerical methods. Our primary finding is that the contact angle $\theta$ is not continuously adjustable but is restricted to a discrete set of values, constrained by the characteristic exponent $\lambda$. Analysis of the complex potential established $\text{Re}[\lambda] \ge 1$ as the critical condition for a non-singular electric field; conversely, singular solutions ($\text{Re}[\lambda] < 1$) are localized exclusively in the acute-angle regime ($\theta < \pi/2$). The high-order solution region exhibits a degeneracy phenomenon at specific angles, implying the local field structure is geometrically stable and universally applicable for a wide range of permittivity ratios $k$. Furthermore, we determined that the onset of electric field oscillation requires the simultaneous satisfaction of two critical conditions: the geometry must approach a flat boundary ($\theta \to \pi$) and the dielectric ratio must approach homogeneity ($k \to 1$). These findings provide a solid theoretical basis for designing non-singular electric fields and mitigating the common contact angle saturation phenomenon. - oai:arXiv.org:2511.11556v2 - physics.flu-dyn + $su(2)$ 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 math-ph - math.CV math.MP - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 replace-cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Dhairya Shah, Yuan Liu, Samuel Brzezicki + Nicolas Cramp\'e, Rafael I. Nepomechie, Luc Vinet, Nabi Zare Harofteh - Revealing POMDPs: Qualitative and Quantitative Analysis for Parity Objectives - https://arxiv.org/abs/2511.13134 - arXiv:2511.13134v2 Announce Type: replace-cross -Abstract: Partially observable Markov decision processes (POMDPs) are a central model for uncertainty in sequential decision making. The most basic objective is the reachability objective, where a target set must be eventually visited, and the more general parity objectives can model all omega-regular specifications. For such objectives, the computational analysis problems are the following: (a) qualitative analysis that asks whether the objective can be satisfied with probability 1 (almost-sure winning) or probability arbitrarily close to 1 (limit-sure winning); and (b) quantitative analysis that asks for the approximation of the optimal probability of satisfying the objective. For general POMDPs, almost-sure analysis for reachability objectives is EXPTIME-complete, but limit-sure and quantitative analyses for reachability objectives are undecidable; almost-sure, limit-sure, and quantitative analyses for parity objectives are all undecidable. A special class of POMDPs, called revealing POMDPs, has been studied recently in several works, and for this subclass the almost-sure analysis for parity objectives was shown to be EXPTIME-complete. In this work, we show that for revealing POMDPs the limit-sure analysis for parity objectives is EXPTIME-complete, and even the quantitative analysis for parity objectives can be achieved in EXPTIME. - oai:arXiv.org:2511.13134v2 - cs.CC - cs.SY - eess.SY + 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 - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 replace-cross - http://creativecommons.org/publicdomain/zero/1.0/ - Ali Asadi, Krishnendu Chatterjee, David Lurie, Raimundo Saona + 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) - Homogeneous potentials, Lagrange's identity and Poisson geometry - https://arxiv.org/abs/2511.19903 - arXiv:2511.19903v2 Announce Type: replace-cross -Abstract: The Lagrange identity expresses the second derivative of the moment of inertia of a system of material points through kinetic energy and homogeneous potential energy, from which follows the Jacobi well-known result on the instability of a system of gravitating bodies. In this work, it is proven that if a Hamiltonian system satisfies the Lagrange identity, then it possesses additional tensor invariants that are not expressed through the basic invariants existing for all Hamiltonian systems. A new class of Hamiltonian systems with inhomogeneous potentials is considered, which also possess similar additional tensor invariants. - oai:arXiv.org:2511.19903v2 - nlin.SI - math-ph - math.DS - math.MP - math.SG - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + cs.IT + math.IT + Wed, 10 Dec 2025 00:00:00 -0500 replace-cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - A. V. Tsiganov + Md Kamran Chowdhury Shisher, Vishrant Tripathi, Mung Chiang, Christopher G. Brinton - Microscopic Variability Alters Macroscopic Rotation Speed in Stochastic Spiral Waves - https://arxiv.org/abs/2511.21710 - arXiv:2511.21710v2 Announce Type: replace-cross -Abstract: We present a general theory for noise-induced corrections to the angular velocity of spiral waves. Stochasticity produces two second-order effects: an instantaneous term from heterogeneity that always slows rotation, and an orbital-drift term from temporal fluctuations that can either accelerate or decelerate it. For our parameters, orbital drift is weaker, producing a net slowdown. Analytical predictions match Barkley-model simulations with temporal noise. Examination of additional noise types in silico confirms angular velocity slowing. This mechanism provides a robust route by which stochasticity reshapes spiral dynamics in excitable media, with direct implications for arrhythmias and neural wave propagation. - oai:arXiv.org:2511.21710v2 - nlin.PS - math-ph - math.MP - physics.bio-ph - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + math.ST + stat.TH + Wed, 10 Dec 2025 00:00:00 -0500 replace-cross - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Jolien Kamphuis, Desmond Kabus, Hermen Jan Hupkes, Tim De Coster + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Zhen Li - Degenerate Addition Formulas of the KP hierarchy and Applications - https://arxiv.org/abs/2511.22876 - arXiv:2511.22876v2 Announce Type: replace-cross -Abstract: It is well known that tau functions of the KP hierarchy satisfy addition formulas. We consider the general addition formula in the determinant form and take a certain limit of it. It expresses certain shifts of a tau function in terms of the Wronskian determinants of wave functions at various values of the spectral parameter. As an application the relation between solutions created by vertex operators and those created by Darboux transformations is clarified. As another application the new addition formula for Riemann's theta functions of Riemann surfaces is obtained by considering theta function solutions of the KP hierarchy. This addition formula is different from any of formulas in Fay's book. - oai:arXiv.org:2511.22876v2 - nlin.SI + 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 + hep-th math-ph - math.AG math.MP - math.RT - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 replace-cross - http://creativecommons.org/licenses/by/4.0/ - Atsushi Nakayashiki + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Gwena\"el Ferrando, Florian Loebbert, Amelie Pitters, Sven F. Stawinski - Correlation-Weighted Communicability Curvature as a Structural Driver of Dengue Spread: A Bayesian Spatial Analysis of Recife (2015-2024) - https://arxiv.org/abs/2512.00315 - arXiv:2512.00315v2 Announce Type: replace-cross -Abstract: We investigate whether the structural connectivity of urban road networks helps explain dengue incidence in Recife, Brazil (2015--2024). For each neighborhood, we compute the average \emph{communicability curvature}, a graph-theoretic measure capturing the ability of a locality to influence others through multiple network paths. We integrate this metric into Negative Binomial models, fixed-effects regressions, SAR/SAC spatial models, and a hierarchical INLA/BYM2 specification. Across all frameworks, curvature is the strongest and most stable predictor of dengue risk. In the BYM2 model, the structured spatial component collapses ($\phi \approx 0$), indicating that functional network connectivity explains nearly all spatial dependence typically attributed to adjacency-based CAR terms. The results show that dengue spread in Recife is driven less by geographic contiguity and more by network-mediated structural flows. - oai:arXiv.org:2512.00315v2 - physics.soc-ph - math.PR - q-bio.PE - stat.AP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace-cross - http://creativecommons.org/licenses/by/4.0/ - Marc\'ilio Ferreira dos Santos, Cleiton de Lima Ricardo, Andreza dos Santos Rodrigues de Melo + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + 10.1016/j.nuclphysb.2025.117257 + Mustapha Azreg-A\"inou, Yassine Sekhmani - Linearized instability of Couette flow in stress-power law fluids - https://arxiv.org/abs/2512.00404 - arXiv:2512.00404v2 Announce Type: replace-cross -Abstract: This paper examines the linearized stability of plane Couette flow for stress-power law fluids, which exhibit non-monotonic stress-strain rate behavior. The constitutive model is derived from a thermodynamic framework using a non-convex rate of dissipation potential. Under velocity boundary conditions, the system may admit three steady-state solutions. Linearized stability analysis reveals that the two solutions on ascending constitutive branches are unconditionally stable, while the solution on the descending branch is unconditionally unstable. For mixed traction-velocity boundary conditions, the base state is unique. Stability depends solely on whether the prescribed traction lies on an ascending (stable) or descending (unstable) branch of the constitutive curve. The results demonstrate that flow stability in these complex fluids is fundamentally governed by both boundary conditions and constitutive non-monotonicity. - oai:arXiv.org:2512.00404v2 - physics.flu-dyn - cond-mat.soft + 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 - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 replace-cross - http://creativecommons.org/licenses/by-nc-nd/4.0/ - Krishna Kaushik Yanamundra (Department of Mechanical Engineering, Texas A&M University, College Station, TX, USA), Lorenzo Fusi (Dipartimento di Matematica e Informatica "U. Dini'', Universit\`a degli Studi di Firenze, 50134, Firenze, Italy) + http://creativecommons.org/licenses/by/4.0/ + Jack C. M. Hughes, Fedor V. Kusmartsev - Enhanced Single-Photon Detector: A framework for Superconducting-Level Performance without cryogenic cooling - https://arxiv.org/abs/2512.01328 - arXiv:2512.01328v2 Announce Type: replace-cross -Abstract: High-performance single-photon detectors (SPDs) are indispensable components for a wide range of quantum optical applications. However, the reliance of state-of-the-art devices on superconducting materials imposes severe technological demands and necessitates challenging operational conditions, such as cryogenics, thereby hindering scalable implementation. To address this, we propose the Enhanced Single-Photon Detector (ESPD) framework, a novel paradigm for achieving high-performance SPDs through the iterative enhancement of conventional room-temperature SPDs. Relying entirely on non-superconducting components and eliminating cryogenic cooling requirements, the ESPD scheme can upgrade a legacy SPD, with detection efficiency (DE) about $59\%$ and dark count rate (DCR) of $10^{-2}$, to a device with superior performance metrics, achieving DE exceeding $93\%$ and DCR below $10^{-9}$. This performance rivals or even surpasses that of state-of-the-art superconducting SPDs, allowing the minimal tolerable channel transmission rate for quantum key distribution (QKD) protocols to be reduced by several orders of magnitude. Although the architecture requires substantial integration effort, the scheme can provide superconducting-level performance without cryogenic cooling, offering a clear path toward the widespread deployment of high-performance SPDs as well as related quantum technologies in infrastructure-constrained environments. - oai:arXiv.org:2512.01328v2 + 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 quant-ph + cs.IT math-ph + math.IT math.MP - math.OC - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 replace-cross http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Hao Shu + Kaiyuan Ji, Bartosz Regula - Quasinormal modes of a static black hole in nonlinear electrodynamics - https://arxiv.org/abs/2512.02714 - arXiv:2512.02714v2 Announce Type: replace-cross -Abstract: We investigate the axial electromagnetic quasinormal modes of a static, asymptotically Anti--de Sitter (AdS) black hole sourced by a nonlinear electrodynamics model of Pleba\'{n}ski type. Starting from the master equation governing axial perturbations, we impose ingoing boundary conditions at the event horizon and normalizable (Dirichlet) behavior at the AdS boundary. Following the approach of Jansen, we recast the radial equation into a linear generalized eigenvalue problem by using an ingoing Eddington--Finkelstein formulation, compactifying the radial domain, and regularizing the asymptotic coefficients. The resulting problem is solved using a Chebyshev--Lobatto pseudospectral discretization. We compute the fundamental quasinormal mode frequencies for both the purely electric ($Q_m=0$) and purely magnetic ($Q_e=0$) sectors, emphasizing the role of the nonlinearity parameter $\beta$ and the effective charge magnitude $Q$. Our results show that increasing either $\beta$ or $Q$ raises both the oscillation frequency $\omega_R$ and the damping rate $-\omega_I$, leading to faster but more rapidly decaying ringdown profiles. Nonlinear electrodynamics breaks the isospectrality between electric and magnetic configurations: magnetic modes are systematically less oscillatory and more weakly damped than their electric counterparts. For sufficiently large $\beta$ and small $Q_m$, the fundamental mode becomes purely imaginary ($\omega_R \approx 0$), in agreement with the absence of a trapping potential barrier in this regime. These findings reveal qualitative signatures of nonlinear electromagnetic effects on black hole perturbations and may have implications for high-field or high-charge astrophysical environments. - oai:arXiv.org:2512.02714v2 - gr-qc - astro-ph.HE - hep-th - math-ph - math.MP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 + eess.SY + cs.SY + math.OC + Wed, 10 Dec 2025 00:00:00 -0500 replace-cross - http://creativecommons.org/licenses/by/4.0/ - Mohsen Fathi, Ariel Guzm\'an, J. R. Villanueva + http://creativecommons.org/licenses/by-nc-nd/4.0/ + Yiqian Wu, Ming Yi, Bolun Xu, James Anderson - An Information Theory of Finite Abstractions and their Fundamental Scalability Limits - https://arxiv.org/abs/2512.03977 - arXiv:2512.03977v3 Announce Type: replace-cross -Abstract: Finite abstractions are discrete approximations of dynamical systems, such that the set of abstraction trajectories contains all system trajectories. There is a consensus that abstractions suffer from the curse of dimensionality: for the same ``accuracy" (how closely the abstraction represents the system), the abstraction size scales poorly with system dimensions. And yet, after decades of research on abstractions, there are no formal results on their accuracy-size tradeoff. In this work, we derive a statistical, quantitative theory of abstractions' accuracy-size tradeoff and uncover fundamental limits on their scalability, through rate-distortion theory -- the information theory of lossy compression. Abstractions are viewed as encoder-decoder pairs, encoding trajectories of dynamical systems. Rate measures abstraction size, while distortion describes accuracy, defined as the spatial average deviation between abstract trajectories and system ones. We obtain a fundamental lower bound on the minimum achievable abstraction distortion, given the system dynamics and the abstraction size; and vice-versa a lower bound on the minimum size, for given distortion. The bound depends on the complexity of the dynamics, through trajectory entropy. We demonstrate its tightness on some dynamical systems. Finally, we showcase how this new theory enables constructing minimal abstractions, optimizing the size-accuracy tradeoff, through an example on a chaotic system. - oai:arXiv.org:2512.03977v3 - eess.SY - cs.IT - cs.SY - math.DS - math.IT + 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 - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 replace-cross - http://arxiv.org/licenses/nonexclusive-distrib/1.0/ - Giannis Delimpaltadakis, Gabriel Gleizer + http://creativecommons.org/licenses/by/4.0/ + Vitor Gelsleichter Probst Curtarelli, Stephan Paul, Anderson Wedderhoff Spengler - AI-Assisted Game Management Decisions: A Fuzzy Logic Approach to Real-Time Soccer Substitutions - https://arxiv.org/abs/2512.04480 - arXiv:2512.04480v2 Announce Type: replace-cross -Abstract: In elite soccer, substitution decisions entail significant financial and sporting consequences yet remain heavily reliant on intuition or predictive models that merely mimic historical biases. This paper introduces a Fuzzy Logic based Decision Support System (DSS) designed for real time, prescriptive game management. Unlike traditional Machine Learning approaches that encounter a predictive ceiling by attempting to replicate human behavior, our system audits performance through an objective, rule based inference engine. We propose a methodological advancement by reformulating the PlayeRank metric into a Cumulative Mean with Role Aware Normalization, eliminating the play time exposure bias inherent in cumulative sum models to enable accurate intra match comparison. The system integrates this refined metric with physiological proxies (fatigue) and contextual variables (disciplinary risk modulated by tactical role) to calculate a dynamic Substitution Priority (P final). Validation via a case study of the 2018 FIFA World Cup match between Brazil and Belgium demonstrates the system's ecological validity: it not only aligned with expert consensus on executed substitutions (for example Gabriel Jesus) but, crucially, identified high risk scenarios ignored by human decision makers. Specifically, the model flagged the "FAGNER Paradox" - a maximum priority defensive risk - minutes before a critical yellow card, and detected the "Lukaku Paradox", where an isolated assist masked a severe drop in participation. These results confirm that Fuzzy Logic offers a transparent, explainable, and superior alternative to black box models for optimizing real time tactical decisions. - oai:arXiv.org:2512.04480v2 - cs.AI - cs.CE - cs.SY - eess.SY + 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 - Tue, 09 Dec 2025 00:00:00 -0500 + Wed, 10 Dec 2025 00:00:00 -0500 replace-cross - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Pedro Passos + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Daniele Masti, Francesco Basciani, Arianna Fedeli, Girgio Gnecco, Francesco Smarra - Structured Light at the Extreme: Harnessing Spatiotemporal Control for High-Field Laser-Matter Interactions - https://arxiv.org/abs/2512.05042 - arXiv:2512.05042v2 Announce Type: replace-cross -Abstract: This review charts the emerging paradigm of intelligent structured light for high-field laser-matter interactions, where the precise spatiotemporal and vectorial control of light is a critical degree of freedom. We outline a transformative framework built upon three synergistic pillars. First, we survey the advanced electromagnetic toolkit, moving beyond conventional spatial light modulators to include robust static optics and the promising frontier of plasma light modulators. Second, we detail the optimization engine for this high-dimensional design space, focusing on physics-informed digital twins and AI-driven inverse design to automate the discovery of optimal light structures. Finally, we explore the groundbreaking applications enabled by this integrated approach, including programmable electron beams, orbital-angular-momentum-carrying {\gamma}-rays, compact THz accelerators, and robust communications. The path forward necessitates overcoming grand challenges in material science, real-time adaptive control at MHz rates, and the extension of these principles to the quantum realm. This review serves as a call to action for a coordinated, interdisciplinary effort to command, rather than merely observe, light-matter interactions at the extreme. - oai:arXiv.org:2512.05042v2 - physics.optics + 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 math-ph + math.DS math.MP - physics.comp-ph - Tue, 09 Dec 2025 00:00:00 -0500 + math.PR + Wed, 10 Dec 2025 00:00:00 -0500 replace-cross - http://creativecommons.org/licenses/by/4.0/ - Sergio Carbajo, Seung-Whan Bahk, Justin Baker, Andrea Bertozzi, Abhimanyu Borthakur, Antonino Di Piazza, Andrew Forbes, Spencer Gessner, Jack Hirschman, Maciej Lewenstein, Yuhang Li, Inhyuk Nam, Eileen Otte, James Rozensweig, Yijie Shen, Liwei Song, Ye Tian, Yu Wang, Yuntian Wang, Logan Wright, Xiaojun Wu, Hao Zhang + http://arxiv.org/licenses/nonexclusive-distrib/1.0/ + Philippe Rigollet - Semantic Faithfulness and Entropy Production Measures to Tame Your LLM Demons and Manage Hallucinations - https://arxiv.org/abs/2512.05156 - arXiv:2512.05156v2 Announce Type: replace-cross -Abstract: Evaluating faithfulness of Large Language Models (LLMs) to a given task is a complex challenge. We propose two new unsupervised metrics for faithfulness evaluation using insights from information theory and thermodynamics. Our approach treats an LLM as a bipartite information engine where hidden layers act as a Maxwell demon controlling transformations of context $C $ into answer $A$ via prompt $Q$. We model Question-Context-Answer (QCA) triplets as probability distributions over shared topics. Topic transformations from $C$ to $Q$ and $A$ are modeled as transition matrices ${\bf Q}$ and ${\bf A}$ encoding the query goal and actual result, respectively. Our semantic faithfulness (SF) metric quantifies faithfulness for any given QCA triplet by the Kullback-Leibler (KL) divergence between these matrices. Both matrices are inferred simultaneously via convex optimization of this KL divergence, and the final SF metric is obtained by mapping the minimal divergence onto the unit interval [0,1], where higher scores indicate greater faithfulness. Furthermore, we propose a thermodynamics-based semantic entropy production (SEP) metric in answer generation, and show that high faithfulness generally implies low entropy production. The SF and SEP metrics can be used jointly or separately for LLM evaluation and hallucination control. We demonstrate our framework on LLM summarization of corporate SEC 10-K filings. - oai:arXiv.org:2512.05156v2 - cs.AI - cs.CL - cs.IT - cs.LG - math.IT - q-fin.CP - Tue, 09 Dec 2025 00:00:00 -0500 + 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 replace-cross - http://creativecommons.org/licenses/by-nc-sa/4.0/ - Igor Halperin + http://creativecommons.org/licenses/by-nc-nd/4.0/ + Zamir Martinez, Daniel Zelazo