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ee3efb0992368a5a8786cca15fb756251135781f43c2a75ee04941c9590e110c | 2026-01-13T00:00:00-05:00 | Lagrange multiplier expressions for matrix polynomial optimization and tight relaxations | arXiv:2506.12579v2 Announce Type: replace Abstract: This paper studies matrix constrained polynomial optimization. We investigate how to get explicit expressions for Lagrange multiplier matrices from the first order optimality conditions. The existence of these expressions can be shown under the nondegeneracy condition... | https://arxiv.org/abs/2506.12579 | Academic Papers | svg |
4c6c26c66c8796190f1ef691edb155856265c6e8bbe3e807a06a7fcfa8e44cf5 | 2026-01-13T00:00:00-05:00 | Generalized Frobenius Manifold Structures on the Orbit Spaces of Affine Weyl Groups I | arXiv:2506.13656v3 Announce Type: replace Abstract: We present an approach to construct a class of generalized Frobenius manifold structures on the orbit spaces of affine Weyl groups, and prove that their monodromy groups are parabolic subgroups of the associated affine Weyl groups. | https://arxiv.org/abs/2506.13656 | Academic Papers | svg |
9c7b44da7393e0029885e5bc44151e4ff4bf8124730b970b85350c9053d6659e | 2026-01-13T00:00:00-05:00 | Automorphism groups and linearizability of rational Fano conic bundle threefolds | arXiv:2506.15042v2 Announce Type: replace Abstract: We generalize the equivariant intermediate Jacobian torsor obstruction over $\mathbb{C}$ to algebraically closed fields of characteristic zero. It is an obstruction to the (projective) linearizability problem of finite group actions on threefolds. In addition, we calc... | https://arxiv.org/abs/2506.15042 | Academic Papers | svg |
7d962ae2ae1de83e96aa4f7aef019a4f068fb32025e663d17622fdda6eff09b7 | 2026-01-13T00:00:00-05:00 | Transporting a Dirac mass in a mean field planning problem | arXiv:2506.16041v2 Announce Type: replace Abstract: We study a mean field planning problem in which the initial density is a Dirac mass. We show that there exists a unique solution which converges to a self-similar profile as time tends to $0$. We proceed by studying a continuous rescaling of the solution, and characte... | https://arxiv.org/abs/2506.16041 | Academic Papers | svg |
63a5dd7c2a35be3a16844e3793e958b727ac0044d098474bffaba1580e6e1ff5 | 2026-01-13T00:00:00-05:00 | Deep random difference method for high-dimensional quasilinear parabolic partial differential equations | arXiv:2506.20308v2 Announce Type: replace Abstract: Solving high-dimensional parabolic partial differential equations (PDEs) with deep learning methods is often computationally and memory intensive, primarily due to the need for automatic differentiation (AD) to compute large Hessian matrices in the PDE. In this work, ... | https://arxiv.org/abs/2506.20308 | Academic Papers | svg |
96de19c4a9efa1a90c0578670acf1beb5b72ef2098443cba1d7ac59cdaba8c4e | 2026-01-13T00:00:00-05:00 | On a minimal free resolution of the residue field over a local ring of codepth 3 of class $T$ | arXiv:2506.21505v2 Announce Type: replace Abstract: Let $R$ be any noetherian local ring with residue field $k$, and $A$ the homology of the Koszul complex on a minimal set of generators of the maximal ideal of $R$. In this paper, we show that a minimal free resolution of $k$ over $R$ can be obtained from a graded mini... | https://arxiv.org/abs/2506.21505 | Academic Papers | svg |
daf73ddffa04c182faacd504738d94b5e5c359e073a3220e633a9b9aad8db191 | 2026-01-13T00:00:00-05:00 | The Dedekind-Hasse Criterion in Quaternion Algebras | arXiv:2506.22651v2 Announce Type: replace Abstract: We show that a criterion for an integral domain to be a principal ideal domain (PID), due to Dedekind and Hasse, can also be applied in quaternion orders, and that it can be used to build a finite algorithm to determine if a given order is a principal left (or right) ... | https://arxiv.org/abs/2506.22651 | Academic Papers | svg |
677f61dda199c8c309ae2e37799f2d328d1a73d6a90583acae7189dbbf261a2f | 2026-01-13T00:00:00-05:00 | An infinite family of pairs of distinct quartic Galois CM-fields with the same discriminant and regulator | arXiv:2506.23541v2 Announce Type: replace Abstract: We construct an infinite family of pairs of distinct imaginary biquadratic fields and pairs of distinct imaginary cyclic quartic fields with the same discriminant and regulator. We also construct an infinite family of imaginary biquadratic fields and imaginary cyclic ... | https://arxiv.org/abs/2506.23541 | Academic Papers | svg |
57b5c6eee927be1b74359124858a665946b62243643d6755533497dd277061e2 | 2026-01-13T00:00:00-05:00 | Existence and Incompressible Limit of Weak and Classical Solutions to the Cauchy Problem for Compressible Navier-Stokes Equations with Large Bulk Viscosity and Large Initial Data | arXiv:2507.02497v2 Announce Type: replace Abstract: This paper investigates the Cauchy problem for the barotropic compressible Navier-Stokes equations in $\mathbb{R}^2$ with the constant state as far field, which could be vacuum or non-vacuum. Under the assumption of a sufficiently large bulk viscosity coefficient, we ... | https://arxiv.org/abs/2507.02497 | Academic Papers | svg |
18ac072d0b69839f2f5d35f173a3084bc802a8e9388e9322cbe2d1cb6574091e | 2026-01-13T00:00:00-05:00 | Skew Laurent Series and General Cyclic Convolutional Codes | arXiv:2507.05022v2 Announce Type: replace Abstract: Convolutional codes were originally conceived as vector subspaces of a finite-dimensional vector space over a field of Laurent series having a polynomial basis. Piret and Roos modeled cyclic structures on them by adding a module structure over a finite-dimensional alg... | https://arxiv.org/abs/2507.05022 | Academic Papers | svg |
35d2b8eec4abbd8d1c00de668c0adad91f67c4a0d6036a5c17b3ad684a6003bc | 2026-01-13T00:00:00-05:00 | Covering Complete Geometric Graphs by Monotone Paths | arXiv:2507.10840v2 Announce Type: replace Abstract: Given a set $A$ of $n$ points (vertices) in general position in the plane, the \emph{complete geometric graph} $K_n[A]$ consists of all $\binom{n}{2}$ segments (edges) between the elements of $A$. It is known that the edge set of every complete geometric graph on $n$ ... | https://arxiv.org/abs/2507.10840 | Academic Papers | svg |
717df43a9b14a9f308389bc7f4ef666d955a2903fd54cfe267de0ed50cea51a0 | 2026-01-13T00:00:00-05:00 | Hierarchical Secure Aggregation with Heterogeneous Security Constraints and Arbitrary User Collusion | arXiv:2507.14768v2 Announce Type: replace Abstract: In hierarchical secure aggregation (HSA), a server communicates with clustered users through an intermediate layer of relays to compute the sum of users' inputs under two security requirements -- server security and relay security. Server security requires that the se... | https://arxiv.org/abs/2507.14768 | Academic Papers | svg |
0ff882ec9a029418e3d3c65ca4ab45edc4adfed063ea553f309e2f59ef52e616 | 2026-01-13T00:00:00-05:00 | A result on spanning trees with bounded total excess | arXiv:2507.15139v2 Announce Type: replace Abstract: Let $G$ be a connected graph and $T$ a spanning tree of $G$. Let $\rho(G)$ denote the adjacency spectral radius of $G$. The $k$-excess of a vertex $v$ in $T$ is defined as $\max\{0,d_T(v)-k\}$. The total $k$-excess $\mbox{te}(T,k)$ is defined by $\mbox{te}(T,k)=\sum\l... | https://arxiv.org/abs/2507.15139 | Academic Papers | svg |
0298c46d849780b96aa0840d3d686fa89c9d197fbc13516333ab104c72b42687 | 2026-01-13T00:00:00-05:00 | Riesz representers for the rest of us | arXiv:2507.19413v3 Announce Type: replace Abstract: The application of semiparametric efficient estimators, particularly those that leverage machine learning, is rapidly expanding within epidemiology and causal inference. This literature is increasingly invoking the Riesz representation theorem and Riesz regression. Th... | https://arxiv.org/abs/2507.19413 | Academic Papers | svg |
0877e07ff9b92c664391659923d85b470fbdf6b6e663fdaf0e4d25ba9860ceed | 2026-01-13T00:00:00-05:00 | Time-complexity of sampling from a multimodal distribution using sequential Monte Carlo | arXiv:2508.02763v2 Announce Type: replace Abstract: We study a sequential Monte Carlo algorithm to sample from the Gibbs measure with a non-convex energy function at a low temperature. We use the practical and popular geometric annealing schedule, and use a Langevin diffusion at each temperature level. The Langevin dif... | https://arxiv.org/abs/2508.02763 | Academic Papers | svg |
527508042d4353351c7aec85468e8e1b9f7a5e1a8f70deb1a209bf38870bbf67 | 2026-01-13T00:00:00-05:00 | Extendability of $1$-decomposable complexes | arXiv:2508.04555v3 Announce Type: replace Abstract: A well-known conjecture of Simon (1994) states that any pure $d$-dimensional shellable complex on $n$ vertices can be extended to $\Delta_{n-1}^{(d)}$, the $d$-skeleton of the $(n-1)$-dimensional simplex, by attaching one facet at a time while maintaining shellability... | https://arxiv.org/abs/2508.04555 | Academic Papers | svg |
b2e5319b61bcb9511238294f662e5ea9cf18c6b2ac59d7ebaf3eb9035ffac01a | 2026-01-13T00:00:00-05:00 | The modified diagonal cycles of Hypergeometric curves | arXiv:2508.06008v2 Announce Type: replace Abstract: For each $N\geq 2$, Asakura and Otsubo have recently introduced a smooth family of algebraic curves $\{X_{N,\lambda}\}_{\lambda \in \mathbb{P}^1\setminus \{0, 1, \infty\}}$ in characteristic 0 that is closely related to hypergeometric functions and the Fermat curve of... | https://arxiv.org/abs/2508.06008 | Academic Papers | svg |
98a82862bedc77348e7d263b4137255dfb536dd5bcb4f9f1b3fc90605c6171dc | 2026-01-13T00:00:00-05:00 | Connected components of Berkovich fixed locus: Potential good reduction | arXiv:2508.07156v2 Announce Type: replace Abstract: Let $\mathbbm{P}^{1,an}$ be the Berkovich projective line over a complete, algebraically closed, non-Archimedean field. Let $\phi$ be a degree $\geq 2$ rational map with potential good reduction, acting on $\mathbbm{P}^{1,an}$. In this article, we study the topology o... | https://arxiv.org/abs/2508.07156 | Academic Papers | svg |
86c3a0040e9313190ddee79b4a1b66d5313ba1298b381d227cfac1c390137fa8 | 2026-01-13T00:00:00-05:00 | A Generalized Crystalline Equivalence Principle | arXiv:2508.10978v3 Announce Type: replace Abstract: We prove a general version of the crystalline equivalence principle which gives an equivalence of categories between a category of TQFTs defined on a generic space with $G$-symmetry, and a category of TQFTs with internal symmetry. We give a definition and classificati... | https://arxiv.org/abs/2508.10978 | Academic Papers | svg |
c8072f045f6b8b26c23c370af95554283365b5384ed7e578d3a0402335457844 | 2026-01-13T00:00:00-05:00 | Reciprocity for GL(2) L-functions twisted by Dirichlet characters | arXiv:2508.12401v2 Announce Type: replace Abstract: A formula connecting a moment of L-functions and a dual moment in a way that interchanges the roles of certain key parameters on both sides is known as a reciprocity relation. We establish a reciprocity relation for a first moment of GL(2) L-functions twisted by Diric... | https://arxiv.org/abs/2508.12401 | Academic Papers | svg |
4c745990fc41630b1d8d639a91232dc0e4743029e1c351feb1e8aab5d402a90b | 2026-01-13T00:00:00-05:00 | Stabilized automorphism groups and full groups of odometers | arXiv:2508.20005v2 Announce Type: replace Abstract: In this article, we show that the stabilized automorphism group of free exact odometers arising from actions of finitely generated residually finite groups coincides with the topological full group of the odometer acting on itself by right multiplication. We then prov... | https://arxiv.org/abs/2508.20005 | Academic Papers | svg |
99a7bfc343f1ad9d7f98b64792edb1227d34f6f320e55b50ba0f69cde6a73736 | 2026-01-13T00:00:00-05:00 | The linear minimal 4-chart with three crossings | arXiv:2509.04114v2 Announce Type: replace Abstract: Charts are oriented labeled graphs in a disk. Any simple surface braid (2-dimensional braid) can be described by using a chart. Also, a chart represents an oriented closed surface embedded in 4-space. In this paper, we investigate embedded surfaces in 4-space by using... | https://arxiv.org/abs/2509.04114 | Academic Papers | svg |
8b2c8e77f451862d92db72d40753209b8370a3471c5a180aa27560211e936237 | 2026-01-13T00:00:00-05:00 | Unitary equivalence in Generalized Uncertainty Principle theories | arXiv:2509.05477v2 Announce Type: replace Abstract: We analyze the issue of unitary equivalence within Generalized Uncertainty Principle (GUP) theories in the one-dimensional case. For a deformed Heisenberg algebra, its representation in terms of Hilbert space and conjugate operators is not uniquely determined, raising... | https://arxiv.org/abs/2509.05477 | Academic Papers | svg |
e51caec39948373a2ef0b3a152c92dc6f4614d181eebee91d2c77681c45edd62 | 2026-01-13T00:00:00-05:00 | Robust Confidence Intervals for a Binomial Proportion: Local Optimality and Adaptivity | arXiv:2509.05568v2 Announce Type: replace Abstract: This paper revisits the classical problem of interval estimation of a binomial proportion under Huber contamination. Our main result derives the rate of optimal interval length when the contamination proportion is unknown under a local minimax framework, where the per... | https://arxiv.org/abs/2509.05568 | Academic Papers | svg |
27800406464f34d46af7347037c4f666ff833a46955363a7743e90d07dbc96b1 | 2026-01-13T00:00:00-05:00 | Convergence analysis for the Barrett--Garcke--Nurnberg method of transport type for evolving curves | arXiv:2509.07834v2 Announce Type: replace Abstract: In this paper, we propose a Barrett-Garcke-Nurnberg (BGN) method for evolving geometries under general flows and present the corresponding convergence analysis. Specifically, we examine the scenario where a closed curve evolves according to a prescribed background vel... | https://arxiv.org/abs/2509.07834 | Academic Papers | svg |
0e059185625dc2369cf96aa2ab54f82e2b24f3f1ece3bac16b9ede0c7a816ac4 | 2026-01-13T00:00:00-05:00 | Finite time blow-up and global solutions for the viscoelastic wave equation with combined power-type nonlinearities | arXiv:2509.08462v3 Announce Type: replace Abstract: The main objective of this manuscript is to investigate the global behavior of the solutions to the viscoelastic wave equation with a linear memory term of Boltzmann type, and a nonlinear damping modeling friction, as well as a supercritical source term which is a com... | https://arxiv.org/abs/2509.08462 | Academic Papers | svg |
107c53188dbd84e153531aa86e6d773aa8a96c090101c31fdf55b7ced4e71bd1 | 2026-01-13T00:00:00-05:00 | Rank of the family of elliptic curves $y^2 = x^3- 5px$ | arXiv:2509.09169v3 Announce Type: replace Abstract: This article considers the family of elliptic curves given by $E_{p}: y^2=x^3-5px$ and certain conditions on an odd prime $p$. More specifically, we have shown that if $p \equiv 7, 23 \pmod {40}$, then the rank of $E_{p}$ is zero for both $ \mathbb{Q} $ and $ \mathbb{... | https://arxiv.org/abs/2509.09169 | Academic Papers | svg |
330def60830d4a799d562a9abfc51a7e599bfab2a31b87c47c25f15369688e9d | 2026-01-13T00:00:00-05:00 | Long-time behavior of a nonlocal Cahn-Hilliard equation with nonlocal dynamic boundary condition and singular potentials | arXiv:2509.10304v2 Announce Type: replace Abstract: We investigate the long-time behavior of a nonlocal Cahn-Hilliard equation in a bounded domain $\Omega\subset\mathbb{R}^d$ $(d\in\{2,3\})$, subject to a kinetic rate-dependent nonlocal dynamic boundary condition. The kinetic rate $1/L$, with $L\in[0,+\infty)$, disting... | https://arxiv.org/abs/2509.10304 | Academic Papers | svg |
35c990fb23e81a59cf65e6b6734a98e49396d72d65913db9fc50ea37e8fbd9d2 | 2026-01-13T00:00:00-05:00 | Decomposition of the Tschirnhausen module for coverings on decomposable $\mathbb{P}^1$-bundles | arXiv:2509.11227v3 Announce Type: replace Abstract: In this note, we show that for a smooth algebraic variety $Y$ and a smooth $m$-section $X$ of the $\mathbb{P}^1$-bundle \[ f : \mathbb{P}(\mathcal{O}_Y \oplus \mathcal{O}_Y(E)) \longrightarrow Y, \] where $E$ is an effective divisor on $Y$ satisfying $H^1(Y, \mathcal{... | https://arxiv.org/abs/2509.11227 | Academic Papers | svg |
3e4391cf27d7706d58a885de3babed3e5daad2f6c6b13ae77756e71830288cb0 | 2026-01-13T00:00:00-05:00 | Spotlight inversion by orthogonal projections | arXiv:2509.15512v2 Announce Type: replace Abstract: Many computational problems involve solving a linear system of equations, although only a subset of the entries of the solution are needed. In inverse problems, where the goal is to estimate unknown parameters from indirect noisy observations, it is not uncommon that ... | https://arxiv.org/abs/2509.15512 | Academic Papers | svg |
6ce61d31c67b5dbb229d2769e698e6bd335d86290645ce6718b4d7c2fb31c809 | 2026-01-13T00:00:00-05:00 | Quantum Howe duality and Schur duality of type AIII | arXiv:2509.18982v2 Announce Type: replace Abstract: We establish a new connection between the iHowe duality of type AIII established by Luo-Xu and the iSchur duality established by Bao-Wang. We show that iweight $\overline{\rho}$ space in the iHowe duality is naturally isomorphic to the tensor space in the iSchur duali... | https://arxiv.org/abs/2509.18982 | Academic Papers | svg |
c8e293e328ed74bec3e8d14fdf4206afdf094693426691555b2a5663672dbae3 | 2026-01-13T00:00:00-05:00 | Higher-order Sobolev and Rellich inequalities via iterated Talenti's principle | arXiv:2509.19198v2 Announce Type: replace Abstract: In this paper we establish higher-order Sobolev and Rellich-type inequalities on non-compact Riemannian manifolds supporting an isoperimetric inequality. We highlight two notable settings: manifolds with non-negative Ricci curvature and having Euclidean volume growth ... | https://arxiv.org/abs/2509.19198 | Academic Papers | svg |
b5b967576202ec8fab99c340c38463615dc9e168552229fbba31b989cd595730 | 2026-01-13T00:00:00-05:00 | ALNS for Tugboat Scheduling in Inland Waterway | arXiv:2509.19718v2 Announce Type: replace Abstract: This paper focuses on the barges shipping problem, also known as the tugboats scheduling problem, within the context of a scenario where a single tugboat has the capacity to tow multiple barges and conduct multiple trips in a drop-and-pull mode during a daily work shi... | https://arxiv.org/abs/2509.19718 | Academic Papers | svg |
46431be3d783f9b29b5c6e92ddeff485629d94f9d8bf396360e3f960193fe258 | 2026-01-13T00:00:00-05:00 | Souriau-Fisher metric and Completely integrable system on Lie groups SO(2) and SO(3) | arXiv:2509.20910v2 Announce Type: replace Abstract: We study the generalize Fisher metric on SO(2) and SO(3) via the thermodynamics Lie group theories of Souriau. Then we give the effect of 2-cocycle on the integrability of gradient systems due to the Fisher metric and Souriau-Fisher metric. In addition, we show how th... | https://arxiv.org/abs/2509.20910 | Academic Papers | svg |
d9981c83e0f1c7ef39df573ba001f99998dc9c4339141f02e642776cc80b0f5e | 2026-01-13T00:00:00-05:00 | Optimal Control of a Navier-Stokes-Cahn-Hilliard System for Membrane-fluid Interaction | arXiv:2509.22069v2 Announce Type: replace Abstract: We consider an optimal control problem for a two-dimensional Navier-Stokes-Cahn-Hilliard system arising in the modeling of fluid-membrane interaction. The fluid dynamics is governed by the incompressible Navier-Stokes equations, which are nonlinearly coupled with a si... | https://arxiv.org/abs/2509.22069 | Academic Papers | svg |
8cd92cfe8a90d7e10364bc11ef56c8e2ca642269c1e5543199d1753a78800b3d | 2026-01-13T00:00:00-05:00 | Advances in the Shannon Capacity of Graphs | arXiv:2509.24600v2 Announce Type: replace Abstract: We derive exact values and new bounds for the Shannon capacity of two families of graphs: the $q$-Kneser graphs and the tadpole graphs. We also construct a countably infinite family of connected graphs whose Shannon capacity is not attained by the independence number ... | https://arxiv.org/abs/2509.24600 | Academic Papers | svg |
9732d2f77a6945aae0d6a4f8c9a72a9c0cb9c14694094ae09fa13a5c185e7b9d | 2026-01-13T00:00:00-05:00 | The Euler characteristic of $\ell$-adic local systems on $\mathcal{A}_n$ | arXiv:2510.00656v2 Announce Type: replace Abstract: We study the Euler characteristic of $\ell$-adic local systems on the moduli stack $\mathcal{A}_n$ of principally polarized abelian varieties of dimension $n$ associated to algebraic representations of $\mathbf{GSp}_{2n}$, as virtual representations of the absolute Ga... | https://arxiv.org/abs/2510.00656 | Academic Papers | svg |
c6d02c1bd68af6c1dee1765e5d61d8e26c6203b23741e2d788195d8b22656bdd | 2026-01-13T00:00:00-05:00 | Agile Tradespace Exploration for Space Rendezvous Mission Design via Transformers | arXiv:2510.03544v2 Announce Type: replace Abstract: Spacecraft rendezvous enables on-orbit servicing, debris removal, and crewed docking, forming the foundation for a scalable space economy. Designing such missions requires rapid exploration of the tradespace between control cost and flight time across multiple candida... | https://arxiv.org/abs/2510.03544 | Academic Papers | svg |
f042ed95a4dc4a53832e096fa2ee74a28235b3bbed7cde245c6bc23c9e460ab2 | 2026-01-13T00:00:00-05:00 | The $\mathbb{A}^1$-Euler characteristic of symmetric powers | arXiv:2510.06922v2 Announce Type: replace Abstract: The $\mathbb{A}^1$-Euler characteristic is a refinement in algebraic geometry of the classical topological Euler characteristic, which can be constructed using motivic homotopy theory. This invariant is a quadratic form rather than an integer, which carries a lot of i... | https://arxiv.org/abs/2510.06922 | Academic Papers | svg |
fd31859667576421e72efb2757527789b8ffa48683feda5294616f2cfb29d87e | 2026-01-13T00:00:00-05:00 | A quantum N-dimer model | arXiv:2510.07543v2 Announce Type: replace Abstract: We study a quantum version of the $n$-dimer model from statistical mechanics, based on the formalism from quantum topology developed by Reshetikhin and Turaev (the latter which, in particular, can be used to construct the Jones polynomial of a knot in $\mathbb{R}^3$).... | https://arxiv.org/abs/2510.07543 | Academic Papers | svg |
74bd5fc4a7683f84672ba4d2b9cd83423832186b76de4a8d2c3c66c80395fdaf | 2026-01-13T00:00:00-05:00 | Metaplectic time-frequency representations | arXiv:2510.09322v3 Announce Type: replace Abstract: Time-frequency representations stemmed in 1932 with the introduction of the Wigner distribution. For most of the 20th century, research in this area primarily focused on defining joint probability distributions for position and momentum in quantum mechanics. Applicati... | https://arxiv.org/abs/2510.09322 | Academic Papers | svg |
04465aaff4ee60ccaa446a8382da9552c46356e1f4a2d42e270f9e25858ed233 | 2026-01-13T00:00:00-05:00 | Elliptic Harnack inequalities for mixed local and nonlocal $p$-energy form on metric measure spaces | arXiv:2510.12404v2 Announce Type: replace Abstract: In the context of metric measure spaces, we introduce an axiomatic formulation of mixed local and nonlocal $p$-energy forms. Within this framework, we use the Poincar\'{e} inequality, the cutoff Sobolev inequality, and mild assumptions on the jump measure to establish... | https://arxiv.org/abs/2510.12404 | Academic Papers | svg |
d69667e0020b92125fbaffa3370b3801f7e602f9008e7583b8eb0f5f16115a84 | 2026-01-13T00:00:00-05:00 | Approximation by elements of finite spectra for C* Algebras of higher real rank | arXiv:2510.17271v3 Announce Type: replace Abstract: In this article, we extend a well known result about real rank zero C* Algebras to higher real rank C* Algebras. The main technique used here is similar to the method in which we approximate continuous functions using projections. What we reach at the end, is similar ... | https://arxiv.org/abs/2510.17271 | Academic Papers | svg |
18ca9ffeeeb21015774b35c88652dd643da6a27c04241aa27c31f2572e165564 | 2026-01-13T00:00:00-05:00 | Twisted commutativity and conjugacy ratio in groups | arXiv:2510.18980v2 Announce Type: replace Abstract: In this paper we introduce and study the degree of twisted commutativity and the twisted conjugacy ratio of a finitely generated group $G$. The degree of twisted commutativity $\mathrm{tdc}_X(\varphi, G)$ generalises the degree of commutativity of $G$, by measuring th... | https://arxiv.org/abs/2510.18980 | Academic Papers | svg |
1625aaa0e6ef8240d9bebd4c93c3f13781d1056813c2d23ea9778d0baededc50 | 2026-01-13T00:00:00-05:00 | On $2n+4$ normals conjecture for convex polytopes in $\mathbb{R}^n$ | arXiv:2510.22695v2 Announce Type: replace Abstract: We prove that for $n>3$ each generic simple polytope in $\mathbb{R}^n$ contains a point with at least $2n+4$ emanating normals to the boundary. This result is a piecewise-linear counterpart of a long-standing problem about normals to smooth convex bodies. | https://arxiv.org/abs/2510.22695 | Academic Papers | svg |
4e2e4ed6d33db8f8da4a4d4eeb617295f8ad52a0b15bc105f7f0196864f00b85 | 2026-01-13T00:00:00-05:00 | Monomial algebras and G_a^n-equivariant embeddings into toric varieties | arXiv:2510.22820v2 Announce Type: replace Abstract: An induced additive action on a projective variety X in P^n is a regular action of the group G_a^n on X with an open orbit that can be extended to a regular action on P^n. Such actions are described with pairs (A, U), where A is a local algebra and U is a generating s... | https://arxiv.org/abs/2510.22820 | Academic Papers | svg |
b33373e8edb5038c73afb6f6c3a7ebf1d32cbd984c4afa7b792cc883ef31dcb5 | 2026-01-13T00:00:00-05:00 | Injective envelopes of $C^*$-algebras as maximal rigid multiplier covers | arXiv:2510.24441v3 Announce Type: replace Abstract: We present a non-commutative analogue of B{\l}aszczyk's elegant two-step construction of the Gleason cover: first maximise irreducibility, then compactify. The key insight is that extremal disconnectedness (respectively, injectivity) emerges naturally from a maximalit... | https://arxiv.org/abs/2510.24441 | Academic Papers | svg |
504cd1f2af9388ba681fa49c791e7e2186f6dda20d39a3f96126fe4112191e77 | 2026-01-13T00:00:00-05:00 | Modular Periodicity of Random Initialized Recurrences | arXiv:2510.24882v4 Announce Type: replace Abstract: Classical studies of the Fibonacci sequence focus on its periodicity modulo $m$ (the Pisano periods) with canonical initialization. We investigate instead the complete periodic structure arising from all $m^2$ possible initializations in $\mathbb{Z}/m\mathbb{Z}$. We d... | https://arxiv.org/abs/2510.24882 | Academic Papers | svg |
e0b828225db132d56219f6913862e18dd79f658e9a244bbab6700e315969c28f | 2026-01-13T00:00:00-05:00 | The product measures of cross $t$-intersecting families | arXiv:2510.26642v2 Announce Type: replace Abstract: We investigate the product measures of intersection problems in extremal combinatorics. Invoking a recent result of He--Li--Wu--Zhang, we prove that for any $ n \geq t \geq 3$ and $ p_1, p_2 \in (0, \frac{1}{t+1})$, if $ \mathcal{F}_1, \mathcal{F}_2 \subseteq 2^{[n]}$... | https://arxiv.org/abs/2510.26642 | Academic Papers | svg |
99659768f667b7d4e765064409682f0305c1354e06efdf0a3227d1048c908f10 | 2026-01-13T00:00:00-05:00 | Forget BIT, It is All about TOKEN: Towards Semantic Information Theory for LLMs | arXiv:2511.01202v2 Announce Type: replace Abstract: Large language models (LLMs) have demonstrated remarkable capabilities in numerous real-world applications. While the vast majority of research conducted from an experimental perspective is progressing rapidly, it demands substantial computational power, data, and oth... | https://arxiv.org/abs/2511.01202 | Academic Papers | svg |
a75891eba5bb50126d4662670fa4f17fa33dfe5e0ff6b211693c4ef24fe4bdd4 | 2026-01-13T00:00:00-05:00 | Lectures on local theta correspondence | arXiv:2511.07849v2 Announce Type: replace Abstract: This set of lecture notes on local theta correspondence is the written version of a mini-course the author gave in March of 2025 for the program ``Representation Theory and Noncommutative Geometry" at the Institut Henri Poincar\'e, Paris. The emphasis is on the Archim... | https://arxiv.org/abs/2511.07849 | Academic Papers | svg |
a4438fb124215566d3be924556e6e72210f27fe744c3d4d0fb508a445979ee54 | 2026-01-13T00:00:00-05:00 | Conditional stability in determining source terms of semilinear parabolic partial differential equations | arXiv:2511.08460v3 Announce Type: replace Abstract: We study an inverse source problem for a semilinear parabolic equation in a bounded domain, where the nonlinearity depends on the unknown function and its gradient through a quadratic reaction term and a Burgers-type convection term. From partial boundary observation ... | https://arxiv.org/abs/2511.08460 | Academic Papers | svg |
1cee9108ccf87466cc5ac152be7ee316741d4b0c71bd3fcec754ad9599ebbc01 | 2026-01-13T00:00:00-05:00 | Instantaneous Type I blow-up and non-uniqueness of smooth solutions of the Navier-Stokes equations | arXiv:2511.09556v2 Announce Type: replace Abstract: For any smooth, divergence-free initial data, we construct a solution of the Navier--Stokes equations that exhibits Type~I blow-up of the $L^\infty$ norm at time $T_*>0$, while remaining smooth in space and time on $\mathbb T^d\times([0,T]\setminus\{T_*\})$. An instan... | https://arxiv.org/abs/2511.09556 | Academic Papers | svg |
4c2095c86df09b2978a4709f5fb8cff9092727e98050bf62bcbd45a5817bd85f | 2026-01-13T00:00:00-05:00 | Surface homeomorphisms with big rotation set | arXiv:2511.15220v2 Announce Type: replace Abstract: This article consists in applications of [arXiv:2511.14232] in the case of homemomorphisms of higher genus surfaces whose homological rotation set is big enough -- a class of dynamics that is open. We first prove a structure theorem for the rotation set of such homeom... | https://arxiv.org/abs/2511.15220 | Academic Papers | svg |
70fc1ca8e210aacf0ad494df388f447924a254984529cdca8d353766f6ddcd13 | 2026-01-13T00:00:00-05:00 | A Stochastic Approach to the Definition of the Path Integral Measure | arXiv:2511.15772v3 Announce Type: replace Abstract: We to define a Path Integral in Lorentzian time by restricting the relevant domain of integration on $C([0,1],M)$ over a Riemannian configuration manifold $(M,g)$ and considering the dynamics of a particle evolving between to fixed endpoints with a referential non-deg... | https://arxiv.org/abs/2511.15772 | Academic Papers | svg |
e7e420d6910f242eb14c13715c6f0c04966248b76bb2b0c88e9d663159374cc1 | 2026-01-13T00:00:00-05:00 | Optimal local central limit theorems on Wiener chaos | arXiv:2511.21496v2 Announce Type: replace Abstract: This paper investigates a local central limit theorem for a normalized sequence of random variables belonging to a fixed order Wiener chaos and converging to the standard normal distribution. We prove, without imposing any additional conditions, that the optimal rate ... | https://arxiv.org/abs/2511.21496 | Academic Papers | svg |
61ec9d7c45eaab0c56b0df925ef666932084b7e5be9108582a0c5604d81609b0 | 2026-01-13T00:00:00-05:00 | Logistic elliptic and parabolic problem for the fractional $p$-Laplacian | arXiv:2511.23272v2 Announce Type: replace Abstract: In this paper we prove existence, uniqueness of weak solutions of the following nonlocal nonlinear logistic equation \begin{equation*} \begin{cases} (-\Delta)_p^s u_\lambda=\lambda u_\lambda^q - b(x)u_\lambda^r \quad \text{in} \;\Omega,\\ u_\lambda=0 \quad \text{in} \... | https://arxiv.org/abs/2511.23272 | Academic Papers | svg |
e180319abba3fce969749347e278cfe66adec0e2d9d8e925046c267a28ce939d | 2026-01-13T00:00:00-05:00 | Nonsmooth bifurcations in families of one-dimensional piecewise-linear quasiperiodically forced maps | arXiv:2512.04234v2 Announce Type: replace Abstract: We study nonsmooth bifurcations of four types of families of one-dimensional quasiperiodically forced maps of the form $F_i(x,\theta) = (f_i(x,\theta), \theta+\omega)$ for $i=1,\dots,4$, where $x$ is real, $\theta\in\mathbb{T}$ is an angle, $\omega$ is an irrational f... | https://arxiv.org/abs/2512.04234 | Academic Papers | svg |
5ac1a9f7b18dc9df0991716bcbd83c2adaa45b7f92e27c9df5ed8252b0b6e070 | 2026-01-13T00:00:00-05:00 | A poset representation for stable contracts in a two-sided market generated by integer choice functions | arXiv:2512.05942v2 Announce Type: replace Abstract: Generalizing a variety of earlier problems on stable contracts in two-sided markets, Alkan and Gale introduced in 2003 a general stability model on a bipartite graph $G=(V,E)$ in which the vertices are interpreted as ``agents'', and the edges as possible ``contract'' ... | https://arxiv.org/abs/2512.05942 | Academic Papers | svg |
52c0138266121a9cdbf4f203a082cd4a27278bba9e2e63d8229cd4f014383325 | 2026-01-13T00:00:00-05:00 | Spoke topological Hochschild homology | arXiv:2512.11338v2 Announce Type: replace Abstract: Fix primes $p$ and $\ell$, and let $C_p$ be the cyclic group of order $p$. We compute the $C_p$-equivariant spoke topological Hochschild homology of $\underline{\mathbb{F}}_{\ell}$ and prove it exhibits a form of B\"okstedt periodicity. Here spoke topological Hochschi... | https://arxiv.org/abs/2512.11338 | Academic Papers | svg |
44e33259219807e9bc6aeaeb64c7a01ce6d91162fe553fa0f4e27f6e58f12d62 | 2026-01-13T00:00:00-05:00 | Decomposition theorems for unmatchable pairs in groups and field extensions | arXiv:2512.12942v2 Announce Type: replace Abstract: A theory of matchings for finite subsets of an abelian group, introduced in connection with a conjecture of Wakeford on canonical forms for symmetric tensors, has since been extended to the setting of field extensions and to that of matroids. Earlier approaches have p... | https://arxiv.org/abs/2512.12942 | Academic Papers | svg |
122ff14fa196f21907642d0beac4c8dc1c35dca0d1e4ed115c1d3756c836a93d | 2026-01-13T00:00:00-05:00 | Ensemble Parameter Estimation for the Lumped Parameter Linear Superposition (LPLSP) Framework: A Rapid Approach to Reduced-Order Modeling for Transient Thermal Systems | arXiv:2512.14467v2 Announce Type: replace Abstract: This work introduces an ensemble parameter estimation framework that enables the Lumped Parameter Linear Superposition (LPLSP) method to generate reduced order thermal models from a single transient dataset. Unlike earlier implementations that relied on multiple param... | https://arxiv.org/abs/2512.14467 | Academic Papers | svg |
7cc919124fca9db0fc0c91857074c104fae0437f6353e69d6c5631d20b296d55 | 2026-01-13T00:00:00-05:00 | Using the Jones Polynomial to Prove Infinite Families of Knots Satisfy the Cosmetic Surgery Conjecture | arXiv:2512.20511v2 Announce Type: replace Abstract: This paper computes the Jones polynomial and the invariants obstructing cosmetic surgery which are derived from it for two infinite families of knots, proving they satisfy the Purely Cosmetic Surgery Conjecture. Both the method of computation and the method for genera... | https://arxiv.org/abs/2512.20511 | Academic Papers | svg |
0a18b93f501ca45c9da46c34071ae1f3e070e56bd5582979ae6fe42dd32e9e6b | 2026-01-13T00:00:00-05:00 | Relation between generalized and ordinary cluster algebras | arXiv:2512.21062v2 Announce Type: replace Abstract: Recently, Ramos and Whiting showed that any generalized cluster algebra of geometric type is isomorphic to a quotient of a subalgebra of a certain cluster algebra. Based on their idea and method, we show that the same property holds for any generalized cluster algebra... | https://arxiv.org/abs/2512.21062 | Academic Papers | svg |
f2872660dd84938eb729ed35a2d33874ec0f28b6be102acff4352b59bb52aee9 | 2026-01-13T00:00:00-05:00 | On Rayleigh scattering in the massless Nelson model | arXiv:2512.21307v2 Announce Type: replace Abstract: Asymptotic completeness of Rayleigh scattering in models of atoms and molecules of non-relativistic QED is expected, but for a proof we still lack sufficient control on the number of emitted soft photons. So far, this obstacle has only been overcome for the spin-boson... | https://arxiv.org/abs/2512.21307 | Academic Papers | svg |
b82087d526fea92f8873c1d88f1cdffe0fcf6b63a76aad106ee076f5b31a1433 | 2026-01-13T00:00:00-05:00 | Data-Free Asymptotics-Informed Operator Networks for Singularly Perturbed PDEs | arXiv:2512.22006v2 Announce Type: replace Abstract: Recent advances in machine learning (ML) have opened new possibilities for solving partial differential equations (PDEs), yet robust performance in challenging regimes remains limited. In particular, singularly perturbed differential equations exhibit sharp boundary o... | https://arxiv.org/abs/2512.22006 | Academic Papers | svg |
a485ed917d3d1989390a0abee97e57e2564d5838a7e4bea213eee61c5f97d239 | 2026-01-13T00:00:00-05:00 | Generalized binomial edge ideals are Cartwright-Sturmfels | arXiv:2512.22012v2 Announce Type: replace Abstract: Binomial edge ideals associated to a simple graph G were introduced by Herzog and collaborators and, independently, by Ohtani. They became an ``instant classic" in combinatorial commutative algebra with more than 100 papers devoted to their investigation over the past... | https://arxiv.org/abs/2512.22012 | Academic Papers | svg |
681c9052ed5e1d12966b7ea2a5d18c32bd5eada10abcecd867f7687b1290a2d1 | 2026-01-13T00:00:00-05:00 | Infinitesimal moments in free and c-free probability and Motzkin paths | arXiv:2512.22700v3 Announce Type: replace Abstract: Infinitesimal moments associated with infinitesimal freeness and infinitesimal conditional freeness are studied. For free random variables, we consider continuous deformations of moment functionals associated with Motzkin paths $w$, which provide a decomposition of th... | https://arxiv.org/abs/2512.22700 | Academic Papers | svg |
6a55294ecc21e795f64be92a2408d56bf5879ddbdf1141409dbccc3ce98dc6ba | 2026-01-13T00:00:00-05:00 | Small-time global controllability of a class of bilinear fourth-order parabolic equations | arXiv:2512.23339v2 Announce Type: replace Abstract: In this work, we investigate the small-time global controllability properties of a class of fourth-order nonlinear parabolic equations driven by a bilinear control posed on the one-dimensional torus. The controls depend only on time and act through a prescribed family... | https://arxiv.org/abs/2512.23339 | Academic Papers | svg |
9d816fdc3b1729077f1e3575d2aa9e273e2896010b901d5612255ec3125be7a6 | 2026-01-13T00:00:00-05:00 | Completeness and reflexivity type properties of $B_1(X)$ | arXiv:2601.00733v2 Announce Type: replace Abstract: For a Tychonoff space $X$, $B_1(X)$ denotes the space of all Baire-one functions on $X$ endowed with the pointwise topology. We prove that the following assertions are equivalent: (1) $B_1(X)$ is a (semi-)Montel space, (2) $B_1(X)$ is a (semi-)reflexive space, (3) $B_... | https://arxiv.org/abs/2601.00733 | Academic Papers | svg |
8970800dfc47168fc0e7aed38a01d63a6b2d3034e3652856321c1f5d542e1926 | 2026-01-13T00:00:00-05:00 | Characterizations of harmonic quasiregular mappings in function spaces | arXiv:2601.01017v2 Announce Type: replace Abstract: We study conjugate-type phenomena for complex-valued harmonic quasiregular mappings in the unit disk across three function space families: $Q(n,p,\alpha)$, $F(p,q,s)$, and the non-derivative $M(p,q,s)$. For a harmonic $K$-quasiregular mapping $f=u+iv$, we first show t... | https://arxiv.org/abs/2601.01017 | Academic Papers | svg |
4b0b7fa5026f9a4a29c999375a59373c259b02971ad37bcaa23cdf8bcbd885bf | 2026-01-13T00:00:00-05:00 | Notes on Poisson deformations of symplectic varieties | arXiv:2601.01131v2 Announce Type: replace Abstract: In this article we give corrections and addendum to the article ``Flops and Poisson deformations of symplectic varieties, Publ. Res. Inst. Math. Sci. {\bf 44} (2008) 259 - 314''. | https://arxiv.org/abs/2601.01131 | Academic Papers | svg |
3e7f1c196c50220f46b304fe5ab44cfdab3ad57cbf3afcd5a90cb2744eda89c9 | 2026-01-13T00:00:00-05:00 | Stochastic Control Methods for Optimization | arXiv:2601.01248v2 Announce Type: replace Abstract: In this work, we investigate a stochastic control framework for global optimization over both Euclidean spaces and the Wasserstein space of probability measures, where the objective function may be non-convex and/or non-differentiable. In the Euclidean setting, the or... | https://arxiv.org/abs/2601.01248 | Academic Papers | svg |
7e4a610073f9813394f83b25ada7375a9575ab42fd30ea302b6f957f68c9b430 | 2026-01-13T00:00:00-05:00 | On Hahn-Banach smoothness of $L_1$-preduals and related $w^*-w$ point of continuity of unit balls of dual spaces | arXiv:2601.01567v2 Announce Type: replace Abstract: In this article, we intend to study possible $(U)$-embeddings of a Banach space $X$ into $X^{**}$. The canonical embedding of $X$ in $X^{**}$ which possesses $(U)$-embedding is of particular interest and such spaces are known as Hahn-Banach smooth spaces. Separable $L... | https://arxiv.org/abs/2601.01567 | Academic Papers | svg |
e4681d30d4f4f4d907972a8233a575516bc20bcd4c559acc3f62385a7a59a4eb | 2026-01-13T00:00:00-05:00 | On a Smoothed Dirichlet Divisor Problem | arXiv:2601.01905v2 Announce Type: replace Abstract: Hardy showed that $\sum_{n \ioe x}\tau(n)-x(\log x +2\gamma -1)$ is not $o(x^{1/4})$. In this article, we prove that $\sum_{n \ioe x}\tau(n)(1-\frac{x}{n})-xP(\log x)=\frac{1}{4}+O \left( \frac{\log x}{x^{1/4}} \right)$, where $P$ is a polynomial of degree 2. As a cor... | https://arxiv.org/abs/2601.01905 | Academic Papers | svg |
53c77d4148ef3fb8925daf022f54bf3865a667b8787fd96949a74f9c96e81f28 | 2026-01-13T00:00:00-05:00 | On the sizes of the maximal prime powers divisors of factorials | arXiv:2601.03414v2 Announce Type: replace Abstract: Let p be any prime, and $p^(\nu_p(n!))$ the maximal power of $p$ dividing $n!$. It is proved that there exists a positive integer $n_0$, which depends only on $p$, such that $q^(\nu_q(n!)) p$. For twin primes $p$ and $q = p + 2$ it is proved that the minimal $n_0$ sat... | https://arxiv.org/abs/2601.03414 | Academic Papers | svg |
66f166cf7ae36827dee25ddf04edc40a74ced5324ebf6c39f4db7eca8ec51acd | 2026-01-13T00:00:00-05:00 | Mean-field limits for interacting particle systems on general adaptive dynamical networks | arXiv:2601.03742v2 Announce Type: replace Abstract: We study the large-population limit of interacting particle systems evolving on adaptive dynamical networks, motivated in particular by models of opinion dynamics. In such systems, agents interact through weighted graphs whose structure evolves over time in a coupled ... | https://arxiv.org/abs/2601.03742 | Academic Papers | svg |
2b6247397b77f7adc82fec8c2448fcf8dc661c8fa7d2664e4398bcb0fa5c537c | 2026-01-13T00:00:00-05:00 | Notes on Ecalle's and Brown's solutions to the double shuffle relations modulo products | arXiv:2601.03828v2 Announce Type: replace Abstract: We investigate relationships between polar/polynomial solutions to the double shuffle relations modulo products, which were independently introduced by Brown and Ecalle. | https://arxiv.org/abs/2601.03828 | Academic Papers | svg |
910ce1d0713d7e7b3cfa1fd621ca8cd67382dd942b3aa557a1b3e6bc2cf44ff7 | 2026-01-13T00:00:00-05:00 | The Feldman-H\'ajek Dichotomy for Countable Gaussian Mixtures and their Asymptotic Separability in High Dimensions | arXiv:2601.03911v2 Announce Type: replace Abstract: This paper establishes the theoretical foundations for the asymptotic separability of Gaussian Mixture Models (GMMs) in high dimensions by extending the classical Feldman-H\'ajek theorem. We first prove that a countable mixture of Gaussian measures is a well-defined p... | https://arxiv.org/abs/2601.03911 | Academic Papers | svg |
712ba2c96da427cb5b72d6a6b35511fe57ed762845a974feeaa77b6792370cc8 | 2026-01-13T00:00:00-05:00 | Non-Existence of Linear-Quartic Factorization for the Second Cuboid Quintic | arXiv:2601.04241v2 Announce Type: replace Abstract: Let $Q_{p,q}(t)\in\mathbb{Z}[t]$ be Sharipov's even monic degree-$10$ second cuboid polynomial depending on coprime integers $p\neq q>0$. Writing $Q_{p,q}(t)$ as a quintic in $t^{2}$ produces an associated monic quintic polynomial. After the weighted normalization $r=... | https://arxiv.org/abs/2601.04241 | Academic Papers | svg |
8c95866b326d0db453ed8a64dfaa3362fab394cc93921faa50ff5906142f84d5 | 2026-01-13T00:00:00-05:00 | Sobre los teoremas de Shafarevich y Siegel | arXiv:2601.04284v2 Announce Type: replace Abstract: Presentaremos una nueva demostraci\'on del teorema de Shafarevich sobre finitud de curvas el\'ipticas con buena reducci\'on fuera de un conjunto finito de primos dado. Esto da un nuevo punto de entrada a teoremas fundamentales de finitud diofantina tales como el teore... | https://arxiv.org/abs/2601.04284 | Academic Papers | svg |
482ddadf0114032269930d778119539239ec085b2267007cd6426a10411d51be | 2026-01-13T00:00:00-05:00 | Infinitesimal Variations of Hodge Structure for Singular Curves I | arXiv:2601.04410v2 Announce Type: replace Abstract: We study the infinitesimal variation of Hodge structure associated with families of reduced algebraic curves with singularities. The analysis applies to curves beyond the nodal case and is not restricted to plane curves, encompassing curves lying on smooth projective ... | https://arxiv.org/abs/2601.04410 | Academic Papers | svg |
cf7bf1a3955aaf0c12b8462c6164e788e5ee528f81c3b06cc774dbaffca7e519 | 2026-01-13T00:00:00-05:00 | Automorphic vector-forms using the Cohn-Elkies magic functions | arXiv:2601.04704v2 Announce Type: replace Abstract: In this study, we introduce the theory of what we call Hecke vector-forms. A Hecke vector-form can be viewed as a vector function representation of some quasiautomorphic form that transforms like an automorphic form on an arbitrarily chosen Hecke triangle group. In ot... | https://arxiv.org/abs/2601.04704 | Academic Papers | svg |
93d9fe3c63aec265d13ffc535bfd5f91480f07f5de0bfe3e7b20dcf8b9121481 | 2026-01-13T00:00:00-05:00 | Spectral Properties of $ C_{0}$-Semigroups of Positive Operators on C$^*$-Algebras | arXiv:2601.05025v2 Announce Type: replace Abstract: Let $ (T(t))_{t\geq0} $ be a positive $C_{0}$-semigroup with generator $A$ on a C$^*$-algebra or on the predual of a W$^*$-algebra. Then the growth bound $\omega_{0}$ equals $s(A)$. If the spectrum of $A$ is not empty, then $s(A)$, the spectral bound of $A$, is a spec... | https://arxiv.org/abs/2601.05025 | Academic Papers | svg |
bef51e97f3c382e2ef3f3eaabe1c444def25bb837c88b4a677aac2f9c942665a | 2026-01-13T00:00:00-05:00 | Information-Theoretic Limits on Exact Subgraph Alignment Problem | arXiv:2601.05173v2 Announce Type: replace Abstract: The graph alignment problem aims to identify the vertex correspondence between two correlated graphs. Most existing studies focus on the scenario in which the two graphs share the same vertex set. However, in many real-world applications, such as computer vision, soci... | https://arxiv.org/abs/2601.05173 | Academic Papers | svg |
83332478e4502e5929ed33d41c2ada7d8d0d6d700f67c4516775d53655864727 | 2026-01-13T00:00:00-05:00 | Markovian Compression: Looking to the Past Helps Accelerate the Future | arXiv:2601.05398v2 Announce Type: replace Abstract: This paper deals with distributed optimization problems that use compressed communication to achieve efficient performance and mitigate communication bottleneck. We propose a family of compression schemes in which operators transform vectors fed to their input accordi... | https://arxiv.org/abs/2601.05398 | Academic Papers | svg |
73bed4702029bfc2c052d4fcb7282cda122911f24d3334fc35b40b882f3d4b19 | 2026-01-13T00:00:00-05:00 | The B\'enabou-Roubaud theorem via string diagrams | arXiv:2601.05691v2 Announce Type: replace Abstract: We give a complete proof of the B\'enabou-Roubaud monadic descent theorem using the graphical calculus of string diagrams. Our proof links the monadic and Grothendieck's original viewpoint on descent via an internal-category-based characterization of the category of d... | https://arxiv.org/abs/2601.05691 | Academic Papers | svg |
9c93fe150be74d1a58475a4ef30fe23e0ec4d04abea2fb2c5432226cbbf47d39 | 2026-01-13T00:00:00-05:00 | Approximating Persistent Homology for Large Datasets | arXiv:2204.09155v3 Announce Type: replace-cross Abstract: Persistent homology is an important methodology in topological data analysis which adapts theory from algebraic topology to data settings. Computing persistent homology produces persistence diagrams, which have been successfully used in diverse domains. Despite ... | https://arxiv.org/abs/2204.09155 | Academic Papers | svg |
c8043f7a240679359f453591766481787e9935626b9097ea47d8bf308fbd3db3 | 2026-01-13T00:00:00-05:00 | Field Theory Equivalences as Spans of $L_\infty$-algebras | arXiv:2305.05473v3 Announce Type: replace-cross Abstract: Semi-classically equivalent field theories are related by a quasi-isomorphism between their underlying $L_\infty$-algebras, but such a quasi-isomorphism is not necessarily a homotopy transfer. We demonstrate that all quasi-isomorphisms can be lifted to spans of ... | https://arxiv.org/abs/2305.05473 | Academic Papers | svg |
5710fc49b4bd55762d8fc66e819ee1d2953c2d13e1f8e441a305e012c8633d4a | 2026-01-13T00:00:00-05:00 | Asymptotic Error Analysis of Multilevel Stochastic Approximations for the Value-at-Risk and Expected Shortfall | arXiv:2311.15333v4 Announce Type: replace-cross Abstract: Cr\'epey, Frikha, and Louzi (2023) introduced a nested stochastic approximation algorithm and its multilevel acceleration to compute the value-at-risk and expected shortfall of a random financial loss. We hereby establish central limit theorems for the renormali... | https://arxiv.org/abs/2311.15333 | Academic Papers | svg |
15f6fc6f8f7ef027a8585d7417d39cdc81751f68d417a03629b90d80b4475dbe | 2026-01-13T00:00:00-05:00 | Learning Operators with Stochastic Gradient Descent in General Hilbert Spaces | arXiv:2402.04691v4 Announce Type: replace-cross Abstract: This study investigates leveraging stochastic gradient descent (SGD) to learn operators between general Hilbert spaces. We propose weak and strong regularity conditions for the target operator to depict its intrinsic structure and complexity. Under these conditi... | https://arxiv.org/abs/2402.04691 | Academic Papers | svg |
0b8537b985e86821720df994f9ffda1b12fb97dd08c70b313e0b7dc871664bad | 2026-01-13T00:00:00-05:00 | $\texttt{skwdro}$: a library for Wasserstein distributionally robust machine learning | arXiv:2410.21231v2 Announce Type: replace-cross Abstract: We present skwdro, a Python library for training robust machine learning models. The library is based on distributionally robust optimization using Wasserstein distances, popular in optimal transport and machine learnings. The goal of the library is to make the ... | https://arxiv.org/abs/2410.21231 | Academic Papers | svg |
1f462b6c4868f382cbd84f9c78d398d378f496f06e9721159cf90dd6dd2bac34 | 2026-01-13T00:00:00-05:00 | Schmidt Decomposition of Multipartite States | arXiv:2411.02473v4 Announce Type: replace-cross Abstract: Quantum states can be written in infinitely many ways depending on the choices of basis. Schmidt decomposition of a quantum state has a lot of properties useful in the study of entanglement. All bipartite states admit Schmidt decomposition, but this does not ext... | https://arxiv.org/abs/2411.02473 | Academic Papers | svg |
682cd0ec8445eaac82b904e7c0dca8dfa91f012c3017f7156812d4c88eb82591 | 2026-01-13T00:00:00-05:00 | Point processes with event time uncertainty | arXiv:2411.02694v2 Announce Type: replace-cross Abstract: Point processes are widely used statistical models for continuous-time discrete event data, such as medical records, crime reports, and social network interactions, to capture the influence of historical events on future occurrences. In many applications, howeve... | https://arxiv.org/abs/2411.02694 | Academic Papers | svg |
795788bebfa78924fd00dead91afb97d51d26127debb1bd70e95e13bb93d265d | 2026-01-13T00:00:00-05:00 | Color symmetry and ferromagnetism in Potts spin glass | arXiv:2412.20607v2 Announce Type: replace-cross Abstract: We consider the Potts spin glass with additional ferromagnetic interaction parametrized by $t$. It has long been observed that the Potts color symmetry breaking for the spin glass order parameter is closely related to the ferromagnetic phase transition. To clari... | https://arxiv.org/abs/2412.20607 | Academic Papers | svg |
54d20088c80156be1b133f1020d47bcca0ccea8545f4f7741a2f889a6b22ae49 | 2026-01-13T00:00:00-05:00 | Coverage and Spectral Efficiency of NOMA-Enabled LEO Satellite Networks with Ordering Schemes | arXiv:2501.05946v2 Announce Type: replace-cross Abstract: This paper investigates an analytical model for low-earth orbit (LEO) multi-satellite downlink non-orthogonal multiple access (NOMA) networks. The satellites transmit data to multiple NOMA user terminals (UTs), each employing successive interference cancellation... | https://arxiv.org/abs/2501.05946 | Academic Papers | svg |
09f4a84676f10cf17d5fa084e459c1472d13668d4667a2969d84d02dca815bf1 | 2026-01-13T00:00:00-05:00 | Ordinary Least Squares as an Attention Mechanism | arXiv:2504.09663v2 Announce Type: replace-cross Abstract: I show that ordinary least squares (OLS) predictions can be rewritten as the output of a restricted attention module, akin to those forming the backbone of large language models. This connection offers an alternative perspective on attention beyond the conventio... | https://arxiv.org/abs/2504.09663 | Academic Papers | svg |
5810134f6d6f347eb502bcf65263f8e832863fac956687f312ab755de63dd013 | 2026-01-13T00:00:00-05:00 | SAD Neural Networks: Divergent Gradient Flows and Asymptotic Optimality via o-minimal Structures | arXiv:2505.09572v3 Announce Type: replace-cross Abstract: We study gradient flows for loss landscapes of fully connected feedforward neural networks with commonly used continuously differentiable activation functions such as the logistic, hyperbolic tangent, softplus or GELU function. We prove that the gradient flow ei... | https://arxiv.org/abs/2505.09572 | Academic Papers | svg |
c45aadf927752a58e4a4f62ba580709bea1589fbbd5e393eebf2d62381a69d96 | 2026-01-13T00:00:00-05:00 | Efficient Online Random Sampling via Randomness Recycling | arXiv:2505.18879v3 Announce Type: replace-cross Abstract: This article studies the fundamental problem of using i.i.d. coin tosses from an entropy source to efficiently generate random variables $X_i \sim P_i$ $(i \ge 1)$, where $(P_1, P_2, \dots)$ is a random sequence of rational discrete probability distributions sub... | https://arxiv.org/abs/2505.18879 | Academic Papers | svg |
693732402b0b62bf424bd141f41f48ae5e8bd7b3130cc3d1ceed29cde4d59ef2 | 2026-01-13T00:00:00-05:00 | Conformable Scaling and Critical Dynamics: A Unified Framework for Phase Transitions | arXiv:2507.11782v2 Announce Type: replace-cross Abstract: We investigate the application of conformable derivatives to model critical phenomena near continuous phase transitions. By incorporating a deformation parameter into the differential structure, we derive unified expressions for thermodynamic observables such as... | https://arxiv.org/abs/2507.11782 | Academic Papers | svg |
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