Tootfinder

The Hidden Rules Behind Rust Functions & Closures
Demystifying fn, Fn, FnMut, and FnOnce from everyday usage to compiler magic under the hood
🦀 https://blog.cuongle.dev/p/the-hidden-rules-behind-rust-functions

The Hidden Rules Behind Rust Functions & Closures
Demystifying fn, Fn, FnMut, and FnOnce from everyday usage to compiler magic under the hood

Transition Matrices between Plethystic Bases of Polysymmetric Functions via Bijective Methods
Aditya Khanna
https://arxiv.org/abs/2510.12723 https://arxiv.…

Transition Matrices between Plethystic Bases of Polysymmetric Functions via Bijective Methods
Many identities involving symmetric functions can be proved through bijective manipulations of tableaux. In this paper, we prove identities involving polysymmetric functions through bijections and sign-reversing involutions. In their paper titled "Polysymmetric functions and motivic measures of configuration spaces", Asvin G and Andrew O'Desky introduced the algebra of polysymmetric functions (PSym) which can be defined as the tensor product of copies of the symmetric functions algebra (Sym) wh…

Appell Functions for General Lattices
Aradhita Chattopadhyaya, Jan Manschot
https://arxiv.org/abs/2510.10204 https://arxiv.org/pdf/2510.10204

Appell Functions for General Lattices
We study Appell functions associated to an arbitrary positive definite lattice $Λ$ and a choice of $M\leq {\rm dim}(Λ)$ linearly independent vectors $d_r\in Λ$, $r=1,\dots,M$. These functions are instances of multi-variable quasi-elliptic functions, and specific examples have appeared at various places in mathematics and theoretical physics. For example, if $Λ$ is chosen to be one-dimensional, these functions reduce to the classical Appell function, which is a prominent example in the theor…

Lets be honest, we spend too much time cleaning data. {janitor} can help with that: #rstats #datasciece

Euclidean Correlation Functions in Quantum Gravity
Jack Laiho, Kenny Ratliff
https://arxiv.org/abs/2510.11888 https://arxiv.org/pdf/2510.11888

Euclidean Correlation Functions in Quantum Gravity
We calculate Euclidean correlation functions through next-to-leading order in the low energy effective theory of gravity. We focus on correlation functions of curvature and volume operators, calculating these functions through one-loop order. We show that quantum fluctuations of the background spacetime must be taken into account in order to obtain gauge invariant expressions, and we point out a subtlety associated with the analytic continuation of the conformal mode. Our final expressions for …

Probabilistic Links Between Quantum Classification of Patterns of Boolean Functions and Hamming Distance
Theodore Andronikos, Constantinos Bitsakos, Konstantinos Nikas, Georgios I. Goumas, Nectarios Koziris
https://arxiv.org/abs/2510.12736

Probabilistic Links Between Quantum Classification of Patterns of Boolean Functions and Hamming Distance
This article investigates the probabilistic relationship between quantum classification of Boolean functions and their Hamming distance. By integrating concepts from quantum computing, information theory, and combinatorics, we explore how Hamming distance serves as a metric for analyzing deviations in function classification. Our extensive experimental results confirm that the Hamming distance is a pivotal metric for validating nearest neighbors in the process of classifying random functions. O…

Fascinating talk on "Compiling with Generating Functions"
Presented by Jianlin Li, joint work with Yizhou Zhang.
#icfpsplash25

Division algebras of slice-Nash functions
Cinzia Bisi, Antonio Carbone
https://arxiv.org/abs/2510.09779 https://arxiv.org/pdf/2510.09779

Division algebras of slice-Nash functions
The purpose of this paper is to introduce the notion of Nash functions in the context of slice regular functions of one quaternionic or octonionic variable. We begin with a detailed analysis of the possible definitions of Nash slice regular functions which leads us to the definition of \textit{slice-Nash} function proposed in this paper (and which we strongly believe to be the natural generalisation of the classical real and complex Nash functions to this context). Once the `correct' definition…

DE-Sinc approximation for unilateral rapidly decreasing functions and its computational error bound
Tomoaki Okayama
https://arxiv.org/abs/2510.11411 https://

DE-Sinc approximation for unilateral rapidly decreasing functions and its computational error bound
The Sinc approximation is known to be a highly efficient approximation formula for rapidly decreasing functions. For unilateral rapidly decreasing functions, which rapidly decrease as $x\to\infty$ but does not as $x\to-\infty$, an appropriate variable transformation makes the functions rapidly decreasing. As such a variable transformation, Stenger proposed $t = \sinh(\log(\operatorname{arsinh}(\exp x)))$, which enables the Sinc approximation to achieve root-exponential convergence. Recently, an…

Reinforced sequential Monte Carlo for amortised sampling
Sanghyeok Choi, Sarthak Mittal, V\'ictor Elvira, Jinkyoo Park, Nikolay Malkin
https://arxiv.org/abs/2510.11711 https…

Reinforced sequential Monte Carlo for amortised sampling
This paper proposes a synergy of amortised and particle-based methods for sampling from distributions defined by unnormalised density functions. We state a connection between sequential Monte Carlo (SMC) and neural sequential samplers trained by maximum-entropy reinforcement learning (MaxEnt RL), wherein learnt sampling policies and value functions define proposal kernels and twist functions. Exploiting this connection, we introduce an off-policy RL training procedure for the sampler that uses …

On Korovkin-type theorems including exponential test functions on infinite intervals through power series convergence
Dilek S\"oylemez, Mehmet \"Unver
https://arxiv.org/abs/2510.12568

On Korovkin-type theorems including exponential test functions on infinite intervals through power series convergence
Approximation theory has long been concerned with the development of positive linear operators that effectively approximate classes of functions. Among the most well-known results in this area are Korovkin-type approximation theorems, which provide simple and elegant criteria for convergence by testing only on a small set of functions. Motivated by these classical results and their extensions, we focus on versions that preserve exponential functions and incorporate modern summability techniques…

Properties of generalized Jacobi elliptic functions with three parameters
Hajime Sato, Nagi Suzuki, Shingo Takeuchi
https://arxiv.org/abs/2510.11443 https://

Properties of generalized Jacobi elliptic functions with three parameters
Jacobi elliptic functions and complete elliptic integrals are generalized using three parameters. These generalized functions and integrals are closely related to ordinary differential equations involving $p$-Laplacian. In this paper, Wallis-type integral formulae are constructed for the generalized Jacobi elliptic functions. Moreover, for the generalized complete elliptic integrals, a Legendre-type relation is derived, which is equivalent to Elliott's identity for Gaussian hypergeometric serie…

On the Walsh spectra of quadratic APN functions
Sophie Hannah B\'en\'eteau, Nicolas Goluboff, Lukas K\"olsch, Divyesh Vaghasiya
https://arxiv.org/abs/2510.12008 htt…

On the Walsh spectra of quadratic APN functions
APN functions play a central role as building blocks in the design of many block ciphers, serving as optimal functions to resist differential attacks. One of the most important properties of APN functions is their linearity, which is directly related to the Walsh spectrum of the function. In this paper, we establish two novel connections that allow us to derive strong conditions on the Walsh spectra of quadratic APN functions. We prove that the Walsh transform of a quadratic APN function $F$ op…

congrats to the authors of RFC 9861, which "defines four eXtendable-Output Functions (#XOFs), hash functions with output of arbitrary length, named #TurboSHAKE128, #TurboSHAKE256, KT128, and KT256.…

New Classes of Non-monotone Variational Inequality Problems Solvable via Proximal Gradient on Smooth Gap Functions
Lei Zhao, Daoli Zhu, Shuzhong Zhang
https://arxiv.org/abs/2510.12105

New Classes of Non-monotone Variational Inequality Problems Solvable via Proximal Gradient on Smooth Gap Functions
In this paper, we study the local linear convergence behavior of proximal-gradient (PG) descent algorithm on a parameterized gap-function reformulation of a smooth but non-monotone variational inequality problem (VIP). The aim is to solve the non-monotone VI problem without assuming the existence of a Minty-type solution. We first introduce and study various error bound conditions for the gap functions in relation to the VI model. In particular, we show that uniform type error bounds imply leve…

Designing Control Barrier Functions Using a Dynamic Backup Policy
Victor Freire, Marco M. Nicotra
https://arxiv.org/abs/2510.09810 https://arxiv.org/pdf/25…

Designing Control Barrier Functions Using a Dynamic Backup Policy
This paper presents a systematic approach to construct control barrier functions for nonlinear control affine systems subject to arbitrary state and input constraints. Taking inspiration from the reference governor literature, the proposed method defines a family of backup policies, parametrized by the equilibrium manifold of the system. The control barrier function is defined on the augmented state-and-reference space: given a state-reference pair, the approach quantifies the distance to const…

Continuous Inverse Ambiguous Functions on Lie Groups
David Schmitz, Sadman Rahman, Anthony Kindness
https://arxiv.org/abs/2510.09958 https://arxiv.org/pdf/…

Continuous Inverse Ambiguous Functions on Lie Groups
In a previous study, the first author defines an inverse ambiguous function on a group $G$ to be a bijective function $f : G \to G$ satisfying the functional equation $f^{-1}(x) = f(x^{-1})$ for all $x \in G$. In this paper, we investigate the existence of continuous inverse ambiguous functions on classical Lie groups. In particular, we look at tori, elliptic curves over various fields, vector spaces, additive matrix groups, and multiplicative matrix groups.

Approximate Proximal Operators for Analog Compressed Sensing Using PN-junction Diode
Soma Furusawa, Taisei Kato, Ryo Hayakawa, Kazunori Hayashi
https://arxiv.org/abs/2510.12065 …

Approximate Proximal Operators for Analog Compressed Sensing Using PN-junction Diode
In order to realize analog compressed sensing, the paper considers approximate proximal operators of the $\ell_1$ and minimax concave penalty (MCP) regularization functions. Specifically, we propose to realize the approximate functions by an electric analog circuit using forward voltage-current (V-I) characteristics of the PN-junction diodes. To confirm the validity of the proposed approach, we employ the proposed approximate proximal operators for the $\ell_1$ and MCP regularization functions …

SLD-Spec: Enhancement LLM-assisted Specification Generation for Complex Loop Functions via Program Slicing and Logical Deletion
Zehan Chen, Long Zhang, Zhiwei Zhang, JingJing Zhang, Ruoyu Zhou, Yulong Shen, JianFeng Ma, Lin Yang
https://arxiv.org/abs/2509.09917

SLD-Spec: Enhancement LLM-assisted Specification Generation for Complex Loop Functions via Program Slicing and Logical Deletion
Automatically generating formal specifications from program code can greatly enhance the efficiency of program verification and enable end-to-end automation from requirements to reliable software. However, existing LLM-based approaches often struggle with programs that include complex loop structures, leading to irrelevant specifications. Moreover, the rigorous proof obligations and design constraints imposed by verification tools can further result in incomplete and ambiguous specifications. T…

On real functions with graphs either connected or locally connected
Gerald Kuba
https://arxiv.org/abs/2510.12450 https://arxiv.org/pdf/2510.12450

On real functions with graphs either connected or locally connected
Let S denote the family of all subspaces of the plane that are graphs of functions from the real line R to itself. We prove that S has two subfamilies G,H of spaces such that the cardinality of G is c (the cardinality of the continuum) and the cardinality of H is 2^c, every space in the family G is completely metrizable, each element of H is a dense subset of the plane and the elements of the union of G and H are pairwise non-embeddable (i.p. pairwise non-homeomorphic) subspaces of the plane. O…

Entropy and Learning of Lipschitz Functions under Log-Concave Measures
Pierre Bizeul, Boaz Klartag
https://arxiv.org/abs/2509.10355 https://arxiv.org/pdf/2…

Entropy and Learning of Lipschitz Functions under Log-Concave Measures
We study regression of $1$-Lipschitz functions under a log-concave measure $μ$ on $\mathbb{R}^d$. We focus on the high-dimensional regime where the sample size $n$ is subexponential in $d$, in which distribution-free estimators are ineffective. We analyze two polynomial-based procedures: the projection estimator, which relies on knowledge of an orthogonal polynomial basis of $μ$, and the least-squares estimator over low-degree polynomials, which requires no knowledge of $μ$ whatsoever. Their…

from my link log —
A bestiary of mathematical functions for systems designers.
https://brunodias.dev/2021/03/19/functions-for-system-designers.html
saved 2021-03-19

The new Affinity editor is a bit disappointing. There are some AI functions, like "remove background,” that seem to be gated behind a paywall. Feels like a pretty basic feature :\

$L$-functions of elliptic curves in ring class extensions of real quadratic fields via regularized theta liftings
Jeanine Van Order
https://arxiv.org/abs/2510.10277 https://

$L$-functions of elliptic curves in ring class extensions of real quadratic fields via regularized theta liftings
We derive new integral presentations for central derivative values of $L$-functions of elliptic curves defined over the rationals, basechanged to a real quadratic field $K$, twisted by ring class characters of $K$ in terms of sums along ``geodesics" corresponding to the class group of $K$ of automorphic Green's functions for certain Hirzebruch-Zagier-like arithmetic divisors on Hilbert modular surfaces. We also relate these sums to Birch-Swinnerton-Dyer constants and periods.

Sparse modeling study of extracting charmonium spectral functions from lattice QCD at finite temperature
Junichi Takahashi, Hiroshi Ohno, Akio Tomiya
https://arxiv.org/abs/2509.10386

Sparse modeling study of extracting charmonium spectral functions from lattice QCD at finite temperature
We present spectral functions extracted from Euclidean-time correlation functions using sparse modeling (SpM). SpM solves inverse problems by considering only the sparsity of the target solution. To assess the applicability of the method, we first test it with mock data that mimic charmonium correlation functions. We show that, while resonance peaks in the spectral functions can be reconstructed using this method, it is difficult to reconstruct transport peaks without further assumptions beyond…

Zeros of Holomorphic Functions in Commuting and Non-commuting Variables as Spectral Data
Poornendu Kumar, Jeet Sampat
https://arxiv.org/abs/2510.12718 https://

Zeros of Holomorphic Functions in Commuting and Non-commuting Variables as Spectral Data
We characterize the zero sets of functions in the Schur--Agler class over the unit polydisk as well as functions in the unit ball of the multiplier algebra of the Drury--Arveson space via operators associated with a unitary realization formula for these functions. To this end, new notions of `eigenvalues' for tuples of operators are introduced, where the eigenvalues depend on the operator space structure of the ambient domain. Several examples showcasing the properties of these eigenvalues and …

Linear fractional relative risk aversion
Kristian Behrens, Yasusada Murata
https://arxiv.org/abs/2509.09865 https://arxiv.org/pdf/2509.09865

Linear fractional relative risk aversion
We characterize the family of utility functions satisfying linear fractional relative risk aversion (LFRRA) in terms of the Gauss hypergeometric functions. We apply this family, which nests various utility functions used in different strands of literature, to monopolistic competition and obtain a closed-form solution for the profit-maximizing price by generalizing the Lambert W function. We let firm-level data decide whether the RRA in each sector or in the aggregate economy is increasing, decr…

Universal behaviors of the multi-time correlation functions of random processes with renewal: the step noise case (the random velocity of a L\'evy walk)
Marco Bianucci, Mauro Bologna, Daniele Lagomarsino-Oneto, Riccardo Mannella
https://arxiv.org/abs/2510.11747

Universal behaviors of the multi-time correlation functions of random processes with renewal: the step noise case (the random velocity of a Lévy walk)
Stochastic processes with renewal properties are powerful tools for modeling systems where memory effects and long-time correlations play a significant role. In this work, we study a broad class of renewal processes where a variable's value changes according to a prescribed Probability Density Function (PDF), $p(ξ)$, after random waiting times $θ$. This model is relevant across many fields, including classical chaos, nonlinear hydrodynamics, quantum dots, cold atom dynamics, biological motion…

Accelerated prediction of dielectric functions in solar cell materials with graph neural networks
Caden Ginter, Kamal Choudhary, Subhasish Mandal
https://arxiv.org/abs/2510.08738

Accelerated prediction of dielectric functions in solar cell materials with graph neural networks
We present an atomistic line graph neural network (ALIGNN) model for predicting dielectric functions directly from crystal structures. Trained on $\sim$7000 dielectric functions from the JARVIS-DFT database computed with a meta-GGA exchange-correlation functional, the model accurately reproduces spectral features, including peak intensities and overall line shapes, while enabling efficient high-throughput screening. Applied to the recently developed Alexandria materials database, containing ove…

From Morse Functions to Lefschetz Fibrations on Cotangent Bundles
Emmanuel Giroux
https://arxiv.org/abs/2510.10669 https://arxiv.org/pdf/2510.10669

From Morse Functions to Lefschetz Fibrations on Cotangent Bundles
We prove that, for any Morse function on a compact manifold and any adapted gradient satisfying the Morse-Smale condition, there is a homotopically unique complex-valued symplectic Lefschetz fibration on the cotangent bundle whose restriction to the zero-section is the given function, whose imaginary part is the evaluation of covectors on the gradient, and which is equivariant under the actions of the fiberwise antipodal involution and the complex conjugation. Then we study the topology and sym…

{testthat} is great for automatic testing. Here are some tricks for the heavy user: #rstats

Gravitational lensing by Lema\^{\i}tre-Tolman-Bondi wormholes in a Friedmann universe
Kirill A. Bronnikov, Valeria A. Ishkaeva, Sergey V. Sushkov
https://arxiv.org/abs/2509.09797

Gravitational lensing by Lema\^ıtre-Tolman-Bondi wormholes in a Friedmann universe
The Lema\^ıtre-Tolman-Bondi (LTB) solution to the Einstein equations describes the dynamics of a self-gravitating spherically symmetric dust cloud with an arbitrary density profile and any distribution of initial velocities, encoded in three arbitrary functions $f(R)$, $F(R)$, and $τ_0(R)$, where $R$ is a radial coordinate in the comoving reference frame. A particular choice of these functions corresponds to a wormhole geometry with a throat defined as a sphere of minimum radius at a fixed ti…

Fast and Interpretable Protein Substructure Alignment via Optimal Transport
Zhiyu Wang, Bingxin Zhou, Jing Wang, Yang Tan, Weishu Zhao, Pietro Li\`o, Liang Hong
https://arxiv.org/abs/2510.11752

Fast and Interpretable Protein Substructure Alignment via Optimal Transport
Proteins are essential biological macromolecules that execute life functions. Local motifs within protein structures, such as active sites, are the most critical components for linking structure to function and are key to understanding protein evolution and enabling protein engineering. Existing computational methods struggle to identify and compare these local structures, which leaves a significant gap in understanding protein structures and harnessing their functions. This study presents PLAS…

Service Function Chaining Architecture for Multi-hop Split Inference and Learning
Takanori Hara, Masahiro Sasabe
https://arxiv.org/abs/2509.10001 https://a…

Service Function Chaining Architecture for Multi-hop Split Inference and Learning
Service Function Chaining (SFC) is a networking technique that ensures traffic traverses a predefined sequence of service functions, realizing arbitrary network services through dynamic and efficient communication paths. Inspired by this concept, we propose an SFC-based architecture for Multi-hop Split Inference (MSI), where split sub-models are interpreted as service functions and their composition forms a service chain representing the global model. By leveraging SFC, the proposed architectur…

On the $v$-adic values of G-functions II
Georgios Papas
https://arxiv.org/abs/2510.11814 https://arxiv.org/pdf/2510.11814

On the $v$-adic values of G-functions II
This is the second in a series of papers by the author centered around the study of values of G-functions associated to $1$-parameter families of abelian varieties $f:\CX\rightarrow S$ and a point $s_0\in S(K)$ with smooth fiber over some number field $K$. Here we study the case where $f:\CX\rightarrow S$ is a family of elliptic curves. We construct relations among the values of G-functions in this setting at points whose fiber is a CM elliptic curve. These lead to bounds for the height of su…

Loop functions of sunset graphs in 2 1 space-time dimensions
N. Kaiser
https://arxiv.org/abs/2510.08704 https://arxiv.org/pdf/2510.08704

Loop functions of sunset graphs in 2+1 space-time dimensions
In these notes the relativistic $n$-body phase-phase is calculated iteratively in $2+1$ space-time dimensions for all $n$. The obtained result shows a simple power-law behavior $α_n (μ-M)^{n-2}/μ$ with a dependence only on the total mass $M=m_1+\dots + m_n$. As a consequence of this feature, the $(n-1)$-loop integrals $J_n(-q^2)$ associated to sunset graphs with $n$ internal lines can be expressed through of elementary (arctangent and logarithmic) functions, modulo polynomial terms in $q^2$ …

Computing Safe Control Inputs using Discrete-Time Matrix Control Barrier Functions via Convex Optimization
James Usevitch, Juan Augusto Paredes Salazar, Ankit Goel
https://arxiv.org/abs/2510.09925

Computing Safe Control Inputs using Discrete-Time Matrix Control Barrier Functions via Convex Optimization
Control barrier functions (CBFs) have seen widespread success in providing forward invariance and safety guarantees for dynamical control systems. A crucial limitation of discrete-time formulations is that CBFs that are nonconcave in their argument require the solution of nonconvex optimization problems to compute safety-preserving control inputs, which inhibits real-time computation of control inputs guaranteeing forward invariance. This paper presents a novel method for computing safety-prese…

Construction of Basis Functions for the Geometry Conforming Immersed Finite Element Method
Slimane Adjerid, Tao Lin, Haroun Meghaichi
https://arxiv.org/abs/2510.12018 https://…

Construction of Basis Functions for the Geometry Conforming Immersed Finite Element Method
The Frenet apparatus is a new framework for constructing high order geometry-conforming immersed finite element functions for interface problems. In this report, we present a procedure for constructing the local IFE bases in some detail as well as a new approach for constructing orthonormal bases using the singular value decomposition of the local generalized Vandermonde matrix. A sample implementation in MATLAB is provided to showcase the simplicity and extensionability of the framework.

How well can LLMs provide planning feedback in grounded environments?
Yuxuan Li, Victor Zhong
https://arxiv.org/abs/2509.09790 https://arxiv.org/pdf/2509.0…

How well can LLMs provide planning feedback in grounded environments?
Learning to plan in grounded environments typically requires carefully designed reward functions or high-quality annotated demonstrations. Recent works show that pretrained foundation models, such as large language models (LLMs) and vision language models (VLMs), capture background knowledge helpful for planning, which reduces the amount of reward design and demonstrations needed for policy learning. We evaluate how well LLMs and VLMs provide feedback across symbolic, language, and continuous c…

A minimal and universal representation of fermionic wavefunctions (fermions = bosons one)
Liang Fu
https://arxiv.org/abs/2510.11431 https://arxiv.org/pdf…

A minimal and universal representation of fermionic wavefunctions (fermions = bosons + one)
Representing fermionic wavefunctions efficiently is a central problem in quantum physics, chemistry and materials science. In this work, we introduce a universal and exact representation of continuous antisymmetric functions by lifting them to continuous symmetric functions defined on an enlarged space. Building on this lifting, we obtain a \emph{parity-graded representation} of fermionic wavefunctions, expressed in terms of symmetric feature variables that encode particle configuration and ant…

CodePlot-CoT: Mathematical Visual Reasoning by Thinking with Code-Driven Images
Chengqi Duan, Kaiyue Sun, Rongyao Fang, Manyuan Zhang, Yan Feng, Ying Luo, Yufang Liu, Ke Wang, Peng Pei, Xunliang Cai, Hongsheng Li, Yi Ma, Xihui Liu
https://arxiv.org/abs/2510.11718

CodePlot-CoT: Mathematical Visual Reasoning by Thinking with Code-Driven Images
Recent advances in Large Language Models (LLMs) and Vision Language Models (VLMs) have shown significant progress in mathematical reasoning, yet they still face a critical bottleneck with problems requiring visual assistance, such as drawing auxiliary lines or plotting functions to solve the problems. Most LLMs and VLMs are constrained to text-only reasoning chains, while multimodal unified models that can generate interleaved text and images lack the necessary precision and controllability for…

Exploiting higher-order correlation functions for photon-statistics-based characterization and reconstruction of arbitrary Gaussian states
Philip Heinzel, Ren\'e Sondenheimer
https://arxiv.org/abs/2510.09083

Exploiting higher-order correlation functions for photon-statistics-based characterization and reconstruction of arbitrary Gaussian states
Gaussian states are an essential building block for various applications in quantum optics and quantum information science, yet the precise relation between their second- and third-order correlation functions remains not fully explored. We discuss connections between these correlation functions by constructing an explicit decomposition formula for arbitrary sixth-order moments of ladder operators for general Gaussian states and demonstrate how the derived relations enable state classification f…

!MSA at BAREC Shared Task 2025: Ensembling Arabic Transformers for Readability Assessment
Mohamed Basem, Mohamed Younes, Seif Ahmed, Abdelrahman Moustafa
https://arxiv.org/abs/2509.10040

!MSA at BAREC Shared Task 2025: Ensembling Arabic Transformers for Readability Assessment
We present MSAs winning system for the BAREC 2025 Shared Task on fine-grained Arabic readability assessment, achieving first place in six of six tracks. Our approach is a confidence-weighted ensemble of four complementary transformer models (AraBERTv2, AraELECTRA, MARBERT, and CAMeLBERT) each fine-tuned with distinct loss functions to capture diverse readability signals. To tackle severe class imbalance and data scarcity, we applied weighted training, advanced preprocessing, SAMER corpus relabe…

Initial Algebras of Domains via Quotient Inductive-Inductive Types
Simcha van Collem, Niels van der Weide, Herman Geuvers
https://arxiv.org/abs/2509.10187 https://

Initial Algebras of Domains via Quotient Inductive-Inductive Types
Domain theory has been developed as a mathematical theory of computation and to give a denotational semantics to programming languages. It helps us to fix the meaning of language concepts, to understand how programs behave and to reason about programs. At the same time it serves as a great theory to model various algebraic effects such as non-determinism, partial functions, side effects and numerous other forms of computation. In the present paper, we present a general framework to construct …

IntrinTrans: LLM-based Intrinsic Code Translator for RISC-V Vector
Liutong Han, Zhiyuan Tan, Hongbin Zhang, Pengcheng Wang, Chu Kang, Mingjie Xing, Yanjun Wu
https://arxiv.org/abs/2510.10119

IntrinTrans: LLM-based Intrinsic Code Translator for RISC-V Vector
The use of intrinsic functions to exploit hardware-specific capabilities is an important approach for optimizing library performance. Many mainstream libraries implement a large number of vectorized algorithms on Arm or x86 SIMD intrinsic functions. With the rapid expansion of the RISC-V hardware-software ecosystem, there is a growing demand for support of the RISC-V Vector (RVV) extension. Translating existing vectorized intrinsic code onto RVV intrinsics is a practical and effective approach.…

On Thompson Sampling and Bilateral Uncertainty in Additive Bayesian Optimization
Nathan Wycoff
https://arxiv.org/abs/2510.11792 https://arxiv.org/pdf/2510.…

On Thompson Sampling and Bilateral Uncertainty in Additive Bayesian Optimization
In Bayesian Optimization (BO), additive assumptions can mitigate the twin difficulties of modeling and searching a complex function in high dimension. However, common acquisition functions, like the Additive Lower Confidence Bound, ignore pairwise covariances between dimensions, which we'll call \textit{bilateral uncertainty} (BU), imposing a second layer of approximations. While theoretical results indicate that asymptotically not much is lost in doing so, little is known about the practical e…

Trump only functions in any international context if the other leaders are adults.

Two Trumps would be impossible / conflict when both sides had no impulse control and towering self regard.

Having a toddler as a leader only works 1 country at a time.

Minimizing smooth Kurdyka-{\L}ojasiewicz functions via generalized descent methods: Convergence rate and complexity
Masoud Ahookhosh, Susan Ghaderi, Alireza Kabgani, Morteza Rahimi
https://arxiv.org/abs/2511.10414 https://arxiv.org/pdf/2511.10414 https://arxiv.org/html/2511.10414
arXiv:2511.10414v1 Announce Type: new
Abstract: This paper addresses the generalized descent algorithm (DEAL) for minimizing smooth functions, which is analyzed under the Kurdyka-{\L}ojasiewicz (KL) inequality. In particular, the suggested algorithm guarantees a sufficient decrease by adapting to the cost function's geometry. We leverage the KL property to establish the global convergence, convergence rates, and complexity. A particular focus is placed on the linear convergence of generalized descent methods. We show that the constant step-size and Armijo line search strategies along a generalized descent direction satisfy our generalized descent condition. Additionally, for nonsmooth functions by leveraging the smoothing techniques such as forward-backward and high-order Moreau envelopes, we show that the boosted proximal gradient method (BPGA) and the boosted high-order proximal-point (BPPA) methods are also specific cases of DEAL, respectively. It is notable that if the order of the high-order proximal term is chosen in a certain way (depending on the KL exponent), then the sequence generated by BPPA converges linearly for an arbitrary KL exponent. Our preliminary numerical experiments on inverse problems and LASSO demonstrate the efficiency of the proposed methods, validating our theoretical findings.
toXiv_bot_toot

Gaussian Semantic Field for One-shot LiDAR Global Localization
Pengyu Yin, Shenghai Yuan, Haozhi Cao, Xingyu Ji, Ruofei Bai, Siyu Chen, Lihua Xie
https://arxiv.org/abs/2510.12101

Gaussian Semantic Field for One-shot LiDAR Global Localization
We present a one-shot LiDAR global localization algorithm featuring semantic disambiguation ability based on a lightweight tri-layered scene graph. While landmark semantic registration-based methods have shown promising performance improvements in global localization compared with geometric-only methods, landmarks can be repetitive and misleading for correspondence establishment. We propose to mitigate this problem by modeling semantic distributions with continuous functions learned from a popu…

Arithmetic Hirzebruch-Zagier divisors and central derivative values of Rankin-Selberg $L$-functions
Jeanine Van Order
https://arxiv.org/abs/2510.10303 https://

Arithmetic Hirzebruch-Zagier divisors and central derivative values of Rankin-Selberg $L$-functions
We give two distinct proofs of the Gross-Zagier formula in terms of sums of automorphic Green's functions realized as regularized theta lifts, including one involving arithmetic Hirzebruch-Zagier divisors on the Hilbert modular surface $X_0(N) \times X_0(N)$. We then describe applications to the refined conjecture of Birch and Swinnerton-Dyer. Through these calculations, we also describe known and conjectural relations of the central derivative values of Rankin-Selberg $L$-functions that appear…

Boundary behavior of analytic functions on certain Banach spaces
Hector N. Salas
https://arxiv.org/abs/2510.10373 https://arxiv.org/pdf/2510.10373

Boundary behavior of analytic functions on certain Banach spaces
For Banach spaces of analytic functions on the disc for which the polynomials are dense and their pointt evaluations continuous, we prove the following: If they contain a function such that the limit superior of its modulus is infinite almost everywhere on the unit circle, then the same is true for a residual set of functions.

On the monodromy conjecture for determinantal varieties
Yifan Chen, Huaiqing Zuo
https://arxiv.org/abs/2510.11425 https://arxiv.org/pdf/2510.11425

On the monodromy conjecture for determinantal varieties
This paper presents a proof of the monodromy conjecture for determinantal varieties. Our strategy centers on an in-depth analysis of monodromy zeta functions, leveraging a generalized A'Campo formula, an examination of multiple contact loci, and the exploitation of the intrinsic symmetric structures inherent to these varieties. Keywords. monodromy conjecture, determinantal varieties, monodromy zeta function.

Newton series representation of completely monotone functions
Thomas Lamby, Jean-Luc Marichal, Na\"im Zena\"idi
https://arxiv.org/abs/2510.11577 https://

Newton series representation of completely monotone functions
We prove that every completely monotone function defined on a right-unbounded open interval admits a Newton series expansion at every point of that interval. This result can be viewed as an analog of Bernstein's little theorem for absolutely monotone functions. As an application, we use it to study principal indefinite sums, which are constructed via a broad generalization of Bohr-Mollerup's theorem.

H-harmonic reproducing kernels on the ball
Mat\v{e}j Morav\'ik
https://arxiv.org/abs/2510.11821 https://arxiv.org/pdf/2510.11821

H-harmonic reproducing kernels on the ball
We consider the Szegő reproducing kernel associated with the space of $H$-harmonic functions on the unit ball in n-dimensional space, i.e. functions that are characterized by being annihilated by the hyperbolic Laplacian. This paper derives an explicit series expansion for the reproducing kernel in terms of a triple hypergeometric function introduced of Exton. Moreover, we demonstrate that the Szegő kernel admits a representation as a finite sum of hypergeometric functions. We further show th…

New nickle release today. This adds complex numbers, adds more math functions and fixes some existing ones. I'm using all of this to generate test vectors for picolibc math functions. More news about that when I manage to get the tests through CI.
Here's the nickle bits:
https://github.com/keith-…

Beyond the Silence: How Men Navigate Infertility Through Digital Communities and Data Sharing
Tawfiq Ammari, Zarah Khondoker, Yihan Wang, Nikki Roda
https://arxiv.org/abs/2509.10003

Beyond the Silence: How Men Navigate Infertility Through Digital Communities and Data Sharing
Men experiencing infertility face unique challenges navigating Traditional Masculinity Ideologies that discourage emotional expression and help-seeking. This study examines how Reddit's r/maleinfertility community helps overcome these barriers through digital support networks. Using topic modeling (115 topics), network analysis (11 micro-communities), and time-lagged regression on 11,095 posts and 79,503 comments from 8,644 users, we found the community functions as a hybrid space: informal dia…

I have to say, spending a decade organizing (for bike/ped/transit infrastructure) has done more for my understanding of how the world _actually_ functions than working at any company or startup, taking any classes*, or really anything else. It's the weird interactions between businesses, the public, technology, and the political landscape that really shape our society.
* Not that classes aren't useful! I took a law class in college and use the knowledge I gained there on a wee…

Off Policy Lyapunov Stability in Reinforcement Learning
Sarvan Gill, Daniela Constantinescu
https://arxiv.org/abs/2509.09863 https://arxiv.org/pdf/2509.098…

Off Policy Lyapunov Stability in Reinforcement Learning
Traditional reinforcement learning lacks the ability to provide stability guarantees. More recent algorithms learn Lyapunov functions alongside the control policies to ensure stable learning. However, the current self-learned Lyapunov functions are sample inefficient due to their on-policy nature. This paper introduces a method for learning Lyapunov functions off-policy and incorporates the proposed off-policy Lyapunov function into the Soft Actor Critic and Proximal Policy Optimization algorit…

Serial Polar Automorphism Ensemble Decoders for Physical Unclonable Functions
Marvin R\"ubenacke, Sebastian Cammerer, Michael Sullivan, Alexander Keller
https://arxiv.org/abs/2510.09220

Serial Polar Automorphism Ensemble Decoders for Physical Unclonable Functions
Physical unclonable functions (PUFs) involve challenging practical applications of error-correcting codes (ECCs), requiring extremely low failure rates on the order of $10^{-6}$ and below despite raw input bit error rates as high as 22%. These requirements call for an efficient ultra-low rate code design. In this work, we propose a novel coding scheme tailored for PUFs based on Polar codes and a low-complexity version of automorphism ensemble decoding (AED). Notably, our serial AED scheme reuse…

Sustaining Research Software: A Fitness Function Approach
Philipp Zech, Irdin Pekaric
https://arxiv.org/abs/2509.10085 https://arxiv.org/pdf/2509.10085

Sustaining Research Software: A Fitness Function Approach
The long-term sustainability of research software is a critical challenge, as it usually suffers from poor maintainability, lack of adaptability, and eventual obsolescence. This paper proposes a novel approach to addressing this issue by leveraging the concept of fitness functions from evolutionary architecture. Fitness functions are automated, continuously evaluated metrics designed to ensure that software systems meet desired non-functional, architectural qualities over time. We define a set …

On the $v$-adic values of G-functions I
Georgios Papas
https://arxiv.org/abs/2510.11806 https://arxiv.org/pdf/2510.11806

On the $v$-adic values of G-functions I
This is the first in a series of papers aimed at studying families of G-functions associated to $1$-parameter families of abelian schemes. In particular, the construction of relations, in both the archimedean and non-archimedean settings, at values of specific interest to problems of unlikely intersections. In this first text in this series, we record what we expect to be the theoretical foundations of this series in a uniform way. After this, we study values corresponding to ``splittings'' i…

Topological Signatures of ReLU Neural Network Activation Patterns
Vicente Bosca, Tatum Rask, Sunia Tanweer, Andrew R. Tawfeek, Branden Stone
https://arxiv.org/abs/2510.12700 htt…

Topological Signatures of ReLU Neural Network Activation Patterns
This paper explores the topological signatures of ReLU neural network activation patterns. We consider feedforward neural networks with ReLU activation functions and analyze the polytope decomposition of the feature space induced by the network. Mainly, we investigate how the Fiedler partition of the dual graph and show that it appears to correlate with the decision boundary -- in the case of binary classification. Additionally, we compute the homology of the cellular decomposition -- in a regr…

Variational Analysis in Spectral Decomposition Systems
H\`oa T. B\`ui, Minh N. B\`ui, Christian Clason
https://arxiv.org/abs/2510.11433 https://arxiv.org/p…

Variational Analysis in Spectral Decomposition Systems
This work is concerned with variational analysis of so-called spectral functions and spectral sets of matrices that only depend on eigenvalues of the matrix. Based on our previous work [H. T. Bùi, M. N. Bùi, and C. Clason, Convex analysis in spectral decomposition systems, arXiv 2503.14981] on convex analysis of such functions, we consider the question in the abstract framework of spectral decomposition systems, which covers a wide range of previously studied settings, including eigenvalue de…

Evaluation of Black-Box XAI Approaches for Predictors of Values of Boolean Formulae
Stav Armoni-Friedmann, Hana Chockler, David A. Kelly
https://arxiv.org/abs/2509.09982 https:/…

Evaluation of Black-Box XAI Approaches for Predictors of Values of Boolean Formulae
Evaluating explainable AI (XAI) approaches is a challenging task in general, due to the subjectivity of explanations. In this paper, we focus on tabular data and the specific use case of AI models predicting the values of Boolean functions. We extend the previous work in this domain by proposing a formal and precise measure of importance of variables based on actual causality, and we evaluate state-of-the-art XAI tools against this measure. We also present a novel XAI tool B-ReX, based on the e…

Trump only functions in any international context if the other leaders are adults.

Two Trumps would be impossible / conflict when both sides had no impulse control and towering self regard.

Having a toddler as a leader only works 1 country at a time.

Fourier transform pairs and Eisenstein-type series related to Jacobi elliptic functions
Peng-Cheng Hang, Alexey Kuznetsov
https://arxiv.org/abs/2510.08823 https://

Fourier transform pairs and Eisenstein-type series related to Jacobi elliptic functions
We compute Fourier transforms of functions expressed as a ratio of one of the Jacobi elliptic functions divided by $\sinh(πx)$ or $\cosh(πx)$. In many cases, the resulting Fourier transform remains within the same class of functions. Applying the Mellin transform, we obtain sixteen Eisenstein-type series $ζ_{j,l}(s,τ)$, for which we establish several results: analytic continuation with respect to the variable $s$, a functional equation connecting $ζ_{j,l}(s,τ)$ and $ζ_{l,j}(1-s,-1/τ)$, …

A Representer Theorem for Hawkes Processes via Penalized Least Squares Minimization
Hideaki Kim, Tomoharu Iwata
https://arxiv.org/abs/2510.08916 https://ar…

A Representer Theorem for Hawkes Processes via Penalized Least Squares Minimization
The representer theorem is a cornerstone of kernel methods, which aim to estimate latent functions in reproducing kernel Hilbert spaces (RKHSs) in a nonparametric manner. Its significance lies in converting inherently infinite-dimensional optimization problems into finite-dimensional ones over dual coefficients, thereby enabling practical and computationally tractable algorithms. In this paper, we address the problem of estimating the latent triggering kernels--functions that encode the interac…

Monte Carlo quasi-interpolation of spherical data
Zhengjie Sun, Mengyuan Lv, Xingping Sun
https://arxiv.org/abs/2510.12027 https://arxiv.org/pdf/2510.12027…

Monte Carlo quasi-interpolation of spherical data
We establish a deterministic and stochastic spherical quasi-interpolation framework featuring scaled zonal kernels derived from radial basis functions on the ambient Euclidean space. The method incorporates both quasi-Monte Carlo and Monte Carlo quadrature rules to construct easily computable quasi-interpolants, which provide efficient approximation to Sobolev-space functions for both clean and noisy data. To enhance the approximation power and robustness of our quasi-interpolants, we develop a…

Analytic results in conformal field theory
Philine van Vliet, Emilio Trevisani, Ingo Runkel, Bernardo Zan, Yifei He, Xin Sun, Volker Schomerus
https://arxiv.org/abs/2510.09868 h…

Analytic results in conformal field theory
Since the 1980s, many exact results have been discovered in $2d$ CFT, from critical exponents to correlation functions to complete solutions of certain models. In $d>2$, there is a wealth of numerical results as well as promising analytic approaches, but comparably fewer exact answers. The aim of this conference was to review the most promising analytic methods and results in CFT in any dimension. In particular we tried to understand to which extent the $2d$ methods can be extended to $d>2$, …

Crosslisted article(s) found for math.AG. https://arxiv.org/list/math.AG/new
[1/1]:
- On the $v$-adic values of G-functions I
Georgios Papas
https://

Boundary-Guided Policy Optimization for Memory-efficient RL of Diffusion Large Language Models
Nianyi Lin, Jiajie Zhang, Lei Hou, Juanzi Li
https://arxiv.org/abs/2510.11683 http…

Boundary-Guided Policy Optimization for Memory-efficient RL of Diffusion Large Language Models
A key challenge in applying reinforcement learning (RL) to diffusion large language models (dLLMs) lies in the intractability of their likelihood functions, which are essential for the RL objective, necessitating corresponding approximation in each training step. While existing methods approximate the log-likelihoods by their evidence lower bounds (ELBOs) via customized Monte Carlo (MC) sampling, the forward computational graphs of all MC samples need to be retained for the gradient computation…

Viscosity CBFs: Bridging the Control Barrier Function and Hamilton-Jacobi Reachability Frameworks in Safe Control Theory
Dylan Hirsch, Jaime Fern\'andez Fisac, Sylvia Herbert
https://arxiv.org/abs/2510.09929

Viscosity CBFs: Bridging the Control Barrier Function and Hamilton-Jacobi Reachability Frameworks in Safe Control Theory
Control barrier functions (CBFs) and Hamilton-Jacobi reachability (HJR) are central frameworks in safe control. Traditionally, these frameworks have been viewed as distinct, with the former focusing on optimally safe controller design and the latter providing sufficient conditions for safety. A previous work introduced the notion of a control barrier value function (CB-VF), which is defined similarly to the other value functions studied in HJR but has certain CBF-like properties. In this work, …

The Fractional Two-Sided Quaternionic Dunkl Transform and Heisenberg-Type Inequalities
Mohamed Essenhajy
https://arxiv.org/abs/2510.11597 https://arxiv.org…

The Fractional Two-Sided Quaternionic Dunkl Transform and Heisenberg-Type Inequalities
This report investigates the main definitions and fundamental properties of the fractional two-sided quaternionic Dunkl transform in two dimensions. We present key results concerning its structure and emphasize its connections to classical harmonic analysis. Special attention is given to inversion, boundedness, spectral behavior, and explicit formulas for structured functions such as radial or harmonic functions. Within this framework, we establish a generalized form of the classical Heisenberg…

Inclusive Fitness as a Key Step Towards More Advanced Social Behaviors in Multi-Agent Reinforcement Learning Settings
Andries Rosseau, Rapha\"el Avalos, Ann Now\'e
https://arxiv.org/abs/2510.12555

Inclusive Fitness as a Key Step Towards More Advanced Social Behaviors in Multi-Agent Reinforcement Learning Settings
The competitive and cooperative forces of natural selection have driven the evolution of intelligence for millions of years, culminating in nature's vast biodiversity and the complexity of human minds. Inspired by this process, we propose a novel multi-agent reinforcement learning framework where each agent is assigned a genotype and where reward functions are modelled after the concept of inclusive fitness. An agent's genetic material may be shared with other agents, and our inclusive reward f…

Semiclassical analytical solutions of the eigenstate thermalization hypothesis in a quantum billiard
Yaoqi Ye, Chengkai Lin, Xiao Wang
https://arxiv.org/abs/2510.12517 https://

Semiclassical analytical solutions of the eigenstate thermalization hypothesis in a quantum billiard
We derive semiclassical analytical solutions for both the diagonal and off-diagonal functions in the eigenstate thermalization hypothesis (ETH) in a quarter-stadium quantum billiard. For a representative observable, we obtain an explicit expression and an asymptotic closed-form solution that naturally separate into a local contribution and a phase-space correlation term. These analytical results predict the band structure of the observable matrix, including its bandwidth and scaling behavior. W…

Neural network-based singularity detection and applications
Nadiia Derevianko, Ioannis G. Kevrekidis, Felix Dietrich
https://arxiv.org/abs/2509.10110 https://

Neural network-based singularity detection and applications
We present a method for constructing a special type of shallow neural network that learns univariate meromorphic functions with pole-type singularities. Our method is based on using a finite set of Laurent coefficients as input information, which we compute by FFT, employing values of the investigated function on some contour $Γ$ in the complex plane. The primary components of our methodology are the following: (1) the adaptive construction of rational polynomial activation functions, (2) a no…

The Second Moment of $\mathrm{GL}_3 \times \mathrm{GL}_2$ $L$-functions at Special Points
Zhi Qi
https://arxiv.org/abs/2510.11191 https://arxiv.org/pdf/251…

The Second Moment of $\mathrm{GL}_3 \times \mathrm{GL}_2$ $L$-functions at Special Points
Let $ϕ$ be a fixed Hecke--Maass form for $\mathrm{SL}_3 (\mathbb{Z})$ and $u_j $ traverse an orthonormal basis of Hecke--Maass forms for $\mathrm{SL}_2 (\mathbb{Z}) $. Let $1/4+t_j^2$ be the Laplace eigenvalue of $u_j $. In this paper, we prove the mean Lindelöf hypothesis for the second moment of $ L (1/2+it_j, ϕ\times u_j) $ on $ T < t_j \leqslant T + \sqrt{T} $. Previously, this was proven by Young on $ t_j \leqslant T$. Our approach is more direct as we do not apply the Poisson summation…

Directed lattice paths avoiding periodic subset of points on "time"-axis
S. Tarasov
https://arxiv.org/abs/2510.11367 https://arxiv.org/pdf/2510.1…

Directed lattice paths avoiding periodic subset of points on "time"-axis
We compute generating functions of the set of directed lattice paths starting from the origin and avoiding a periodic set of even point on OX = "time"-axis. As an application we prove a combinatorial identity proposed by P. Hajnal and G.V. Nagy.

Approximating the coefficients of the Bessel functions
Andrew Yao
https://arxiv.org/abs/2510.10370 https://arxiv.org/pdf/2510.10370

Approximating the coefficients of the Bessel functions
For the type A, BC, and D root systems, we determine equivalent conditions between the coefficients of an exponential holomorphic function and the asymptotic values taken by the Dunkl bilinear form when one of its entries is the function. We establish these conditions over the $|θN| \rightarrow\infty$ regime for the type A and D root systems and over the $|θ_0 N|\rightarrow \infty, \frac{θ_1}{θ_0 N}\rightarrow c\in\mathbb{C}$ regime for the type BC root system. We also g…

Adapting Noise to Data: Generative Flows from 1D Processes
Jannis Chemseddine, Gregor Kornhardt, Richard Duong, Gabriele Steidl
https://arxiv.org/abs/2510.12636 https://

Adapting Noise to Data: Generative Flows from 1D Processes
We introduce a general framework for constructing generative models using one-dimensional noising processes. Beyond diffusion processes, we outline examples that demonstrate the flexibility of our approach. Motivated by this, we propose a novel framework in which the 1D processes themselves are learnable, achieved by parameterizing the noise distribution through quantile functions that adapt to the data. Our construction integrates seamlessly with standard objectives, including Flow Matching an…

If $\sum_n n! c_n z^n$ is entire and $c_n$ does not terminate, then $\sum_n c_n z^n$ has infinitely many zeros
Alann Rosas
https://arxiv.org/abs/2510.10054 https://

If $\sum_n n! c_n z^n$ is entire and $c_n$ does not terminate, then $\sum_n c_n z^n$ has infinitely many zeros
We prove that if $\sum_n n! c_n z^n$ is entire and $c_n$ does not terminate, then $\sum_n c_n z^n$ has infinitely many zeros. We then use this result to give alternative proofs that the Le Roy functions $f_r(z)=\sum_{n=0}^\infty \frac{z^n}{(n!)^r}$ for $r>1$ and Bessel functions $J_α(z)=\sum_{m=0}^\infty \frac{(-1)^m}{m!Γ(m+α+1)}\left(\frac{z}{2}\right)^{2m+α}$ for $α\in\mathbb R$ have infinitely many zeros.

Crosslisted article(s) found for math.AG. https://arxiv.org/list/math.AG/new
[1/1]:
- Division algebras of slice-Nash functions
Cinzia Bisi, Antonio Carbone
htt…

Replaced article(s) found for cs.LG. https://arxiv.org/list/cs.LG/new
[1/14]:
- Meta-Learning Adaptive Loss Functions
Christian Raymond, Qi Chen, Bing Xue, Mengjie Zhang

The Second Moment of $\mathrm{GL}_4 \times \mathrm{GL}_2$ $L$-functions at Special Points
Zhi Qi, Ruihua Qiao
https://arxiv.org/abs/2510.11186 https://arxi…

The Second Moment of $\mathrm{GL}_4 \times \mathrm{GL}_2$ $L$-functions at Special Points
In this paper, we provide an alternative proof of Chandee and Li's result on the second moment of $\mathrm{GL}_4 \times \mathrm{GL}_2$ special $L$-values. Our method is conceptually more direct as it neither detects the `Eisenstein--Kloosterman' cancellation nor uses the Poisson summation.

Locally Linear Convergence for Nonsmooth Convex Optimization via Coupled Smoothing and Momentum
Reza Rahimi Baghbadorani, Sergio Grammatico, Peyman Mohajerin Esfahani
https://arxiv.org/abs/2511.10239 https://arxiv.org/pdf/2511.10239 https://arxiv.org/html/2511.10239
arXiv:2511.10239v1 Announce Type: new
Abstract: We propose an adaptive accelerated smoothing technique for a nonsmooth convex optimization problem where the smoothing update rule is coupled with the momentum parameter. We also extend the setting to the case where the objective function is the sum of two nonsmooth functions. With regard to convergence rate, we provide the global (optimal) sublinear convergence guarantees of O(1/k), which is known to be provably optimal for the studied class of functions, along with a local linear rate if the nonsmooth term fulfills a so-call locally strong convexity condition. We validate the performance of our algorithm on several problem classes, including regression with the l1-norm (the Lasso problem), sparse semidefinite programming (the MaxCut problem), Nuclear norm minimization with application in model free fault diagnosis, and l_1-regularized model predictive control to showcase the benefits of the coupling. An interesting observation is that although our global convergence result guarantees O(1/k) convergence, we consistently observe a practical transient convergence rate of O(1/k^2), followed by asymptotic linear convergence as anticipated by the theoretical result. This two-phase behavior can also be explained in view of the proposed smoothing rule.
toXiv_bot_toot

On the distinction between Kloosterman sums and multiplicative functions
Yang Zhang
https://arxiv.org/abs/2510.10721 https://arxiv.org/pdf/2510.10721

On the distinction between Kloosterman sums and multiplicative functions
Let $S(a,b;n)$ be the Kloosterman sum. For any integers $a\neq0,b\neq0,k\geqslant2$, any given complex number $η\not=0$ and multiplicative function $f: \mathbb{N} \rightarrow \mathbb{C}$, we show that \[ |\{n\leqslant X:S(a,b;n)=ηf(n), n \text{ square-free }k\text{-almost prime}\}|\leqslant π(\dfrac{X}{L_k})+O(X^{1-\frac{1}{2k}}) \] and \[ |\{n\leqslant X:S(a,b;n)=ηf(n), n \text{ square-free}\}|\leqslant π(X)+O(Xe^{-\sqrt{\log X}}) \] as $X\rightarrow \infty$. Here, $L_…

One-dimensional tunneling of the two-body bound state
N. Shypka, O. Hryhorchak, V. Pastukhov
https://arxiv.org/abs/2510.11932 https://arxiv.org/pdf/2510.11…

One-dimensional tunneling of the two-body bound state
We consider bound and scattering states of the one-dimensional dimer formed by two coupled non-identical atoms when one of them also interacts with the zero-range potential located at the origin. By calculating the dimer localized and scattering wave functions, we identify properties of the system without the two-body bound-state collapse. In general, we predict an enhancement of the dimer reflection compared to a single atom, except for a narrow region on the attractive side of the external po…

Bounded Littlewood identities with fixed number of odd rows or odd columns
JiSun Huh, Jang Soo Kim, Christian Krattenthaler, Soichi Okada
https://arxiv.org/abs/2510.11054 https:…

Bounded Littlewood identities with fixed number of odd rows or odd columns
A Littlewood identity is an identity equating a sum of Schur functions with an infinite product. A bounded Littlewood identity is one where the sum is taken over the partitions with a bounded number of rows or columns. The price to pay is that the infinite product has to be replaced by a determinant. The focus of this article is on refinements of such bounded Littlewood identities where one also prescribes the number of odd-length rows or columns of the partitions. Goulden [{\it Discrete Math.}…

Project-Level C-to-Rust Translation via Synergistic Integration of Knowledge Graphs and Large Language Models
Zhiqiang Yuan, Wenjun Mao, Zhuo Chen, Xiyue Shang, Chong Wang, Yiling Lou, Xin Peng
https://arxiv.org/abs/2510.10956

Project-Level C-to-Rust Translation via Synergistic Integration of Knowledge Graphs and Large Language Models
Translating C code into safe Rust is an effective way to ensure its memory safety. Compared to rule-based translation which produces Rust code that remains largely unsafe, LLM-based methods can generate more idiomatic and safer Rust code because LLMs have been trained on vast amount of human-written idiomatic code. Although promising, existing LLM-based methods still struggle with project-level C-to-Rust translation. They typically partition a C project into smaller units (\eg{} functions) base…

Equivalence criteria for the two--term functional equations for Herglotz--Zagier functions
Sumukha Sathyanarayana, N. Guru Sharan
https://arxiv.org/abs/2510.10088 https://

Equivalence criteria for the two--term functional equations for Herglotz--Zagier functions
We establish Kronecker limit type formula for the generalized Mordell-Tornheim zeta function $Θ(r,r,t,x)$ as a function of the third argument around $t=1-r$. We then show that the above Kronecker limit type formula is equivalent to the two-term functional equation for the higher Herglotz function obtained by Vlasenko and Zagier. We also show the equivalence between a previously known Kronecker limit type formula for $Θ(1,1,t,x)$ around $t=0$ and the two-term functional equation for the Herglo…

Crosslisted article(s) found for math.OC. https://arxiv.org/list/math.OC/new
[1/1]:
- Optimal control of Volterra integral diffusions and application to contract theory
Dylan Possama\"i, Mehdi Talbi
https://arxiv.org/abs/2511.09701 https://mastoxiv.page/@arXiv_mathPR_bot/115547093766733637
- Generalized infinite dimensional Alpha-Procrustes based geometries
Salvish Goomanee, Andi Han, Pratik Jawanpuria, Bamdev Mishra
https://arxiv.org/abs/2511.09801 https://mastoxiv.page/@arXiv_statML_bot/115547135711272091
- Sample Complexity of Quadratically Regularized Optimal Transport
Alberto Gonz\'alez-Sanz, Eustasio del Barrio, Marcel Nutz
https://arxiv.org/abs/2511.09807 https://mastoxiv.page/@arXiv_mathST_bot/115546975796760368
- On the Convergence of Overparameterized Problems: Inherent Properties of the Compositional Struct...
Arthur Castello Branco de Oliveira, Dhruv Jatkar, Eduardo Sontag
https://arxiv.org/abs/2511.09810 https://mastoxiv.page/@arXiv_csLG_bot/115547543989283588
- Implicit Multiple Tensor Decomposition
Kunjing Yang, Libin Zheng, Minru Bai
https://arxiv.org/abs/2511.09916 https://mastoxiv.page/@arXiv_mathNA_bot/115547169767663335
- Theoretical Analysis of Resource-Induced Phase Transitions in Estimation Strategies
Takehiro Tottori, Tetsuya J. Kobayashi
https://arxiv.org/abs/2511.10184 https://mastoxiv.page/@arXiv_physicsbioph_bot/115546979073652600
- Zeroes and Extrema of Functions via Random Measures
Athanasios Christou Micheas
https://arxiv.org/abs/2511.10293 https://mastoxiv.page/@arXiv_statME_bot/115547493525198835
- Operator Models for Continuous-Time Offline Reinforcement Learning
Nicolas Hoischen, Petar Bevanda, Max Beier, Stefan Sosnowski, Boris Houska, Sandra Hirche
https://arxiv.org/abs/2511.10383 https://mastoxiv.page/@arXiv_statML_bot/115547254989932993
- On topological properties of closed attractors
Wouter Jongeneel
https://arxiv.org/abs/2511.10429 https://mastoxiv.page/@arXiv_mathDS_bot/115547276594491411
- Learning parameter-dependent shear viscosity from data, with application to sea and land ice
Gonzalo G. de Diego, Georg Stadler
https://arxiv.org/abs/2511.10452 https://mastoxiv.page/@arXiv_mathNA_bot/115547323782478749
- Formal Verification of Control Lyapunov-Barrier Functions for Safe Stabilization with Bounded Con...
Jun Liu
https://arxiv.org/abs/2511.10510 https://mastoxiv.page/@arXiv_eessSY_bot/115547429321496393
- Direction-of-Arrival and Noise Covariance Matrix joint estimation for beamforming
Vitor Gelsleichter Probst Curtarelli
https://arxiv.org/abs/2511.10639 https://mastoxiv.page/@arXiv_eessAS_bot/115547188796143762
toXiv_bot_toot

Multi-Copy Security in Unclonable Cryptography
Alper \c{C}akan, Vipul Goyal, Fuyuki Kitagawa, Ryo Nishimaki, Takashi Yamakawa
https://arxiv.org/abs/2510.12626 https://

Multi-Copy Security in Unclonable Cryptography
Unclonable cryptography leverages the quantum no-cloning principle to copy-protect cryptographic functionalities. While most existing works address the basic single-copy security, the stronger notion of multi-copy security remains largely unexplored. We introduce a generic compiler that upgrades collusion-resistant unclonable primitives to achieve multi-copy security, assuming only one-way functions. Using this framework, we obtain the first multi-copy secure constructions of public-key quant…

On the enumeration of records of rooted trees and rooted forests
Adri\'an Lillo, Mercedes Rosas, Stefan Trandafir
https://arxiv.org/abs/2510.12536 https://

On the enumeration of records of rooted trees and rooted forests
A record of a rooted Cayley tree is a node whose label is the largest along the unique path to the root. In this work, we find elegant functional equations relating the generating functions for records of rooted Cayley trees and for records of forests of rooted trees with the Cayley tree function, and explore the consequences of our results.

Quantum variance for cubic moment of Hecke--Maass cusp forms and Eisenstein series
Bingrong Huang, Liangxun Li
https://arxiv.org/abs/2510.12322 https://arx…

Quantum variance for cubic moment of Hecke--Maass cusp forms and Eisenstein series
In this paper, we give the upper bounds on the variance for cubic moment of Hecke--Maass cusp forms and Eisenstein series respectively. For the cusp form case, the bound comes from a large sieve inequality for symmetric cubes. We also give some nontrivial bounds for higher moments of symmetric cube $L$-functions. For the Eisenstein series case, the upper bound comes from Lindelöf-on-average type bounds for various $L$-functions. In particular, we establish the sharp upper bounds for the fourth…

Confined few-particle systems beyond mean-field theory adopting Gaussian-type orbitals and Morse interparticle interaction
Matee ur Rehman, Paul Winter, Fabio Revuelta, Alejandro Saenz
https://arxiv.org/abs/2509.10347

Confined few-particle systems beyond mean-field theory adopting Gaussian-type orbitals and Morse interparticle interaction
Recent advancements in optical tweezers enable the trapping of arbitrary numbers of neutral atoms and molecules, even arrays of tweezers with variable geometry can be realized. These fascinating breakthroughs require novel full-dimensional beyond mean-field treatments for systems with more than two confined particles spread over traps that are arranged arbitrarily in space. In this work, the suitability of a quantum-chemistry inspired approach adopting Cartesian Gaussians as basis functions is …

Directional Subdifferentials at Infinity and Its Applications
Le Ngoc Kien, Nguyen Van Tuyen, Tran Van Nghi
https://arxiv.org/abs/2510.09179 https://arxiv.…

Directional Subdifferentials at Infinity and Its Applications
This paper investigates the behavior of sets and functions at infinity by introducing new concepts, namely directional normal cones at infinity for unbounded sets, along with limiting and singular subdifferentials at infinity in the direction for extended real-valued functions. We develop several calculus rules for these concepts and then apply them to nonsmooth optimization problems. The applications include establishing directional optimality conditions at infinity, analyzing the coercivity, …

Linear Convergence of a Unified Primal--Dual Algorithm for Convex--Concave Saddle Point Problems with Quadratic Growth
Cody Melcher, Afrooz Jalilzadeh, Erfan Yazdandoost Hamedani
https://arxiv.org/abs/2510.11990

Linear Convergence of a Unified Primal--Dual Algorithm for Convex--Concave Saddle Point Problems with Quadratic Growth
In this paper, we study saddle point (SP) problems, focusing on convex-concave optimization involving functions that satisfy either two-sided quadratic functional growth (QFG) or two-sided quadratic gradient growth (QGG)--novel conditions tailored specifically for SP problems as extensions of quadratic growth conditions in minimization. These conditions relax the traditional requirement of strong convexity-strong concavity, thereby encompassing a broader class of problems. We propose a generali…

Hybrid Ridgelet Deep Neural Networks for Data-Driven Arbitrage Strategies
Bahadur Yadav, Sanjay Kumar Mohanty
https://arxiv.org/abs/2510.10599 https://arxi…

Hybrid Ridgelet Deep Neural Networks for Data-Driven Arbitrage Strategies
In this study, we propose a novel model framework that integrates deep neural networks with the Ridgelet Transform. The Ridgelet Transform on Borel measurable functions is used for arbitrage detection on high-dimensional sparse structures. This transform also enhances the expressive power of neural networks, enabling them to capture complex and high-dimensional market structures. Theoretically, we determine profitable trading strategies by optimizing hybrid ridgelet deep neural networks. Furthe…

Mordell--Tornheim zeta function: Kronecker limit type formulas and Special values
Sumukha Sathyanarayana, N. Guru Sharan
https://arxiv.org/abs/2510.10093 https://

Mordell--Tornheim zeta function: Kronecker limit type formulas and Special values
In this paper, we establish Kronecker limit type formulas for the generalized Mordell--Tornheim zeta function $Θ(r,s,t,x)$ as a function of the third variable, in terms of Riemann-zeta and Gamma values. We also give series evaluations of $Θ(r,s,t,x)$ in terms of Herglotz-Zagier type functions, and their derivatives. As applications of this, we derive Kronecker limit type formula in the second variable and a new infinite family of modular relations called mixed functional equations. We also st…

Periods detecting Eisenstein series and sums of $L$-values I
Weixiao Lu, Guodong Xi
https://arxiv.org/abs/2510.12446 https://arxiv.org/pdf/2510.12446

Periods detecting Eisenstein series and sums of $L$-values I
We study the automorphic period associated to a $G$-Hamiltonian variety $M$ whose dual is $\check{M} = T^*(\check{G}/\check{L})$, where $\check{G}$ is a general linear group and $\check{L}$ is a Levi subgroup. For certain cuspidal Eisenstein series, we prove that their period is equal to a finite sum of special values of $L$-functions. This sum is indexed by the fixed points of the associated extended $L$-parameter on $\check{M}$, confirming a conjecture by Ben-Zvi-Sakellaridis-Venkatesh in thi…