id
stringlengths
64
64
published
stringlengths
19
25
title
stringlengths
7
262
description
stringlengths
6
54.4k
link
stringlengths
31
227
category
stringclasses
6 values
image
stringlengths
3
247
46599c3a77eea6b3f9e2b454f3d22b5843710550391de0fa43938f810e0eaab4
2026-01-21T00:00:00-05:00
Three-chromatic geometric hypergraphs
arXiv:2112.01820v2 Announce Type: replace Abstract: We prove that for any planar convex body C there is a positive integer m with the property that any finite point set P in the plane can be three-colored such that there is no translate of C containing at least m points of P, all of the same color. As a part of the pro...
https://arxiv.org/abs/2112.01820
Academic Papers
svg
1292a1a7995f2eaa30cdb69c33550864ef43da44f19b929929a682dc823ab76e
2026-01-21T00:00:00-05:00
p-adic adelic metrics and Quadratic Chabauty I
arXiv:2112.03873v4 Announce Type: replace Abstract: We give a new construction of $p$-adic heights on varieties over number fields using $p$-adic Arakelov theory. In analogy with Zhang's construction of real-valued heights in terms of adelic metrics, these heights are given in terms of $p$-adic adelic metrics on line b...
https://arxiv.org/abs/2112.03873
Academic Papers
svg
f7c1a414253a575eaff78a5bd08dc1b28bceda7dc84df513bc335844a758c991
2026-01-21T00:00:00-05:00
Reconstruction for the time-dependent coefficients of a quasilinear dynamical Schr{\"o}dinger equation
arXiv:2201.09809v2 Announce Type: replace Abstract: We study an inverse problem related to the dynamical Schr{\"o}dinger equation in a bounded domain of $\Rb^n,n\geq 2$. Since the concerned non-linear Schr\"odinger equation possesses a trivial solution, we linearize the equation around the trivial solution. Demonstrati...
https://arxiv.org/abs/2201.09809
Academic Papers
svg
b6172b8e6882899c44e19f13f9a68b6c97ac6f8676c79909c0316e28643b5992
2026-01-21T00:00:00-05:00
Improvements in $L^2$ Restriction bounds for Neumann Data along closed curves
arXiv:2203.01208v2 Announce Type: replace Abstract: We seek to improve the restriction bounds of Neumann data of Laplace eigenfunctions $u_h$ by studying the $L^2$ restriction bounds of Neumann data and their $L^2$ concentration as measured by defect measures. Let $\gamma$ be a closed smooth curve with unit exterior no...
https://arxiv.org/abs/2203.01208
Academic Papers
svg
dcc33839cf9503d98073ce93b96b7b7dc0cb7ba950056b3ca324a398bf58c656
2026-01-21T00:00:00-05:00
Holomorphic foliations of degree two and arbitrary dimension
arXiv:2207.12880v5 Announce Type: replace Abstract: We prove a complete classification of degree-$2$ foliations on $\mathbb{P}^n$ in any dimension, assuming they are not algebraically integrable. If $\mathcal{F}$ is such a foliation, then either $\mathcal{F}$ is the linear pull-back of a degree-$2$ foliation by curves ...
https://arxiv.org/abs/2207.12880
Academic Papers
svg
cfd66bb6fc279cc060e04c7d5d6c0f665b94217d8db454c02ee41c342f8e8d46
2026-01-21T00:00:00-05:00
Tame class field theory over local fields
arXiv:2209.02953v2 Announce Type: replace Abstract: For a quasi-projective scheme $X$ admitting a smooth compactification over a local field of residue characteristic $p > 0$, we construct a continuous reciprocity homomorphism from a tame class group to the abelian tame etale fundamental group of $X$. We describe the p...
https://arxiv.org/abs/2209.02953
Academic Papers
svg
13950b65070c5a28283c31d0e5f05e23356f2f531d7ad578e74bec1f03777fd9
2026-01-21T00:00:00-05:00
Functional dimension of feedforward ReLU neural networks
arXiv:2209.04036v2 Announce Type: replace Abstract: It is well-known that the parameterized family of functions representable by fully-connected feedforward neural networks with ReLU activation function is precisely the class of piecewise linear functions with finitely many pieces. It is less well-known that for every ...
https://arxiv.org/abs/2209.04036
Academic Papers
svg
52f816a6c6084ed10900c5578a9774083fe01205cd1b37170340fab4e283ac3b
2026-01-21T00:00:00-05:00
Nondivergence of Reductive group action on Homogeneous Spaces
arXiv:2209.06463v2 Announce Type: replace Abstract: Let $X=G/\Gamma$ be the quotient of a semisimple Lie group $G$ by its non-cocompact arithmetic lattice. Let $H$ be a reductive algebraic subgroup of $G$ acting on $X$. We give several equivalent algebraic conditions on $H$ for the existence of a fixed compact set in $...
https://arxiv.org/abs/2209.06463
Academic Papers
svg
9bb860686b17f2a163782183b07f48d281da850e0afc20ad2fcf50c1512dfa10
2026-01-21T00:00:00-05:00
Prime Solutions of Diagonal Diophantine Systems
arXiv:2209.06934v2 Announce Type: replace Abstract: An asymptotic formula for the number of prime solutions of a general diagonal system of Diophantine equations is established, contingent on the existence of an appropriate mean value bound and on local solvability. In conjunction with the Vinogradov Mean Value Theorem...
https://arxiv.org/abs/2209.06934
Academic Papers
svg
c26dfff9c795db1cf97b85f36818334c9002e310a868c751188e25328c242cd1
2026-01-21T00:00:00-05:00
Expander graphs are globally synchronizing
arXiv:2210.12788v4 Announce Type: replace Abstract: The Kuramoto model is fundamental to the study of synchronization. It consists of a collection of oscillators with interactions given by a network, which we identify respectively with vertices and edges of a graph. In this paper, we show that a graph with sufficient e...
https://arxiv.org/abs/2210.12788
Academic Papers
svg
be1828c50a391d0a748796d39e871bcfa81f9c7fff4800a3262def58535c9504
2026-01-21T00:00:00-05:00
Turing meets Moore-Penrose: Computing the Pseudoinverse on Turing Machines
arXiv:2212.02940v2 Announce Type: replace Abstract: The pseudoinverse of a matrix, a generalized notion of the inverse, is of fundamental importance in linear algebra and, thereby, in many different fields. Despite its proven existence, an algorithmic approach is typically necessary to obtain the pseudoinverse in pract...
https://arxiv.org/abs/2212.02940
Academic Papers
svg
c4e02f4134d4133771c88e2eaa3a3f5e376e780f51641288cca4785607e1b109
2026-01-21T00:00:00-05:00
Diophantine Criterion for Non-trivial Shafarevich-Tate Groups
arXiv:2301.03486v3 Announce Type: replace Abstract: The solvability of Diophantine quartic equations is a contemporary area of interest due to its connection with \textit{generalized Fermat's equation}. In this work, we are interested in the integer solutions of a similar quartic equation $pu^{2} = v^{2}+w^{2}$. For a ...
https://arxiv.org/abs/2301.03486
Academic Papers
svg
0d2dd4c856fd1d4986b36e120ae7d6ad96056c2272329cf39b52ed295a01b252
2026-01-21T00:00:00-05:00
Relations between e, $\pi$, golden ratios and $\sqrt{2}$
arXiv:2301.09643v4 Announce Type: replace Abstract: We write out relations between the base of natural logarithms ($e$), the ratio of the circumference of a circle to its diameter ($\pi$), the golden ratios ($\Phi_p$) of the additive $p$-sequences, and the ratio of the diagonal of a square to its side ($\sqrt{2}$). An ...
https://arxiv.org/abs/2301.09643
Academic Papers
svg
6a0513ebd92d2c4553690a9b185578bdddd7fd2cb514f823aa5024728779d4f1
2026-01-21T00:00:00-05:00
A relative Nadel-type vanishing theorem
arXiv:2302.11080v3 Announce Type: replace Abstract: Let $f:X\rightarrow Y$ be a K\"{a}hler fibration from a complex manifold $X$ to an analytic space $Y$. We show several relative Nadel-type vanishing theorems.
https://arxiv.org/abs/2302.11080
Academic Papers
svg
f30ff57baf1f7c9ac5202effbacdcfb8041e2dadb7b6fdceabca13650a34550d
2026-01-21T00:00:00-05:00
Controlled Interacting Branching Diffusion Processes: Relaxed Formulation in the Mean-Field Regime
arXiv:2304.07064v3 Announce Type: replace Abstract: The focus of this article is studying an optimal control problem for branching diffusion processes. Initially, we introduce the problem in its strong formulation and expand it to include linearly growing drifts. Then, we present a relaxed formulation that provides a s...
https://arxiv.org/abs/2304.07064
Academic Papers
svg
a2def47fd29ae770eb70826347af973e47b941533d7f485d3020272bf9f5d06c
2026-01-21T00:00:00-05:00
Continuous-time extensions of discrete-time cocycles
arXiv:2305.07338v2 Announce Type: replace Abstract: We consider linear cocycles taking values in $\textup{SL}_d(\mathbb{R})$ driven by homeomorphic transformations of a smooth manifold, in discrete and continuous time. We show that any discrete-time cocycle can be extended to a continuous-time cocycle, while preserving...
https://arxiv.org/abs/2305.07338
Academic Papers
svg
76ac07abb1734a170b617d779076eed9fa33d82ed07d74bfdf884079d40f38de
2026-01-21T00:00:00-05:00
Quasimaps to quivers with potentials
arXiv:2306.01302v2 Announce Type: replace Abstract: This paper is concerned with a non-compact GIT quotient of a vector space, in the presence of an abelian group action and an equivariant regular function (potential) on the quotient. We define virtual counts of quasimaps from prestable curves to the critical locus of ...
https://arxiv.org/abs/2306.01302
Academic Papers
svg
d77e3d67b96e6e5c4ce93763cab9d951fd28a61b1d9ba3c92dc5b2588312cb8c
2026-01-21T00:00:00-05:00
The distribution of Ridgeless least squares interpolators
arXiv:2307.02044v2 Announce Type: replace Abstract: The Ridgeless minimum $\ell_2$-norm interpolator in overparametrized linear regression has attracted considerable attention in recent years in both machine learning and statistics communities. While it seems to defy conventional wisdom that overfitting leads to poor p...
https://arxiv.org/abs/2307.02044
Academic Papers
svg
ecc0da5df116ece8296a1034b142fa055aa613f61c368ffbb872c4e635593324
2026-01-21T00:00:00-05:00
A First-Order Algorithm for Decentralised Min-Max Problems
arXiv:2308.11876v2 Announce Type: replace Abstract: In this work, we consider a connected network of finitely many agents working cooperatively to solve a min-max problem with convex-concave structure. We propose a decentralised first-order algorithm which can be viewed as a non-trivial combination of two algorithms: P...
https://arxiv.org/abs/2308.11876
Academic Papers
svg
2c03a50debcf8e109c2df19fcadbc185114b21a43c7fe678d5fad04aad2f3c75
2026-01-21T00:00:00-05:00
Fast and Inverse-Free Algorithms for Deflating Subspaces
arXiv:2310.00193v4 Announce Type: replace Abstract: This paper explores a key question in numerical linear algebra: how can we compute projectors onto the deflating subspaces of a regular matrix pencil $(A,B)$, in particular without using matrix inversion or defaulting to an expensive Schur decomposition? We focus spec...
https://arxiv.org/abs/2310.00193
Academic Papers
svg
221ed213f19c4821363331881fde7c69561b24568d9f35b04927fe5dfde2206b
2026-01-21T00:00:00-05:00
Global well-posedness and large-time behavior of the compressible Navier-Stokes equations with hyperbolic heat conduction
arXiv:2310.13461v2 Announce Type: replace Abstract: The classical Fourier's law, which states that the heat flux is proportional to the temperature gradient, induces the paradox of infinite propagation speed for heat conduction. To accurately simulate the real physical process, the hyperbolic model of heat conduction n...
https://arxiv.org/abs/2310.13461
Academic Papers
svg
ce9175122c4f4ae8cd631fdff10ad602368e4bb0c490649ed6bb55ab8a510669
2026-01-21T00:00:00-05:00
The asymptotic behavior of rarely visited edges of the simple random walk
arXiv:2310.16657v2 Announce Type: replace Abstract: In this paper, we study the asymptotic behavior of the number of rarely visited edges (i.e., edges that visited only once) of a simple symmetric random walk on $\mathbb{Z}$. Let $\alpha(n)$ be the number of rarely visited edges up to time $n$. First, we evaluate $\mat...
https://arxiv.org/abs/2310.16657
Academic Papers
svg
abbe22bc7372d1be620bd429b96b8da51ebd44f0824febd146b411955e204df6
2026-01-21T00:00:00-05:00
Factorization structures, cones, and polytopes
arXiv:2311.07328v4 Announce Type: replace Abstract: Factorization structures occur in toric differential and discrete geometry, and can be viewed in multiple ways, e.g., as objects determining substantial classes of explicit toric Sasaki and K\"ahler geometries, as special coordinates on such, or as an apex generalisat...
https://arxiv.org/abs/2311.07328
Academic Papers
svg
196588446301f41d97ea49bb8e2633e214ac9260e624c90d85c1715f01cb3d56
2026-01-21T00:00:00-05:00
Abelian gauge-like groups of $L_\infty$-algebras
arXiv:2311.08512v3 Announce Type: replace Abstract: Given a finite type degree-wise nilpotent $L_\infty$-algebra, we construct an abelian group that acts on the set of Maurer-Cartan elements of the given $L_\infty$-algebra so that the quotient by this action becomes the moduli space of equivalence classes of Maurer-Car...
https://arxiv.org/abs/2311.08512
Academic Papers
svg
54571ac0725232239005205972256b2907e831d4083941e2ff8ad00c8370eac7
2026-01-21T00:00:00-05:00
Quaternion-Valued Wavelets on the Plane: A Construction via the Douglas-Rachford Approach
arXiv:2311.12614v2 Announce Type: replace Abstract: This paper presents a reformulation of the construction of nonseparable multiresolution quaternion-valued wavelets on the plane as a feasibility problem. The constraint sets in the feasibility problem are derived from the standard conditions of smoothness, compact sup...
https://arxiv.org/abs/2311.12614
Academic Papers
svg
691c0004c71fec5d0a97bce209532a0c4ea2f2f7d6673bbc9c3258242ac86866
2026-01-21T00:00:00-05:00
On the equivalence of static and dynamic weak optimal transport
arXiv:2311.13872v3 Announce Type: replace Abstract: We show that there is a PDE formulation in terms of Fokker-Planck equations for weak optimal transport problems. The main novelty is that we introduce a minimization problem involving Fokker-Planck equations in the extended sense of measure-valued solutions and prove ...
https://arxiv.org/abs/2311.13872
Academic Papers
svg
4f3b41662208e6d8d8bbf1ebc3e3597b28fd5efb3d41a40ffce3d42dc1e715b2
2026-01-21T00:00:00-05:00
Ancient mean curvature flows from minimal hypersurfaces
arXiv:2311.15278v4 Announce Type: replace Abstract: For $n\geq 2$, we construct $I$-dimensional family of embedded ancient solutions to mean curvature flow arise from an unstable minimal hypersurface $\Sigma$ with finite total curvature in $\mathbb{R}^{n+1}$, where $I$ is the Morse index of the Jacobi operator on $\Sig...
https://arxiv.org/abs/2311.15278
Academic Papers
svg
8fa76dba51c90644a82723828ce62154381ca3c2fe0f7e3e7ed5b36a4c13cc8a
2026-01-21T00:00:00-05:00
Propagating front solutions in a time-fractional Fisher-KPP equation
arXiv:2311.15651v5 Announce Type: replace Abstract: In this paper, we treat the Fisher-KPP equation with a Caputo-type time fractional derivative and discuss the propagation speed of the solution. The equation is a mathematical model that describes the processes of sub-diffusion, proliferation, and saturation. We first...
https://arxiv.org/abs/2311.15651
Academic Papers
svg
db2332ac75ab82a080cd39896857bf962641f5055d0dd54397bc8918b8d9e248
2026-01-21T00:00:00-05:00
Non-vanishing of Kolyvagin systems and Iwasawa theory
arXiv:2312.09301v2 Announce Type: replace Abstract: Let $E/\mathbb{Q}$ be an elliptic curve and $p$ an odd prime. In 1991 Kolyvagin conjectured that the system of cohomology classes for torsion quotients of the $p$-adic Tate module of $E$ derived from Heegner points over ring class fields of a suitable imaginary quadra...
https://arxiv.org/abs/2312.09301
Academic Papers
svg
d53292e1b63d3035673790e0aafe2cf2367a9cbf570d73878d5cea506163feaa
2026-01-21T00:00:00-05:00
On the mixed monotonicity of polynomial functions
arXiv:2312.15517v2 Announce Type: replace Abstract: In this paper, it is shown that every polynomial function is mixed monotone globally with a polynomial decomposition function. For univariate polynomials, the decomposition functions can be constructed from the Gram matrix representation of polynomial functions. The t...
https://arxiv.org/abs/2312.15517
Academic Papers
svg
54d06df007db9ae668deacd33f3ca3d719530a14b8d88d5e93390c737a009cb2
2026-01-21T00:00:00-05:00
Virtual Holonomic and Nonholonomic Constraints on Lie groups
arXiv:2312.17531v2 Announce Type: replace Abstract: This paper develops a geometric framework for virtual constraints on Lie groups, with emphasis on mechanical systems modeled as affine connection systems. Virtual holonomic and virtual nonholonomic constraints, including linear and affine nonholonomic constraints, are...
https://arxiv.org/abs/2312.17531
Academic Papers
svg
99818173f6d8c37be74f6439e8a58e2bb8794476a738092a6457ce948f2472c7
2026-01-21T00:00:00-05:00
Separable homology of graphs and the separability complex
arXiv:2401.01320v2 Announce Type: replace Abstract: We introduce the separability complex, a one-complex associated to a finite regular cover of the rose and show that it is connected if and only if the fundamental group of the associated cover is generated by its intersection with the set of elements in proper free fa...
https://arxiv.org/abs/2401.01320
Academic Papers
svg
b06621019b69332ecc149a37d7b231dc9ebda1fcfca53f142850ca78af09cc3f
2026-01-21T00:00:00-05:00
A classification of neighborhoods around leaves of a singular foliation
arXiv:2401.05966v3 Announce Type: replace Abstract: We classify singular foliations admitting a given leaf and a given transverse singular foliation.
https://arxiv.org/abs/2401.05966
Academic Papers
svg
a2771c7e13f132df1a7d1b5b27d785e5a9bc0239f6222b705edcbd303d70cbec
2026-01-21T00:00:00-05:00
Local dimension spectrum for dominated planar self-affine sets
arXiv:2401.13626v2 Announce Type: replace Abstract: The local dimension spectrum provides a framework for quantifying the fractal properties of a measure, and it is well understood for non-overlapping self-similar measures. In this article, we study the local dimension spectrum for dominated self-affine measures. By an...
https://arxiv.org/abs/2401.13626
Academic Papers
svg
b02fff27c51cd32d86e18f5535ac454f521729ceb1fb9b7a85f6fa894b86c338
2026-01-21T00:00:00-05:00
On generalized Beauville decompositions
arXiv:2402.08861v2 Announce Type: replace Abstract: Motivated by the Beauville decomposition of an abelian scheme and the "Perverse = Chern" phenomenon for a compactified Jacobian fibration, we study in this paper splittings of the perverse filtration for compactified Jacobian fibrations. On the one hand, we prove for ...
https://arxiv.org/abs/2402.08861
Academic Papers
svg
70c4473f24a4f0464b439c7a2cf64144d963fdf1c998fd8da7cbaf1ddb588c0e
2026-01-21T00:00:00-05:00
Uniform bounds for bilinear symbols with linear K-quasiconformally embedded singularity
arXiv:2402.11661v2 Announce Type: replace Abstract: We prove bounds in the strict local $L^{2}(\mathbb{R}^{d})$ range for trilinear Fourier multiplier forms with a $d$-dimensional singular subspace. Given a fixed parameter $K \ge 1$, we treat multipliers with non-degenerate singularity that are push-forwards by $K$-qua...
https://arxiv.org/abs/2402.11661
Academic Papers
svg
d5c19cae4a15de550c76019e6955e8f8e9dabd13a4499c77ec2c64056e3e27c9
2026-01-21T00:00:00-05:00
On transverse-universality of twist knots
arXiv:2402.12585v3 Announce Type: replace Abstract: In the search for transverse-universal knots in the standard contact structure on $\mathbb{S}^3$, we present a classification of the transverse twist knots with maximal self-linking number, that admit only overtwisted contact branched covers. As a direct consequence, ...
https://arxiv.org/abs/2402.12585
Academic Papers
svg
9b8ebd580dd38b0cfcb3444d95dfcf7762ec972cd78691babf68eaa6139408c9
2026-01-21T00:00:00-05:00
Hyperuniformity and optimal transport of point processes
arXiv:2402.13705v4 Announce Type: replace Abstract: We examine optimal matchings or transport between two stationary random measures. It covers allocation from the Lebesgue measure to a point process and matching a point process to a regular (shifted) lattice. The main focus of the article is the impact of hyperuniform...
https://arxiv.org/abs/2402.13705
Academic Papers
svg
7ed55fa5bf0aed7b00f3f92303908adbccd159fd1df3a064bc71c4e92eefa3e5
2026-01-21T00:00:00-05:00
Bilinear Rough Singular Integrals near the Critical Integrability via Sharp Fourier Multiplier Criteria
arXiv:2402.15785v2 Announce Type: replace Abstract: We establish boundedness results for bilinear singular integral operators with rough homogeneous kernels whose restriction to the unit sphere belongs to the Orlicz space $L(\log L)^\alpha$. This improves the previously best known condition for boundedness of such bili...
https://arxiv.org/abs/2402.15785
Academic Papers
svg
ebbc1cf2abbbdb9dfa10d852d36114fbf671daa63241c6eec4313040471c9515
2026-01-21T00:00:00-05:00
Counting rationals and diophantine approximation in missing-digit Cantor sets
arXiv:2402.18395v2 Announce Type: replace Abstract: We establish a new upper bound for the number of rationals up to a given height in a missing-digit set, making progress towards a conjecture of Broderick, Fishman, and Reich. This enables us to make novel progress towards another conjecture of those authors about the ...
https://arxiv.org/abs/2402.18395
Academic Papers
svg
d6ce7ff7335c9a03deb82faca24b957db8f620e6769956db755fed8319045bcb
2026-01-21T00:00:00-05:00
A restricted additive smoother for finite cell flow problems
arXiv:2403.11636v2 Announce Type: replace Abstract: In this work, we propose an adaptive geometric multigrid method for the solution of large-scale finite cell flow problems. The finite cell method seeks to circumvent the need for a boundary-conforming mesh through the embedding of the physical domain in a regular back...
https://arxiv.org/abs/2403.11636
Academic Papers
svg
9ce4cf0c9c71ac7daf34e2fbc31bf5b42e385adbc6ccc91317c57fd1e64e9252
2026-01-21T00:00:00-05:00
What Is a Good Imputation Under MAR Missingness?
arXiv:2403.19196v5 Announce Type: replace Abstract: Missing values pose a persistent challenge in modern data science. Consequently, there is an ever-growing number of publications introducing new imputation methods in various fields. The present paper attempts to take a step back and provide a more systematic analysis...
https://arxiv.org/abs/2403.19196
Academic Papers
svg
251adc3f0c082036eac9b8e6b1efeb878794fefbdc403fc4c667142f700dec2c
2026-01-21T00:00:00-05:00
Analytic holonomicity of real C$^{{\mathrm{exp}}}$-class distributions
arXiv:2403.20167v2 Announce Type: replace Abstract: We introduce a notion of distributions on $\mathbb{R}^n$, called distributions of C$^{{\mathrm{exp}}}$-class, based on wavelet transforms of distributions and the theory from Cluckers, Comte, Miller, Rolin, Servi (2018) about C$^{{\mathrm{exp}}}$-class functions. We p...
https://arxiv.org/abs/2403.20167
Academic Papers
svg
e8563bdf0ce79798edc81202403f7cf6c55365556f45315866d26a72c478c803
2026-01-21T00:00:00-05:00
Constructive proofs for some semilinear PDEs on $H^2(e^{|x|^2/4},\mathbb{R}^d)$
arXiv:2404.04054v2 Announce Type: replace Abstract: We develop computer-assisted tools to study semilinear equations of the form \begin{equation*} -\Delta u -\frac{x}{2}\cdot \nabla{u}= f(x,u,\nabla u) ,\quad x\in\mathbb{R}^d. \end{equation*} Such equations appear naturally in several contexts, and in particular when l...
https://arxiv.org/abs/2404.04054
Academic Papers
svg
f453c32c9c826d72e03379cf76098b4358120f54f4d5b14c774dcce32e1d74fb
2026-01-21T00:00:00-05:00
Monochromatic polynomial sumset structures on $\mathbb{N}$
arXiv:2404.05226v4 Announce Type: replace Abstract: In the paper, we search for monochromatic infinite additive structures involving polynomials over $\mathbb{N}$. It is proved that for any $r\in \mathbb{N}$, any two distinct natural numbers $a,b$, and any $2$-coloring of $\mathbb{N}$, there exist two sets $B,C\subset ...
https://arxiv.org/abs/2404.05226
Academic Papers
svg
5b715e73f1c0f14a3b3104d6aeee7d2c8c9b32db473650976f0f0a16cf66fc48
2026-01-21T00:00:00-05:00
Cohen-Macaulay representations of Artin-Schelter Gorenstein algebras of dimension one
arXiv:2404.05925v4 Announce Type: replace Abstract: Tilting theory is one of the central tools in modern representation theory, in particular in the study of Cohen-Macaulay representations. We study Cohen-Macaulay representations of $\mathbb N$-graded Artin-Schelter Gorenstein algebras $A$ of dimension one, without ass...
https://arxiv.org/abs/2404.05925
Academic Papers
svg
4d87b700b116b1d364c31d9e95cb131baab6cf99c046fffe7c10b33cd3bed60e
2026-01-21T00:00:00-05:00
Lower bound for the first eigenvalue of $p-$Laplacian and applications in asymptotically hyperbolic Einstein manifolds
arXiv:2405.02669v2 Announce Type: replace Abstract: This paper investigates the first Dirichlet eigenvalue for the $p$-Laplacian in Riemannian manifolds. Firstly, we establish a lower bound for this eigenvalue under the condition that the domain includes a specific function which fulfills certain criteria related to di...
https://arxiv.org/abs/2405.02669
Academic Papers
svg
053d8e06e4ed5f6fa616403d16fd91d545f6d2d7b73c4e9d7c4ba83275796183
2026-01-21T00:00:00-05:00
Fast Two-Time-Scale Stochastic Gradient Method with Applications in Reinforcement Learning
arXiv:2405.09660v4 Announce Type: replace Abstract: Two-time-scale optimization is a framework introduced in Zeng et al. (2024) that abstracts a range of policy evaluation and policy optimization problems in reinforcement learning (RL). Akin to bi-level optimization under a particular type of stochastic oracle, the two...
https://arxiv.org/abs/2405.09660
Academic Papers
svg
a13b7a791de0da39d12b69f87ef50f0eb7ead34fa4df21c9c2898cc1dbe9fec8
2026-01-21T00:00:00-05:00
On a Conjecture by Hayashi on Finite Connected Quandles
arXiv:2405.11660v2 Announce Type: replace Abstract: A quandle is an algebraic structure whose binary operation is idempotent, right-invertible and right self-distributive. Right-invertibility ensures right translations are permutations and right self-distributivity ensures further they are automorphisms. For finite con...
https://arxiv.org/abs/2405.11660
Academic Papers
svg
03dd82c0605b4cfb2e6d3c1aefa9195df6b278839dc021f7a68edab48399e5ee
2026-01-21T00:00:00-05:00
Rate Optimality and Phase Transition for User-Level Local Differential Privacy
arXiv:2405.11923v3 Announce Type: replace Abstract: Most of the literature on differential privacy considers the item-level case where each user has a single observation, but a growing field of interest is that of user-level privacy where each of the $n$ users holds $T$ observations and wishes to maintain the privacy o...
https://arxiv.org/abs/2405.11923
Academic Papers
svg
165cede06af6d169f27f02a99a029f8a705e64c2e66ae78863ba04f5aeb51288
2026-01-21T00:00:00-05:00
Distribution Steering for Discrete-Time Uncertain Ensemble Systems
arXiv:2405.12415v2 Announce Type: replace Abstract: Ensemble systems appear frequently in many engineering applications and, as a result, they have become an important research topic in control theory. These systems are best characterized by the evolution of their underlying state distribution. Despite the work to date...
https://arxiv.org/abs/2405.12415
Academic Papers
svg
a6a4600c7090af8882369439897fe9f5dbf3c661d7c13a8a883595a0d4f6a706
2026-01-21T00:00:00-05:00
On non-topologizable semigroups
arXiv:2405.16992v3 Announce Type: replace Abstract: We find anti-isomorphic submonoids $\mathscr{C}_{+}(a,b)$ and $\mathscr{C}_{-}(a,b)$ of the bicyclic monoid $\mathscr{C}(a,b)$ with the following properties: every Hausdorff left-continuous (right-continuous) topology on $\mathscr{C}_{+}(a,b)$ ($\mathscr{C}_{-}(a,b)$)...
https://arxiv.org/abs/2405.16992
Academic Papers
svg
8e961179b12718fc596f1dd8c10da1697131ded3d4f3a006c2c80bb750b58029
2026-01-21T00:00:00-05:00
CHANI: Correlation-based Hawkes Aggregation of Neurons with bio-Inspiration
arXiv:2405.18828v2 Announce Type: replace Abstract: The present work aims at proving mathematically that a neural network inspired by biology can learn a classification task thanks to local transformations only. In this purpose, we propose a spiking neural network named CHANI (Correlation-based Hawkes Aggregation of Ne...
https://arxiv.org/abs/2405.18828
Academic Papers
svg
fbd147f5d6c13a9d94244f33892351180cd25a42b894abb4e7c28dbd16ad991b
2026-01-21T00:00:00-05:00
Uniform Resolvent Estimates for Subwavelength Resonators: The Minnaert Bubble Case
arXiv:2406.02192v4 Announce Type: replace Abstract: Subwavelength resonators are small scaled objects that exhibit contrasting medium properties (eigher in intensity or sign) while compared to the ones of a uniform background. Such contrasts allow them to resonate at specific frequencies. There are two ways to mathemat...
https://arxiv.org/abs/2406.02192
Academic Papers
svg
b98724b7b1d4d86a25948c82b57a67b8c42daca79aabe8fcb450c8b192bcb37c
2026-01-21T00:00:00-05:00
Solutions to the exercises from the book "Albert algebras over commutative rings"
arXiv:2406.02933v3 Announce Type: replace Abstract: This document presents the solutions to the exercises in the book "Albert algebras over commutative rings" published by Cambridge University Press, 2024, as well as errata and addenda.
https://arxiv.org/abs/2406.02933
Academic Papers
svg
818b1805ca8a8c949498d769498ad0be61e2562045100b597f0d8ecf39c18666
2026-01-21T00:00:00-05:00
Exact formulae for ranks of partitions
arXiv:2406.06294v2 Announce Type: replace Abstract: In 2009, Bringmann arXiv:0708.0691 [math.NT] used the circle method to prove an asymptotic formula for the Fourier coefficients of rank generating functions. In this paper, we prove that Bringmann's formula, when summing up to infinity and in the case of prime modulus...
https://arxiv.org/abs/2406.06294
Academic Papers
svg
405a2d53e29f9d71430c6accd4f1fce661e28671e4f3c31ff316dd3269d6578a
2026-01-21T00:00:00-05:00
Multivariate extreme values for dynamical systems
arXiv:2406.14807v3 Announce Type: replace Abstract: We establish a theory for multivariate extreme value analysis of dynamical systems. Namely, we provide conditions adapted to the dynamical setting which enable the study of dependence between extreme values of the components of $\R^d$-valued observables evaluated alon...
https://arxiv.org/abs/2406.14807
Academic Papers
svg
1de7dcc42a8a1d7192d28c625686cf86f00d765268f0610fdc8034d0433f9f69
2026-01-21T00:00:00-05:00
Geometric structures for maximal representations and pencils
arXiv:2407.01254v2 Announce Type: replace Abstract: We study fibrations of the projective model for the symmetric space associated with $\text{SL}(2n,\mathbb{R})$ by codimension $2$ projective subspaces, or pencils of quadrics. In particular we show that if such a smooth fibration is equivariant with respect to a repre...
https://arxiv.org/abs/2407.01254
Academic Papers
svg
a729d7fdc8acc5167e45fb3928b9db004f90b82b5222f23508d8adc4072a3666
2026-01-21T00:00:00-05:00
Heights of Ceresa and Gross-Schoen cycles
arXiv:2407.01304v4 Announce Type: replace Abstract: We study the Beilinson-Bloch heights of Ceresa and Gross-Schoen cycles in families. We construct that for any $g\ge 3$, a Zariski open dense subset $\mathcal{M}_g^{\mathrm{amp}}$ of $\mathcal{M}_g$, the coarse moduli of curves of genus $g$ over $\mathbb{Q}$, such that...
https://arxiv.org/abs/2407.01304
Academic Papers
svg
6ee5772d80cb1cfe324e392101030b9d23d7384f36d21ce3e12db1e287e49c9d
2026-01-21T00:00:00-05:00
A uniform-in-time nonlocal approximation of the standard Fokker-Planck equation
arXiv:2407.03870v4 Announce Type: replace Abstract: We study a nonlocal approximation of the Fokker-Planck equation in which we can estimate the speed of convergence to equilibrium in a way which does not degenerate as we approach the local limit of the equation. This uniform estimate cannot be easily obtained with sta...
https://arxiv.org/abs/2407.03870
Academic Papers
svg
e5c360c4a257a1dd6263a16027957a9c0160b63aedcadce677cd878afcd3a6a5
2026-01-21T00:00:00-05:00
Lipschitz regularity for solutions to an orthotropic $q$-Laplacian-type equation in the Heisenberg group
arXiv:2407.07548v3 Announce Type: replace Abstract: We establish the local Lipschitz regularity for solutions to an orthotropic q-Laplacian-type equation within the Heisenberg group. Our approach is largely inspired by the works of X. Zhong, who investigated the q-Laplacian in the same setting and proved the H\"older r...
https://arxiv.org/abs/2407.07548
Academic Papers
svg
78d0ba9e932e7e6af11bf98db34909f045d1a15b9a29944e90646b278c41be68
2026-01-21T00:00:00-05:00
An Adaptive Proximal ADMM for Nonconvex Linearly Constrained Composite Programs
arXiv:2407.09927v3 Announce Type: replace Abstract: This paper develops an adaptive proximal alternating direction method of multipliers (ADMM) for solving linearly constrained, composite optimization problems under the assumption that the smooth component of the objective is weakly convex, while the non-smooth compone...
https://arxiv.org/abs/2407.09927
Academic Papers
svg
a96e7e8684860eeb40b25cbe4469c84ee6a9857a6bf1ab609e1afe3fe8ea62bc
2026-01-21T00:00:00-05:00
A short nonstandard proof of the Spectral Theorem for unbounded self-adjoint operators
arXiv:2407.16136v3 Announce Type: replace Abstract: By nonstandard analysis, a very short and elementary proof of the Spectral Theorem for unbounded self-adjoint operators is given.
https://arxiv.org/abs/2407.16136
Academic Papers
svg
a2a07d523065306e0e006e136dcc6f08d8fba2eaa897d8c6138bb81ee52b95a5
2026-01-21T00:00:00-05:00
Winners with Confidence: Discrete Argmin Inference with an Application to Model Selection
arXiv:2408.02060v4 Announce Type: replace Abstract: We study the problem of finding the index of the minimum value of a vector from noisy observations. This problem is relevant in population/policy comparison, discrete maximum likelihood, and model selection. We develop an asymptotically normal test statistic, even in ...
https://arxiv.org/abs/2408.02060
Academic Papers
svg
0459f75c5c630213448a67b309af75ced50a24f0cd5e7b93c152987a351a8fc2
2026-01-21T00:00:00-05:00
Long-time behaviour of a multidimensional age-dependent branching process with a singular jump kernel modelling telomere shortening
arXiv:2408.02476v2 Announce Type: replace Abstract: In this article, we investigate the ergodic behaviour of a multidimensional age-dependent branching process with a singular jump kernel, motivated by studying the phenomenon of telomere shortening in cell populations. Our model tracks individuals evolving within a con...
https://arxiv.org/abs/2408.02476
Academic Papers
svg
d2a76996468dcd69cc77493ace72910f4c1f68013c2c2e22b811cceaf78f65c1
2026-01-21T00:00:00-05:00
Poisson Approximation of prime divisors of shifted primes
arXiv:2408.03803v4 Announce Type: replace Abstract: We develop an analog for shifted primes of the Kubilius model of prime factors of integers. We prove a total variation distance estimate for the difference between the model and actual prime factors of shifted primes, and apply it to show that the prime factors of shi...
https://arxiv.org/abs/2408.03803
Academic Papers
svg
ebbda67ef2ecf50f61e2ebdab3faf6301c2b0d0a6425ce09c042a710b5c4f67b
2026-01-21T00:00:00-05:00
On a family of arithmetic series related to the M\"obius function
arXiv:2409.02754v5 Announce Type: replace Abstract: Let $P^-(n)$ denote the smallest prime factor of a natural integer $n>1$. Furthermore let $\mu$ and $\omega$ denote respectively the M\"obius function and the number of distinct prime factors function. We show that, given any set ${{\scr P}}$ of prime numbers with a n...
https://arxiv.org/abs/2409.02754
Academic Papers
svg
557f55f8fd931e205cb0d7980633291e4fa58decf8b69ef7e127aab271e47a7d
2026-01-21T00:00:00-05:00
Counting points on generic character varieties
arXiv:2409.04735v3 Announce Type: replace Abstract: We count points on character varieties associated with punctured surfaces and regular semisimple generic conjugacy classes in reductive groups. We find that the number of points are palindromic polynomials. This suggests a $P=W$ conjecture for these varieties. We also...
https://arxiv.org/abs/2409.04735
Academic Papers
svg
594cecd9a68830e7f828e14da47d0c510529020fed1f0a647deb4a76fb106faf
2026-01-21T00:00:00-05:00
A Complexity Dichotomy for Temporal Valued Constraint Satisfaction Problems
arXiv:2409.07285v2 Announce Type: replace Abstract: We study the complexity of the valued constraint satisfaction problem (VCSP) for every valued structure with the domain ${\mathbb Q}$ that is preserved by all order-preserving bijections. Such VCSPs will be called temporal, in analogy to the (classical) constraint sat...
https://arxiv.org/abs/2409.07285
Academic Papers
svg
ab3401596963694fae26a0d4e580eaba4890a3e5ca2d7910aaf9a929a721f6fb
2026-01-21T00:00:00-05:00
Matrix perturbation analysis of methods for extracting singular values from approximate singular subspaces
arXiv:2409.09187v2 Announce Type: replace Abstract: Given (orthonormal) approximations $\tilde{U}$ and $\tilde{V}$ to the left and right subspaces spanned by the leading singular vectors of a matrix $A$, we discuss methods to approximate the leading singular values of $A$ and study their accuracy. In particular, we foc...
https://arxiv.org/abs/2409.09187
Academic Papers
svg
cf4a9748a861277433e2939c1d6ccb7b7002ab7b7d9904103adbd930c81ed48b
2026-01-21T00:00:00-05:00
Averaging theory and catastrophes
arXiv:2409.11054v2 Announce Type: replace Abstract: When a dynamical system is subject to a periodic perturbation, the averaging method can be applied to obtain an autonomous leading order "guiding system", placing the time dependence at higher orders. Recent research focused on investigating invariant structures in no...
https://arxiv.org/abs/2409.11054
Academic Papers
svg
604334c839c3de3a952e59b9c0a681938ef297e55a58c23233a14a22198c72f0
2026-01-21T00:00:00-05:00
QMC integration based on arbitrary (t,m,s)-nets yields optimal convergence rates on several scales of function spaces
arXiv:2409.12879v2 Announce Type: replace Abstract: We study the integration problem over the $s$-dimensional unit cube on four types of Banach spaces of integrands. First we consider Haar wavelet spaces, consisting of functions whose Haar wavelet coefficients exhibit a certain decay behavior measured by a parameter $\...
https://arxiv.org/abs/2409.12879
Academic Papers
svg
c68c5683637690d0058e79be120cece814c1c3ebdd069364f210b47c2ad54801
2026-01-21T00:00:00-05:00
D2D Coded Caching from Two Classes of Optimal DPDAs using Cross Resolvable Designs
arXiv:2409.14350v2 Announce Type: replace Abstract: Device to device (D2D) communication is one of the most promising techniques for fifth-generation and beyond wireless communication systems. This paper considers coded caching in a wireless D2D network, in which a central server initially places the data in the user c...
https://arxiv.org/abs/2409.14350
Academic Papers
svg
cc20b8b58e0f301040c9096d47ee6cc27e353bfe14f7f2aa8af5baa4fa90dd72
2026-01-21T00:00:00-05:00
Crystallinity for syntomic cohomology, \'etale cohomology, and algebraic $K$-theory
arXiv:2409.20543v2 Announce Type: replace Abstract: We prove for $n\geq c-1$ that the functor taking an animated ring $R$ to its mod $(p^c,v_1^{p^n})$ syntomic cohomology factors through the functor $R \mapsto R/p^{c(n+2)}$, a phenomenon we term crystallinity for mod $(p^c,v_1^{p^n})$ syntomic cohomology. As an applica...
https://arxiv.org/abs/2409.20543
Academic Papers
svg
d7666bdf2688df4b94a90644400173fee799c518cc0433fb00918b512040e3bc
2026-01-21T00:00:00-05:00
Entropy contraction of the Gibbs sampler under log-concavity
arXiv:2410.00858v2 Announce Type: replace Abstract: The Gibbs sampler (a.k.a. Glauber dynamics and heat-bath algorithm) is a popular Markov Chain Monte Carlo algorithm which iteratively samples from the conditional distributions of a probability measure $\pi$ of interest. Under the assumption that $\pi$ is strongly log...
https://arxiv.org/abs/2410.00858
Academic Papers
svg
7da4827fbd09637366e4a543b273c0f57e7bec915dad9f076f685902cc89309b
2026-01-21T00:00:00-05:00
The Conjecture of Dixmier for the first Weyl algebra is true
arXiv:2410.06959v5 Announce Type: replace Abstract: Let $K$ be a field of characteristic zero, let $A_1=K[x][\partial ]$ be the first Weyl algebra. In this paper we prove that the Dixmier conjecture for the first Weyl algebra is true, i.e. each algebra endomorphism of the algebra $A_1$ is an automorphism.
https://arxiv.org/abs/2410.06959
Academic Papers
svg
890c2cd35b93813ee4ddc487e33fd60f7146d4562e7f8f53921abc8300bb6ed7
2026-01-21T00:00:00-05:00
Uniform Space and Time Behavior for Acoustic Resonators
arXiv:2410.09630v2 Announce Type: replace Abstract: We deal with the time-domain acoustic wave propagation in the presence of a subwavelength resonator given by a Minneart bubble. This bubble is small scaled and enjoys high contrasting mass density and bulk modulus. It is well known that, under certain regimes between ...
https://arxiv.org/abs/2410.09630
Academic Papers
svg
ae00040ad34421ee4d1e7ea34b0c1c00da4101aa60630f6311d1685d1d5326a3
2026-01-21T00:00:00-05:00
Safety on the Fly: Constructing Robust Safety Filters via Policy Control Barrier Functions at Runtime
arXiv:2410.11157v3 Announce Type: replace Abstract: Control Barrier Functions (CBFs) have proven to be an effective tool for performing safe control synthesis for nonlinear systems. However, guaranteeing safety in the presence of disturbances and input constraints for high relative degree systems is a difficult problem...
https://arxiv.org/abs/2410.11157
Academic Papers
svg
b372d9e799309ccde34a4256c0c6024408d8a635ba3d09bab0510dbcd435a917
2026-01-21T00:00:00-05:00
Subspace method based on neural networks for eigenvalue problems
arXiv:2410.13358v2 Announce Type: replace Abstract: In this paper, we propose a subspace method based on neural networks for eigenvalue problems with high accuracy and low cost. We first construct a neural network-based orthogonal basis by some deep learning method and dimensionality reduction technique, and then calcu...
https://arxiv.org/abs/2410.13358
Academic Papers
svg
9c5847bfe22097083f7bfd73e87345164e14d5e9b91c3cb351bf7e720c2c2081
2026-01-21T00:00:00-05:00
Two-stage Online Reusable Resource Allocation: Reservation, Overbooking and Confirmation Call
arXiv:2410.15245v2 Announce Type: replace Abstract: We study a two-stage online reusable resource allocation problem over T days involving advance reservations and walk-ins. Each day begins with a reservation stage (Stage I), where reservation requests arrive sequentially. When service starts (Stage II), both reserved ...
https://arxiv.org/abs/2410.15245
Academic Papers
svg
4d240dcb25339b0115e5d03e190e01366114c7594f53a1346d5462ee3ad39736
2026-01-21T00:00:00-05:00
Entrance boundary for standard processes with no negative jumps and its application to exponential convergence to the Yaglom limit
arXiv:2410.15447v3 Announce Type: replace Abstract: We study standard processes with no negative jumps under the entrance boundary condition. Similarly to one-dimensional diffusions, we show that the process can be made into a Feller process by attaching the boundary point to the state space. We investigate the spectru...
https://arxiv.org/abs/2410.15447
Academic Papers
svg
984e44617fe2e5c64355fdf20026c01f5ce2218aacd3ccf3b4410249b6b9b0a1
2026-01-21T00:00:00-05:00
Information-Based Martingale Optimal Transport
arXiv:2410.16339v3 Announce Type: replace Abstract: Randomised arcade processes are a class of continuous stochastic processes that interpolate in a strong sense, i.e., omega by omega, between any given ordered set of random variables, at fixed pre-specified times. Utilising these processes as generators of partial inf...
https://arxiv.org/abs/2410.16339
Academic Papers
svg
faad20a8ec7d1d64537abcb94124d2b1ef3d3b3af1d5aebf91607d6fa00d1bde
2026-01-21T00:00:00-05:00
Polynomials with exponents in compact convex sets and associated weighted extremal functions -- Approximations and regularity
arXiv:2410.20370v3 Announce Type: replace Abstract: We study various regularization operators on plurisubharmonic functions that preserve Lelong classes with growth given by certain compact convex sets. The purpose is to show that the weighted Siciak-Zakharyuta functions associated with these Lelong classes are lower s...
https://arxiv.org/abs/2410.20370
Academic Papers
svg
9b1c324ce891e6b4c78f879fef3f812f3b68b13794d9947e2e1dd9d5dcf44b98
2026-01-21T00:00:00-05:00
Erd\H{o}s-P\'osa property of $A$-paths in unoriented group-labelled graphs
arXiv:2411.05372v2 Announce Type: replace Abstract: We characterize the obstructions to the Erd\H{o}s-P\'osa property of $A$-paths in unoriented group-labelled graphs. As a result, we prove that for every finite abelian group $\Gamma$ and for every subset $\Lambda$ of $\Gamma$, the family of $\Gamma$-labelled $A$-paths...
https://arxiv.org/abs/2411.05372
Academic Papers
svg
45473decdfc9503d84d528f7d58fa42291c27691cbf27e2a5dc34d82a3b71111
2026-01-21T00:00:00-05:00
Torsion and semi-degeneracy of second-order maximally superintegrable systems
arXiv:2411.06994v3 Announce Type: replace Abstract: The isotropic harmonic oscillator and the Kepler-Coulomb system are pivotal models in the Sciences. They are two examples of second-order (maximally) superintegrable (Hamiltonian) systems. These systems are classified in dimension two. A partial classification exists ...
https://arxiv.org/abs/2411.06994
Academic Papers
svg
51e9459a87db9efbb2b50100e371086a380bdfa9bd5e65be0f5eda88b7c3a7f4
2026-01-21T00:00:00-05:00
Accelerating Benders decomposition for solving a sequence of sample average approximation replications
arXiv:2411.09091v2 Announce Type: replace Abstract: Sample average approximation (SAA) is a technique for obtaining approximate solutions to stochastic programs that uses the average from a random sample to approximate the expected value that is being optimized. Since the outcome from solving an SAA is random, statisti...
https://arxiv.org/abs/2411.09091
Academic Papers
svg
3d2bf155f37135aebf41fd6a98b67e9a155d91b28cd310655b85538f4b70cb5c
2026-01-21T00:00:00-05:00
Harmonic forms on ALE Ricci-flat 4-manifolds
arXiv:2411.09561v4 Announce Type: replace Abstract: In this paper, we compute the expansion of some harmonic functions and 1-forms on ALE Ricci-flat 4-manifolds.
https://arxiv.org/abs/2411.09561
Academic Papers
svg
30e2635a414d5b91876c3502cd348a4866913263b12053a063af2f4f81965881
2026-01-21T00:00:00-05:00
Equivalent spectral theory for fundamental graph cut problems
arXiv:2411.11077v2 Announce Type: replace Abstract: We introduce and develop equivalent spectral graph theory for several fundamental graph cut problems including maxcut, mincut, Cheeger cut, anti-Cheeger cut, dual Cheeger problem and their useful variants. A specified strategy for achieving an equivalent eigenproblem ...
https://arxiv.org/abs/2411.11077
Academic Papers
svg
ac0b10721f2ef0af9036feb12f84bb525195d77180ec87e8a96c033969361607
2026-01-21T00:00:00-05:00
A star is born: Explosive Crump-Mode-Jagers branching processes
arXiv:2411.18749v2 Announce Type: replace Abstract: We study a family of Crump--Mode--Jagers branching processes in random environment that explode, i.e. that grow infinitely large in finite time with positive probability. Building on recent work of the author and Iyer (``On the structure of genealogical trees associat...
https://arxiv.org/abs/2411.18749
Academic Papers
svg
a50104d1742cdc75153aeaca8553b177419be51ba2540a55d322f61cbaf60cb0
2026-01-21T00:00:00-05:00
Characterization of Trees with Maximum Security
arXiv:2411.19188v3 Announce Type: replace Abstract: The rank (also known as protection number or leaf-height) of a vertex in a rooted tree is the minimum distance between the vertex and any of its leaf descendants. We consider the sum of ranks over all vertices (known as the security) in binary trees, and produce a cla...
https://arxiv.org/abs/2411.19188
Academic Papers
svg
e3a71464e325e7df4a875be521170b18bc216efb7c09970853474173bc4e2381
2026-01-21T00:00:00-05:00
Arithmetic level raising theorem for some unitary Shimura varieties mod $p$
arXiv:2412.03519v4 Announce Type: replace Abstract: Let $F$ be a real quadratic field in which a fixed prime $p$ is inert, and $E_0$ be an imaginary quadratic field in which $p$ splits; put $E=E_0 F$. Let ${{\rm Sh}}_{1,n-1}$ be the special fiber over $\mathbb{F}_{p^2}$ of the Shimura variety for $G(U(1,n-1)\times U(n-...
https://arxiv.org/abs/2412.03519
Academic Papers
svg
13dd3dbc2e64f0f7aaacfb74ffea61f7f798b6acc6e59e2e4418261cd7664f21
2026-01-21T00:00:00-05:00
Rational First Integrals and Relative Killing Tensors
arXiv:2412.04151v2 Announce Type: replace Abstract: We relate rational integrals of the geodesic flow of a (pseudo-)Riemannian metric to relative Killig tensors, describe the spaces they span and discuss upper bounds on their dimensions.
https://arxiv.org/abs/2412.04151
Academic Papers
svg
233c2ade977ea7e338aac5aa1e54272d7238f9ce009a7270fe7b5725c4550618
2026-01-21T00:00:00-05:00
MPAX: Mathematical Programming in JAX
arXiv:2412.09734v3 Announce Type: replace Abstract: We present MPAX (Mathematical Programming in JAX), an open-source first-order solver for large-scale linear programming (LP) and convex quadratic programming (QP) built natively in JAX. The primary goal of MPAX is to exploit modern machine learning infrastructure for ...
https://arxiv.org/abs/2412.09734
Academic Papers
svg
8a6cb5844705bc50fdb43b5159e39283687bec86d52a5fdb6a1a26c20f80f654
2026-01-21T00:00:00-05:00
Finite type as fundamental objects even non-single-valued and non-continuous
arXiv:2412.11675v5 Announce Type: replace Abstract: In this paper, inspired by the elegant work of Good and Meddaugh \cite{GM} and the graph models for zero-dimensional systems developed by several authors, like Gambaudo and Martens \cite{GM06}, Shimomura \cite{Sh14}. We try to discover a connection among some objects,...
https://arxiv.org/abs/2412.11675
Academic Papers
svg
a9caf223f639cd5cf00bb3c6c8b9ef7c6dc32b973199063966cddc0793bbac23
2026-01-21T00:00:00-05:00
Rare events statistics for $\mathbb Z^d$ map lattices coupled by collision
arXiv:2412.12803v3 Announce Type: replace Abstract: Understanding the statistics of collisions among locally confined gas particles poses a major challenge. In this work we investigate $\mathbb Z^d$-map lattices coupled by collision with simplified local dynamics that offer significant insights for the above challengin...
https://arxiv.org/abs/2412.12803
Academic Papers
svg
dd1dd82c5c073b5726ef7802fd603fb9d669cc64c69734b7d4109a1b22aac9a5
2026-01-21T00:00:00-05:00
On some Sobolev and P\'olya-Szeg\"o type inequalities with weights and applications
arXiv:2412.15490v3 Announce Type: replace Abstract: We are motivated by studying a boundary-value problem for a class of semilinear degenerate elliptic equations \begin{align}\tag{P}\label{P} \begin{cases} - \Delta_x u - |x|^{2\alpha} \dfrac{\partial^2 u}{\partial y^2} = f(x,y,u), & \textrm{in } \Omega, u = 0, & \textr...
https://arxiv.org/abs/2412.15490
Academic Papers
svg
bbf6b846d7a321919d7e466981468ab8393d96ae08d48e5c2544e8a862d2812e
2026-01-21T00:00:00-05:00
On the ergodicity of anti-symmetric skew products with singularities and its applications
arXiv:2412.21067v2 Announce Type: replace Abstract: We introduce a novel method for proving ergodicity for skew products of interval exchange transformations (IETs) with piecewise smooth cocycles having singularities at the ends of exchanged intervals. This approach is inspired by Borel-Cantelli-type arguments from Fay...
https://arxiv.org/abs/2412.21067
Academic Papers
svg
95a81a680e0773a11d5554743245da879486fb840dc3acdc89880a2ff8d6196f
2026-01-21T00:00:00-05:00
Subspaces of $L^2(\mathbb{R}^n)$ Invariant Under Crystallographic Shifts
arXiv:2501.02130v2 Announce Type: replace Abstract: In this thesis we consider crystal groups in dimension $n$ and their natural unitary representation on $L^2(\mathbb{R}^n)$. We show that this representation is unitarily equivalent to a direct integral of factor representations, and use this to characterize the subspa...
https://arxiv.org/abs/2501.02130
Academic Papers
svg
9a83075ffb772c411b836351555b3bd62c7ab010f4ddeda3e415d870e2f141ab
2026-01-21T00:00:00-05:00
Towards a constructive framework for control theory
arXiv:2501.02267v2 Announce Type: replace Abstract: This work presents a framework for control theory based on constructive analysis to account for discrepancy between mathematical results and their implementation in a computer, also referred to as computational uncertainty. In control engineering, the latter is usuall...
https://arxiv.org/abs/2501.02267
Academic Papers
svg
34a66b600952fd1b4cbc683f6421b6b993be1053458d9d1294e9e083787d99ec
2026-01-21T00:00:00-05:00
The{N/D}-Conjecture for Nonresonant Hyperplane Arrangements
arXiv:2501.05189v3 Announce Type: replace Abstract: This paper studies Bernstein--Sato polynomials $b_{f,0}$ for homogeneous polynomials $f$ of degree $d$ with $n$ variables. It is open to know when $-{n\over d}$ is a root of $b_{f,0}$. For essential indecomposable hyperplane arrangements, this is a conjecture by Budur...
https://arxiv.org/abs/2501.05189
Academic Papers
svg