Tootfinder

Prime graphical parking functions and strongly recurrent configurations of the Abelian sandpile model
Thomas Selig, Haoyue Zhu
https://arxiv.org/abs/2506.23237

Prime graphical parking functions and strongly recurrent configurations of the Abelian sandpile model
This work investigates the duality between two discrete dynamical processes: parking functions, and the Abelian sandpile model (ASM). Specifically, we are interested in the extension of classical parking functions, called $G$-parking functions, introduced by Postnikov and Shapiro in 2004. $G$-parking functions are in bijection with recurrent configurations of the ASM on $G$. In this work, we define a notion of prime $G$-parking functions. These are parking functions that are in a sense "indecom…

Have Object-Oriented Languages Missed a Trick with Class Function and its Subclasses?
Lloyd Allison
https://arxiv.org/abs/2507.00488 https://

Have Object-Oriented Languages Missed a Trick with Class Function and its Subclasses?
Compared to functions in mathematics, functions in programming languages seem to be under classified. Functional programming languages based on the lambda calculus famously treat functions as first-class values. Object-oriented languages have adopted ``lambdas'', notably for call-back routines in event-based programming. Typically a programming language has functions, a function has a type, and some functions act on other functions and/or return functions but there is generally a lack of (i) ``…

Cute comics of R functions by @…: https://allisonhorst.com/r-packages-functions

Allison Horst - R Packages & Functions

Convergence rates of Newton's method for strongly self-concordant minimization
Nick Tsipinakis, Panos Parpas
https://arxiv.org/abs/2507.23558 https://a…

Convergence rates of Newton's method for strongly self-concordant minimization
Newton's method has been thoroughly studied for the class of self-concordant functions. However, a local analysis specific to strongly self-concordant functions (a subclass of the former) is missing from the literature. The local quadratic rate of strongly self-concordant functions follows, of course, from the known results for self-concordant functions. However, it is not known whether strongly self-concordant functions enjoy better theoretical properties. In this paper, we study the local con…

An Ohsawa-Takegoshi-type $L^2$ extension for upper semi-continuous $L^2$-optimal functions
Zhuo Liu
https://arxiv.org/abs/2506.22834 https://

An Ohsawa-Takegoshi-type $L^2$ extension for upper semi-continuous $L^2$-optimal functions
In this article, we obtain an Ohsawa-Takegoshi-type $L^2$-extension for upper semi-continuous $L^2$-optimal functions via a Lebesgue-type differentiation theorem. As applications, we give a characterization of plurisubharmonic functions via the multiple coarse $L^2$-estimate property for (strongly) upper semi-continuous functions and show that (strongly) upper semi-continuous $L^2$-optimal functions satisfy Skoda's integrability theorem and the strong openness property.

More about cofinally Bourbaki quasi-complete metric spaces
Argha Ghosh
https://arxiv.org/abs/2507.00541 https://arxiv.org/pdf/2507.00…

More about cofinally Bourbaki quasi-complete metric spaces
We characterize cofinally Bourbaki quasi-complete metric spaces and their completions in terms of certain Lipschitz-type functions. To this end, we introduce and study a new class of functions, namely strongly uniformly locally Lipschitz functions, which lie strictly between Lipschitz functions and uniformly locally Lipschitz functions. We show that a metric space is cofinally Bourbaki quasi-complete if and only if the class of strongly uniformly locally Lipschitz functions on coi…

Inhomogeneous mark correlation functions for general marked point processes
Mehdi Moradi, Matthias Eckardt
https://arxiv.org/abs/2505.24501 https://…

Inhomogeneous mark correlation functions for general marked point processes
Spatial phenomena in environmental and biological contexts often involve events that are unevenly distributed across space and carry attributes, whose associations/variations are space-dependent. In this paper, we introduce the class of inhomogeneous mark correlation functions, capturing mark associations/variations, while explicitly accounting for the spatial inhomogeneity of events. The proposed functions are designed to quantify how, on average, marks vary or associate with one another as a …

Extended Non-Markovian Stochastic Schr\"odinger Equation with Complex Frequency Modes for General Basis Functions
Yukai Guo, Zeyu Huang, Xing Gao
https://arxiv.org/abs/2506.22738

Extended Non-Markovian Stochastic Schrödinger Equation with Complex Frequency Modes for General Basis Functions
We present an extended formulation of the non-Markovian stochastic Schrödinger equation with complex frequency modes (extended cNMSSE), enabling the treatment of open quantum system dynamics under general spectral densities. This extension employs complete non-exponential basis expansions for the bath correlation functions, thereby generalizing the applicability of the cNMSSE framework beyond environments with Debye-type spectral structures. By preserving the wavefunction-based description and…

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization
Sergii Kavun
https://arxiv.org/abs/2507.22090 https://

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization
Activation functions are critical components in deep neural networks, directly influencing gradient flow, training stability, and model performance. Traditional functions like ReLU suffer from dead neuron problems, while sigmoid and tanh exhibit vanishing gradient issues. We introduce two novel hybrid activation functions: S3 (Sigmoid-Softsign) and its improved version S4 (smoothed S3). S3 combines sigmoid for negative inputs with softsign for positive inputs, while S4 employs a smooth transiti…

Susceptibilities of rotating quark matter in Fourier-Bessel basis
Mamiya Kawaguchi, Kazuya Mameda
https://arxiv.org/abs/2507.00494 https://

Susceptibilities of rotating quark matter in Fourier-Bessel basis
We analyze various two-point correlation functions of fermionic bilinears in a rotating finite-size cylinder at finite temperatures, with a focus on susceptibility functions. Due to the noninvariance of radial translation, the susceptibility functions are constructed using the Dirac propagator in the Fourier-Bessel basis instead of the plane-wave basis. As a specific model to demonstrate the susceptibility functions in an interacting theory, we employ the two-flavor Nambu-Jona-Lasinio model. We…

A Minimal Substitution Basis for the Kalmar Elementary Functions
Mihai Prunescu, Lorenzo Sauras-Altuzarra, Joseph M. Shunia
https://arxiv.org/abs/2505.23787

A Minimal Substitution Basis for the Kalmar Elementary Functions
We show that the class of Kalmar elementary functions can be inductively generated from the addition, the integer remainder and the base-two exponentiation, hence improving previous results by Marchenkov and Mazzanti. In addition, we further prove that the substitution basis defined by these three operations is minimal.

The completed Kirillov model and local-global compatibility for functions on Igusa varieties
Sean Howe
https://arxiv.org/abs/2506.24089 https://

The completed Kirillov model and local-global compatibility for functions on Igusa varieties
We describe the cuspidal functions $\mathbb{V}_b^{\mathrm{cusp}}$ on the ordinary Caraiani-Scholze Igusa variety for $\mathrm{GL}_2$ as a completion of the smooth Kirillov model for classical cuspidal modular forms, and identify a variant of Hida's ordinary $p$-adic modular forms with the coinvariants of an action of $\tildeμ_{p^\infty}$ on $\mathbb{V}_b^{\mathrm{cusp}}$. As a consequence of these results, we establish a weak local-global compatibility theorem for eigenspaces in $\mathbb{V}_b^…

Weighted $K$-$k$-Schur functions and their application to the $K$-$k$-Schur alternating conjecture
Yaozhou Fan, Xing Gao
https://arxiv.org/abs/2507.23222 https://

Weighted $K$-$k$-Schur functions and their application to the $K$-$k$-Schur alternating conjecture
We introduce the new concept of weighted $K$-$k$-Schur functions -- a novel family within the broader class of Katalan functions -- that unifies and extends both $K$-$k$-Schur functions and closed $k$-Schur Katalan functions. This new notion exhibits a fundamental alternating property under certain conditions on the indexed $k$-bounded partitions. As a central application, we resolve the $K$-$k$-Schur alternating conjecture -- posed by Blasiak, Morse, and Seelinger in 2022 -- for a wide class o…

Abstractions of Sequences, Functions and Operators
Louis Rustenholz, Pedro Lopez-Garcia, Manuel V. Hermenegildo
https://arxiv.org/abs/2507.23151 https://ar…

Abstractions of Sequences, Functions and Operators
We present theoretical and practical results on the order theory of lattices of functions, focusing on Galois connections that abstract (sets of) functions - a topic known as higher-order abstract interpretation. We are motivated by the challenge of inferring closed-form bounds on functions which are defined recursively, i.e. as the fixed point of an operator or, equivalently, as the solution to a functional equation. This has multiple applications in program analysis (e.g. cost analysis, loo…

Conditions for solving polynomial equations using algebraic and hypergeometric functions
Nikos Mantzakouras, Carlos L\'opez Zapata, Nid Na Ratch
https://arxiv.org/abs/2507.00027

Conditions for solving polynomial equations using algebraic and hypergeometric functions
In this paper, we focus on clarifying the concept of solving equations of degree greater than six using continuous functions or hypergeometric functions and providing another proof of the non-existence of algebraic solutions for equations of degree greater than four. According to the Kolmogorov-Arnold theorem, we will prove that equations of degree greater than five cannot be solved without special conditions between their coefficients using hypergeometric functions. However, we prove that trin…

The dbcooper package turns a database connection into a collection of functions. #rstats

GitHub - pipeline-tools/dbcooper: Create user-friendly accessor functions from a database connection
Create user-friendly accessor functions from a database connection - pipeline-tools/dbcooper

Differentiable Radar Ambiguity Functions: Mathematical Formulation and Computational Implementation
Marc Bara Iniesta
https://arxiv.org/abs/2506.22935 http…

Differentiable Radar Ambiguity Functions: Mathematical Formulation and Computational Implementation
The ambiguity function is fundamental to radar waveform design, characterizing range and Doppler resolution capabilities. However, its traditional formulation involves non-differentiable operations, preventing integration with gradient-based optimization methods and modern machine learning frameworks. This paper presents the first complete mathematical framework and computational implementation for differentiable radar ambiguity functions. Our approach addresses the fundamental technical challe…

Uncentered Fractional Maximal functions and mean oscillation spaces associated with dyadic Hausdorff content
Riju Basak, You-Wei Benson Chen, Prasun Roychowdhury
https://arxiv.org/abs/2506.23206

Uncentered Fractional Maximal functions and mean oscillation spaces associated with dyadic Hausdorff content
We study the action of uncentered fractional maximal functions on mean oscillation spaces associated with the dyadic Hausdorff content $\mathcal{H}_{\infty}^β$ with $0<β\leq n$. For $0 < α< n$, we refine existing results concerning the action of the Euclidean uncentered fractional maximal function $\mathcal{M}_α$ on the functions of bounded mean oscillations (BMO) and vanishing mean oscillations (VMO). In addition, for $0 < β_1 \leq β_2 \leq n$, we establish the boundedness of the $β_2$-…

Sources: Salesforce and ServiceNow are in talks to invest ~$750M each in Genesys, which uses AI to automate customer service functions, valuing Genesys at ~$15B (Bloomberg)
https://www.bloomberg.com/news/articles/2025-07-31/salesforc…

Lya2pcf: an efficient pipeline to estimate two- and three-point correlation functions of the Lyman-$\alpha$ forest
Josue De-Santiago, Rafael Guti\'errez-Balboa, Gustavo Niz, Alma X. Gonz\'alez-Morales
https://arxiv.org/abs/2507.00129

Lya2pcf: an efficient pipeline to estimate two- and three-point correlation functions of the Lyman-$α$ forest
Studying the matter distribution in the universe through the Lyman-$α$ forest allows us to constrain small-scale physics in the high-redshift regime. Spectroscopic quasar surveys are generating increasingly large datasets that require efficient algorithms to compute correlation functions. Moreover, cosmological analyses based on Lyman-$α$ forests can significantly benefit from incorporating higher-order statistics alongside traditional two-point correlations. In this work, we present Lya2pcf,…

This https://arxiv.org/abs/2308.13135 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Nonparametric Additive Value Functions: Interpretable Reinforcement Learning with an Application to Surgical Recovery
We propose a nonparametric additive model for estimating interpretable value functions in reinforcement learning, with an application in optimizing postoperative recovery through personalized, adaptive recommendations. While reinforcement learning has achieved significant success in various domains, recent methods often rely on black-box approaches such as neural networks, which hinder the examination of individual feature contributions to a decision-making policy. Our novel method offers a fle…

Weak but influential: Nonlinear contributions of structural connectivity to human cognitive abilities and brain functions
Rong Wang, Zhao Chang, Xuechun Liu, Daniel Kristanto, \'Etienne G\'erard Guy Gartner, Xinyang Liu, Mianxin Liu, Ying Wu, Ming Lui, Changsong Zhou
https://arxiv.org/abs/2505.24125

Weak but influential: Nonlinear contributions of structural connectivity to human cognitive abilities and brain functions
Diverse human cognitive abilities are rooted in brain structural connectivity which has weights spanning several orders of magnitude. However, due to false-positive challenges in tractography, weak connectivity has been often treated as noise and ignored - despite its prevalence across mammalian brains. Here we show that weak connectivity significantly predicts human cognitive abilities and supports brain functions through amplification of its small weight in a nonlinear manner. Using the Human…

Some results about varextropy and weighted varextropy functions
Faranak Goodarzi
https://arxiv.org/abs/2506.22996 https://arxiv.org/p…

Some results about varextropy and weighted varextropy functions
In this paper, we investigate several properties of the weighted varextropy measure and obtain it for specific distribution functions, such as the equilibrium and weighted distributions. We also obtain bounds for the weighted varextropy, as well as for weighted residual varextropy and weighted past varextropy. Additionally, we derive an expression for the varextropy of the lifetime of coherent systems. A new stochastic ordering, referred to as weighted varextopy orderind, is introduced, and som…

Hybrid Character Sums From Vectorial Dual-Bent Functions and Asymptotically Optimal Complex Codebooks With Small Alphabet Sizes
Ziling Heng, Peng Wang, Chengju Li
https://arxiv.org/abs/2506.23198

Hybrid Character Sums From Vectorial Dual-Bent Functions and Asymptotically Optimal Complex Codebooks With Small Alphabet Sizes
Hybrid character sums are an important class of exponential sums which have nice applications in coding theory and sequence design. Let $\gf_{p^m}$ be the finite field with $p^m$ elements for a prime $p$ and a positive integer $m$. Let $V_n^{(p)}$ be an $n$-dimensional vector space over $\gf_p$ for a prime $p$. In this paper, we study the hybrid character sums of the form \begin{eqnarray*} \sum_{x \in V_n^{(p)}}ψ\left(F(x)\right)χ_1\left(a x\right), \end{eqnarray*} where $F$ is a function fro…

Towards Large-Scale Condensed Phase Simulations using Machine Learned Energy Functions
Eric D. Boittier, Silvan K\"aser, Markus Meuwly
https://arxiv.org/abs/2506.23272

Towards Large-Scale Condensed Phase Simulations using Machine Learned Energy Functions
Accurate, yet computationally efficient energy functions are essential for state-of-the art molecular dynamics (MD) studies of condensed phase systems. Here, a generic workflow based on a combination of machine learning-based and empirical representations of intra- and intermolecular interactions is presented. The total energy is decomposed into internal contributions, and electrostatic and van der Waals interactions between monomers. The monomer potential energy surface is described using a ne…

This https://arxiv.org/abs/2504.01163 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Minimal pole representation for spectral functions
Representing spectral densities, real-frequency, and real-time Green's functions of continuous systems by a small discrete set of complex poles is an ubiquitous problem in condensed matter physics, with applications ranging from quantum transport simulations to the simulation of strongly correlated electron systems. This paper introduces a method for obtaining a compact, approximate representation of these functions, based on their parameterization on the real axis and a given approximate preci…

Universal Time Evolution of Holographic and Quantum Complexity
Masamichi Miyaji, Shan-Ming Ruan, Shono Shibuya, Kazuyoshi Yano
https://arxiv.org/abs/2507.23667 https://

Universal Time Evolution of Holographic and Quantum Complexity
Holographic complexity, as the bulk dual of quantum complexity, encodes the geometric structure of black hole interiors. Motivated by the complexity=anything proposal, we introduce the spectral representation for generating functions associated with codimension-one and codimension-zero holographic complexity measures. These generating functions exhibit a universal slope-ramp-plateau structure, analogous to the spectral form factor in chaotic quantum systems. In such systems, quantum complexity …

Toponogov comparison and the collar theorem for complete surfaces with an appendix on the level sets of distance functions
Peter Buser, Jose M. Rodriguez
https://arxiv.org/abs/2507.00104

Toponogov comparison and the collar theorem for complete surfaces with an appendix on the level sets of distance functions
In the 1970s, the collar theorem was proven, establishing the existence of uniform tubular neighborhoods of simple closed geodesics on compact surfaces, whose widths depend only on the lengths of the geodesics and the lower bound of the curvature, but not on the surface. In this paper, we improve this result by eliminating the compactness hypothesis. To achieve this result, we needed to prove new Toponogov-type triangle comparison theorems. We also add a new theorem to the literature on the rec…

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations
Melissa Antonelli, Arnaud Durand, Juha Kontinen
https://arxiv.org/abs/2506.23404

Characterizing Small Circuit Classes from FAC^0 to FAC^1 via Discrete Ordinary Differential Equations
In this paper, we provide a uniform framework for investigating small circuit classes and bounds through the lens of ordinary differential equations (ODEs). Following an approach recently introduced to capture the class of polynomial-time computable functions via ODE-based recursion schemas and later applied to the context of functions computed by unbounded fan-in circuits of constant depth (FAC^0), we study multiple relevant small circuit classes. In particular, we show that natural restrictio…

One of the goals I've set for further development of #Python eclasses in #Gentoo was to avoid needless complexity. Unfortunately, the subject matter sometimes requires them. However, many of the functions added lately were already manually done in ebuilds for years.
We've started disabling plugin autoloading years ago. First we just did that for individual packages that caused issues. Then, for these where tests ended up being really slow. Finally, pretty much anywhere `python_test()` was declared. Doing it all manually was particularly cumbersome — all I needed for `EPYTEST_PLUGINS` is a good idea how to generalize it.
Similarly, `EPYTEST_XDIST` was added after we have been adding manually `epytest -p xdist -n "$(makeopts_jobs)" --dist=worksteal` — and while at it, I've added `EPYTEST_JOBS` to override the job count.
Perhaps `EPYTEST_TIMEOUT` wasn't that common. However, it was meant to help CI systems that could otherwise get stuck on hanging test.
Similarly, "standard library" version (like `3.9`) matching to `python_gen_cond_dep` was added after a long period of explicitly stating `python3_9 pypy3`. As an extra benefit, this also resolved the problem that at the time `pypy3` could mean different Python versions.

ViscoReg: Neural Signed Distance Functions via Viscosity Solutions
Meenakshi Krishnan, Ramani Duraiswami
https://arxiv.org/abs/2507.00412 https://

ViscoReg: Neural Signed Distance Functions via Viscosity Solutions
Implicit Neural Representations (INRs) that learn a Signed Distance Function (SDF) are a powerful tool for continuous 3D scene reconstruction. These models are trained by enforcing the Eikonal equation. We demonstrate theoretically that despite the ill-posedness of the Eikonal equation, generalization error estimates may be obtained for Neural SDFs in terms of the training error. However, training with the Eikonal loss can lead to unstable gradient flows, necessitating alternate stabilization t…

Biobjective optimization with M-convex functions
Ellen H. Fukuda, Satoru Iwata, Itsuki Nakagawa
https://arxiv.org/abs/2507.23423 https://arxiv.org/pdf/2507…

Biobjective optimization with M-convex functions
In this paper, we deal with two ingredients that, as far as we know, have not been combined until now: multiobjective optimization and discrete convex analysis. First, we show that the entire Pareto optimal value set can be obtained in polynomial time for biobjective optimization problems with discrete convex functions, in particular, involving an M$^\natural$-convex function and a linear function with binary coefficients. We also observe that a more efficient algorithm can be obtained in the s…

Reducing Profile-Based Matching to the Maximum Weight Matching Problem
Seongbeom Park
https://arxiv.org/abs/2507.00047 https://arxiv.…

Reducing Profile-Based Matching to the Maximum Weight Matching Problem
The profile-based matching problem is the problem of finding a matching that optimizes profile from an instance $(G, r, \langle u_1, \dots, u_r \rangle)$, where $G$ is a bipartite graph $(A \cup B, E)$, $r$ is the number of utility functions, and $u_i: E \to \{ 0, 1, \dots, U_i \}$ is utility functions for $1 \le i \le r$. A matching is optimal if the matching maximizes the sum of the 1st utility, subject to this, maximizes the sum of the 2nd utility, and so on. The profile-based matching can e…

What’s the difference between ordinary functions and arrow functions in JavaScript?
Arrow functions (also known as ‘rocket’ functions) are concise and convenient. However, they have subtle differences compared to function declarations and function expressions. So how do you know which one to use, and when?
🧑‍💻

What’s the difference between ordinary functions and arrow functions in JavaScript?
Arrow functions (also known as ‘rocket’ functions) are concise and convenient. However, they have subtle differences compared to function declarations and function expressions. So how do you know which one to use, and when?

Sensitivity analysis of epidemic forecasting and spreading on networks with probability generating functions
Mariah C. Boudreau, William H. W. Thompson, Christopher M. Danforth, Jean-Gabriel Young, Laurent H\'ebert-Dufresne
https://arxiv.org/abs/2506.24103

Sensitivity analysis of epidemic forecasting and spreading on networks with probability generating functions
Epidemic forecasting tools embrace the stochasticity and heterogeneity of disease spread to predict the growth and size of outbreaks. Conceptually, stochasticity and heterogeneity are often modeled as branching processes or as percolation on contact networks. Mathematically, probability generating functions provide a flexible and efficient tool to describe these models and quickly produce forecasts. While their predictions are probabilistic-i.e., distributions of outcome-they depend determinist…

Stochastic Neural Control Barrier Functions
Hongchao Zhang, Manan Tayal, Jackson Cox, Pushpak Jagtap, Shishir Kolathaya, Andrew Clark
https://arxiv.org/abs/2506.21697

Stochastic Neural Control Barrier Functions
Control Barrier Functions (CBFs) are utilized to ensure the safety of control systems. CBFs act as safety filters in order to provide safety guarantees without compromising system performance. These safety guarantees rely on the construction of valid CBFs. Due to their complexity, CBFs can be represented by neural networks, known as neural CBFs (NCBFs). Existing works on the verification of the NCBF focus on the synthesis and verification of NCBFs in deterministic settings, leaving the stochast…

Exploring Many-Body Quantum Geometry Beyond the Quantum Metric with Correlation Functions: A Time-Dependent Perspective
Yuntao Guan, Barry Bradlyn
https://arxiv.org/abs/2507.23028

Exploring Many-Body Quantum Geometry Beyond the Quantum Metric with Correlation Functions: A Time-Dependent Perspective
The quantum geometric tensor and quantum Fisher information have recently been shown to provide a unified geometric description of the linear response of many-body systems. However, a similar geometric description of higher-order perturbative phenomena including nonlinear response in generic quantum systems is lacking. In this work, we develop a general framework for the time-dependent quantum geometry of many-body systems by treating external perturbing fields as coordinates on the space of de…

Complex wave functions, CPT and quantum field theory for classical generalized Ising models
Christof Wetterich
https://arxiv.org/abs/2505.24392 https://

Complex wave functions, CPT and quantum field theory for classical generalized Ising models
The quantum or quantum field theory concept of a complex wave function is useful for understanding the information transport in classical statistical generalized Ising models. We relate complex conjugation to the discrete transformations charge conjugation ($C$), parity ($P$) and time reversal ($T$). A subclass of generalized Ising models are probabilistic cellular automata (PCA) with deterministic updating and probabilistic initial conditions. Two-dimensional PCA correspond to discretize…

A linear topological invariant for weighted spaces of holomorphic functions
Andreas Debrouwere, Quinten Van Boxstael
https://arxiv.org/abs/2506.23695 https…

A linear topological invariant for weighted spaces of holomorphic functions
We study the linear topological invariant $(Ω)$ for a class of Fréchet spaces of holomorphic functions of rapid decay on strip-like domains in the complex plane, defined via weight function systems. We obtain a complete characterization of the property $(Ω)$ for such spaces in terms of an explicit condition on the defining weight function systems. As an application, we investigate the surjectivity of the Cauchy-Riemann operator on certain weighted spaces of vector-valued smooth functions.

Pok\'eAI: A Goal-Generating, Battle-Optimizing Multi-agent System for Pokemon Red
Zihao Liu, Xinhang Sui, Yueran Song, Siwen Wang
https://arxiv.org/abs/2506.23689

PokéAI: A Goal-Generating, Battle-Optimizing Multi-agent System for Pokemon Red
We introduce PokéAI, the first text-based, multi-agent large language model (LLM) framework designed to autonomously play and progress through Pokémon Red. Our system consists of three specialized agents-Planning, Execution, and Critique-each with its own memory bank, role, and skill set. The Planning Agent functions as the central brain, generating tasks to progress through the game. These tasks are then delegated to the Execution Agent, which carries them out within the game environment. Up…

Replaced article(s) found for cs.LO. https://arxiv.org/list/cs.LO/new
[1/1]:
- On the Number of Quantifiers Needed to Define Boolean Functions
Marco Carmosino, Ronald Fagin, Neil Immerman, Phokion Kolaitis, Jonathan Lenchner, Rik Sengupta

Distributed Neural Policy Gradient Algorithm for Global Convergence of Networked Multi-Agent Reinforcement Learning
Pengcheng Dai, Yuanqiu Mo, Wenwu Yu, Wei Ren
https://arxiv.org/abs/2505.24113

Distributed Neural Policy Gradient Algorithm for Global Convergence of Networked Multi-Agent Reinforcement Learning
This paper studies the networked multi-agent reinforcement learning (NMARL) problem, where the objective of agents is to collaboratively maximize the discounted average cumulative rewards. Different from the existing methods that suffer from poor expression due to linear function approximation, we propose a distributed neural policy gradient algorithm that features two innovatively designed neural networks, specifically for the approximate Q-functions and policy functions of agents. This distri…

Verifying Properties of Index Arrays in a Purely-Functional Data-Parallel Language
Nikolaj Hey Hinnerskov, Robert Schenck, Cosmin E. Oancea
https://arxiv.org/abs/2506.23058

Verifying Properties of Index Arrays in a Purely-Functional Data-Parallel Language
This paper presents a novel approach to automatically verify properties of pure data-parallel programs with non-linear indexing -- expressed as pre- and post-conditions on functions. Programs consist of nests of second-order array combinators (e.g., map, scan, and scatter) and loops. The key idea is to represent arrays as index functions: programs are index function transformations over which properties are propagated and inferred. Our framework proves properties on index functions by distillin…

An improved upper bound for the distribution of iterated Euler totient functions
Pei Gao, Qiyu Yang
https://arxiv.org/abs/2506.23882 https://

An improved upper bound for the distribution of iterated Euler totient functions
Let $ϕ(n)$ be the Euler totient function and $ϕ_k(n)$ its $k$-fold iterate. In this note, we improve the upper bound for the number of positive $n\leqslant x$ such that $ϕ_{k+1}(n)\geqslant cn$. Comparing with the upper bound which was obtained from Pollack's asymptotic formula of the summation of $ϕ_{k+1}(n)$ for $n\leqslant x$, we have successfully increased the denominator exponent of the main term of the upper bound from $k$ to $k+1$.

Dicritical divisors and hypercurvettes
Enrique Artal Bartolo, Willem Veys
https://arxiv.org/abs/2505.24648 https://arxiv.org/pdf/2505…

Dicritical divisors and hypercurvettes
Germs of rational functions~$h$ on points $p$ of smooth varieties~$S$ define germs of rational maps to the projective line. Assume that $p$ is in the indeterminacy locus of $h$. If $π:\hat{S}\to S$ is a birational map which is an isomorphism outside $p$, then $h$ lifts to a germ of a rational map on $(\hat{S}, π^{-1}(p))$. The exceptional components $E_i$ of $π^{-1}(p)$ are classified according to the restriction of (the lift of) $h$ to $E_i$; the dicritical components are those where this r…

Single-shot HDR using conventional image sensor shutter functions and optical randomization
Xiang Dai, Kyrollos Yanny, Kristina Monakhova, Nicholas Antipa
https://arxiv.org/abs/2506.22426

Single-shot HDR using conventional image sensor shutter functions and optical randomization
High-dynamic-range (HDR) imaging is an essential technique for overcoming the dynamic range limits of image sensors. The classic method relies on multiple exposures, which slows capture time, resulting in motion artifacts when imaging dynamic scenes. Single-shot HDR imaging alleviates this issue by encoding HDR data into a single exposure, then computationally recovering it. Many established methods use strong image priors to recover improperly exposed image detail. These approaches struggle wi…

Real Noncommutative Convexity II: Extremality and nc convex functions
David P. Blecher, Caleb Becker McClure
https://arxiv.org/abs/2507.22833 https://arxiv…

Real Noncommutative Convexity II: Extremality and nc convex functions
We continue with the theory of real noncommutative (nc) convexity, following the recent and profound complex case developed by Davidson and Kennedy. The present paper focuses on the theory of nc extreme (and pure and maximal) points and the nc Choquet boundary in the real case, and on the theory of real nc convex and semicontinuous functions and real nc convex envelopes. Our main emphasis is on how these interact with complexification. For example some of our paper analyzes carefully how variou…

Stealtooth: Breaking Bluetooth Security Abusing Silent Automatic Pairing
Keiichiro Kimura, Hiroki Kuzuno, Yoshiaki Shiraishi, Masakatu Morii
https://arxiv.org/abs/2507.00847

Stealtooth: Breaking Bluetooth Security Abusing Silent Automatic Pairing
Bluetooth is a pervasive wireless communication technology used by billions of devices for short-range connectivity. The security of Bluetooth relies on the pairing process, where devices establish shared long-term keys for secure communications. However, many commercial Bluetooth devices implement automatic pairing functions to improve user convenience, creating a previously unexplored attack surface. We present Stealtooth, a novel attack that abuses unknown vulnerabilities in the automatic …

CodableLLM: Automating Decompiled and Source Code Mapping for LLM Dataset Generation
Dylan Manuel, Paul Rad
https://arxiv.org/abs/2507.22066 https://arxiv.…

CodableLLM: Automating Decompiled and Source Code Mapping for LLM Dataset Generation
The generation of large, high-quality datasets for code understanding and generation remains a significant challenge, particularly when aligning decompiled binaries with their original source code. To address this, we present CodableLLM, a Python framework designed to automate the creation and curation of datasets by mapping decompiled functions to their corresponding source functions. This process enhances the alignment between decompiled and source code representations, facilitating the devel…

On completely monotonic functions
Mostafa Najafi, Ali Morassaei
https://arxiv.org/abs/2505.23767 https://arxiv.org/pdf/2505.23767

On completely monotonic functions
Let $ f:(0,\infty)\rightarrow \Bbb{R} $ be a completely monotonic function. In this paper, we present some properties of this functions and several new classes of completely monotonic functions. We also give some special functions such that its have completely monotonic condition.

Cosmology with Distinct Functions $f$ of the Non-metricity Scalar $Q$ : A Dynamical System Approach
Promila Biswas, Subhajit Pal, Ritabrata Biswas, Satyajit Pal
https://arxiv.org/abs/2506.21646

Cosmology with Distinct Functions $f$ of the Non-metricity Scalar $Q$ : A Dynamical System Approach
Symmetric teleparallel gravity is one among the general relativistic trinity which deals with the non-metricity scalar $Q$. In the Einstein Hilbert action, a function of $Q$ is chosen to be the main contributory part of the Lagrangian and a modified theory of gravity is constructed. In literature, different structures of the function of $Q$ are found which sustain several astrophysical observations like Big Bang nucleosynthesis, late-time cosmic acceleration etc. Autonomous systems for each suc…

A Novel Discrete Memristor-Coupled Heterogeneous Dual-Neuron Model and Its Application in Multi-Scenario Image Encryption
Yi Zou, Mengjiao Wang, Xinan Zhang, Herbert Ho-Ching Iu
https://arxiv.org/abs/2505.24294

A Novel Discrete Memristor-Coupled Heterogeneous Dual-Neuron Model and Its Application in Multi-Scenario Image Encryption
Simulating brain functions using neural networks is an important area of research. Recently, discrete memristor-coupled neurons have attracted significant attention, as memristors effectively mimic synaptic behavior, which is essential for learning and memory. This highlights the biological relevance of such models. This study introduces a discrete memristive heterogeneous dual-neuron network (MHDNN). The stability of the MHDNN is analyzed with respect to initial conditions and a range of neuro…

The Clear Winner in Trump v. CASA: The Supreme Court (Jack Goldsmith/Executive Functions)
https://executivefunctions.substack.com/p/the-clear-winner-in-trump-v-casa
http://www.memeorandum.com/250629/p66#a250629p66

A note on D-functions and P-covariances on Hilbert spaces and related inequalities
Sergio Scarlatti
https://arxiv.org/abs/2507.00009 https://

A note on D-functions and P-covariances on Hilbert spaces and related inequalities
In this note we first review the concept of D-function, closely connected with Cauchy-Schwarz inequality, and then introduce the notion of P-covariance on a Hilbert space, where $P$ is an orthogonal projection. We show that when P is specialized to be one-dimensional many well-known inequalities such as Buzano, Richard and Walker inequalities are simple consequences of P-covariance inequalities and their relation with D-functions. By means of these concepts enhancements of the previous mentione…

The ArborX library: version 2.0
Andrey Prokopenko, Daniel Arndt, Damien Lebrun-Grandi\'e, Bruno Turcksin
https://arxiv.org/abs/2507.23700 https://arxiv…

The ArborX library: version 2.0
This paper provides an overview of the 2.0 release of the ArborX library, a performance portable geometric search library based on Kokkos. We describe the major changes in ArborX 2.0 including a new interface for the library to support a wider range of user problems, new search data structures (brute force, distributed), support for user functions to be executed on the results (callbacks), and an expanded set of the supported algorithms (ray tracing, clustering).

Scaling functions in the soft-wall AdS/QCD models
Zhongzheng Zhang, Danning Li, Lang Yu, Zhibin Li, Xinyang Wang
https://arxiv.org/abs/2507.22724 https://a…

Scaling functions in the soft-wall AdS/QCD models
We investigate the static scaling behavior of the chiral condensate near the two-flavor critical point within the framework of the soft-wall AdS/QCD. The scaling functions are extracted from the chiral order parameters and are found to precisely match those obtained through mean-field calculations. Additionally, it is also checked that the scaling functions are independent of the specific construction of the holographic model. Furthermore, we develop the formalism for calculating the chiral sus…

Enhanced Thermodynamic Framework for Third-Order Galaxy Correlation Functions: From Theory to Observations
Sameer Choudhary, Naseer Iqbal
https://arxiv.org/abs/2506.23829

Enhanced Thermodynamic Framework for Third-Order Galaxy Correlation Functions: From Theory to Observations
We present a comprehensive thermodynamic derivation and observational validation of the third-order galaxy correlation function, extending the seminal work of Iqbal et al [ 1, 2]. Using the statistical mechanics framework for gravitating systems, we derive the governing partial differential equation and provide explicit analytical solutions. Our enhanced framework includes: (1) comparison with N-body simulations and SDSS/BOSS galaxy survey data showing excellent agreement (\c{hi}2/dof = 1.27), …

Quadrature Over-the-Air-Computing for Multimodal Dual-Stream Signal Processing
Hyeon Seok Rou, Kengo Ando, Giuseppe Thadeu Freitas de Abreu, David Gonz\'alez G
https://arxiv.org/abs/2507.00508

Quadrature Over-the-Air-Computing for Multimodal Dual-Stream Signal Processing
We propose a novel quadrature over-the-air computing (Q-OTAC) framework that enables the simultaneously computation of two independent functions and/or data stream within a single transmission. In contrast to conventional OTAC schemes, where a single function is computed by treating each complex signal as a single component, the proposed Q-OTAC exploits both in-phase and quadrature (IQ) components of a complex signal, encoding two distinct functions and/or data streams at the edge devices (EDs)…

Simultaneous Sieve Estimation and Inference for Time-Varying Nonlinear Time Series Regression
Xiucai Ding, Zhou Zhou
https://arxiv.org/abs/2506.23069 https…

Simultaneous Sieve Estimation and Inference for Time-Varying Nonlinear Time Series Regression
In this paper, we investigate time-varying nonlinear time series regression for a broad class of locally stationary time series. First, we propose sieve nonparametric estimators for the time-varying regression functions that achieve uniform consistency. Second, we develop a unified simultaneous inferential theory to conduct both structural and exact form tests on these functions. Additionally, we introduce a multiplier bootstrap procedure for practical implementation. Our methodology and theory…

On compact sets possessing $q$-convex functions
Thomas Pawlaschyk, Nikolay Shcherbina
https://arxiv.org/abs/2505.24588 https://arxiv.…

On compact sets possessing $q$-convex functions
We show that there exists a $q$-convex function in a neighborhood of a compact set $K$ in a complex manifold $\mathcal{M}$ if and only if the $q$-nucleus of this compact set is empty. The latter can be characterized as the maximal $q$-pseudoconcave subset of $K$, i.e., a subset of $K$ containing all other compact $q$-pseudoconcave subsets in $K$.

On Weary Drivers, Records of Trees, and Parking Functions
Adri\'an Lillo, Mercedes Rosas, Stefan Trandafir
https://arxiv.org/abs/2506.22145 https://

On Weary Drivers, Records of Trees, and Parking Functions
This work builds on a decomposition of a Cayley tree using the notion of a record, a concept closely related to the blob encoding of a tree introduced by Kreweras and Moszkowski, and Picciotto, that we explore and extend. We provide an alternative definition of parking functions and derive from it a record-preserving bijection between Cayley trees and parking functions. Finally, we use this bijection to establish an equidistribution between a sextuple of statistics on Cayley trees and a corresp…

Applications of Fa\`{a} di Bruno's formula to partition traces
Toshiki Matsusaka
https://arxiv.org/abs/2507.00404 https://arxiv.o…

Applications of Faà di Bruno's formula to partition traces
We revisit several partition-theoretic generating functions, including the theta quotients from Ramanujan's lost notebook, MacMahon's partition functions, and reciprocal sums of parts in partitions, through the lens of the classical Faà di Bruno formula. This approach offers a unified and natural reinterpretation of known results and provides a systematic framework for deriving new identities of a similar type.

Analyzing Time-Varying Scalar Fields using Piecewise-Linear Morse-Cerf Theory
Amritendu Dhar, Apratim Chakraborty, Vijay Natarajan
https://arxiv.org/abs/2507.00725

Analyzing Time-Varying Scalar Fields using Piecewise-Linear Morse-Cerf Theory
Morse-Cerf theory considers a one-parameter family of smooth functions defined on a manifold and studies the evolution of their critical points with the parameter. This paper presents an adaptation of Morse-Cerf theory to a family of piecewise-linear (PL) functions. The vertex diagram and Cerf diagram are introduced as representations of the evolution of critical points of the PL function. The characterization of a crossing in the vertex diagram based on the homology of the lower links of verti…

{slider} helps with aggregation over (sliding) windows, both index and time period based: #rstats

GitHub - r-lib/slider: Sliding Window Functions
Sliding Window Functions. Contribute to r-lib/slider development by creating an account on GitHub.

Scientific Machine Learning with Kolmogorov-Arnold Networks
Salah A. Faroughi, Farinaz Mostajeran, Amin Hamed Mashhadzadeh, Shirko Faroughi
https://arxiv.org/abs/2507.22959 http…

Scientific Machine Learning with Kolmogorov-Arnold Networks
The field of scientific machine learning, which originally utilized multilayer perceptrons (MLPs), is increasingly adopting Kolmogorov-Arnold Networks (KANs) for data encoding. This shift is driven by the limitations of MLPs, including poor interpretability, fixed activation functions, and difficulty capturing localized or high-frequency features. KANs address these issues with enhanced interpretability and flexibility, enabling more efficient modeling of complex nonlinear interactions and effe…

Lower bounds for trace estimation via Block Krylov and other methods
Shi Jie Yu
https://arxiv.org/abs/2506.22701 https://arxiv.org/pd…

Lower bounds for trace estimation via Block Krylov and other methods
This paper studies theoretical lower bounds for estimating the trace of a matrix function, $\text{tr}(f(A))$, focusing on methods that use Hutchinson's method along with Block Krylov techniques. These methods work by approximating matrix-vector products like $f(A)V$ using a Block Krylov subspace. This is closely related to approximating functions with polynomials. We derive theoretical upper bounds on how many Krylov steps are needed for functions such as $A^{-1/2}$ and $A^{-1}$ by analyzing th…

Agentic Enterprise: AI-Centric User to User-Centric AI
Arpit Narechania, Alex Endert, Atanu R Sinha
https://arxiv.org/abs/2506.22893 https://

Agentic Enterprise: AI-Centric User to User-Centric AI
After a very long winter, the Artificial Intelligence (AI) spring is here. Or, so it seems over the last three years. AI has the potential to impact many areas of human life - personal, social, health, education, professional. In this paper, we take a closer look at the potential of AI for Enterprises, where decision-making plays a crucial and repeated role across functions, tasks, and operations. We consider Agents imbued with AI as means to increase decision-productivity of enterprises. We hi…

Explicit formulas for extremals in sub-Lorentzian and Finsler problems on 2- and 3-dimensional Lie groups
E. A. Ladeishchikov, L. V. Lokutsievskiy, N. V. Prilepin
https://arxiv.org/abs/2507.00250

Explicit formulas for extremals in sub-Lorentzian and Finsler problems on 2- and 3-dimensional Lie groups
In this paper, we consider the problem of finding geodesics in a series of left-invariant problems endowed with sub-Lorentzian and Finsler structures. Explicit formulas for extremals are obtained in terms of convex trigonometric functions. In the sub-Lorentzian setting, the new trigonometric functions $\cosh_Ω$ and $\sinh_Ω$, developed here, prove especially useful; they generalize the classical $\cosh$ and $\sinh$ to the case of an unbounded convex set $Ω\subset\mathbb{R}^2$.

Fant\^omas Unconfined: global QCD fits with B\'ezier parameterizations
Lucas Kotz, Aurore Courtoy, T. J. Hobbs, Pavel Nadolsky, Fredrick Olness, Maximiliano Ponce-Chavez, Varada Purohit
https://arxiv.org/abs/2507.22969

Fantômas Unconfined: global QCD fits with Bézier parameterizations
Fantômas is a C++ toolkit for exploring the parametrization dependence of parton distribution functions (PDFs) and other correlator functions in quantum chromodynamics (QCD). Fantômas facilitates the generation of adaptable polynomial parametrizations for PDFs, called metamorphs, to find best-fit PDF solutions and quantify the epistemic uncertainty associated with the parametrizations during their fitting. The method employs Bézier curves as universal approximators for a variety of PDF shape…

The Multivariate Herglotz-Nevanlinna Class: Superresolution
Mainak Bhowmik, Mihai Putinar
https://arxiv.org/abs/2505.24425 https://ar…

The Multivariate Herglotz-Nevanlinna Class: Superresolution
Unique solutions of bounded, or equivalently, non-negative real part, holomorphic interpolation in several complex variables with finite prescribed data are very rare, with rational inner functions in a polydisk as the best understood examples. We analyze the continuity of global solutions as functions of the finite interpolation data in neighborhoods of elements distinguished by this uniqueness property. Our study covers rational inner functions in the polydisk and automorphisms of the Euclide…

One-Parametric Presburger Arithmetic has Quantifier Elimination
Alessio Mansutti, Mikhail R. Starchak
https://arxiv.org/abs/2506.23730 https://

One-Parametric Presburger Arithmetic has Quantifier Elimination
We give a quantifier elimination procedure for one-parametric Presburger arithmetic, the extension of Presburger arithmetic with the function $x \mapsto t \cdot x$, where $t$ is a fixed free variable ranging over the integers. This resolves an open problem proposed in [Bogart et al., Discrete Analysis, 2017]. As conjectured in [Goodrick, Arch. Math. Logic, 2018], quantifier elimination is obtained for the extended structure featuring all integer division functions $x \mapsto \lfloor{\frac{x}{f(…

On Higher Order Busy Beaver Function
Zining Cao
https://arxiv.org/abs/2507.20321 https://arxiv.org/pdf/2507.20321…

On Higher Order Busy Beaver Function
In this paper, we extend Busy Beaver function to a class of higher order Busy Beaver functions based on Turing oracle machine. We prove some results about the relation between decidability of number theoretical formula and higher order Busy Beaver functions, and the relation between computability of max-min partial recursive functions and higher order Busy Beaver functions. We also present some conjectures on higher order Busy Beaver functions.

This https://arxiv.org/abs/2502.03503 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Analyzing limits for in-context learning
We examine limits of in-context learning (ICL) in transformer models trained from scratch, focusing on function approximation tasks as a controlled setting to uncover fundamental behaviors. While we show empirically that transformer models can generalize, approximating unseen classes of polynomial (non linear) functions, they cannot generalize beyond certain values. We provide both empirical and mathematical arguments explaining that these limitations stem from architectural components, namely …

AutoBridge: Automating Smart Device Integration with Centralized Platform
Siyuan Liu, Zhice Yang, Huangxun Chen
https://arxiv.org/abs/2507.23178 https://ar…

AutoBridge: Automating Smart Device Integration with Centralized Platform
Multimodal IoT systems coordinate diverse IoT devices to deliver human-centered services. The ability to incorporate new IoT devices under the management of a centralized platform is an essential requirement. However, it requires significant human expertise and effort to program the complex IoT integration code that enables the platform to understand and control the device functions. Therefore, we propose AutoBridge to automate IoT integration code generation. Specifically, AutoBridge adopts a …

Generalized chord diagrams and weight systems
M. Kazarian, E. Krasilnikov, S. Lando, M. Shapiro
https://arxiv.org/abs/2505.24491 https://

Generalized chord diagrams and weight systems
Weight systems are functions on chord diagrams satisfying Vassiliev's $4$-term relations. They originate in the theory of finite type knot invariants. Recent developments in understanding weight systems arising from Lie algebras are based on extending these weight systems from chord diagrams (which can be interpreted as involutions without fixed points, considered modulo cyclic shifts) to arbitrary permutations (also modulo cyclic shifts). We suggest relations for functions on permutations, whi…

Deep learning-derived arterial input function
Junyu Chen, Zirui Jiang, Jennifer M. Coughlin, Martin G. Pomper, Yong Du
https://arxiv.org/abs/2505.24166 htt…

Deep learning-derived arterial input function
Dynamic positron emission tomography (PET) imaging combined with radiotracer kinetic modeling is a powerful technique for visualizing biological processes in the brain, offering valuable insights into brain functions and neurological disorders such as Alzheimer's and Parkinson's diseases. Accurate kinetic modeling relies heavily on the use of a metabolite-corrected arterial input function (AIF), which typically requires invasive and labor-intensive arterial blood sampling. While alternative non…

Equidistribution and arithmetic $\Lambda$-distributions
Matthew Bertucci, Sean Howe
https://arxiv.org/abs/2505.24748 https://arxiv.or…

Equidistribution and arithmetic $Λ$-distributions
We formulate an abstract notion of equidistribution for families of $λ$-probability spaces parameterized by admissible $\mathbb{Z}$-sets. Under the assumption of equidistribution, we show that the $σ$-moment generating functions of certain infinite sums of random variables can be computed as motivic Euler products. Combining this result with earlier generalizations of Poonen's sieve, we compute the asymptotic $Λ$-distributions for several natural families of function field $L$-functions and …

Bounded Pluriharmonic Functions and Holomorphic Functions on Teichm\"uller Space II -- Poisson integral formula --
Hideki Miyachi
https://arxiv.org/abs/2507.19930 https://

Bounded Pluriharmonic Functions and Holomorphic Functions on Teichmüller Space II -- Poisson integral formula --
In this paper, we establish the Poisson integral formula for bounded pluriharmonic functions on the Teichmüller space of analytically finite Riemann surfaces of type $(g,m)$ with $2g-2+m>0$. We also discuss a version of the F. and M. Riesz theorem concerning the value distribution of plurisubharmonic functions on the Teichmüller space, as well as a Teichmüller-theoretic interpretation of the mean value theorem for pluriharmonic functions.

Soft and virtual corrections to semi-inclusive DIS up to four loops in QCD
Saurav Goyal, Sven-Olaf Moch, Vaibhav Pathak, Narayan Rana, V. Ravindran
https://arxiv.org/abs/2506.24078

Soft and virtual corrections to semi-inclusive DIS up to four loops in QCD
We apply the threshold resummation formalism for semi-inclusive deep-inelastic scattering (SIDIS) to derive the soft and virtual corrections for the SIDIS cross section up to four loops in QCD. Using the recently computed next-to-next-to-leading order QCD corrections for the SIDIS cross section together with known results for the form factor and splitting functions in QCD up to four loops, we derive the complete soft and collinear contributions to the SIDIS coefficient functions at four-loop or…

Hidden shift problem for complex functions
Serge Adonsou, Peter Bruin, Maris Ozols, Joppe Stokvis
https://arxiv.org/abs/2507.19440 https://arxiv.org/pdf/25…

Hidden shift problem for complex functions
We study quantum algorithms for the hidden shift problem of complex scalar- and vector-valued functions on finite abelian groups. Given oracle access to a shifted function and the Fourier transform of the unshifted function, the goal is to find the hidden shift. We analyze the success probability of our algorithms when using a constant number of queries. For bent functions, they succeed with probability 1, while for arbitrary functions the success probability depends on the `bentness' of the fu…

This https://arxiv.org/abs/2505.13182 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

Information Science Principles of Machine Learning: A Causal Chain Meta-Framework Based on Formalized Information Mapping
[Objective] This study focuses on addressing the current lack of a unified formal theoretical framework in machine learning, as well as the deficiencies in interpretability and ethical safety assurance. [Methods] A formal information model is first constructed, utilizing sets of well-formed formulas to explicitly define the ontological states and carrier mappings of typical components in machine learning. Learnable and processable predicates, along with learning and processing functions, are in…

Universal Modelling of Autocovariance Functions via Spline Kernels
Lachlan Astfalck
https://arxiv.org/abs/2506.21953 https://arxiv.or…

Universal Modelling of Autocovariance Functions via Spline Kernels
Flexible modelling of the autocovariance function (ACF) is central to time-series, spatial, and spatio-temporal analysis. Modern applications often demand flexibility beyond classical parametric models, motivating non-parametric descriptions of the ACF. Bochner's Theorem guarantees that any positive spectral measure yields a valid ACF via the inverse Fourier transform; however, existing non-parametric approaches in the spectral domain rarely return closed-form expressions for the ACF itself. We…

Sensitivity and Query Complexity under Uncertainty
Deepu Benson, Balagopal Komarath, Nikhil Mande, Sai Soumya Nalli, Jayalal Sarma, Karteek Sreenivasaiah
https://arxiv.org/abs/2507.00148

Sensitivity and Query Complexity under Uncertainty
In this paper, we study the query complexity of Boolean functions in the presence of uncertainty, motivated by parallel computation with an unlimited number of processors where inputs are allowed to be unknown. We allow each query to produce three results: zero, one, or unknown. The output could also be: zero, one, or unknown, with the constraint that we should output ''unknown'' only when we cannot determine the answer from the revealed input bits. Such an extension of a Boolean function is ca…

The functions in the {withr} package allow to change your environment temporarily. E.g. create a temp file for a {testthat} test and clean it up afterwards. #rstats

Run Code With Temporarily Modified Global State
A set of functions to run code with safely and temporarily modified global state. Many of these functions were originally a part of the devtools package, this provides a simple package with limited dependencies to provide access to these functions.

A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm
Marco Rando, Cheik Traor\'e, Cesare Molinari, Lorenzo Rosasco, Silvia Villa
https://arxiv.org/abs/2506.23758

A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm
Minimizing finite sums of functions is a central problem in optimization, arising in numerous practical applications. Such problems are commonly addressed using first-order optimization methods. However, these procedures cannot be used in settings where gradient information is unavailable. Finite-difference methods provide an alternative by approximating gradients through function evaluations along a set of directions. For finite-sum minimization problems, it was shown that incorporating varian…

This https://arxiv.org/abs/2504.00847 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

From learnable objects to learnable random objects
We consider the relationship between learnability of a "base class" of functions on a set $X$, and learnability of a class of statistical functions derived from the base class. For example, we refine results showing that learnability of a family $h_p: p \in Y$ of functions implies learnability of the family of functions $h_μ=λp: Y. E_μ(h_p)$, where $E_μ$ is the expectation with respect to $μ$, and $μ$ ranges over probability distributions on $X$. We will look at both Probably Approximatel…

Coh zeta functions for inert quadratic orders
Yifeng Huang
https://arxiv.org/abs/2507.21966 https://arxiv.org/pdf/2507.21966…

Coh zeta functions for inert quadratic orders
We study the Coh zeta function for a family of inert quadratic orders, which we conjecture to be given by $t$-deformed Bressoud $q$-series. This completes a trilogy connecting the zeta functions of ramified and split quadratic orders to the classical Andrews--Gordon and Bressoud identities, respectively. We provide strong evidence for this conjecture by deriving the first explicit formulas for the finitized Coh zeta function of the simplest order in the family, and for the $t=1$ specialization …

A tableaux formula for $q$-rook numbers
Tirtharaj Basu, Aritra Bhattacharya
https://arxiv.org/abs/2507.00766 https://arxiv.org/pdf/25…

A tableaux formula for $q$-rook numbers
We provide a formula for the Garsia-Remmel $q$-rook numbers as a sum over standard Young tableaux. We connect our formula with the coefficients in $q$-Whittaker expansion of unicellular LLT functions.

Approximation of starshaped sets using polynomials
Chiara Meroni, Jared Miller, Mauricio Velasco
https://arxiv.org/abs/2505.24352 https://

Approximation of starshaped sets using polynomials
We introduce polystar bodies: compact starshaped sets whose gauge or radial functions are expressible by polynomials, enabling tractable computations, such as that of intersection bodies. We prove that polystar bodies are uniformly dense in starshaped sets and obtain asymptotically optimal approximation guarantees. We develop tools for the construction of polystar approximations and illustrate them via several computational examples, including numerical estimations of largest volume slices and …

Sudakov evolution without unitarity
Javira Altmann, Hai Tao Li, Ludovic Scyboz, Peter Skands
https://arxiv.org/abs/2507.00111 https://

Sudakov evolution without unitarity
We present a method for sampling singular functions defined on (nested) multi-particle phase spaces, based on a generalisation of parton-shower phase-space generation techniques. At the heart of the method are three key ingredients: 1) the Sudakov sampling by which shower-style calculations sweep across phase space in an ordered manner, from hard to soft; 2) the sequential nesting of multiparticle phase spaces; and 3) the factorisations obeyed by singular multiparton amplitudes on the edges of …

This https://arxiv.org/abs/2505.00489 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Weighted averages of $\operatorname{SL}_2(\mathbb{R})$ automorphic kernel, Part I: non-oscillatory functions
We prove a theorem that evaluates weighted averages of sums parametrised by congruence subgroups of $\operatorname{SL}_2(\mathbb{Z})$. In the proof, spectral methods are applied directly to the automorphic kernel instead of going over sums of Kloosterman sums. In number theoretical applications this better preserves the specific symmetries throughout the application of spectral methods. In a separate paper we apply the main theorem to quadratic polynomials and obtain new results about their gre…

Hall--Littlewood expansions of chromatic quasisymmetric polynomials using linked rook placements
Jang Soo Kim, Seung Jin Lee, Meesue Yoo
https://arxiv.org/abs/2506.23082

Hall--Littlewood expansions of chromatic quasisymmetric polynomials using linked rook placements
In this work, we obtain a Hall--Littlewood expansion of the chromatic quasisymmetric function arising from a natural unit interval order and describe the coefficients in terms of linked rook placements. Applying the Carlsson--Mellit relation between chromatic quasisymmetric functions and unicellular LLT polynomials, we also obtain a combinatorial description for the coefficients of the unicellular LLT polynomials expanded in terms of the modified transformed Hall--Littlewood polynomials.

Swapping objectives accelerates Davis-Yin splitting
Edward Duc Hien Nguyen, Jaewook J. Suh, Xin Jiang, Shiqian Ma
https://arxiv.org/abs/2506.23475 https://…

Swapping objectives accelerates Davis-Yin splitting
In this work, we investigate the application of Davis-Yin splitting (DYS) to convex optimization problems and demonstrate that swapping the roles of the two nonsmooth convex functions can result in a faster convergence rate. Such a swap typically yields a different sequence of iterates, but its impact on convergence behavior has been largely understudied or often overlooked. We address this gap by establishing best-known convergence rates for DYS and its swapped counterpart, using the primal--d…

This https://arxiv.org/abs/2503.17228 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Mean value of cubic $L$-funcitons with fixed genus
We investigate the mean value of the first moment of primitive cubic $L$-functions over $\mathbb{F}_q(T)$ in the non-Kummer setting. Specifically, we study the sum \begin{equation*} \sum_{\substack{χ primitive\ cubic\\ genus(χ)=g}}L_q(\frac{1}{2}, χ), \end{equation*} where $L_q(s,χ)$ denotes the $L$-function associated with primitive cubic character $χ$. Using double Dirichlet series, we derive an error term of size $q^{(\frac{7}{8}+\varepsilon)g}$.

Homogeneous Linear Calculus of Order 1 and a $\lambda$-Taylor Formula
Ronald Orozco L\'opez
https://arxiv.org/abs/2506.22976 https://

Homogeneous Linear Calculus of Order 1 and a $λ$-Taylor Formula
In this paper, a new calculus on sequences is defined. Also, the $λ$-derivative and the $λ$-integration are investigated. The fundamental theorem of $λ$-calculus is included. A suitable function basis for the $λ$-derivative and the $λ$-integral is provided, and various properties of this basis are given. A $λ$-Taylor formula for functions is given.

Consensus-based optimization for closed-box adversarial attacks and a connection to evolution strategies
Tim Roith, Leon Bungert, Philipp Wacker
https://arxiv.org/abs/2506.24048

Consensus-based optimization for closed-box adversarial attacks and a connection to evolution strategies
Consensus-based optimization (CBO) has established itself as an efficient gradient-free optimization scheme, with attractive mathematical properties, such as mean-field convergence results for non-convex loss functions. In this work, we study CBO in the context of closed-box adversarial attacks, which are imperceptible input perturbations that aim to fool a classifier, without accessing its gradient. Our contribution is to establish a connection between the so-called consensus hopping as introd…

A Selberg-type zero-density result for twisted $\rm GL_2$ $L$-functions and its application
Qingfeng Sun, Hui Wang, Yanxue Yu
https://arxiv.org/abs/2505.23573

A Selberg-type zero-density result for twisted $\rm GL_2$ $L$-functions and its application
Let $f$ be a fixed holomorphic primitive cusp form of even weight $k$, level $r$ and trivial nebentypus $χ_r$. Let $q$ be an odd prime with $(q,r)=1$ and let $χ$ be a primitive Dirichlet character modulus $q$ with $χ\neqχ_r$. In this paper, we prove an unconditional Selberg-type zero-density estimate for the family of twisted $L$-functions $L(s, f \otimes χ)$ in the critical strip. As an application, we establish an asymptotic formula for the even moments of the argument function $S(t, f…

An evident corollary arising from Newton--Thorne
Shenghao Hua
https://arxiv.org/abs/2507.23656 https://arxiv.org/pdf/2507.23656

An evident corollary arising from Newton--Thorne
We present a special class of examples of automorphic lifts of multiple tensor products of automorphic representations in the sense of matching $L$-functions, motivated by combinatorial identities for Schur polynomials and a celebrated result of Newton and Thorne.

Discrete restrictions from Laurent monomial systems for multiple Dirichlet series
Shenghao Hua
https://arxiv.org/abs/2507.23477 https://arxiv.org/pdf/2507.…

Discrete restrictions from Laurent monomial systems for multiple Dirichlet series
We introduce a special class of multiple Dirichlet series whose terms are supported on a variety and which admit an Euler product structure. We show that these series arise naturally from twisted moments of automorphic \( L \)-functions associated with Dirichlet twists. We proposed several conjectures on the analytic properties of these series.

A Rigorous Error Bound for the TG Kernel in Prime Counting
Bugra Kilictas, Faruk Alpay
https://arxiv.org/abs/2506.22634 https://arxiv…

A Rigorous Error Bound for the TG Kernel in Prime Counting
We establish rigorous error bounds for prime counting using a truncated Gaussian (TG) kernel in the explicit formula framework. Our main theorem proves that the approximation error remains globally below 1/2 for all sufficiently large arguments, guaranteeing exact computation of π(x) through simple rounding, without relying on unproven hypotheses. The TG kernel construction employs Gaussian-like test functions with compact support, engineered with vanishing moments to eliminate main terms. F…