Tootfinder

Almost Maiorana-McFarland bent functions
Sadmir Kudin, Enes Pasalic, Alexandr Polujan, Fengrong Zhang, Haixia Zhao
https://arxiv.org/abs/2508.14265 https://

Almost Maiorana-McFarland bent functions
In this article, we study bent functions on $\mathbb{F}_2^{2m}$ of the form $f(x,y) = x \cdot ϕ(y) + h(y)$, where $x \in \mathbb{F}_2^{m-1} $ and $ y \in \mathbb{F}_2^{m+1}$, which form the generalized Maiorana-McFarland class (denoted by ${GMM}_{m+1}$) and are referred to as almost Maiorana-McFarland bent functions. We provide a complete characterization of the bent property for such functions and determine their duals. Specifically, we show that $f$ is bent if and only if the mapping $ϕ$ pa…

Multiple $\wp$-Functions and Their Applications
Hayato Kanno, Katsumi Kina
https://arxiv.org/abs/2507.14118 https://arxiv.org/pdf/250…

Multiple $\wp$-Functions and Their Applications
In this paper, we introduce and study multiple $\wp$-functions, which generalize the classical Weierstrass $\wp$-function to iterated sums over lattice points, and we establish explicit formulas expressing them in terms of single $\wp$-functions with coefficients given by multiple Eisenstein series. As an application, we derive some relations among multiple Eisenstein series and multiple zeta values by exploiting the double periodicity of the multiple $\wp$-functions.

Representation theory of monoids consisting of order-preserving functions and order-reversing functions on an n-set
Itamar Stein
https://arxiv.org/abs/2507.14873

Representation theory of monoids consisting of order-preserving functions and order-reversing functions on an n-set
Let $\operatorname{OD}_{n}$ be the monoid of all order-preserving functions and order-reversing functions on the set $\{1,\ldots,n\}$. We describe a quiver presentation for the monoid algebra $\Bbbk\operatorname{OD}_{n}$ where $\Bbbk$ is a field whose characteristic is not 2. We show that the quiver consists of two straightline paths, one with $n-1$ vertices and one with $n$ vertices, and that all compositions of consecutive arrows are equal to $0$. As part of the proof we obtain a complete des…

Total Loss Functions for Measuring the Accuracy of Nonnegative Cross-Sectional Predictions
Charles D. Coleman
https://arxiv.org/abs/2507.15136 https://

Total Loss Functions for Measuring the Accuracy of Nonnegative Cross-Sectional Predictions
The total loss function associated with a set of cross-sectional predictions, that is, estimates or forecasts, summarizes the set's overall accuracy. Its arguments are the individual cross-sectional units' loss functions. Under general assumptions, including impartiality, about the forms of the individual loss functions, and the specific assumptions that the total loss function is anonymous and monotonic, only the additive, multiplicative and L-type (with restrictions) total loss functions are …

from my link log —
Functions are vectors.
https://thenumb.at/Functions-are-Vectors/
saved 2025-08-20 https://dotat.at/:/83TED.html

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?

CPED-NCBFs: A Conformal Prediction for Expert Demonstration-based Neural Control Barrier Functions
Sumeadh MS, Kevin Dsouza, Ravi Prakash
https://arxiv.org/abs/2507.15022

CPED-NCBFs: A Conformal Prediction for Expert Demonstration-based Neural Control Barrier Functions
Among the promising approaches to enforce safety in control systems, learning Control Barrier Functions (CBFs) from expert demonstrations has emerged as an effective strategy. However, a critical challenge remains: verifying that the learned CBFs truly enforce safety across the entire state space. This is especially difficult when CBF is represented using neural networks (NCBFs). Several existing verification techniques attempt to address this problem including SMT-based solvers, mixed-integer …

On a dense set of functions determined by sampled Gabor magnitude
Matthias Wellershoff
https://arxiv.org/abs/2507.14556 https://arxiv…

On a dense set of functions determined by sampled Gabor magnitude
We study the problem of recovering a function from the magnitude of its Gabor transform sampled on a discrete set. While it is known that uniqueness fails for general square integrable functions, we show that phase retrieval is possible for a dense class of signals: specifically, those whose Bargmann transforms are entire functions of exponential type. Our main result characterises when such functions can be uniquely recovered (up to a global phase) from magnitude only data sampled on uniformly…

One-point functions in AdS/dCFT: MPS and twisted Yangian
Xin Qian
https://arxiv.org/abs/2507.15462 https://arxiv.org/pdf/2507.15462…

One-point functions in AdS/dCFT: MPS and twisted Yangian
I focus on the scalar one-point functions in SO(6) sector of D5-D3 probe-brane set-up. Start with a general introduction of integrability, I explore both coordinate Bethe ansatz and algebraic Bethe ansatz, with possible generalization. I then shortly review how to use the Bethe ansatz in $N = 4$ super Yang-Mills theory, and then apply such procedure to the D5-D3 system. The dual field theory of such system corresponds to a defected version of $N = 4$ super Yang-Mills theory, where the one-point…

An Optimal In-Situ Multipole Algorithm for the Isotropic Three-Point Correlation Functions
Wenjie Ju, Longlong Feng, Zhiqi Huang, Xin Sun, Weishan Zhu
https://arxiv.org/abs/2507.15209

An Optimal In-Situ Multipole Algorithm for the Isotropic Three-Point Correlation Functions
We present an optimised multipole algorithm for computing the three-point correlation function (3PCF), tailored for application to large-scale cosmological datasets. The algorithm builds on a $in\, situ$ interpretation of correlation functions, wherein spatial displacements are implemented via translation window functions. In Fourier space, these translations correspond to plane waves, whose decomposition into spherical harmonics naturally leads to a multipole expansion framework for the 3PCF. …

K-rings of smooth toric varieties via piecewise-exponential functions
Melody Chan, Emily Clader, Caroline Klivans, Dustin Ross
https://arxiv.org/abs/2507.13610

K-rings of smooth toric varieties via piecewise-exponential functions
We describe an explicit presentation of the ring of integral piecewise-exponential functions on a unimodular fan as a quotient of the Stanley-Reisner ring of the fan. This gives rise to a presentation of K-rings of smooth toric varieties that is parallel to the well-known presentation of integral Chow rings as quotients of Stanley-Reisner rings.

Polyconvex double well functions
Didier Henrion (LAAS-POP), Martin Kru\v{z}\'ik (UTIA / CAS)
https://arxiv.org/abs/2508.14541 https://arxiv.org/pdf/250…

Polyconvex double well functions
We investigate polyconvexity of the double well function $f(X)\,:= |X-X_1|^2|X-X_2|^2$ for given matrices $X_1, X_2 \in R^{n \times n}$. Such functions are fundamental in the modeling of phase transitions in materials, but their non-convex nature presents challenges for the analysis of variational problems. We prove that $f$ is polyconvex if and only if the singular values of the matrix difference $X_1 - X_2$ are all equal. This condition allows the function to be decomposed…

Estimating Rate-Distortion Functions Using the Energy-Based Model
Shitong Wu, Sicheng Xu, Lingyi Chen, Huihui Wu, Wenyi Zhang
https://arxiv.org/abs/2507.15700

Estimating Rate-Distortion Functions Using the Energy-Based Model
The rate-distortion (RD) theory is one of the key concepts in information theory, providing theoretical limits for compression performance and guiding the source coding design, with both theoretical and practical significance. The Blahut-Arimoto (BA) algorithm, as a classical algorithm to compute RD functions, encounters computational challenges when applied to high-dimensional scenarios. In recent years, many neural methods have attempted to compute high-dimensional RD problems from the perspe…

Databelt: A Continuous Data Path for Serverless Workflows in the 3D Compute Continuum
Cynthia Marcelino, Leonard Guelmino, Thomas Pusztai, Stefan Nastic
https://arxiv.org/abs/2508.15351

Databelt: A Continuous Data Path for Serverless Workflows in the 3D Compute Continuum
Typically, serverless functions rely on remote storage services for managing state, which can result in increased latency and network communication overhead. In a dynamic environment such as the 3D (Edge-Cloud-Space) Compute Continuum, serverless functions face additional challenges due to frequent changes in network topology. As satellites move in and out of the range of ground stations, functions must make multiple hops to access cloud services, leading to high-latency state access and unnece…

Families of Morse functions for manifolds with boundary
Maciej Borodzik, Weronika Buczy\'nska
https://arxiv.org/abs/2507.15847 https://arxiv.org/pdf/25…

Families of Morse functions for manifolds with boundary
We study 1-parameter families of Morse functions for manifolds with boundary. We list all degeneracies that may occur in generic 1-parameter families.

Determination of Fragmentation Functions from Charge Asymmetries in Hadron Production
Jun Gao, ChongYang Liu, Bin Zhou
https://arxiv.org/abs/2507.14637 htt…

Determination of Fragmentation Functions from Charge Asymmetries in Hadron Production
We propose a novel method for extracting non-singlet (NS) fragmentation functions (FFs) of light charged hadrons from charge asymmetries measured in hadron fragmentation, using data from both single-inclusive electron-positron annihilation and semi-inclusive deep-inelastic scattering processes. We determine the NS FFs for pions and kaons at next-to-next-to-leading order in Quantum Chromodynamics, including a comprehensive uncertainty analysis. The extracted FFs reveal a scaling index of about 0…

Fixed time convergence guarantees for Higher Order Control Barrier Functions
Janani S K, Shishir Kolathaya
https://arxiv.org/abs/2507.13888 https://…

Fixed time convergence guarantees for Higher Order Control Barrier Functions
We present a novel method for designing higher-order Control Barrier Functions (CBFs) that guarantee convergence to a safe set within a user-specified finite. Traditional Higher Order CBFs (HOCBFs) ensure asymptotic safety but lack mechanisms for fixed-time convergence, which is critical in time-sensitive and safety-critical applications such as autonomous navigation. In contrast, our approach imposes a structured differential constraint using repeated roots in the characteristic polynomial, en…

Set Contribution Functions for Quantitative Bipolar Argumentation and their Principles
Filip Naudot, Andreas Br\"annstr\"om, Vicen\c{c} Torra, Timotheus Kampik
https://arxiv.org/abs/2509.14963

Set Contribution Functions for Quantitative Bipolar Argumentation and their Principles
We present functions that quantify the contribution of a set of arguments in quantitative bipolar argumentation graphs to (the final strength of) an argument of interest, a so-called topic. Our set contribution functions are generalizations of existing functions that quantify the contribution of a single contributing argument to a topic. Accordingly, we generalize existing contribution function principles for set contribution functions and provide a corresponding principle-based analysis. We in…

$\zeta$-functions via contour integrals and universal sum rules
Guglielmo Fucci, Mateusz Piorkowski, Jonathan Stanfill
https://arxiv.org/abs/2508.15699 https://

$ζ$-functions via contour integrals and universal sum rules
This work develops an analytic framework for the study of the $ζ$-function associated with general sequences of complex numbers. We show that a contour integral representation, commonly used when studying spectral $ζ$-functions associated with self-adjoint differential operators, can be extended far beyond its traditional setting. In contrast to representations utilizing integrals of $θ$-functions, our method applies to arbitrary sequences of complex numbers with minimal assumptions. This le…

Explicit Runge-Kutta Methods with MQ and IMQ-Radial Basis Functions
Shipra Mahata, Samala Rathan
https://arxiv.org/abs/2507.14474 https://

Explicit Runge-Kutta Methods with MQ and IMQ-Radial Basis Functions
This article presents a class of explicit Runge-Kutta methods with multiquadric (MQ) and inverse multiquadric (IMQ) radial basis functions (RBFs) to improve the accuracy of time integration for ordinary differential equations. By introducing RBF-based corrections derived from Taylor series expansions and optimally selecting the shape parameter, the method achieves a one-order increase in accuracy without additional stages. Convergence and stability analyses support the theoretical claims, and n…

Quantum algebra approach to univariate and multivariate rational functions of $q$-Racah type
Wolter Groenevelt, Carel Wagenaar
https://arxiv.org/abs/2507.13483

Quantum algebra approach to univariate and multivariate rational functions of $q$-Racah type
In this paper, we study rational functions of $q$-Racah type and a multivariate extension, using representation theory of $\mathcal U_q(\mathfrak{sl}_2)$. Eigenfunctions of twisted primitive elements in $\mathcal U_q(\mathfrak{su}_2)$ can be expressed in terms of $q^{-1}$-Krawtchouk polynomials. Using this, we show that overlap coefficients of solutions of a generalized eigenvalue problem (GEVP) and an eigenvalue problem (EVP) can be expressed in terms of a rational function of $_4φ_3$-type. W…

Challenges of Virtual Validation and Verification for Automotive Functions
Beatriz Cabrero-Daniel, Mazen Mohamad
https://arxiv.org/abs/2508.14747 https://a…

Challenges of Virtual Validation and Verification for Automotive Functions
Verification and validation of vehicles is a complex yet critical process, particularly for ensuring safety and coverage through simulations. However, achieving realistic and useful simulations comes with significant challenges. To explore these challenges, we conducted a workshop with experts in the field, allowing them to brainstorm key obstacles. Following this, we distributed a survey to consolidate findings and gain further insights into potential solutions. The experts identified 17 key c…

On Strongly Convex Sets and Farthest Distance Functions
Juan Enrique Mart\'inez-Legaz
https://arxiv.org/abs/2507.15053 https://ar…

On Strongly Convex Sets and Farthest Distance Functions
A polarity notion for sets in a Banach space is introduced in such a way that the second polar of a set coincides with the smallest strongly convex set with respect to R that contains it. Strongly convex sets are characterized in terms of their associated farthest distance functions, and farthest distance functions associated with strongly convex sets are characterized, too.

Closure Conversion, Flat Environments, and the Complexity of Abstract Machines
Beniamino Accattoli (Inria & LIX, \'Ecole Polytechnique), Dan Ghica (Huawei Central Software Institute, University of Birmingham), Giulio Guerrieri (University of Sussex), Cl\'audio Belo Louren\c{c}o (Huawei Central Software Institute), Claudio Sacerdoti Coen (Universit\`a di Bologna)

Closure Conversion, Flat Environments, and the Complexity of Abstract Machines
Closure conversion is a program transformation at work in compilers for functional languages to turn inner functions into global ones, by building closures pairing the transformed functions with the environment of their free variables. Abstract machines rely on similar and yet different concepts of closures and environments. In this paper, we study the relationship between the two approaches. We adopt a very simple λ-calculus with tuples as source language and study abstract machines for bot…

Pixel 10 gets a 10.8 MP telephoto lens; 10 Pro and Pro XL get an AI-driven Pro Res Zoom capable of up to 100x zoom; all models get AI features like Camera Coach (Damien Wilde/9to5Google)
https://9to5google.com/2025/08/20/pixel-10-camera-features/

Pixel 10 camera adds ‘Camera Coach’, 100x ‘Pro Res Zoom’ 24fps video, plus more new features
The Pixel 10 series has officially been unveiled with new camera features and upgrades for existing functions. Here's what you need to know.

State Space Models Naturally Produce Traveling Waves, Time Cells, and Scale to Abstract Cognitive Functions
Sen Lu, Xiaoyu Zhang, Mingtao Hu, Eric Yeu-Jer Lee, Soohyeon Kim, Wei D. Lu
https://arxiv.org/abs/2507.13638

State Space Models Naturally Produce Traveling Waves, Time Cells, and Scale to Abstract Cognitive Functions
A grand challenge in modern neuroscience is to bridge the gap between the detailed mapping of microscale neural circuits and a mechanistic understanding of cognitive functions. While extensive knowledge exists about neuronal connectivity and biophysics, a significant gap remains in how these elements combine to produce flexible, learned behaviors. Here, we propose that a framework based on State-Space Models (SSMs), an emerging class of deep learning architectures, can bridge this gap. We argue…

Connecting Discrete Morse Functions via Birth-Death Transitions
Chong Zheng
https://arxiv.org/abs/2508.15736 https://arxiv.org/pdf/2508.15736

Connecting Discrete Morse Functions via Birth-Death Transitions
We study transformations between discrete Morse functions on a finite simplicial complex via birth-death transitions--elementary chain maps between discrete Morse complexes that either create or cancel pairs of critical simplices.We prove that any two discrete Morse functions f1, f2 on a finite simplicial complex K are linked by a finite sequence of such transitions.As applications, we present alternative proofs of several of Forman's fundamental results in discrete Morse theory and study the t…

Explicit formulas of the relation between multiple zeta functions of Arakawa-Kaneko and Euler-Zagier types
Naho Kawasaki
https://arxiv.org/abs/2507.15034 h…

Explicit formulas of the relation between multiple zeta functions of Arakawa-Kaneko and Euler-Zagier types
Multiple zeta functions of Arakawa-Kaneko and Euler-Zagier types are known as generalizations of the Riemann zeta function. In 2018, Kaneko and Tsumura proved that the multiple zeta functions of Arakawa-Kaneko type can be expressed as a ${\mathbb Q}$-linear combination of products of the ones of Euler-Zagier type and multiple zeta values. In this paper, we give explicit formulas to the above mentioned relation. Moreover, as a key of its proof, we also give certain functional equations among mul…

Exact versus Approximate Representations of Boolean Functions in the De Morgan Basis
Arkadev Chattopadhyay, Yogesh Dahiya, Shachar Lovett
https://arxiv.org/abs/2507.13963

Exact versus Approximate Representations of Boolean Functions in the De Morgan Basis
A seminal result of Nisan and Szegedy (STOC, 1992) shows that for any total Boolean function, the degree of the real polynomial that computes the function, and the minimal degree of a real polynomial that point-wise approximates the function, are at most polynomially separated. Extending this result from degree to other complexity measures like sparsity of the polynomial representation, or total weight of the coefficients, remains poorly understood. In this work, we consider this problem in t…

Fundamental measure theory for predicting many-body correlation functions
Ilian Pihlajamaa, Teunike A. van de Pol, Liesbeth M. C. Janssen
https://arxiv.org/abs/2508.14642 https:…

Fundamental measure theory for predicting many-body correlation functions
We study many-body correlation functions within various Fundamental Measure Theory (FMT) formulations and compare their predictions to Monte Carlo simulations of hard-sphere fluids. FMT accurately captures key features of three- and four-body structure, particularly at low and intermediate wavevectors. We show that the dominant contributions to the four-point structure factor arise from direct triplet correlations, allowing evaluation of four-point correlations to be greatly simplified. In glas…

The Digital Life of Parisian Parks: Multifunctionality and Urban Context Uncovered by Mobile Application Traffic
Andr\'e Felipe Zanella, Linus W. Dietz, Sanja \v{S}\'cepanovi\'c, Ke Zhou, Zbigniew Smoreda, Daniele Quercia
https://arxiv.org/abs/2508.15516

The Digital Life of Parisian Parks: Multifunctionality and Urban Context Uncovered by Mobile Application Traffic
Landscape architecture typically considers urban parks through the lens of form and function. While past research on equitable access has focused mainly on form, studies of functions have been constrained by limited scale and coarse measurement. Existing efforts have partially quantified functions through small-scale surveys and movement data (e.g., GPS) or general usage records (e.g., CDR), but have not captured the activities and motivations underlying park visits. As a result, our understand…

Lorentzian Cheeger-Gromov convergence and temporal functions
Sa\'ul Burgos, Jos\'e L. Flores, Miguel S\'anchez
https://arxiv.org/abs/2508.15441 https://

Lorentzian Cheeger-Gromov convergence and temporal functions
Uniqueness (up to isometries) and existence of limits are analyzed in the context of Cheeger-Gromov convergence of spacetimes. To face the non-compactness of the vector isometry group in the semi-Riemanian setting, standard \em{pointed} convergence is strenghtened to \em{anchored} convergence (which requires the convergence of a timelike direction in the Lorenzian case). Then, a local isometry between the neighborhoods of the basepoints is found, and extended globally under geodesic completenes…

ai but with mood swings to better understand context smh.
science more interested in how menstruation affects ai than it ever was in how it affects women.

"Ohio Bill Would Require Watermarks on AI Imagery"
How exactly does a state enforce this? 🤔 "...it could place restrictions on a consumer's legal uses of a product, or it could place restrictions on what type of functions a producer's product can actually produce."
http…

On the extremal functions of second order uncertainty principles: symmetry and symmetry breaking
Xiao-Ping Chen, Chun-Lei Tang
https://arxiv.org/abs/2508.15221 https://

On the extremal functions of second order uncertainty principles: symmetry and symmetry breaking
This paper focus on the symmetry and symmetry breaking about the second order Hydrogen Uncertainty Principle. \emph{Firstly}, by choosing a suitable test function, we give a negative answer to the conjecture presented by Cazacu, Flynn and Lam in [\emph{J. Funct. Anal.} \textbf{283} (2022), Paper No. 109659, 37 pp] for $N\in\{2,3\}$, and emphasizing the symmetry breaking phenomenon. \emph{Secondly}, we obtain a family of sharp weighted second order Hydrogen Uncertainty Principle, and prove the e…

Conceptual and Design Principles for a Self-Referential Algorithm Mimicking Neuronal Assembly Functions
Paolo Totaro, Alberto Mangiante
https://arxiv.org/abs/2507.14011

Conceptual and Design Principles for a Self-Referential Algorithm Mimicking Neuronal Assembly Functions
This article proposes a method to formalise models of cognitive processes grounded in experience, considering experience from the perspective of a living system and not from that of an observer of the living system. The perspective of a living system is defined by the need of the system to preserve the vital equilibria. The method is based on an algorithmic schema that we call Environment Generative Operator (EGO) and uses a self-referential language developed for this purpose which we call E-l…

Weakly-Convex Regularization for Magnetic Resonance Image Denoising
Akash Prabakar, Abhishek Shreekant Bhandiwad, Abijith Jagannath Kamath, Chandra Sekhar Seelamantula
https://arxiv.org/abs/2508.14438 …

Weakly-Convex Regularization for Magnetic Resonance Image Denoising
Regularization for denoising in magnetic resonance imaging (MRI) is typically achieved using convex regularization functions. Recently, deep learning techniques have been shown to provide superior denoising performance. However, this comes at the price of lack of explainability, interpretability and stability, which are all crucial to MRI. In this work, we present a constructive approach for designing weakly-convex regularization functions for MR image denoising. We show that our technique perf…

Geophysics-informed neural network for model-based seismic inversion using surrogate point spread functions
Marcus Saraiva, Ana Muller, Alexandre Maul
https://arxiv.org/abs/2507.14140

Geophysics-informed neural network for model-based seismic inversion using surrogate point spread functions
Model-based seismic inversion is a key technique in reservoir characterization, but traditional methods face significant limitations, such as relying on 1D average stationary wavelets and assuming an unrealistic lateral resolution. To address these challenges, we propose a Geophysics-Informed Neural Network (GINN) that integrates deep learning with seismic modeling. This novel approach employs a Deep Convolutional Neural Network (DCNN) to simultaneously estimate Point Spread Functions (PSFs) an…

Exploiting scattering-based point spread functions for snapshot 5D and modality-switchable lensless imaging
Ze Zheng, Baolei Liu, Jiaqi Song, Muchen Zhu, Yao Wang, Menghan Tian, Ying Xiong, Zhaohua Yang, Xiaolan Zhong, David McGloin, Fan Wang
https://arxiv.org/abs/2507.13813

Exploiting scattering-based point spread functions for snapshot 5D and modality-switchable lensless imaging
Snapshot multi-dimensional imaging offers a promising alternative to traditional low-dimensional imaging techniques by enabling the simultaneous capture of spatial, spectral, polarization, and other information in a single shot for improved imaging speed and acquisition efficiency. However, existing snapshot multi-dimensional imaging systems are often hindered by their large size, complexity, and high cost, which constrain their practical applicability. In this work, we propose a compact lensle…

Modular transformations of tau functions and conformal blocks on the torus
Fabrizio Del Monte, Harini Desiraju, Pavlo Gavrylenko
https://arxiv.org/abs/2508.14030 https://…

Modular transformations of tau functions and conformal blocks on the torus
The connection problem for isomonodromic tau functions on the one-punctured torus concerns the ratio between the tau function and its modular transform, associated to dual pants decompositions of the torus. In this paper, we study the modular transformations of the tau function and consequently derive the connection constant. Moreover, through the relation with two-dimensional Conformal Field Theory, we also obtain an exact closed formula for the $c=1$ Virasoro modular kernel, whose expression …

A minimal model with stochastically broken reciprocity
Z. C. Tu
https://arxiv.org/abs/2507.14862 https://arxiv.org/pdf/2507.14862

A minimal model with stochastically broken reciprocity
We introduce a minimal model consisting of a two-body system with stochastically broken reciprocity (i.e., random violation of Newton's third law) and then investigate its statistical behaviors, including correlation functions, time evolution of probability distribution functions, energy gain, and entropy production. The effective temperature of this two-body system immersed in a thermal bath is derived. Furthermore, we heuristically present an extremely minimal model where the relative motion …

Entropies of Cox-Ingersoll-Ross and Bessel processes as functions of time and of related parameters
Ivan Kucha, Yuliya Mishura, Kostiantyn Ralchenko
https://arxiv.org/abs/2507.14684

Entropies of Cox-Ingersoll-Ross and Bessel processes as functions of time and of related parameters
We investigate the long-time asymptotic behavior of various entropy measures associated with the Cox-Ingersoll-Ross (CIR) and squared Bessel processes. As the one-dimensional distributions of both processes follow noncentral chi-squared laws, we first derive sufficient conditions for the existence of these entropy measures for a noncentral chi-squared random variable. We then analyze their limiting behavior as the noncentrality parameter approaches zero and apply these results to the CIR and sq…

Projective functions
Laurence Carassus, Massinissa Ferhoune
https://arxiv.org/abs/2507.12605 https://arxiv.org/pdf/2507.12605

Projective functions
We study projective functions. We prove that projective functions generalise lower and upper-semianalytic ones while being stable by composition and difference. We show that the class of projective functions is closed under sums, differences, products, finite suprema and infima, sections and compositions. Assuming the set-theoretical axiom of Projective Determinacy, we also prove measurable selection results, stability under integration, and the existence of $ε$-optimal selectors. Finally, we …

An elementary construction of the ring of dual $K$-$Q$-cancellation property
Shinsuke Iwao
https://arxiv.org/abs/2508.14484 https://arxiv.org/pdf/2508.1448…

An elementary construction of the ring of dual $K$-$Q$-cancellation property
This paper presents an elementary introduction on $K$-theoretic $Q$-functions, which were introduced by Ikeda and Naruse in 2013. These functions, which serve as $K$-theoretic analogs of Schur $Q$-functions, are known to possess combinatorial and algebraic constructions. In a 2022 paper, the author introduced ``$β$-deformed power-sums" to provide a simpler, more algebraic construction of these functions. Since the original approach relies on fermionic operators and vacuum expectation values, t…

High-Frequency First: A Two-Stage Approach for Improving Image INR
Sumit Kumar Dam, Mrityunjoy Gain, Eui-Nam Huh, Choong Seon Hong
https://arxiv.org/abs/2508.15582 https://

High-Frequency First: A Two-Stage Approach for Improving Image INR
Implicit Neural Representations (INRs) have emerged as a powerful alternative to traditional pixel-based formats by modeling images as continuous functions over spatial coordinates. A key challenge, however, lies in the spectral bias of neural networks, which tend to favor low-frequency components while struggling to capture high-frequency (HF) details such as sharp edges and fine textures. While prior approaches have addressed this limitation through architectural modifications or specialized …

Safe and Performant Controller Synthesis using Gradient-based Model Predictive Control and Control Barrier Functions
Aditya Singh, Aastha Mishra, Manan Tayal, Shishir Kolathaya, Pushpak Jagtap
https://arxiv.org/abs/2507.13872

Safe and Performant Controller Synthesis using Gradient-based Model Predictive Control and Control Barrier Functions
Ensuring both performance and safety is critical for autonomous systems operating in real-world environments. While safety filters such as Control Barrier Functions (CBFs) enforce constraints by modifying nominal controllers in real time, they can become overly conservative when the nominal policy lacks safety awareness. Conversely, solving State-Constrained Optimal Control Problems (SC-OCPs) via dynamic programming offers formal guarantees but is intractable in high-dimensional systems. In thi…

Beyond Semantic Similarity: Reducing Unnecessary API Calls via Behavior-Aligned Retriever
Yixin Chen, Ying Xiong, Shangyu Wu, Yufei Cui, Xue Liu, Nan Guan, Chun Jason Xue
https://arxiv.org/abs/2508.14323

Beyond Semantic Similarity: Reducing Unnecessary API Calls via Behavior-Aligned Retriever
Tool-augmented large language models (LLMs) leverage external functions to extend their capabilities, but inaccurate function calls can lead to inefficiencies and increased costs.Existing methods address this challenge by fine-tuning LLMs or using demonstration-based prompting, yet they often suffer from high training overhead and fail to account for inconsistent demonstration samples, which misguide the model's invocation behavior. In this paper, we trained a behavior-aligned retriever (BAR), …

Corridor-based Adaptive Control Barrier and Lyapunov Functions for Safe Mobile Robot Navigation
Nicholas Mohammad, Nicola Bezzo
https://arxiv.org/abs/2507.14700

Corridor-based Adaptive Control Barrier and Lyapunov Functions for Safe Mobile Robot Navigation
Safe navigation in unknown and cluttered environments remains a challenging problem in robotics. Model Predictive Contour Control (MPCC) has shown promise for performant obstacle avoidance by enabling precise and agile trajectory tracking, however, existing methods lack formal safety assurances. To address this issue, we propose a general Control Lyapunov Function (CLF) and Control Barrier Function (CBF) enabled MPCC framework that enforces safety constraints derived from a free-space corridor …

Understanding Action Effects through Instrumental Empowerment in Multi-Agent Reinforcement Learning
Ardian Selmonaj, Miroslav Strupl, Oleg Szehr, Alessandro Antonucci
https://arxiv.org/abs/2508.15652

Understanding Action Effects through Instrumental Empowerment in Multi-Agent Reinforcement Learning
To reliably deploy Multi-Agent Reinforcement Learning (MARL) systems, it is crucial to understand individual agent behaviors within a team. While prior work typically evaluates overall team performance based on explicit reward signals or learned value functions, it is unclear how to infer agent contributions in the absence of any value feedback. In this work, we investigate whether meaningful insights into agent behaviors can be extracted that are consistent with the underlying value functions,…

Quantum Programming in Polylogarithmic Time
Florent Ferrari (ENS de Lyon), Emmanuel Hainry (MOCQUA, LORIA), Romain P\'echoux (LORIA, MOCQUA), M\'ario Silva (LORIA, MOCQUA)
https://arxiv.org/abs/2507.15415

Quantum Programming in Polylogarithmic Time
Polylogarithmic time delineates a relevant notion of feasibility on several classical computational models such as Boolean circuits or parallel random access machines. As far as the quantum paradigm is concerned, this notion yields the complexity class FBQPOLYLOG of functions approximable in polylogarithmic time with a quantum random-access Turing machine. We introduce a quantum programming language with first-order recursive procedures, which provides the first programming-language-based chara…

Quantum Variational Activation Functions Empower Kolmogorov-Arnold Networks
Jiun-Cheng Jiang, Morris Yu-Chao Huang, Tianlong Chen, Hsi-Sheng Goan
https://arxiv.org/abs/2509.14026

Quantum Variational Activation Functions Empower Kolmogorov-Arnold Networks
Variational quantum circuits (VQCs) are central to quantum machine learning, while recent progress in Kolmogorov-Arnold networks (KANs) highlights the power of learnable activation functions. We unify these directions by introducing quantum variational activation functions (QVAFs), realized through single-qubit data re-uploading circuits called DatA Re-Uploading ActivatioNs (DARUANs). We show that DARUAN with trainable weights in data pre-processing possesses an exponentially growing frequency …

Correlations of error terms for weighted prime counting functions
Shubhrajit Bhattacharya, Greg Martin, Reginald M. Simpson
https://arxiv.org/abs/2507.13504

Correlations of error terms for weighted prime counting functions
Standard prime-number counting functions, such as $ψ(x)$, $θ(x)$, and $π(x)$, have error terms with limiting logarithmic distributions once suitably normalized. The same is true of weighted versions of those sums, like $π_r(x) = \sum_{p\le x} \frac1p$ and $π_\ell(x) = \sum_{p\le x} \log(1-\frac1p)^{-1}$, that were studied by Mertens. These limiting distributions are all identical, but passing to the limit loses information about how these error terms are correlated with one another. In t…

A condition equivalent to the H\"{o}lder continuity of harmonic functions on unbounded Lipschitz domains
Marijan Markovic
https://arxiv.org/abs/2507.14511

A condition equivalent to the Hölder continuity of harmonic functions on unbounded Lipschitz domains
Our main result concerns the behavior of bounded harmonic functions on a domain in $\mathbb{R}^N$ which may be represented as a strict epigraph of a Lipschitz function on $\mathbb{R}^{N-1}$. Generally speaking, the result says that the Hölder continuity of a harmonic function on such a domain is equivalent to the uniform Hölder continuity along the straight lines determined by the vector $\mathbf{e}_N$, where $\mathbf{e}_1,\mathbf{e}_2,\dots,\mathbf {e}_N$ is the base of standard vectors in $…

Controlled Optimization of Quadratic Functions in $\mathbb{R}^n$
Jean-Jacques Godeme
https://arxiv.org/abs/2508.15515 https://arxiv.org/pdf/2508.15515

Controlled Optimization of Quadratic Functions in $\mathbb{R}^n$
In this work, we introduce and study the controllability of the trajectories of a linear dynamical system, which can be used to solve the minimization of a quadratic function in finite dimension. We named this dynamical system the controlled quadratic gradient flow. Finally, we introduce what we call the controlled quadratic gradient descent and the controlled proximity operator which are respectively the Euler explicit and implicit discretization of the controlled gradient flow.

AdS$\times$S Mellin Bootstrap, Hidden 10d Symmetry and Five-point Kaluza-Klein Functions in $\mathcal{N}=4$ SYM
Bruno Fernandes, Vasco Goncalves, Zhongjie Huang, Yichao Tang, Joao Vilas Boas, Ellis Ye Yuan
https://arxiv.org/abs/2507.14124

AdS$\times$S Mellin Bootstrap, Hidden 10d Symmetry and Five-point Kaluza-Klein Functions in $\mathcal{N}=4$ SYM
We propose an AdS$\times$S factorization formula at the level of the generating function for correlators with arbitrary Kaluza-Klein configurations, and implement it in the supergravity limit of $\mathcal{N}=4$ super Yang-Mills. By incorporating this mechanism into Mellin space bootstrap, together with an observed $Z_2$ symmetry under AdS$\ \leftrightarrow\ $S, we manage to simultaneously work out unified formulas both for all five-point half-BPS correlators and for all four-point correlators w…

Loss-Complexity Landscape and Model Structure Functions
Alexander Kolpakov
https://arxiv.org/abs/2507.13543 https://arxiv.org/pdf/250…

Loss-Complexity Landscape and Model Structure Functions
We develop a framework for dualizing the Kolmogorov structure function $h_x(α)$, which then allows using computable complexity proxies. We establish a mathematical analogy between information-theoretic constructs and statistical mechanics, introducing a suitable partition function and free energy functional. We explicitly prove the Legendre-Fenchel duality between the structure function and free energy, showing detailed balance of the Metropolis kernel, and interpret acceptance probabilities a…

Vertex functions for bow varieties and their Mirror Symmetry
Tommaso Maria Botta, Hunter Dinkins
https://arxiv.org/abs/2507.13219 https://

Vertex functions for bow varieties and their Mirror Symmetry
In this paper, we study the vertex functions of finite type $A$ bow varieties. Vertex functions are $K$-theoretic analogs of $I$-functions, and 3d mirror symmetry predicts that the $q$-difference equations satisfied by the vertex functions of a variety and its 3d mirror dual are the same after a change of variable swapping the roles of the various parameters. Thus the vertex functions are related by a matrix of elliptic functions, which is expected to be the elliptic stable envelope of M. Agana…

CausalMesh: A Formally Verified Causal Cache for Stateful Serverless Computing
Haoran Zhang, Zihao Zhang, Shuai Mu, Sebastian Angel, Vincent Liu
https://arxiv.org/abs/2508.15647

CausalMesh: A Formally Verified Causal Cache for Stateful Serverless Computing
Stateful serverless workflows consist of multiple serverless functions that access state on a remote database. Developers sometimes add a cache layer between the serverless runtime and the database to improve I/O latency. However, in a serverless environment, functions in the same workflow may be scheduled to different nodes with different caches, which can cause non-intuitive anomalies. This paper presents CausalMesh, a novel approach to causally consistent caching in environments where a comp…

The recoil corrections, correlation functions and possible double-strange hadronic molecules
Xiao-mei Tang, Li-sheng Cheng, Qi Huang, Rui Chen
https://arxiv.org/abs/2508.15640 h…

The recoil corrections, correlation functions and possible double-strange hadronic molecules
In this work, we perform a systematic investigation of ${K}^{(*)}{K}^{(*)}$ interactions within a one-boson-exchange model.The framework incorporates both $S-D$ wave mixing and coupled-channel effects, with effective potentials retained up to order $\mathcal{O}(1/M^2)$. By solving the coupled channel Schrödinger equations, we can predict two double-strange molecular candidates: a $KK^*$ molecule with $I(J^P)=0(1^+)$ and a $K^*K^*$ molecule with $0(1^+)$. Our results also show that the recoil c…

from my link log —
NaN-propagation: a novel method for sparsity detection in black-box computational functions.
https://arxiv.org/abs/2507.23186
saved 2025-08-14

NaN-Propagation: A Novel Method for Sparsity Detection in Black-Box Computational Functions
When numerically evaluating a function's gradient, sparsity detection can enable substantial computational speedups through Jacobian coloring and compression. However, sparsity detection techniques for black-box functions are limited, and existing finite-difference-based methods suffer from false negatives due to coincidental zero gradients. These false negatives can silently corrupt gradient calculations, leading to difficult-to-diagnose errors. We introduce NaN-propagation, which exploits the…

Pseudorandomness of Expander Walks via Fourier Analysis on Groups
Fernando Granha Jeronimo, Tushant Mittal, Sourya Roy
https://arxiv.org/abs/2507.14445 htt…

Pseudorandomness of Expander Walks via Fourier Analysis on Groups
One approach to study the pseudorandomness properties of walks on expander graphs is to label the vertices of an expander with elements from an alphabet $Σ$, and study the mean of functions over $Σ^n$. We say expander walks $\varepsilon$-fool a function if, for any unbiased labeling of the vertices, the expander walk mean is $\varepsilon$-close to the true mean. We show that: - The class of symmetric functions is $O(|Σ|\cdotλ)$-fooled by expander walks over any generic $λ$-expa…

Safety Certification in the Latent space using Control Barrier Functions and World Models
Mehul Anand, Shishir Kolathaya
https://arxiv.org/abs/2507.13871 h…

Safety Certification in the Latent space using Control Barrier Functions and World Models
Synthesising safe controllers from visual data typically requires extensive supervised labelling of safety-critical data, which is often impractical in real-world settings. Recent advances in world models enable reliable prediction in latent spaces, opening new avenues for scalable and data-efficient safe control. In this work, we introduce a semi-supervised framework that leverages control barrier certificates (CBCs) learned in the latent space of a world model to synthesise safe visuomotor po…

Permutations satisfying $(P_1)$ and $(P_2)$ properties and $\ell$-optimal bent functions
Sadmir Kudin, Enes Pasalic, Alexandr Polujan, Fengrong Zhang
https://arxiv.org/abs/2508.14277

Permutations satisfying $(P_1)$ and $(P_2)$ properties and $\ell$-optimal bent functions
An important classification of permutations over $\mathbb{F}_2^m$, suitable for constructing Maiorana-McFarland bent functions on $\mathbb{F}_2^m \times \mathbb{F}_2^m$ with the unique $M$-subspace of maximal dimension, was recently considered in Pasalic et al. (IEEE Trans. Inf. Theory 70(6): 4464-4477, 2024). More precisely, two properties called $(P_1)$ and $(P_2)$ were introduced and a generic method of constructing permutations having the property $(P_1)$ was presented, whereas no such resu…

Shifted moments of cubic and quartic Dirichlet $L$-functions
Peng Gao, Liangyi Zhao
https://arxiv.org/abs/2508.14534 https://arxiv.org/pdf/2508.14534

Shifted moments of cubic and quartic Dirichlet $L$-functions
We establish upper bounds for shifted moments of cubic and quartic Dirichlet $L$-functions under the generalized Riemann hypothesis. As an application, we prove bounds for moments of cubic and quartic Dirichlet character sums.

Basis Construction for Spline Spaces over Arbitrary Partitions from a Dimensional Stable Perspective
Bingru Huang, Falai Chen
https://arxiv.org/abs/2508.14649 https://

Basis Construction for Spline Spaces over Arbitrary Partitions from a Dimensional Stable Perspective
This paper introduces a novel framework for constructing $C^r$ basis functions for polynomial spline spaces of degree $d$ over arbitrary planar polygonal partitions, overturning the belief that basis functions cannot be constructed on dimensionally unstable meshes. We provide a comprehensive comparison of basis construction methods, classifying them as explicit, semi-explicit, and implicit. Our method, a semi-explicit construction using Extended Edge Elimination conditions, uniquely resolves al…

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

Carleman estimates for stationary $Q$-valued maps: a variational approach
Aria Halavati, Luca Spolaor
https://arxiv.org/abs/2508.14388 https://arxiv.org/pd…

Carleman estimates for stationary $Q$-valued maps: a variational approach
We prove a Carleman-type estimate for Dirichlet-stationary multivalued functions and apply it to give a different proof of the optimal dimension of the singular set of Dir-minimizing multivalued functions, originally due to Almgren and to De Lellis-Spadaro.

Elephant random walks with multiple extractions and general reinforcement functions
Moumanti Podder, Archi Roy
https://arxiv.org/abs/2507.14626 https://

Elephant random walks with multiple extractions and general reinforcement functions
We consider a generalized model of elephant random walks wherein the walker, during the $(n+1)$-st time-stamp, draws from the past (i.e. the set $\{1,2,\ldots,n\}$) a sample of $k$ time-stamps, either with replacement or without, where $k$ may either remain fixed as $n$ grows, or $k=k(n)$ may grow with $n$. Letting $\{U_{n,1}, U_{n,2}, \ldots, U_{n,k}\}$ denote the time-stamps sampled, the step taken by the walker during the $(n+1)$-st time-stamp, denoted $X_{n+1}$, is a $\pm 1$-valued random v…

Simulating a Gaussian stochastic gravitational wave background signal in pulsar timing arrays
Reginald Christian Bernardo, Kin-Wang Ng
https://arxiv.org/abs/2507.15756

Simulating a Gaussian stochastic gravitational wave background signal in pulsar timing arrays
We revisit the theoretical modeling and simulation of a Gaussian stochastic gravitational wave background (SGWB) signal in a pulsar timing array (PTA). We show that the correlation between Fourier components of pulsar timing residuals can be expressed using transfer functions; that are indicative of characteristic temporal correlations in a SGWB signal observed in a finite time window. These transfer functions, when convolved with the SGWB power spectrum and spatial correlation (Hellings \& Dow…

Level sets of prevalent Weierstrass functions
Zolt\'an Buczolich, Antti K\"aenm\"aki, Bal\'azs Maga
https://arxiv.org/abs/2507.15591 http…

Level sets of prevalent Weierstrass functions
The $α$-Weierstrass function is defined as $W_g^{α,b}(x) = \sum_{k=0}^{\infty} b^{-αk} g(b^k x)$, where $g$ is a Lipschitz function on the unit circle. For a prevalent $α$-Weierstrass function, we prove that the upper Minkowski dimension of every level set is at most $1-α$, and the Hausdorff dimension of almost every level set equals $1-α$ with respect to its occupation measure. We further demonstrate that the occupation measure of a prevalent $α$-Weierstrass function is absolutely conti…

A lower bound on the number of bent squares
Jan Kristian Haugland
https://arxiv.org/abs/2508.14605 https://arxiv.org/pdf/2508.14605

A lower bound on the number of bent squares
Bent functions are Boolean functions that are maximally nonlinear. They can be represented as bent squares, i.e., square matrices for which each row and each column is the Walsh spectrum of a Boolean function. Using this representation, it is shown in this note that the number of bent functions in $n$ variables is at least $2^{n \cdot 2^{\frac{n}{2}} \left(1 + O\left(\frac{1}{n}\right)\right)}$ for even integers $n$.

Bicomplex Hardy Classes of Solutions to Beltrami Equations and the Schwarz Boundary Value Problem
William L. Blair
https://arxiv.org/abs/2507.15657 https:/…

Bicomplex Hardy Classes of Solutions to Beltrami Equations and the Schwarz Boundary Value Problem
We define Hardy classes of bicomplex-valued functions on the complex unit disk which solve bicomplex versions of the Beltrami and related equations. Using representations in terms of their complex-valued counterparts, we show these bicomplex-valued functions recover the boundary behavior associated with the classic holomorphic Hardy spaces. This work generalizes known results for complex-valued functions and continues recent work in the setting of bicomplex analogues of Hardy spaces of both hol…

Some Optimal and Near Optimal Doppler Resilient Complementary Sequence Sets
Bingsheng Shen, Zhengchun Zhou, Yang Yang, Pingzhi Fan
https://arxiv.org/abs/2508.15325 https://

Some Optimal and Near Optimal Doppler Resilient Complementary Sequence Sets
Sequences with excellent ambiguity functions are very useful in radar detection and modern mobile communications. Doppler resilient complementary sequence (DRCS) is a new type of sequence proposed recently, which can achieve lower ambiguity function sidelobes by summing the ambiguity functions of subsequences. In this paper, we introduce some new constructions of DRCS sets (DRCSSs) based on one-coincidence frequency-hopping sequence sets (OC-FHSSs), almost difference sets (ADSs), some specific …

Homomorphism Calculus for User-Defined Aggregations
Ziteng Wang, Ruijie Fang, Linus Zheng, Dixin Tang, Isil Dillig
https://arxiv.org/abs/2508.15109 https://

Homomorphism Calculus for User-Defined Aggregations
Data processing frameworks like Apache Spark and Flink provide built-in support for user-defined aggregation functions (UDAFs), enabling the integration of domain-specific logic. However, for these frameworks to support \emph{efficient} UDAF execution, the function needs to satisfy a \emph{homomorphism property}, which ensures that partial results from independent computations can be merged correctly. Motivated by this problem, this paper introduces a novel \emph{homomorphism calculus} that can…

Crosslisted article(s) found for cs.LO. https://arxiv.org/list/cs.LO/new
[1/1]:
- Logical Expressivity and Explanations for Monotonic GNNs with Scoring Functions
Matthew Morris, David J. Tena Cucala, Bernardo Cuenca Grau

Improving in-context learning with a better scoring function
Omar Naim, Swarnadeep Bhar, J\'er\^ome Bolte, Nicholas Asher
https://arxiv.org/abs/2508.14685 https://

Improving in-context learning with a better scoring function
Large language models (LLMs) exhibit a remarkable capacity to learn by analogy, known as in-context learning (ICL). However, recent studies have revealed limitations in this ability. In this paper, we examine these limitations on tasks involving first-order quantifiers such as {\em all} and {\em some}, as well as on ICL with linear functions. We identify Softmax, the scoring function in attention mechanism, as a contributing factor to these constraints. To address this, we propose \textbf{scale…

from my link log —
Row polymorphic programming.
https://www.stranger.systems/posts/by-slug/row-polymorphic-programming.html
saved 2025-07-14

Row Polymorphic Programming
Sometimes, especially when dealing with business logic, we have to deal with data that comes in from the real world, or elsewhere, naturally very messily typed, leading to nasty type signatures and messes of macros or code generation to build data structures from a schema. Row polymorphism can help us by abstracting over the fields contained in a record type in the type signature, letting us define records based on data, concatenate records together, and define functions that are generic across…

Enumerating Vector Parking Functions and their Outcomes Based on Specified Lucky Cars
Melanie Ferreri, Pamela E. Harris, Lucy Martinez, Eric Swartz
https://arxiv.org/abs/2508.13917

Enumerating Vector Parking Functions and their Outcomes Based on Specified Lucky Cars
In a parking function, a car is considered lucky if it is able to park in its preferred spot. Extending work of Harris and Martinez, we enumerate outcomes of parking functions with a fixed set of lucky cars. We then consider a generalization of parking functions known as vector parking functions or $\boldsymbol{u}$-parking functions, in which a nonnegative integer capacity is given to each parking spot in the street. With certain restrictions on $\boldsymbol{u}$, we enumerate outcomes of $\bold…

Susceptibilities and Taylor coefficients of magnetic QCD from perturbation theory
Eduardo S. Fraga, Let\'icia F. Palhares, Tulio E. Restrepo
https://arxiv.org/abs/2507.14360

Susceptibilities and Taylor coefficients of magnetic QCD from perturbation theory
We compute the coefficients $c_2(T,B)$ and $c_4(T,B)$ of the Taylor expansion for the pressure in powers of $μ_B/T$ in the presence of a large magnetic field within perturbative QCD at finite temperature and baryon density up to two-loops for $N_f=3$ flavors with physical quark masses. We also present results for the excess of pressure, baryon density and baryon number susceptibility as functions of $μ_B$, as well as susceptibilities as functions of the temperature in the $\{ μ_B,μ_Q,μ_S \…

Limit theorems for random Dirichlet series with summation over primes, with an application to Rademacher random multiplicative functions
Congzao Dong, Alexander Iksanov
https://arxiv.org/abs/2508.15032

Limit theorems for random Dirichlet series with summation over primes, with an application to Rademacher random multiplicative functions
It is shown that two conjectures put forward in the recent article Iksanov and Kostohryz (2025) are true. Namely, we prove a functional central limit theorem (FCLT) and a law of the iterated logarithm (LIL) for a random Dirichlet series $\sum_p \frac{η_p}{p^{1/2+s}}$ as $s\to 0+$, where $η_1$, $η_2,\ldots$ are independent identically distributed random variables with zero mean and finite variance, and $\sum_p$ denotes the summation over the prime numbers. As a consequence, an FCLT and an LIL…

Higher-Point Correlators in N=4 SYM: Generating Functions
Till Bargheer, Albert Bekov, Carlos Bercini, Frank Coronado
https://arxiv.org/abs/2509.14332 https://

Higher-Point Correlators in N=4 SYM: Generating Functions
We construct generating functions of five- and six-point correlators up to two loops at weak 't Hooft coupling in planar N=4 SYM. These generating functions unify the correlators of the lightest scalar operator in the stress-tensor multiplet with those of all higher R-charge single-trace half-BPS scalar operators, thereby extending previous results for four-point loop integrands. At the integrated level, they are represented as sums of conformal integrals with coefficients exhibiting ten-dimens…

Real geometric transcendence for Weierstrass elliptic functions
Arshay Sheth, Matteo Tamiozzo
https://arxiv.org/abs/2508.14645 https://arxiv.org/pdf/2508.1…

Real geometric transcendence for Weierstrass elliptic functions
Given a lattice $Λ\subset \mathbb C\simeq \mathbb R^2$ with associated Weierstrass function $\wp_Λ$, we determine the algebraic curves in $\mathbb R^2$ whose image via $\wp_Λ$ is contained in an algebraic curve.

Search-Based Credit Assignment for Offline Preference-Based Reinforcement Learning
Xiancheng Gao, Yufeng Shi, Wengang Zhou, Houqiang Li
https://arxiv.org/abs/2508.15327 https://…

Search-Based Credit Assignment for Offline Preference-Based Reinforcement Learning
Offline reinforcement learning refers to the process of learning policies from fixed datasets, without requiring additional environment interaction. However, it often relies on well-defined reward functions, which are difficult and expensive to design. Human feedback is an appealing alternative, but its two common forms, expert demonstrations and preferences, have complementary limitations. Demonstrations provide stepwise supervision, but they are costly to collect and often reflect limited exp…

Matrix Control Barrier Functions
Pio Ong, Yicheng Xu, Ryan M. Bena, Faryar Jabbari, Aaron D. Ames
https://arxiv.org/abs/2508.11795 https://arxiv.org/pdf/25…

Matrix Control Barrier Functions
This paper generalizes the control barrier function framework by replacing scalar-valued functions with matrix-valued ones. Specifically, we develop barrier conditions for safe sets defined by matrix inequalities -- both semidefinite and indefinite. Matrix inequalities can be used to describe a richer class of safe sets, including nonsmooth ones. The safety filters constructed from our proposed matrix control barrier functions via semidefinite programming (CBF-SDP) are shown to be continuous. O…

On the Effective Non-vanishing of Hecke--Maass $L$-functions at Special Points
Zhi Qi
https://arxiv.org/abs/2507.14566 https://arxiv.…

On the Effective Non-vanishing of Hecke--Maass $L$-functions at Special Points
In this paper, we consider the non-vanishing problem for the family of special Hecke--Maass $L$-values $ L (1/2+it_f, f) $ with $f (z)$ in an orthonormal basis of (even or odd) Hecke--Maass cusp forms of Laplace eigenvalue $1/4 + t_f^2$ ($t_f > 0$). We prove that 33% of $L (1/2+it_f, f)$ for $ t_f \leqslant T$ do not vanish as $T \rightarrow \infty$. For comparison, it is known that the non-vanishing proportion is at least 25% for the central $L$-values $L (1/2, f)$. Further, 33% may be raised …

Continuity of Functions on Bare Representation of Graphs under Star Topology
Rodolfo E. Maza
https://arxiv.org/abs/2507.13968 https://

Continuity of Functions on Bare Representation of Graphs under Star Topology
This paper introduces a novel topology, referred to as the star topology, on finite graphs. By treating vertices and edges as points in a unified space, we explore continuous maps between Bare representations of a graph and their properties. The key distinction lies in the fact that while every graph homomorphism induces a continuous map, the converse is not generally true due to potential loss of adjacency information.

Twisted Dirac operators and fractional correlations of the massless sine-Gordon model at the free fermion point
Roland Bauerschmidt, Scott Mason, Christian Webb
https://arxiv.org/abs/2508.14806

Twisted Dirac operators and fractional correlations of the massless sine-Gordon model at the free fermion point
For the massless sine-Gordon model at the free fermion point, in infinite volume, we define the fractional (charge or vertex operator) correlation functions from the probabilistic path integral and prove that they are given by renormalized determinants of massive twisted Dirac operators. The fractional correlation functions are the moments of the imaginary multiplicative chaos, a random generalized function that we construct with respect to the infinite-volume massless sine-Gordon measure. The …

Crosslisted article(s) found for cs.AI. https://arxiv.org/list/cs.AI/new
[2/6]:
- Logical Expressivity and Explanations for Monotonic GNNs with Scoring Functions
Matthew Morris, David J. Tena Cucala, Bernardo Cuenca Grau

from my link log —
Perfecting anti-aliasing on signed distance functions.
https://blog.pkh.me/p/44-perfecting-anti-aliasing-on-signed-distance-functions.html
saved 2025-07-26

Perfecting anti-aliasing on signed distance functions

Conditional estimates on the argument of Dirichlet $L$-functions with applications to low-lying zeros
Tianyu Zhao
https://arxiv.org/abs/2508.13301 https://…

Conditional estimates on the argument of Dirichlet $L$-functions with applications to low-lying zeros
Under the generalized Riemann hypothesis, we use Beurling-Selberg extremal functions to bound the mean and mean square of the argument of Dirichlet $L$-functions to a large prime modulus $q$. As applications, we give alternative proofs of several results on low-lying zeros of $L(s,χ)$ and obtain a new lower bound on the proportion of $L(s,χ)$ modulo $q$ with zeros close to the central point. In particular, we show conditionally that for any $β>1/4$, there exist a positive proportion of Diric…

PROD: Palpative Reconstruction of Deformable Objects through Elastostatic Signed Distance Functions
Hamza El-Kebir
https://arxiv.org/abs/2508.12554 https://

PROD: Palpative Reconstruction of Deformable Objects through Elastostatic Signed Distance Functions
We introduce PROD (Palpative Reconstruction of Deformables), a novel method for reconstructing the shape and mechanical properties of deformable objects using elastostatic signed distance functions (SDFs). Unlike traditional approaches that rely on purely geometric or visual data, PROD integrates palpative interaction -- measured through force-controlled surface probing -- to estimate both the static and dynamic response of soft materials. We model the deformation of an object as an elastostati…

Tight cylindric partitions
Shashank Kanade, Matthew C. Russell
https://arxiv.org/abs/2508.15113 https://arxiv.org/pdf/2508.15113

Tight cylindric partitions
In this note, we initiate the study of generating functions for tight cylindric partitions. For general (i.e., $r$-rowed for $r\geq 2$) tight cylindric partitions, we provide analogs of the Corteel--Welsh functional equations. We prove closed forms for the bivariate generating functions for 2-rowed tight cylindric partitions. We also show that these partitions are in bijection with a class of partitions studied by Dousse, Hardiman, and Konan.

Universal quaternary mixed sums involving generalized 3-, 4-, 5- and 8-gonal numbers via products of Ramanujan's theta functions
Nasser Abdo Saeed Bulkhali, A. Vanitha, M. P. Chaudhary
https://arxiv.org/abs/2507.13645

Universal quaternary mixed sums involving generalized 3-, 4-, 5- and 8-gonal numbers via products of Ramanujan's theta functions
Generalized $m$-gonal numbers are those $p_m(x)= [ (m - 2)x^2 - (m - 4)x ]/2 $ where $x$ and $m$ are integers with $m \geq 3$. If any nonnegative integer can be written in the form $ap_r(h)+bp_s(l)+cp_t(m)+dp_u(n)$, where $a,b,c,d$ are positive integers, then we call $ap_r(h)+bp_s(l)+cp_t(m)+dp_u(n)$ a universal quaternary sum. In this paper, we determine the universality of many quaternary sums when $r,s,t,u \in \{3,4,5,8\}$, using the theory of Ramanujan's theta function identities

Adapting A Vector-Symbolic Memory for Lisp ACT-R
Meera Ray, Christopher L. Dancy
https://arxiv.org/abs/2508.15630 https://arxiv.org/pdf/2508.15630

Adapting A Vector-Symbolic Memory for Lisp ACT-R
Holographic Declarative Memory (HDM) is a vector-symbolic alternative to ACT-R's Declarative Memory (DM) system that can bring advantages such as scalability and architecturally defined similarity between DM chunks. We adapted HDM to work with the most comprehensive and widely-used implementation of ACT-R (Lisp ACT-R) so extant ACT-R models designed with DM can be run with HDM without major changes. With this adaptation of HDM, we have developed vector-based versions of common ACT-R functions, …

Combinatorial and Gaussian Foundations of Rational Nth Root Approximations: Theorems and Conjectures
Isaac Wolford
https://arxiv.org/abs/2508.14095 https://

Combinatorial and Gaussian Foundations of Rational Nth Root Approximations: Theorems and Conjectures
We present an approach (the biroot method) for nth root approximation that yields closed-form rational functions with coefficients derived from binomial structures, Gaussian functions, or qualifying DAG structures. The method emerges from an analysis of Newton's method applied to root extraction, revealing that successive iterations generate coefficients following rows of Pascal's triangle in an alternating numerator-denominator pattern. After further exploration of these patterns, we formulate…

On the connection between zero-free regions and the error term in the Prime Number Theorem
Frederik Broucke
https://arxiv.org/abs/2507.13780 https://

On the connection between zero-free regions and the error term in the Prime Number Theorem
We provide for a wide class of zero-free regions an upper bound for the error term in the Prime Number Theorem, refining works of Pintz (1980), Johnston (2024), and Révész (2024). Our method does not only apply to the Riemann zeta function, but to general Beurling zeta functions. Next we construct Beurling zeta functions having infinitely many zeros on a prescribed contour, and none to the right, for a wide class of such contours. We also deduce an oscillation result for the corresponding err…

The Weyl bound for triple product L-functions in the cubic level
Xinchen Miao, Huimin Zhang
https://arxiv.org/abs/2508.13746 https://arxiv.org/pdf/2508.137…

The Weyl bound for triple product L-functions in the cubic level
In this paper, we focus on the strong subconvexity bounds for triple product L-functions in the cubic level aspect. Our proof on the Weyl-type bound synthesizes techniques from classical analytic number theory with methods in automorphic forms and representation theory. The methods include the refined Petersson trace formula for the newforms of cubic level, classical Voronoi summation formula, Jutila's circle method, Kuznetsov trace formula and the spectral large sieve inequality.

Inversions in parking functions
Kyle Celano, Jennifer Elder, Kimberly P. Hadaway, Pamela E. Harris, Amanda Priestley, Gabe Udell
https://arxiv.org/abs/2508.11587 https://…

Inversions in parking functions
In this paper, we obtain a q-exponential generating function for inversions on parking functions via symmetric function theory and also through a direct bijection to rooted labeled forests. We then apply these techniques to unit interval parking functions to give analogous results. We conclude by introducing a probabilistic approach through which we obtain formulas for the total number of inversions and several other statistics across all parking functions and other sets of words closed under r…

Reciprocity for GL(2) L-functions twisted by Dirichlet characters
Agniva Dasgupta, Rizwanur Khan, Ze Sen Tang
https://arxiv.org/abs/2508.12401 https://arxi…

Reciprocity for GL(2) L-functions twisted by Dirichlet characters
A formula connecting a moment of L-functions and a dual moment in a way that interchanges the roles of certain key parameters on both sides is known as a reciprocity relation. We establish a reciprocity relation for a first moment of GL(2) L-functions twisted by Dirichlet characters. This extends, via a new and simple argument, some results of Bettin, Drappeau, and Nordentoft.

Stirling polynomials and multiple zeta (star) functions at non-positive integers
Yoni Ishii, Takeshi Shinohara
https://arxiv.org/abs/2508.12577 https://arx…

Stirling polynomials and multiple zeta (star) functions at non-positive integers
It is known that the values of multiple zeta functions (MZFs) at non-positive integers can be expressed by Bernoulli numbers. This paper gives explicit formulas for the values of MZFs and multiple zeta star functions (MZSFs) at non-positive integers using Stirling polynomials. We also study the following two points: a connection between MZFs and MZSFs at non-positive integers and a connection between reverse values and generalized Gregory coefficients studied by Matsusaka, Murahara, and Onozuka.