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43c6ce2c245a83b9219643a8565c99550b215697e816a4f803a195744e257e20 | 2026-01-13T00:00:00-05:00 | Relative tensor products and Koszul duality in monoidal oo-categories | arXiv:2210.11861v3 Announce Type: replace Abstract: This semi-expository work covers central aspects of the theory of relative tensor products as developed in Higher Algebra, as well as their application to Koszul duality for algebras in monoidal oo-categories. Part of our goal is to expand on the rather condensed acco... | https://arxiv.org/abs/2210.11861 | Academic Papers | svg |
2c626976c99ee92eab1f21ae5ef987949c0c1d73ee58c6853aae8b2f7520d8fa | 2026-01-13T00:00:00-05:00 | Joint Binary-Continuous Fractional Programming: Solution Methods and Applications | arXiv:2211.02152v3 Announce Type: replace Abstract: In this paper, we investigate a class of non-convex sum-of-ratios programs relevant to decision-making in key areas such as product assortment and pricing, and facility location and cost planning. These optimization problems, characterized by both continuous and binar... | https://arxiv.org/abs/2211.02152 | Academic Papers | svg |
46c383a9d670e3f21f75cdab459beed55ab7de072ee6f4d19abdc752e8ffc4c7 | 2026-01-13T00:00:00-05:00 | Partition regularity of infinite parallelepiped sets | arXiv:2212.06887v2 Announce Type: replace Abstract: A proper infinite parallelepiped (IP) set in a semigroup is an infinite set consisting of a sequence $\myseq{a}$ and its finite sums, or a superset of such a set. Hindman's theorem asserts that the proper IP sets of natural numbers are partition regular: for each fini... | https://arxiv.org/abs/2212.06887 | Academic Papers | svg |
7cb9f810edbcce1b45ca977249cf98660301fef5287cfcfa93711a8a71d898a7 | 2026-01-13T00:00:00-05:00 | Cliques and independent subgroups of the Birkhoff polytope graph | arXiv:2212.12655v2 Announce Type: replace Abstract: The Birkhoff polytope $\Omega_n$ is the polytope of doubly stochastic matrices of order $n$. The Birkhoff polytope graph $G(\Omega_n)$ is the skeleton of $\Omega_n$; it is the Cayley graph whose vertex set consists of the elements of the symmetric group ${\rm Sym}(n)$... | https://arxiv.org/abs/2212.12655 | Academic Papers | svg |
7e5779169a681c115f0c39c3999bfd5c38e98e41c6196d6d99865901adfbe433 | 2026-01-13T00:00:00-05:00 | A factorization of metric spaces | arXiv:2212.13409v3 Announce Type: replace Abstract: We first prove that for every metrizable space $X$, for every closed subset $F$ whose complement is zero-dimensional, the space $X$ can be embedded into a product space of the closed subset $F$ and a metrizable zero-dimensional space as a closed subset. Using this the... | https://arxiv.org/abs/2212.13409 | Academic Papers | svg |
1cf8ca49b7dd5307587785172f0513e21bcbc0cf5c299d26cd0bf8e4fbce75a6 | 2026-01-13T00:00:00-05:00 | Topology and convergence on the space of measure-valued functions | arXiv:2301.04361v3 Announce Type: replace Abstract: In these notes, uniform convergence on compacta is studied on the space of functions taking values in the set of finite Borel measures. Related limit theorems, including L\'evy's continuity theorem and functional limit theorems for (classical and non-commutative) addi... | https://arxiv.org/abs/2301.04361 | Academic Papers | svg |
35c0c47a50cbb0b396fbdd4e82518b2d3bf85d1ee3ae8de663f54c35ca0df5bc | 2026-01-13T00:00:00-05:00 | Heat kernel-based p-energy norms on metric measure spaces | arXiv:2303.10414v4 Announce Type: replace Abstract: We investigate heat kernel-based and other $p$-energy norms (1<\infty) on bounded and unbounded metric measure spaces, in particular, on nested fractals and their blowups. With the weak-monotonicity properties for these norms, we generalise the celebrated Bourgain-Bre... | https://arxiv.org/abs/2303.10414 | Academic Papers | svg |
ed81989a6b4b7bc53b999ab6b7c179fe0541e644e923802c8b61a3c91436a5bf | 2026-01-13T00:00:00-05:00 | Generative Modeling via Hierarchical Tensor Sketching | arXiv:2304.05305v2 Announce Type: replace Abstract: We propose a hierarchical tensor-network approach for approximating high-dimensional probability density via empirical distribution. This leverages randomized singular value decomposition (SVD) techniques and involves solving linear equations for tensor cores in this ... | https://arxiv.org/abs/2304.05305 | Academic Papers | svg |
0a7cff32077ec21aa0b49d5f92cd7570f444922bbff51dba1a247808e172ac08 | 2026-01-13T00:00:00-05:00 | Faster List Decoding of AG Codes | arXiv:2304.07083v2 Announce Type: replace Abstract: In this article, we present a fast algorithm performing an instance of the Guruswami-Sudan list decoder for algebraic geometry codes. We show that any such code can be decoded in $\tilde{O}(s^2\ell^{\omega-1}\mu^{\omega-1}(n+g) + \ell^\omega \mu^\omega)$ operations in... | https://arxiv.org/abs/2304.07083 | Academic Papers | svg |
e8c8ccf3c7cb0c30720792419cc11ffba149e9cb1cc768a6ad3edefe0891610c | 2026-01-13T00:00:00-05:00 | Nonorientable genus embedding of nearly complete bipartite graphs | arXiv:2305.10008v2 Announce Type: replace Abstract: The nearly complete bipartite graph $G(m,n,k)$ is obtained by removing $k$ independent edges from the complete bipartite graph $K_{m,n}$. In this paper, we prove that for any nearly complete bipartite graph $G(m,n,k)$ with $m, n\geq 3$, and $(m,n,k)\notin\{(5,4,4)$, $... | https://arxiv.org/abs/2305.10008 | Academic Papers | svg |
5860d39e973a4e490cf418b1ff0b3846477be828aa7e94883a5bd39115cd286d | 2026-01-13T00:00:00-05:00 | Smooth projective surfaces with bounded cohomology property | arXiv:2306.07830v4 Announce Type: replace Abstract: In this paper, we first prove that every Mori dream surface $X$ satisfies the bounded cohomology property (BCP for short). Namely, there exists a constant $c_X>0$ such that $h^1(\mathcal O_X(C))\le c_Xh^0(\mathcal O_X(C))$ for every curve $C$ on $X$. We then prove tha... | https://arxiv.org/abs/2306.07830 | Academic Papers | svg |
e6312771641671849cd36f4363c61f196f619a57a14443a6ca6de06287567068 | 2026-01-13T00:00:00-05:00 | Commutation of Smyth and Hoare Power Constructions in Well-filtered Dcpos | arXiv:2311.14261v3 Announce Type: replace Abstract: Prior work [11] established a commutativity result for the Hoare power construction and a modified version of the Smyth power construction consisting of strongly compact sets, which is defined for Us-admitting dcpos, where Us-admissability is well-filteredness with co... | https://arxiv.org/abs/2311.14261 | Academic Papers | svg |
67f4fdd70d67c8bf9988ee90cf8c01adf105d0c7c0bad0f1667463891d021464 | 2026-01-13T00:00:00-05:00 | M\"obius function and primes: an identity factory with applications | arXiv:2312.05138v3 Announce Type: replace Abstract: We investigate the sums $\sum_{n\le X, (n,q)=1}\frac{\mu(n)}{n^s}\log^k\left(\frac{X}{n}\right)$, where $k\in\{0,1\}$, $s\in\mathbb{C}$, $\Re s>0$. Our goal is to obtain explicit asymptotic estimations for these quantities. To achieve this, we develop a broad framewor... | https://arxiv.org/abs/2312.05138 | Academic Papers | svg |
2d4954b93b30ce3a1ddae53a56bbb943bb461356895bc235a0919b8e7f537373 | 2026-01-13T00:00:00-05:00 | The FBSDE approach to sine-Gordon up to $6\pi$ | arXiv:2401.13648v2 Announce Type: replace Abstract: We develop a stochastic analysis of the sine-Gordon Euclidean quantum field $(\cos (\beta \varphi))_2$ on the full space up to the second threshold, i.e. for $\beta^2 < 6 \pi$. The basis of our method is a forward-backward stochastic differential equation (FBSDE) for ... | https://arxiv.org/abs/2401.13648 | Academic Papers | svg |
bb26997b6e31858e6b9c700293617172f8b34508e3a3a506fc9cef56ddb2decc | 2026-01-13T00:00:00-05:00 | Kubota-type formulas and supports of mixed measures | arXiv:2401.16371v2 Announce Type: replace Abstract: Kubota's integral formula expresses the intrinsic volumes of a convex body as averages over its projections onto linear subspaces. In this work, we introduce a new class of Kubota-type formulas for mixed area measures adapted to rotations around a fixed axis, which en... | https://arxiv.org/abs/2401.16371 | Academic Papers | svg |
7b1aa55549abee8679cdfcabdc37605836b402bf6434323c6436eaf916d8f652 | 2026-01-13T00:00:00-05:00 | Kinetic shock profiles for the Landau equation | arXiv:2402.01581v2 Announce Type: replace Abstract: The physical quantities in a gas should vary continuously across a shock. However, the physics inherent in the compressible Euler equations is insufficient to describe the width or structure of the shock. We demonstrate the existence of weak shock profiles to the kine... | https://arxiv.org/abs/2402.01581 | Academic Papers | svg |
31d191e022c6a39b1dab69a5a5a03ce912fe5b4252ea134ce8fc76f1f956f8e8 | 2026-01-13T00:00:00-05:00 | On smooth adic spaces over $\mathbb{B}_{\mathrm{dR}}^+$ and sheafified $p$-adic Riemann--Hilbert correspondence | arXiv:2403.01363v3 Announce Type: replace Abstract: Let $C$ be a completely algebraic closed non-archimedean field over $\mathbb{Q}_p$ and $\alpha,r$ be two positive integers. Denote by $B_\alpha$ the ring $\mathbb{B}_{\mathrm{dR}}^+(C)/(\ker\theta)^\alpha$. This paper first constructs a sheafified $p$-adic Riemann--Hi... | https://arxiv.org/abs/2403.01363 | Academic Papers | svg |
43b464117bd357603a53c46bef06f74d249bf7a48a9130d3c2d0048b904685d5 | 2026-01-13T00:00:00-05:00 | The classification of homomorphism homogeneous oriented graphs | arXiv:2403.04393v2 Announce Type: replace Abstract: The modern theory of homogeneous structures begins with the work of Roland Fra\"iss\'e. The theory developed in the last seventy years is placed in the border area between combinatorics, model theory, algebra, and analysis. We turn our attention to its combinatorial p... | https://arxiv.org/abs/2403.04393 | Academic Papers | svg |
b94c961c44bd3f15393ce92ac329521d3bb92919dd310b25226d1a6fed0af96c | 2026-01-13T00:00:00-05:00 | Directional testing for one-way MANOVA in divergent dimensions | arXiv:2403.07679v4 Announce Type: replace Abstract: Testing the equality of mean vectors across $g$ different groups plays an important role in many scientific fields. In regular frameworks, likelihood-based statistics under the normality assumption offer a general solution to this task. However, the accuracy of standa... | https://arxiv.org/abs/2403.07679 | Academic Papers | svg |
6e48d2947cebf6121ca3f454f54d741ee0250759d7954f64cc7cd38b96c1ab70 | 2026-01-13T00:00:00-05:00 | Compactly supported $\mathbb{A}^1$-Euler characteristics of symmetric powers of cellular varieties | arXiv:2404.08486v2 Announce Type: replace Abstract: The compactly supported $\mathbb{A}^1$-Euler characteristic, introduced by Hoyois and later refined by Levine and others, is an anologue in motivic homotopy theory of the classical Euler characteristic of complex topological manifolds. It is an invariant on the Grothe... | https://arxiv.org/abs/2404.08486 | Academic Papers | svg |
4bc485b2952618f788d1e12a69da0d36f44d7645d656d7a1043a0bac530260a5 | 2026-01-13T00:00:00-05:00 | Global existence of a strong solution to the initial value problem for the Nernst-Planck-Navier-Stokes system in high space dimensions | arXiv:2404.16433v5 Announce Type: replace Abstract: We study the existence of a strong solution to the initial value problem for the Nernst-Planck-Navier-Stokes (NPNS) system in $\mathbb{R}^N, N\geq 3$. The system describes the electrodiffusion of ions in a viscous Newtonian fluid. A strong solution is obtained in any ... | https://arxiv.org/abs/2404.16433 | Academic Papers | svg |
88db1e46e5304a482dc15de1c0ecdf35752c527cf1a2d4e1826a331c7eefeeb7 | 2026-01-13T00:00:00-05:00 | Parametric set-theoretic Yang-Baxter equation: p-racks, solutions & quantum algebras | arXiv:2405.04088v3 Announce Type: replace Abstract: The theory of the parametric set-theoretic Yang-Baxter equation is established from a purely algebraic point of view. The first step towards this objective is the introduction of certain generalizations of the familiar shelves and racks called parametric (p)-shelves a... | https://arxiv.org/abs/2405.04088 | Academic Papers | svg |
8083a9b6764f41adf0f2da448e0c2429f583bb59299989e621f21a9dd132c065 | 2026-01-13T00:00:00-05:00 | Universal-existential theories of fields | arXiv:2405.12771v4 Announce Type: replace Abstract: We study various universal-existential fragments of first-order theories of fields, in particular of function fields and of equicharacteristic henselian valued fields. For example we discuss to what extent the theory of a field k determines the universal-existential t... | https://arxiv.org/abs/2405.12771 | Academic Papers | svg |
8c020ddd08bc3e65b43a404fc5e98c91bca5a3f0e402cc4d5ffcd701b9a3e1c6 | 2026-01-13T00:00:00-05:00 | The hierarchies of identities and closed products for multiple complexes | arXiv:2405.16271v3 Announce Type: replace Abstract: We consider infinite $\Z_\Z$-index complexes $\mathcal C$ of spaces with elements depending on a number of parameters, complete with respect to a linear associative regular inseparable multilinear product. The existence of nets of vanishing ideals of orders of and pow... | https://arxiv.org/abs/2405.16271 | Academic Papers | svg |
ec1a40ba215d26165f6fe230f106da57af55c84fc3ea680812ff4196e56645b9 | 2026-01-13T00:00:00-05:00 | Bounded geometry for PCF-special subvarieties | arXiv:2405.17343v3 Announce Type: replace Abstract: For each integer $d\geq 2$, let $M_d$ denote the moduli space of maps $f: \mathbb{P}^1\to \mathbb{P}^1$ of degree $d$. We study the geometric configurations of subsets of postcritically finite (or PCF) maps in $M_d$. A complex-algebraic subvariety $Y \subset M_d$ is s... | https://arxiv.org/abs/2405.17343 | Academic Papers | svg |
43acf18af09ae5197f6efb9e2a5712c9b3023d6a94b7359bcbd74783d4b9b396 | 2026-01-13T00:00:00-05:00 | Fast Numerical Approximation of Linear, Second-Order Hyperbolic Problems Using Model Order Reduction and the Laplace Transform | arXiv:2405.19896v2 Announce Type: replace Abstract: We extend our previous work [F. Henr'iquez and J. S. Hesthaven, arXiv:2403.02847 (2024)] to the linear, second-order wave equation in bounded domains. This technique uses two widely known mathematical tools to construct a fast and efficient method for the solution of ... | https://arxiv.org/abs/2405.19896 | Academic Papers | svg |
49862b9a2234d97893729b566cc95fd31f1686a82c4fa04bf4dc05db3d7e41c7 | 2026-01-13T00:00:00-05:00 | Topological Stability and Latschev-type Reconstruction Theorems for Spaces of Curvature Bounded Above | arXiv:2406.04259v4 Announce Type: replace Abstract: We consider the problem of homotopy-type reconstruction of compact subsets $X\subset\R^N$ that have the Alexandrov curvature bounded above ($\leq$ $\kappa$) in the intrinsic length metric. The reconstructed spaces are in the form of Vietoris--Rips complexes computed f... | https://arxiv.org/abs/2406.04259 | Academic Papers | svg |
74659e7c2a4e81eff67ad2127322f1953bc48815001b62d315bafb02f857586e | 2026-01-13T00:00:00-05:00 | Homogeneous G2 and Sasakian instantons on the Stiefel 7-manifold | arXiv:2406.06753v2 Announce Type: replace Abstract: We study homogeneous instantons on the seven dimensional Stiefel manifold V in the context of $G_2$ and Sasakian geometry. According to the reductive decomposition of V we provide an explicit description of all invariant $G_2$ and Sasakian structures. In particular, w... | https://arxiv.org/abs/2406.06753 | Academic Papers | svg |
135249dc12b2ca9ff04390ba362bbd0d4c056699b26600f39b46a3eef38ccfd1 | 2026-01-13T00:00:00-05:00 | Slalom numbers | arXiv:2406.19901v3 Announce Type: replace Abstract: The paper is an extensive and systematic study of cardinal invariants we call slalom numbers, describing the combinatorics of sequences of sets of natural numbers. Our general approach, based on relational systems, covers many such cardinal characteristics, including ... | https://arxiv.org/abs/2406.19901 | Academic Papers | svg |
8a605ac7d63e30cc1b77445c8a38cb3318888d26a05d89f2e4f10e119de1a390 | 2026-01-13T00:00:00-05:00 | The geometry of preperiodic points in families of maps on $\mathbb{P}^N$ | arXiv:2407.10894v2 Announce Type: replace Abstract: We study the dynamics of algebraic families of maps on $\mathbb{P}^N$, over the field $\mathbb{C}$ of complex numbers, and the geometry of their preperiodic points. The goal of this note is to formulate a conjectural characterization of the subvarieties of $S \times\m... | https://arxiv.org/abs/2407.10894 | Academic Papers | svg |
70680b8d87e1b515c8b94eb982626f3e0e8e06bfb3a7f767cb7c5e29cde06023 | 2026-01-13T00:00:00-05:00 | Obstructions to homotopy invariance of loop coproduct via parametrised fixed-point theory | arXiv:2407.13662v2 Announce Type: replace Abstract: Given $f: M \to N$ a homotopy equivalence of compact manifolds with boundary, we use a construction of Geoghegan and Nicas to define its Reidemeister trace $[T] \in \pi_1^{st}(\mathcal{L} N, N)$. We realize the Goresky-Hingston coproduct as a map of spectra, and show ... | https://arxiv.org/abs/2407.13662 | Academic Papers | svg |
9b4f8dbe4d791bfb4cc11dd1a82583791c8de23ca26a90ced4506559806a5d08 | 2026-01-13T00:00:00-05:00 | Universal Approximation of Dynamical Systems by Semi-Autonomous Neural ODEs and Applications | arXiv:2407.17092v3 Announce Type: replace Abstract: In this paper, we introduce semi-autonomous neural ordinary differential equations (SA-NODEs), a variation of the vanilla NODEs, employing fewer parameters. We investigate the universal approximation properties of SA-NODEs for dynamical systems from both a theoretical... | https://arxiv.org/abs/2407.17092 | Academic Papers | svg |
6159236d5d00127bf7ef15cea2d0835bf1750304331a420112fe68c5b2fa7431 | 2026-01-13T00:00:00-05:00 | The flux norm, Bohr-Sommerfeld Quantization Rules and the scattering problem for h $\Psi$DO's on the real line | arXiv:2407.18893v3 Announce Type: replace Abstract: We revisit the well known Bohr-Sommerfeld quantization rule (BS) of order 2 for a self-adjoint 1-D h-Pseudo-differential operator within the algebraic and microlocal framework of Helffer and Sjoestrand; BS holds precisely when Gram matrix consisting of scalar products... | https://arxiv.org/abs/2407.18893 | Academic Papers | svg |
080903a7cc0a0bd1765ba8881081fd0eca1568570b0d3a88b02bd99bca87e865 | 2026-01-13T00:00:00-05:00 | Deterministic approximate counting of colorings with fewer than $2\Delta$ colors via absence of zeros | arXiv:2408.04727v3 Announce Type: replace Abstract: Let $\Delta,q\geq 3$ be integers. We prove that there exists $\eta\geq 0.002$ such that if $q\geq (2-\eta)\Delta$, then there exists an open set $\mathcal{U}\subset \mathbb{C}$ that contains the interval $[0,1]$ such that for each $w\in \mathcal{U}$ and any graph $G=(... | https://arxiv.org/abs/2408.04727 | Academic Papers | svg |
4e4a3ee7245586bd5e89358ebe11203cb802c35bbcbfe09ebbd3ebc838d04f19 | 2026-01-13T00:00:00-05:00 | A multi-objective mixed integer linear programming model for supply chain planning of 3D printing | arXiv:2408.05213v4 Announce Type: replace Abstract: 3D printing is considered the future of production systems and one of the physical elements of the Fourth Industrial Revolution. 3D printing will significantly impact the product lifecycle, considering cost, energy consumption, and carbon dioxide emissions, leading to... | https://arxiv.org/abs/2408.05213 | Academic Papers | svg |
2e568ebca808e9297e85460b82b8ef944558035237869dc866fe105967011056 | 2026-01-13T00:00:00-05:00 | Topology of total cut complexes and cut complexes of grid graphs | arXiv:2408.07646v3 Announce Type: replace Abstract: Inspired by the work of Fr{\"o}berg (1990) and Eagon and Reiner (1998), Bayer et al. recently introduced two new graph complexes: total cut complexes and cut complexes. In this article, we investigate these complexes specifically for (rectangular) grid graphs, focusin... | https://arxiv.org/abs/2408.07646 | Academic Papers | svg |
2b0d2388092ff5f1cd35bc60c960a7a5fff049a0deaae370cb5a589d4b300358 | 2026-01-13T00:00:00-05:00 | Rigidity results for non-K\"ahler Calabi-Yau geometries on threefolds | arXiv:2408.09648v5 Announce Type: replace Abstract: We derive a canonical symmetry reduction associated to a compact non-K\"ahler Bismut-Hermitian-Einstein manifold. In real dimension $6$, the transverse geometry is conformally K\"ahler, and we give a complete description in terms of a single scalar PDE for the underly... | https://arxiv.org/abs/2408.09648 | Academic Papers | svg |
c4956a4b6e41e18013270450236d8ca38d22bc31d04acd90f17aaa26b56967ef | 2026-01-13T00:00:00-05:00 | Turk's head knots and links: a survey | arXiv:2409.20106v3 Announce Type: replace Abstract: We collect and discuss various results on an important family of knots and links called Turk's head knots and links $Th (p,q)$. In the mathematical literature, they also appear under different names such as rosette knots and links or weaving knots and links. Unless be... | https://arxiv.org/abs/2409.20106 | Academic Papers | svg |
df01e60022c488fb8d830aa3d9f6b634fd5fba3b2076c32a511caba8894476ae | 2026-01-13T00:00:00-05:00 | Improved performance guarantees for Tukey's median | arXiv:2410.00219v3 Announce Type: replace Abstract: Is there a natural way to order data in dimension greater than one? The approach based on the notion of data depth, often associated with John Tukey, is among the most popular. Tukey's depth has found applications in robust statistics, graph theory, and the study of e... | https://arxiv.org/abs/2410.00219 | Academic Papers | svg |
0f08363017dcef94f0186b552bb1d06d0f789f1f050925403988c319312f4728 | 2026-01-13T00:00:00-05:00 | Constrained Consensus-Based Optimization and Numerical Heuristics for the Few Particle Regime | arXiv:2410.10361v2 Announce Type: replace Abstract: Consensus-based optimization (CBO) is a versatile multi-particle optimization method for performing nonconvex and nonsmooth global optimizations in high dimensions. Proofs of global convergence in probability have been achieved for a broad class of objective functions... | https://arxiv.org/abs/2410.10361 | Academic Papers | svg |
fc6e1c2df9f76170415eba423105065b49e726248909f5eb9284e7bd06ba4927 | 2026-01-13T00:00:00-05:00 | Semi-boolean and Yosida $\ell$-groups, Martinez and Yosida frames, and the $G+B$ construction | arXiv:2410.11930v2 Announce Type: replace Abstract: The class of semi-boolean $\ell$-groups was introduced in 1968 by A. Bigard. These are the $\ell$-groups $G$ in which the principal convex $\ell$-subgroup $G(a)$ generated by any $a \in G$ is equal to the polar $a^{\perp \perp}$. Examples include all hyperarchimedean ... | https://arxiv.org/abs/2410.11930 | Academic Papers | svg |
ac011d40159f24c6bf51517eadc001fbdc375fe2c0d03039f16ed2f3011cccc5 | 2026-01-13T00:00:00-05:00 | An iterative construction of complete K\"ahler--Einstein metrics | arXiv:2410.12599v3 Announce Type: replace Abstract: We extend Tsuji's iterative construction of complete K\"ahler--Einstein metrics with negative scalar curvature to noncompact K\"ahler manifolds with bounded geometry, using Berndtsson's method from the compact setting. Consequently, given a holomorphic surjective map ... | https://arxiv.org/abs/2410.12599 | Academic Papers | svg |
c36dcd7ceca2ced442866d76ecaad3007dd40e773d28416f6911d672c42437d6 | 2026-01-13T00:00:00-05:00 | Hypoellipticity and Higher Order Gaussian Bounds | arXiv:2410.14456v2 Announce Type: replace Abstract: Let $(\mathfrak{M},\rho,\mu)$ be a metric measure space satisfying a doubling condition, $p_0\in (1,\infty)$, and $T(t):L^{p_0}(\mathfrak{M},\mu)\rightarrow L^{p_0}(\mathfrak{M},\mu)$, $t\geq 0$, a strongly continuous semi-group. We provide sufficient conditions under... | https://arxiv.org/abs/2410.14456 | Academic Papers | svg |
2bf4b6a2cd31385f0aa393b42848ca5772668f6e4c2b9e869e027a7956b71d33 | 2026-01-13T00:00:00-05:00 | $s$-almost $t$-intersecting families for finite sets | arXiv:2410.20185v4 Announce Type: replace Abstract: A family $\mathcal{F}$ of $k$-subsets of an $n$-set is called $s$-almost $t$-intersecting if each member is $t$-disjoint with at most $s$ members. In this paper, we prove that, if $\left|\mathcal{F}\right|$ is maximum, then $\mathcal{F}$ consists of all $k$-subsets co... | https://arxiv.org/abs/2410.20185 | Academic Papers | svg |
10454dc61796f9d53733adeb0a745249299fca33962a59bc57ec4fe2c97402e1 | 2026-01-13T00:00:00-05:00 | Effectively Leveraging Momentum Terms in Stochastic Line Search Frameworks for Fast Optimization of Finite-Sum Problems | arXiv:2411.07102v3 Announce Type: replace Abstract: In this work, we address unconstrained finite-sum optimization problems, with particular focus on instances originating in large scale deep learning scenarios. Our main interest lies in the exploration of the relationship between recent line search approaches for stoc... | https://arxiv.org/abs/2411.07102 | Academic Papers | svg |
b90025f03251950b5b663f56262e82de33a680e6f3077f89a34f03b7d2d16eef | 2026-01-13T00:00:00-05:00 | A Hodge-Tate decomposition with rigid analytic coefficients | arXiv:2411.07366v2 Announce Type: replace Abstract: Let $X$ be a smooth proper rigid analytic space over a complete algebraically closed field extension $K$ of $\mathbb{Q}_p$. We establish a Hodge--Tate decomposition for $X$ with $G$-coefficients, where $G$ is any commutative locally $p$-divisible rigid group. This gen... | https://arxiv.org/abs/2411.07366 | Academic Papers | svg |
c693e54cab3992e4d6a66f31f55381dfcbb730ce51cba2b513cafc5e175b471e | 2026-01-13T00:00:00-05:00 | The transcendence degree of the reals over certain set-theoretical subfields | arXiv:2412.00616v2 Announce Type: replace Abstract: It is a well-known result that, after adding one Cohen real, the transcendence degree of the reals over the ground-model reals is continuum. We extend this result for a set $X$ of finitely many Cohen reals, by showing that, in the forcing extension, the transcendence ... | https://arxiv.org/abs/2412.00616 | Academic Papers | svg |
35375708f872d77ab113ec8217efd0cd8d8d93539f46bcce75d13b603d5e0505 | 2026-01-13T00:00:00-05:00 | Adelic C*-correspondences and parabolic induction | arXiv:2412.02379v2 Announce Type: replace Abstract: In analogy with the construction of representations of adelic groups as restricted products of representations of local groups, we study restricted tensor products of Hilbert C*-modules and of C*-correspondences. The construction produces global C*-correspondences fro... | https://arxiv.org/abs/2412.02379 | Academic Papers | svg |
f63bb328e6eb7385e29b97c98004d708dcda37fbcf2669bd58ccfccd01096b6f | 2026-01-13T00:00:00-05:00 | Convergence of a discrete selection-mutation model with exponentially decaying mutation kernel to a Hamilton-Jacobi equation | arXiv:2412.06657v2 Announce Type: replace Abstract: In this paper we derive a constrained Hamilton-Jacobi equation with obstacle from a discrete non-linear integro-differential model of population dynamics, with exponentially decaying mutation kernel. The exponential decay of the kernel leads to a modification of the c... | https://arxiv.org/abs/2412.06657 | Academic Papers | svg |
882908b29d00c22f1fe185f452e94ed7f3a53d6ec05db275e7fdc71080945f28 | 2026-01-13T00:00:00-05:00 | When entropy meets Tur\'an: new proofs and hypergraph Tur\'an results | arXiv:2412.08075v3 Announce Type: replace Abstract: In this paper, we provide a new proof of a density version of Tur\'an's theorem. We also rephrase both the theorem and the proof using entropy. With the entropic formulation, we show that some naturally defined entropic quantity is closely connected to other common qu... | https://arxiv.org/abs/2412.08075 | Academic Papers | svg |
88aad512408e33ebfe32f13c0f8f93fc8271baf3f9416f1ce45eaefb086b0a2b | 2026-01-13T00:00:00-05:00 | A Detailed Analysis on Sharpened Singular Adams-Type Inequalities | arXiv:2412.11176v3 Announce Type: replace Abstract: We establish a sharp Adams-type inequality in higher-order function spaces with singular weights on $\mathbb{R}^n$. A sharp singular concentration-compactness principle, improving Lions' result, is also proved. The study distinguishes between critical and subcritical ... | https://arxiv.org/abs/2412.11176 | Academic Papers | svg |
9e809a4efeb551b76edeeeb9201d83d5ef33977333c8d5ef8376d60b00494349 | 2026-01-13T00:00:00-05:00 | Defining extended TQFTs via handle attachments | arXiv:2412.14649v2 Announce Type: replace Abstract: We give a finite presentation of the cobordism symmetric monoidal bicategory of (smooth, oriented) closed manifolds, cobordisms and cobordisms with corners as an extension of the bicategory of closed manifolds, cobordisms and diffeomorphisms. The generators are the st... | https://arxiv.org/abs/2412.14649 | Academic Papers | svg |
ad156f6fc20df38791859e30f75899191e8a12fb9f4aabd259fad83742518041 | 2026-01-13T00:00:00-05:00 | Dimension reduction for path signatures | arXiv:2412.14723v2 Announce Type: replace Abstract: This paper focuses on the mathematical framework for reducing the complexity of models using path signatures. The structure of these signatures, which can be interpreted as collections of iterated integrals along paths, is discussed and their applications in areas suc... | https://arxiv.org/abs/2412.14723 | Academic Papers | svg |
13cc35a0ecd912222a73656196ba5b584d08122bb185f5ff746e4b00d8934164 | 2026-01-13T00:00:00-05:00 | Fluctuations in Various Regimes of Non-Hermiticity and a Holographic Principle | arXiv:2412.15854v3 Announce Type: replace Abstract: The variance of the number of particles in a set is an important quantity in understanding the statistics of non-interacting fermionic systems in low dimensions. An exact map of their ground state in a harmonic trap in one and two dimensions to the classical Gaussian ... | https://arxiv.org/abs/2412.15854 | Academic Papers | svg |
6376a03a296c69ad5b3f21133c762defa1303a839ba2633d100ab0b292a9bb2e | 2026-01-13T00:00:00-05:00 | Additive processes on the real line and Loewner chains | arXiv:2412.18742v2 Announce Type: replace Abstract: This paper investigates additive processes with respect to several different independences in non-commutative probability in terms of the convolution hemigroups of the distributions of the increments of the processes. In particular, we focus on the relation of monoton... | https://arxiv.org/abs/2412.18742 | Academic Papers | svg |
497ffd8e28763ab7579b50ba35e205411d4be01508aa2f2f0d262fd80727ad6e | 2026-01-13T00:00:00-05:00 | On reconstructing Morse functions with prescribed level sets on $3$-dimensional manifolds and a necessary and sufficient condition for the reconstruction | arXiv:2412.20626v3 Announce Type: replace Abstract: We discuss a necessary and sufficient condition for reconstruction of Morse functions with prescribed (regular) level sets on $3$-dimensional manifolds. The present work strengthens a previous result of the author where only sufficient conditions are studied. Our new ... | https://arxiv.org/abs/2412.20626 | Academic Papers | svg |
e725d9b54cc6e91560782f04b4836370291df53a29b8d0f3c4475f282453ae4d | 2026-01-13T00:00:00-05:00 | Scalar behavior for a complex multi-soliton arising in blow-up for a semilinear wave equation | arXiv:2501.04505v2 Announce Type: replace Abstract: This paper deals with blow-up for the complex-valued semilinear wave equation with power nonlinearity in dimension 1. Up to a rotation of the solution in the complex plane, we show that near a characteristic blow-up point, the solution behaves exactly as in the real-v... | https://arxiv.org/abs/2501.04505 | Academic Papers | svg |
0fedb712f693d017603ef72b429865a656d4501e4b25ff20d273c9b0c1068597 | 2026-01-13T00:00:00-05:00 | Uniformizable foliated projective structures along singular foliations | arXiv:2501.04626v2 Announce Type: replace Abstract: We consider holomorphic foliations by curves on compact complex manifolds, for which we investigate the existence of projective structures along the leaves varying holomorphically (foliated projective structures), that satisfy particular uniformizability properties. O... | https://arxiv.org/abs/2501.04626 | Academic Papers | svg |
040e8911def2dc5d20453f344a97f3878825a01480bc355bff917d87268a90e4 | 2026-01-13T00:00:00-05:00 | Maximality of the futures of points in globally hyperbolic maximal conformally flat spacetimes | arXiv:2501.05856v2 Announce Type: replace Abstract: Let M be a globally hyperbolic conformally spacetime. We prove that the indecomposable past/future sets (abbrev. IPs/IFs) -in the sense of Penrose, Kronheimer and Geroch -of the universal cover of M are domains of injectivity of the developing map. This relies on the ... | https://arxiv.org/abs/2501.05856 | Academic Papers | svg |
d12bbda9f12fab7521a8a4198f5e4a994814fd401be5b71922dc00a29813f713 | 2026-01-13T00:00:00-05:00 | Fourier Extension Based on Weighted Generalized Inverse | arXiv:2501.16096v4 Announce Type: replace Abstract: This paper introduces a weighted generalized inverse framework for Fourier extensions, designed to suppress spurious oscillations in the extended region while maintaining high approximation accuracy on the original interval. By formulating the Fourier extension proble... | https://arxiv.org/abs/2501.16096 | Academic Papers | svg |
a2abfd1fddcc15d6b6a1070a4bd47fab2e104ee5167e6a91fdcd99159f2cac24 | 2026-01-13T00:00:00-05:00 | Shrinking vs. expanding: the evolution of spatial support in degenerate Keller-Segel systems | arXiv:2501.19119v2 Announce Type: replace Abstract: We consider radially symmetric solutions of the degenerate Keller-Segel system \begin{align*} \begin{cases} \partial_t u=\nabla\cdot (u^{m-1}\nabla u - u\nabla v),\\ 0=\Delta v -\mu +u,\quad\mu =\frac{1}{|\Omega|}\int_\Omega u, \end{cases} \end{align*} in balls $\Omeg... | https://arxiv.org/abs/2501.19119 | Academic Papers | svg |
10b6189d944eb137daae6f7d077a885c74e6d2366dac703c71fb4b5f1994b5b1 | 2026-01-13T00:00:00-05:00 | Density-valued symplectic forms from a multisymplectic viewpoint | arXiv:2502.02224v4 Announce Type: replace Abstract: We give an intrinsic characterization of multisymplectic manifolds that have the linear type of density-valued symplectic forms in each tangent space, prove Darboux-type theorems for these forms, and investigate their symmetries. | https://arxiv.org/abs/2502.02224 | Academic Papers | svg |
754ad6ed5d20753b06d4ee1c673a2b852d3bb936c9b0301ce46bfedac7e4f7ac | 2026-01-13T00:00:00-05:00 | Nondeterministic Behaviours in Double Categorical Systems Theory | arXiv:2502.02517v2 Announce Type: replace Abstract: In this paper, we build double theories capturing the idea of nondeterministic behaviors and trajectories. Following Libkind and Myers' Double Operadic Theory of Systems, we construct monoidal semi double categories of interfaces, along with what we call semimodules o... | https://arxiv.org/abs/2502.02517 | Academic Papers | svg |
eef61d8b28830588704287e85f411049d3eb100dd109f1d2b871e8c32417eec2 | 2026-01-13T00:00:00-05:00 | High-dimensional stochastic finite volumes using the tensor train format | arXiv:2502.04868v3 Announce Type: replace Abstract: A method for the uncertainty quantification of nonlinear hyperbolic conservation laws with many uncertain parameters is presented. The method combines stochastic finite volume methods and tensor trains in a novel way: the dimensions of physical space and time are kept... | https://arxiv.org/abs/2502.04868 | Academic Papers | svg |
67e57705c639494fa311bce9baa888bb9a51c59b6563998dc422854b964e430d | 2026-01-13T00:00:00-05:00 | Fixed-strength spherical designs | arXiv:2502.06002v3 Announce Type: replace Abstract: A spherical $t$-design is a finite subset $X$ of the unit sphere such that every polynomial of degree at most $t$ has the same average over $X$ as it does over the entire sphere. Determining the minimum possible size of spherical designs, especially in a fixed dimensi... | https://arxiv.org/abs/2502.06002 | Academic Papers | svg |
3d23fcf88d1f98591bd091e2ec5242e365bf57e02ca57a132d9abe1c43194247 | 2026-01-13T00:00:00-05:00 | High-order BUG dynamical low-rank integrators based on explicit Runge--Kutta methods | arXiv:2502.07040v5 Announce Type: replace Abstract: In this work, we introduce high-order Basis-Update & Galerkin (BUG) integrators based on explicit Runge-Kutta methods for large-scale matrix differential equations. These dynamical low-rank integrators extend the BUG integrator to arbitrary explicit Runge-Kutta scheme... | https://arxiv.org/abs/2502.07040 | Academic Papers | svg |
58c51aedccad021473ee5b6d1356bf7cda293ea2003aa51bf94a5c4e1ddc2390 | 2026-01-13T00:00:00-05:00 | Convex cocompact groups in real hyperbolic spaces with limit set a Pontryagin sphere | arXiv:2502.09470v3 Announce Type: replace Abstract: We exhibit two examples of convex cocompact subgroups of the isometry groups of real hyperbolic spaces with limit set a Pontryagin sphere: one generated by $50$ reflections of $\mathbb{H}^4$, and the other by a rotation of order $21$ and a reflection of $\mathbb{H}^6$... | https://arxiv.org/abs/2502.09470 | Academic Papers | svg |
01d8f34a501611ae46314d5d2ee0688f1a26296d4641dd4905790aa1ad14b733 | 2026-01-13T00:00:00-05:00 | On the global stability and large time behavior of solutions of the Boussinesq equations | arXiv:2502.16226v3 Announce Type: replace Abstract: We study the two dimensional viscous Boussinesq equations, which model stratified flows in a circular domain under the influence of a general gravitational potential $f$. First, we show that the Boussinesq equations admit steady-state solutions only in the form of hyd... | https://arxiv.org/abs/2502.16226 | Academic Papers | svg |
40bd0588ca49ee8ca8d5a3d83a07ab49ecde41cc76952cf1560c5a269abf5816 | 2026-01-13T00:00:00-05:00 | Novel Constructions for Computation and Communication Trade-offs in Private Coded Distributed Computing | arXiv:2502.17195v2 Announce Type: replace Abstract: Distributed computing enables scalable machine learning by distributing tasks across multiple nodes, but ensuring privacy in such systems remains a challenge. This paper introduces a novel private coded distributed computing model that integrates privacy constraints t... | https://arxiv.org/abs/2502.17195 | Academic Papers | svg |
020bbd93280827af79e7d3c7a11ca5d45207d51e9f5651a62dad037d9eb7b7aa | 2026-01-13T00:00:00-05:00 | The multi-level friendship paradox for sparse random graphs | arXiv:2502.17724v2 Announce Type: replace Abstract: In Hazra, den Hollander and Parvaneh (2025) we analysed the friendship paradox for sparse random graphs. For four classes of random graphs we characterised the empirical distribution of the friendship biases between vertices and their neighbours at distance $1$, provi... | https://arxiv.org/abs/2502.17724 | Academic Papers | svg |
3f8344fcdbfba9852a4723c9d4fc49a0cb185485cd1451425fbb3b8be6f73c9e | 2026-01-13T00:00:00-05:00 | Mass conservation, positivity and energy identical-relation preserving scheme for the Navier-Stokes equations with variable density | arXiv:2503.00405v3 Announce Type: replace Abstract: In this paper, we consider a mass conservation, positivity and energy identical-relation preserving scheme for the Navier-Stokes equations with variable density. Utilizing the square transformation, we first ensure the positivity of the numerical fluid density, which ... | https://arxiv.org/abs/2503.00405 | Academic Papers | svg |
33e9086ce2fc8fcab6919cd73b7f2e7a208e01af53e415020a9b4bcd3ed8a172 | 2026-01-13T00:00:00-05:00 | On the Mordell-Weil rank and $2$-Selmer group of a family of elliptic curves | arXiv:2503.04561v2 Announce Type: replace Abstract: We consider the parametric family of elliptic curves over $\mathbb{Q}$ of the form $E_{m} : y^{2} = x(x - n_{1})(x - n_{2}) + t^{2}$, where $n_{1}$, $n_{2}$ and $t$ are particular polynomial expressions in an integral variable $m$. In this paper, we investigate the to... | https://arxiv.org/abs/2503.04561 | Academic Papers | svg |
4ace4b48e059eb39a58134b384e7863d5a273ede19e73e9016ca22c2305c08f1 | 2026-01-13T00:00:00-05:00 | On Approximate Representation of Fractional Brownian Motion | arXiv:2503.04575v3 Announce Type: replace Abstract: This paper considers the orthogonal expansion of the fractional Brownian motion relative to the Legendre polynomials. Such an expansion has not only theoretical but also practical interest, since it can be applied to approximate and simulate the fractional Brownian mo... | https://arxiv.org/abs/2503.04575 | Academic Papers | svg |
ddc3ebcfedbe79393465f77734e0f59d5f526738875044eddf8425f21b9554da | 2026-01-13T00:00:00-05:00 | Algebraic and Combinatorial Stability of Independence Polynomials in Iterated Strong Products of Cycles | arXiv:2503.07910v2 Announce Type: replace Abstract: This paper investigates the independence polynomials arising from iterated strong products of cycle graphs, examining their algebraic symmetries and combinatorial structures. Leveraging modular arithmetic and Galois theory, we establish precise conditions under which ... | https://arxiv.org/abs/2503.07910 | Academic Papers | svg |
abec732f7fc4d336617396fe42eb6744d35bcb8429062b05ef733bcec3698c93 | 2026-01-13T00:00:00-05:00 | The LZ78 Source | arXiv:2503.10574v3 Announce Type: replace Abstract: We study a family of processes generated according to sequential probability assignments induced by the LZ78 universal compressor. We characterize entropic and distributional properties such as their entropy and relative entropy rates, finite-state compressibility and... | https://arxiv.org/abs/2503.10574 | Academic Papers | svg |
25ec4a6b161ba05e76977a24ed428d976afc958ea9dc805dad3cf2c7e9707fb4 | 2026-01-13T00:00:00-05:00 | Two statistical problems for multivariate mixture distributions | arXiv:2503.12147v4 Announce Type: replace Abstract: We address two important statistical problems: that of estimating for mixtures of multivariate normal distributions and mixtures of $t$-distributions based of univariate projections, and that of measuring the agreement between two different random partitions. The resu... | https://arxiv.org/abs/2503.12147 | Academic Papers | svg |
18ba9cb79060b1707935d1291fee2c16b9881e5a83034cb4294830755ae911b9 | 2026-01-13T00:00:00-05:00 | Strassen's LIL and a Phase transition for the capacity of the random walk under diameter constraints | arXiv:2503.12728v2 Announce Type: replace Abstract: We discuss the relationship between the capacity and the geometry for the range of the random walk for $d=3$. In particular, we consider how efficiently the random walk moves or what shape it forms in order to maximize its capacity. In one of our main results, we show... | https://arxiv.org/abs/2503.12728 | Academic Papers | svg |
f3b9212be68b28d4d3611151ffa54ab88e8b2d915ee42cb268ed94c3f5c41abc | 2026-01-13T00:00:00-05:00 | Disproving two conjectures on the Hamiltonicity of Venn diagrams | arXiv:2503.18554v4 Announce Type: replace Abstract: In 1984, Winkler conjectured that every simple Venn diagram with $n$ curves can be extended to a simple Venn diagram with $n+1$ curves. His conjecture is equivalent to the statement that the dual graph of any simple Venn diagram has a Hamilton cycle. In this work, we ... | https://arxiv.org/abs/2503.18554 | Academic Papers | svg |
58fa1f9693f2806c5313f659243d20e19477c7c6e308042fe4d56c2d8d433906 | 2026-01-13T00:00:00-05:00 | Calibration Bands for Mean Estimates within the Exponential Dispersion Family | arXiv:2503.18896v2 Announce Type: replace Abstract: A statistical model is said to be calibrated if the resulting mean estimates perfectly match the true means of the underlying responses. Aiming for calibration is often not achievable in practice as one has to deal with finite samples of noisy observations. A weaker n... | https://arxiv.org/abs/2503.18896 | Academic Papers | svg |
b6489355af3da5661b1741fc6c1a09f90cd74069d2f3c66aec2fa67c8173e0fd | 2026-01-13T00:00:00-05:00 | Convergent Power Series for Anharmonic Chain with Periodic Forcing | arXiv:2503.23527v5 Announce Type: replace Abstract: We study the propagation of energy in one-dimensional anharmonic chains subject to a periodic, localized forcing. For the purely harmonic case, forcing frequencies outside the linear spectrum produce exponentially localized responses, preventing equi-distribution of e... | https://arxiv.org/abs/2503.23527 | Academic Papers | svg |
68dc0fa01143d94f9008bb81b03d2f3a41c5db4a2a5efbebdef4d498779f8e6a | 2026-01-13T00:00:00-05:00 | A Comparison of Parametric Dynamic Mode Decomposition Algorithms for Thermal-Hydraulics Applications | arXiv:2503.24205v2 Announce Type: replace Abstract: In recent years, algorithms aiming at learning models from available data have become quite popular due to two factors: 1) the significant developments in Artificial Intelligence techniques and 2) the availability of large amounts of data. Nevertheless, this topic has... | https://arxiv.org/abs/2503.24205 | Academic Papers | svg |
dab72c06934f3eb70872facf9bdfc4cacbbd28d1e865e5b78dce7159c3b0614f | 2026-01-13T00:00:00-05:00 | Uniform convergence to the equilibrium of the homogeneous Boltzmann-Fermi-Dirac Equation with moderately soft potential | arXiv:2504.01341v2 Announce Type: replace Abstract: We concern the long-time behavior of mild solutions to the spatially homogeneous Boltzmann--Fermi--Dirac equation with moderately soft potential. Based on the well-posedness results in [X-G. Lu, J. Stat. Phys., 105, (2001), 353-388], we prove that the mild solution de... | https://arxiv.org/abs/2504.01341 | Academic Papers | svg |
c29d5f560aa338cfcdb7b1aaf832ece4a9f3b29e2b2a8d5b5fec25175c5b51f6 | 2026-01-13T00:00:00-05:00 | Certified Model Order Reduction for parametric Hermitian eigenproblems | arXiv:2504.02672v3 Announce Type: replace Abstract: This article deals with the efficient and certified numerical approximation of the smallest eigenvalue and the associated eigenspace of a large-scale parametric Hermitian matrix. For this aim, we rely on projection-based model order reduction (MOR), i.e., we approxima... | https://arxiv.org/abs/2504.02672 | Academic Papers | svg |
4041388f876a5036979990056d11f8deb5d127ea6571f43809ddb63e552f0178 | 2026-01-13T00:00:00-05:00 | Hybrid Nitsche method for distributed computing | arXiv:2504.05036v2 Announce Type: replace Abstract: We extend a distributed finite element method built upon model order reduction to arbitrary polynomial degree using a hybrid Nitsche scheme. The new method considerably simplifies the transformation of the finite element system to the reduced basis for large problems.... | https://arxiv.org/abs/2504.05036 | Academic Papers | svg |
babf77cbb06c02a11f0146932455550d1547177a341f7a023af19ce001f94fee | 2026-01-13T00:00:00-05:00 | Instability of the Standing Pulse in Skew-Gradient Systems and Its Application to FitzHugh-Nagumo Type Systems | arXiv:2504.11211v2 Announce Type: replace Abstract: Classical results from Sturm-Liouville theory establish that the Morse index of a one-dimensional Sturm-Liouville operator defined on $\mathbb{R}$ is equal to the number of its associated conjugate points. Recent advancements by Beck et al.~\cite{BCJLM18} have extende... | https://arxiv.org/abs/2504.11211 | Academic Papers | svg |
46a6b5d04fb2f9abb6390df0cc54d1912f38e841734a3d7df8f57cebc2f6395f | 2026-01-13T00:00:00-05:00 | Theoretical and computational investigations of superposed interacting affine and more complex processes | arXiv:2504.13712v3 Announce Type: replace Abstract: We theoretically and computationally investigate long-memory processes based on the Markovian lifts of affine jump-diffusion processes. A nominal superposition process consisting of an infinite number of interacting affine processes is considered, along with its finit... | https://arxiv.org/abs/2504.13712 | Academic Papers | svg |
0bdb6fdb27d66a604a7e1a18d88014acce99b2f7b0efd3bea58b2b902891bf08 | 2026-01-13T00:00:00-05:00 | Asymptotically well-calibrated Bayesian $p$-value using the Kolmogorov-Smirnov statistic | arXiv:2504.14077v3 Announce Type: replace Abstract: The posterior predictive $p$-value (ppp) is widely used in Bayesian model evaluation. However, due to double use of the data, the ppp may not be a valid $p$-value even in large samples: The asymptotic null distribution of the ppp can be non-uniform unless the underlyi... | https://arxiv.org/abs/2504.14077 | Academic Papers | svg |
52945deaa318babe0834e071de34a189e74f7d8d32fb7583e41d528cfbd4541a | 2026-01-13T00:00:00-05:00 | Jacobson identities for post-Lie algebras in positive characteristic | arXiv:2504.14540v2 Announce Type: replace Abstract: Let $p$ be a prime number. Given a restricted Lie algebra over a field of characteristic $p$ and a post-Lie operation over it, we prove the Jacobson identities for a $p$-structure built from the Lie bracket and the post-Lie operation, called sub-adjacent $p$-structure... | https://arxiv.org/abs/2504.14540 | Academic Papers | svg |
5925179939e3a76de69194164773305330ec802242bba8b4056005458e2cf236 | 2026-01-13T00:00:00-05:00 | Projection Coefficients Estimation in Continuous-Variable Quantum Circuits | arXiv:2504.16246v3 Announce Type: replace Abstract: In this work, we propose a continuous-variable quantum algorithm to compute the projection coefficients of a holomorphic function in the Segal--Bargmann space by leveraging its isometric correspondence with single-mode quantum states. Using CV quantum circuits, we pre... | https://arxiv.org/abs/2504.16246 | Academic Papers | svg |
46de2ec9c967ac3bf31dc7685055df6c48eb6acb8e122e9e8220976fa8e0a07f | 2026-01-13T00:00:00-05:00 | Secret Sharing in the Rank Metric | arXiv:2504.18294v2 Announce Type: replace Abstract: The connection between secret sharing and matroid theory is well established. In this paper, we generalize the concepts of secret sharing and matroid ports to $q$-polymatroids. Specifically, we introduce the notion of an access structure on a vector space, and conside... | https://arxiv.org/abs/2504.18294 | Academic Papers | svg |
68e953952dd34f49a1288b97695818b9301973d8d6869a0c185884a234a638b3 | 2026-01-13T00:00:00-05:00 | Efficient approximations of matrix multiplication using truncated decompositions | arXiv:2504.19308v3 Announce Type: replace Abstract: We exploit the truncated singular value decomposition and the recently proposed circulant decomposition for an efficient first-order approximation of the multiplication of large dense matrices. A decomposition of each matrix into a sum of a sparse matrix with relative... | https://arxiv.org/abs/2504.19308 | Academic Papers | svg |
18e72c533d73b2b2dd7114c53bb7ac72894eba502f14ef6139b0d4226de6b2bb | 2026-01-13T00:00:00-05:00 | Asymptotics of zeta determinants of Laplacians on large degree abelian covers | arXiv:2505.01586v2 Announce Type: replace Abstract: Let $(M,g)$ be some smooth, closed, compact Riemannian manifold and $(M_N\mapsto M)_N$ be an increasing sequence of large degree cyclic covers of $M$ that converges when $N\rightarrow +\infty$, in a suitable sense, to some limit $\mathbb{Z}^p$ cover $M_\infty$ over $M... | https://arxiv.org/abs/2505.01586 | Academic Papers | svg |
0621f67fa6c2953239f168ba6eb7f9d716dc38cdaa3e9978fc483b71ba685f51 | 2026-01-13T00:00:00-05:00 | The raspberries in three dimensions with at most two sizes of berry | arXiv:2505.03408v2 Announce Type: replace Abstract: In three dimensional Euclidean space, a raspberry is defined to be an arrangement of spheres with pairwise disjoint interiors, where all spheres are tangent to a central unit sphere and such that the contact graph of the non-central spheres triangulates the central sp... | https://arxiv.org/abs/2505.03408 | Academic Papers | svg |
266e1bbee4c6e98717e306dc4d6cfc0fcfa92e5ed05c367146998ff6fdafa499 | 2026-01-13T00:00:00-05:00 | m-Accretive Extensions of Friedrichs Operators | arXiv:2505.03657v2 Announce Type: replace Abstract: The introduction of abstract Friedrichs operators in 2007-an operator-theoretic framework for studying classical Friedrichs operators has led to significant developments in the field, including results on well-posedness, multiplicity, and classification. More recently... | https://arxiv.org/abs/2505.03657 | Academic Papers | svg |
c7c120bcc62aafacdb20bc768939d2c79d900be86a35a660c81dc5906baef827 | 2026-01-13T00:00:00-05:00 | On some critical Riemannian metrics and Thorpe-type conditions | arXiv:2505.06990v3 Announce Type: replace Abstract: We study critical metrics of higher-order curvature functionals on compact Riemannian $n$-manifolds $(M,g)$. For an integer $k$ with $2 \leq 2k \leq n$, let $R^k$ denote the $k$-th exterior power of the Riemann curvature tensor. We investigate the Riemannian functiona... | https://arxiv.org/abs/2505.06990 | Academic Papers | svg |
a261d3bbaba9fbfec6638d8084ccaafd97d2cd2472e93f09839b95e7aed14a90 | 2026-01-13T00:00:00-05:00 | A 2-torsion invariant of 2-knots | arXiv:2505.13699v2 Announce Type: replace Abstract: In this paper we describe what should perhaps be called a `type-2' Vassiliev invariant of knots S^2 -> S^4. We give a formula for an invariant of 2-knots, taking values in Z_2 that can be computed in terms of the double-point diagram of the knot. The double-point diag... | https://arxiv.org/abs/2505.13699 | Academic Papers | svg |
74dee641a76369ef7c704985068bbfe2ccaf7cfd8d7d7e3501c31629bd5e188e | 2026-01-13T00:00:00-05:00 | A new measure of dependence: Integrated $R^2$ | arXiv:2505.18146v4 Announce Type: replace Abstract: We introduce a novel measure of dependence that captures the extent to which a random variable $Y$ is determined by a random vector $X$. The measure equals zero precisely when $Y$ and $X$ are independent, and it attains one exactly when $Y$ is almost surely a measurab... | https://arxiv.org/abs/2505.18146 | Academic Papers | svg |
45ee8012e4d179506e30f49a9493f38e8e6a385d4e6974598ba44b70252c116f | 2026-01-13T00:00:00-05:00 | Second Order Properties of Thinned Counts in Finite Birth--Death Processes | arXiv:2505.20174v2 Announce Type: replace Abstract: The paper studies the counting process arising as a subset of births and deaths in a birth--death process on a finite state space. Whenever a birth or death occurs, the process is incremented or not depending on the outcome of an independent Bernoulli experiment whose... | https://arxiv.org/abs/2505.20174 | Academic Papers | svg |
aec1dd0dd083438b168ec4049e25381b787ad78d1a134070b8b6484f67fa674e | 2026-01-13T00:00:00-05:00 | Definable ranks | arXiv:2506.00443v4 Announce Type: replace Abstract: We introduce the notion of the definable rank of an ordered field, ordered abelian group and ordered set, respectively. We study the relation between the definable rank of an ordered field and the definable rank of the value group of its natural valuation. Similarly, ... | https://arxiv.org/abs/2506.00443 | Academic Papers | svg |
3673d7bdd6a95bec59429bdafeeb83e4b4e3c05b7d257e839fa3796089910a7b | 2026-01-13T00:00:00-05:00 | R-PINN: Recovery-type a-posteriori estimator enhanced adaptive PINN | arXiv:2506.10243v2 Announce Type: replace Abstract: In recent years, with the advancements in machine learning and neural networks, algorithms using physics-informed neural networks (PINNs) to solve PDEs have gained widespread applications. While these algorithms are well-suited for a wide range of equations, they ofte... | https://arxiv.org/abs/2506.10243 | Academic Papers | svg |
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