Tootfinder

FPT Constant Approximation Algorithms for Colorful Sum of Radii
Shuilian Liu, Gregory Gutin, Yicheng Xu, Yong Zhang
https://arxiv.org/abs/2506.13191 https:…

FPT Constant Approximation Algorithms for Colorful Sum of Radii
We study the colorful sum of radii problem, where the input is a point set $P$ partitioned into classes $P_1, P_2, \dots, P_ω$, along with per-class outlier bounds $m_1, m_2, \dots, m_ω$, summing to $m$. The goal is to select a subset $\mathcal{C} \subseteq P$ of $k$ centers and assign points to centers in $\mathcal{C}$, allowing up to $m_i$ unassigned points (outliers) from each class $P_i$, while minimizing the sum of cluster radii. The radius of a cluster is defined as the maximum distance…

🤼 To understand America today, study the zero-sum mindset, writes Stefanie Stantcheva
Young people and city-dwellers are among those most likely to see one group’s gain as another’s loss
(great insight into political psychology!)
https://www.

To understand America today, study the zero-sum mindset, writes Stefanie Stantcheva
Young people and city-dwellers are among those most likely to see one group’s gain as another’s loss

Bounded Exponential Sums with Multiplicative Coefficients
Ihor Pylaiev, Fred Tyrrell
https://arxiv.org/abs/2506.12845 https://arxiv.o…

Bounded Exponential Sums with Multiplicative Coefficients
We investigate when the exponential sum $\sum_{n \leq x}f(n)e^{2 πi n α}$ is bounded, for a multiplicative function $f$ and $α\in \mathbb{R}$. We show that under certain natural assumptions, this exponential sum is bounded only when $f$ closely resembles a periodic function. For completely multiplicative functions or those taking only finitely many values, we obtain sharper classification results, including a full classification (up to a measure-zero set of $α$) in the completely multiplica…

The Space-Time Complexity of Sum-Product Queries
Kyle Deeds, Timo Camillo Merkl, Reinhard Pichler, Dan Suciu
https://arxiv.org/abs/2509.11920 https://arxiv…

The Space-Time Complexity of Sum-Product Queries
While extensive research on query evaluation has achieved consistent improvements in the time complexity of algorithms, the space complexity of query evaluation has been largely ignored. This is a particular challenge in settings with strict pre-defined space constraints. In this paper, we examine the combined space-time complexity of conjunctive queries (CQs) and, more generally, of sum-product queries (SPQs). We propose several classes of space-efficient algorithms for evaluating SPQs, and we…

Fully strange tetraquark states via QCD sum rules
Bing-Dong Wan, Ji-Chong Yang
https://arxiv.org/abs/2507.11874 https://arxiv.org/pdf…

Fully strange tetraquark states via QCD sum rules
In this paper, we have systematically explored the mass spectrum of fully strange tetraquark candidates within the framework of QCD sum rules, focusing on states with quantum numbers $J^{PC}=0^{++}$, $0^{-+}$, $0^{--}$, $1^{--}$, $1^{+-}$, and $1^{++}$. The analysis reveals the existence of fully strange tetraquark states with masses ranging from approximately $2.08$ to $3.12$ GeV. These predictions are confronted with existing experimental observations of potential fully strange tetraquark res…

A Parallelizable Approach for Characterizing NE in Zero-Sum Games After a Linear Number of Iterations of Gradient Descent
Taemin Kim, James P. Bailey
https://arxiv.org/abs/2507.11366

A Parallelizable Approach for Characterizing NE in Zero-Sum Games After a Linear Number of Iterations of Gradient Descent
We study online optimization methods for zero-sum games, a fundamental problem in adversarial learning in machine learning, economics, and many other domains. Traditional methods approximate Nash equilibria (NE) using either regret-based methods (time-average convergence) or contraction-map-based methods (last-iterate convergence). We propose a new method based on Hamiltonian dynamics in physics and prove that it can characterize the set of NE in a finite (linear) number of iterations of altern…

Instability of regular planar black holes in four dimensions arising from an infinite sum of curvature corrections
Antonio De Felice, Shinji Tsujikawa
https://arxiv.org/abs/2507.11803

Instability of regular planar black holes in four dimensions arising from an infinite sum of curvature corrections
In four-dimensional scalar-tensor theories derived via dimensional regularization with a conformal rescaling of the metric, we study the stability of planar black holes (BHs) whose horizons are described by two-dimensional compact Einstein spaces with vanishing curvature. By taking an infinite sum of Lovelock curvature invariants, it is possible to construct BH solutions whose metric components remain nonsingular at $r=0$, with a scalar-field derivative given by $ϕ'(r)=1/r$, where $r$ is the r…

Quantum State Recovery via Direct Sum Formalism Without Measurement Outcomes
Taiga Suzuki, Masayuki Ohzeki
https://arxiv.org/abs/2509.11066 https://arxiv.o…

Quantum State Recovery via Direct Sum Formalism Without Measurement Outcomes
This study proposes a new approach to quantum state recovery following measurement. Specifically, we introduce a special operation that transfers the probability amplitude of the quantum state into its orthogonal complement. This operation is followed by a measurement performed on this orthogonal subspace, enabling the undisturbed original quantum state to be regained. Remarkably, this recovery is achieved without dependence of the post-measurement operation on the measurement outcome, thus all…

Tencent and Baidu sold $3.3B combined in offshore bonds this year, the most ever for Chinese tech companies, as companies secure cheap financing for AI buildout (Janice Huang/Bloomberg)
https://www.bloomberg.com/news/articles/2025-…

Convolutive sequences, I: Through the lens of integer partition functions
Shane Chern, Dennis Eichhorn, Shishuo Fu, James A. Sellers
https://arxiv.org/abs/2507.10965

Convolutive sequences, I: Through the lens of integer partition functions
Motivated by the convolutive behavior of the counting function for partitions with designated summands in which all parts are odd, we consider coefficient sequences $(a_n)_{n\ge 0}$ of primitive eta-products that satisfy the generic convolutive property \begin{align*} \sum_{n\ge 0} a_{mn} q^n = \left(\sum_{n\ge 0} a_n q^n\right)^m \end{align*} for a specific positive integer $m$. Given the results of an exhaustive search of the Online Encyclopedia of Integer Sequences for such sequences…

Solvability Issues of Two Classes of Quasilinear and Nonlinear Integral Equations with a Sum-Difference Kernel on the Half-Line
A. Kh. Khachatryan, Kh. A. Khachatryan, H. S. Petrosyan
https://arxiv.org/abs/2507.12231

Solvability Issues of Two Classes of Quasilinear and Nonlinear Integral Equations with a Sum-Difference Kernel on the Half-Line
This paper investigates two classes of quasilinear and essentially nonlinear integral equations with a sum-difference kernel on the half-line. Such equations arise in various areas of physics, including the theory of radiative transfer in spectral lines, the dynamic theory of p-adic strings, and the kinetic theory of gases within the framework of the modified Bhatnagar-Gross-Krook (BGK) model. Under specific conditions on the kernel and the nonlinear terms, we establish constructive existence t…

The Modular Energy Function: Exact Identities and a Primality Equivalence
Es-said En-naoui
https://arxiv.org/abs/2509.10592 https://arxiv.org/pdf/2509.1059…

The Modular Energy Function: Exact Identities and a Primality Equivalence
We introduce and study the arithmetic function E_m(n), defined as the sum of the remainders of n when divided by the first m positive integers. Although the definition is elementary, the function encodes rich arithmetic structure. In this first part we develop exact algebraic and combinatorial identities, including floor-sum and divisor-sum reformulations, quotient-residue decompositions, sharp bounds and extremal classes, and symmetry relations. We also establish a diagonal identity linking E_…

Discrete weakly stable distributions
Matthew Aldridge
https://arxiv.org/abs/2509.12070 https://arxiv.org/pdf/2509.12070

Discrete weakly stable distributions
A random variable X is strictly stable if a sum of independent copies of X has the same distribution as X up to scaling, and is stable (or weakly stable) if the sum has the same distribution as X up to both scaling and shifting. Steutel and Van Harn studied 'discrete strict stability' for random variables taking values in the non-negative integers, replacing scaling by the thinning operation. We extend this to 'discrete (weak) stability', where shifting is replaced by the addition of an indepen…

PROL : Rehearsal Free Continual Learning in Streaming Data via Prompt Online Learning
M. Anwar Ma'sum, Mahardhika Pratama, Savitha Ramasamy, Lin Liu, Habibullah Habibullah, Ryszard Kowalczyk
https://arxiv.org/abs/2507.12305

PROL : Rehearsal Free Continual Learning in Streaming Data via Prompt Online Learning
The data privacy constraint in online continual learning (OCL), where the data can be seen only once, complicates the catastrophic forgetting problem in streaming data. A common approach applied by the current SOTAs in OCL is with the use of memory saving exemplars or features from previous classes to be replayed in the current task. On the other hand, the prompt-based approach performs excellently in continual learning but with the cost of a growing number of trainable parameters. The first ap…

Geometric representation of CP phases $\delta_{\rm PDG}, \delta_{\rm KM}$ in flavor mixing matrix and its sum rule by alternative unitarity triangle and quadrangle
Masaki J. S. Yang
https://arxiv.org/abs/2509.11596

Geometric representation of CP phases $δ_{\rm PDG}, δ_{\rm KM}$ in flavor mixing matrix and its sum rule by alternative unitarity triangle and quadrangle
In this letter, we present a geometric representation of the CP phases $δ_{\rm PDG}$ and $δ_{\rm KM}$ in the PDG and Kobayashi--Maskawa parameterizations of the mixing matrix as angles on the complex plane. The sum rule with the unitarity triangle $δ_{\rm PDG} + δ_{\rm KM} = π- α+ γ$ is geometrically expressed as a quadrangle on the complex plane, combination of a unitarity triangle and an alternative triangle. Furthermore, a new set of inverse unitarity triangles is defined from the inv…

In a short blog post for the MacArthur Foundation, my colleague Veronica Thamaini and I discuss the Abstract Wikipedia proposal, one of five finalists for the ongoing 100&Change program.
A Path to a World Where Everyone Can Share in the Sum of All Knowledge
https://www.

A Path to a World Where Everyone Can Share in the Sum of All Knowledge

On integers with many representations as the sum of $k$th powers of primes
Anay Aggarwal
https://arxiv.org/abs/2509.11558 https://arxiv.org/pdf/2509.11558

On integers with many representations as the sum of $k$th powers of primes
For a natural number $k>1$, let $f_k(n)$ denote the number of distinct representations of a natural number $n$ of the form $p^k+q^k$ for primes $p,q$. We prove that, for all $k>1$, $$\limsup_{n\to\infty}f_k(n)=\infty.$$ This positively answers a conjecture of Erdos, which asks if there are natural numbers $n$ with arbitrarily many distinct representations of the form $p_1^k+p_2^k+\dots+p_k^k$ for primes $p_1,p_2,\dots,p_k$.

Single-trace current correlators for 2d models of 4d gluon scattering
Sean Seet
https://arxiv.org/abs/2509.12200 https://arxiv.org/pdf/2509.12200

Single-trace current correlators for 2d models of 4d gluon scattering
Correlators of affine Kac-Moody currents evaluate to a sum over multi-color-trace contributions. We present a `single-trace current system' defined on a genus 0 Riemann surface, whose correlators evaluate to precisely the single-trace term in the evaluation of a standard affine Kac-Moody at level 1. We demonstrate that using the single-trace current system in genus 0 Berkovits-Witten twistor string correlators gives pure $\mathcal{N} = 4$ super Yang-Mills tree amplitudes, and explain how this w…

ILCL: Inverse Logic-Constraint Learning from Temporally Constrained Demonstrations
Minwoo Cho, Jaehwi Jang, Daehyung Park
https://arxiv.org/abs/2507.11000 …

ILCL: Inverse Logic-Constraint Learning from Temporally Constrained Demonstrations
We aim to solve the problem of temporal-constraint learning from demonstrations to reproduce demonstration-like logic-constrained behaviors. Learning logic constraints is challenging due to the combinatorially large space of possible specifications and the ill-posed nature of non-Markovian constraints. To figure it out, we introduce a novel temporal-constraint learning method, which we call inverse logic-constraint learning (ILCL). Our method frames ICL as a two-player zero-sum game between 1) …

Sum-of-Gaussians tensor neural networks for high-dimensional Schr\"odinger equation
Qi Zhou, Teng Wu, Jianghao Liu, Qingyuan Sun, Hehu Xie, Zhenli Xu
https://arxiv.org/abs/2508.10454

Sum-of-Gaussians tensor neural networks for high-dimensional Schrödinger equation
We propose an accurate, efficient, and low-memory sum-of-Gaussians tensor neural network (SOG-TNN) algorithm for solving the high-dimensional Schrödinger equation. The SOG-TNN utilizes a low-rank tensor product representation of the solution to overcome the curse of dimensionality associated with high-dimensional integration. To handle the Coulomb interaction, we introduce an SOG decomposition to approximate the interaction kernel such that it is dimensionally separable, leading to a tensor re…

ADHO (adho.org) updates at the opening of #DH2025 from Diane and Michael - the Italian Digital Humanities association officially joins ADHO, and announces awards including the Zampoli prize to Stylo software, the conference bursaries winners and Fortier prize nominees. Also note the Code of Conduct!

Sources: Chord Music Partners, a music rights investment vehicle, raised $2B so far in a round due to close in October; Searchlight Capital has invested $400M (Murray Stassen/Music Business Worldwide)
https://www.musicbusiness…

Exclusive: Chord Music Partners raises $2 billion+ in investable capital… with another $1 billion+ on
Chord has raised the sum via a funding round due to close in October…

A Gradient Meta-Learning Joint Optimization for Beamforming and Antenna Position in Pinching-Antenna Systems
Kang Zhou, Weixi Zhou, Donghong Cai, Xianfu Lei, Yanqing Xu, Zhiguo Ding, Pingzhi Fan
https://arxiv.org/abs/2506.12583

A Gradient Meta-Learning Joint Optimization for Beamforming and Antenna Position in Pinching-Antenna Systems
In this paper, we consider a novel optimization design for multi-waveguide pinching-antenna systems, aiming to maximize the weighted sum rate (WSR) by jointly optimizing beamforming coefficients and antenna position. To handle the formulated non-convex problem, a gradient-based meta-learning joint optimization (GML-JO) algorithm is proposed. Specifically, the original problem is initially decomposed into two sub-problems of beamforming optimization and antenna position optimization through equi…

On the Tschirnhausen module of coverings of curves on decomposable ruled surfaces and applications
Youngook Choi, Hristo Iliev, Seonja Kim
https://arxiv.org/abs/2507.11304

On the Tschirnhausen module of coverings of curves on decomposable ruled surfaces and applications
We show that for two classes of $m$-secant curves $X \subset S$, with $m \geq 2$, where $f : S = \mathbb{P} (\mathcal{O}_Y \oplus \mathcal{O}_Y (E)) \to Y$ and $E$ is a non-special divisor on a smooth curve $Y$, the Tschirnhausen module $\mathcal{E}^{\vee}$ of the covering $φ= f_{|_X} : X \to Y$ decomposes completely as a direct sum of line bundles. Specifically, we prove that: for $X \in |\mathcal{O}_S (mH)|$, where $H$ denotes the tautological divisor on $S$, one has $ \mathca…

Improved Rates for Stochastic Variance-Reduced Difference-of-Convex Algorithms
Anh Duc Nguyen, Alp Yurtsever, Suvrit Sra, Kim-Chuan Toh
https://arxiv.org/abs/2509.11657 https://…

Improved Rates for Stochastic Variance-Reduced Difference-of-Convex Algorithms
In this work, we propose and analyze DCA-PAGE, a novel algorithm that integrates the difference-of-convex algorithm (DCA) with the ProbAbilistic Gradient Estimator (PAGE) to solve structured nonsmooth difference-of-convex programs. In the finite-sum setting, our method achieves a gradient computation complexity of $O(N + N^{1/2}\varepsilon^{-2})$ with sample size $N$, surpassing the previous best-known complexity of $O(N + N^{2/3}\varepsilon^{-2})$ for stochastic variance-reduced (SVR) DCA meth…

Ultra-Resilient Superimposed Codes: Near-Optimal Construction and Applications
Gianluca De Marco, Dariusz R. Kowalski
https://arxiv.org/abs/2506.13489 http…

Ultra-Resilient Superimposed Codes: Near-Optimal Construction and Applications
A superimposed code is a collection of binary vectors (codewords) with the property that no vector is contained in the Boolean sum of any $k$ others, enabling unique identification of codewords within any group of $k$. Superimposed codes are foundational combinatorial tools with applications in areas ranging from distributed computing and data retrieval to fault-tolerant communication. However, classical superimposed codes rely on strict alignment assumptions, limiting their effectiveness in as…

Linear representations of the mapping class group of dimension at most $3g-3$
Julian Kaufmann, Nick Salter, Zhong Zhang, Xiyan Zhong
https://arxiv.org/abs/2507.11365

Linear representations of the mapping class group of dimension at most $3g-3$
We classify representations of the mapping class group of a surface of genus $g$ (with at most one puncture or boundary component) up to dimension $3g-3$. Any such representation is the direct sum of a representation in dimension $2g$ or $2g+1$ (given as the action on the (co)homology of the surface or its unit tangent bundle) with a trivial representation. As a corollary, any linear system on the moduli space of Riemann surfaces of genus $g$ in this range is of algebro-geometric origin.

Cohomological Calibration and Curvature Constraints on Product Manifolds: A Topological Lower Bound
Alexander Pigazzini, Magdalena Toda
https://arxiv.org/abs/2509.11834 https://…

Cohomological Calibration and Curvature Constraints on Product Manifolds: A Topological Lower Bound
We establish a quantitative relationship between mixed cohomology classes and the geometric complexity of cohomologically calibrated metric connections with totally skew torsion on product manifolds. Extending the results of Pigazzini--Toda (2025), we show that the dimension of the off-diagonal curvature subspace of a connection $\nabla^C$ is bounded below by the sum of tensor ranks of the mixed Künneth components of its calibration class. The bound depends only on the mixed class $[ω]_{\math…

Additional Constructions of Sequences of Alternating Sum and Difference Dominated Sets
Yorick Herrmann, Connor Hill, Merlin Phillips, Daniel Flores, Steven J. Miller, Steven Senger
https://arxiv.org/abs/2509.12829

Additional Constructions of Sequences of Alternating Sum and Difference Dominated Sets
A More Sums Than Differences (MSTD) set is a finite set of integers $A$ where the cardinality of its sumset, $A+A$, is greater than the cardinality of its difference set, $A-A$. We address a problem posed by Samuel Allen Alexander that asks whether there exists an infinite sequence of sets alternating between being MSTD and More Differences Than Sums (MDTS), where each set properly contains the previous. While a companion paper resolved this using `filling in' techniques, we solve the more chal…

OffsetCrust: Variable-Radius Offset Approximation with Power Diagrams
Zihan Zhao, Pengfei Wang, Minfeng Xu, Shuangmin Chen, Shiqing Xin, Changhe Tu, Wenping Wang
https://arxiv.org/abs/2507.10924

OffsetCrust: Variable-Radius Offset Approximation with Power Diagrams
Offset surfaces, defined as the Minkowski sum of a base surface and a rolling ball, play a crucial role in geometry processing, with applications ranging from coverage motion planning to brush modeling. While considerable progress has been made in computing constant-radius offset surfaces, computing variable-radius offset surfaces remains a challenging problem. In this paper, we present OffsetCrust, a novel framework that efficiently addresses the variable-radius offsetting problem by computing…

Nonrelativistic limit of ground states to $L^2$-supercritical nonlinear Dirac equations
Pan Chen, Yanheng Ding, Qi Guo
https://arxiv.org/abs/2507.11203 htt…

Nonrelativistic limit of ground states to $L^2$-supercritical nonlinear Dirac equations
In this paper, we study the existence and nonrelativistic limit of normalized ground states for the following nonlinear Dirac equation with power-type potentials \begin{equation*} \begin{cases} &-i c\sum\limits_{k=1}^3α_k\partial_k u +mc^2 β{u}- |{u}|^{p-2}{u}=ω{u}, \\ &\displaystyle\int_{\mathbb{R}^3}\vert u \vert^2 dx =1. \end{cases} \end{equation*} We demonstrate the existence of ground states for large $c$ and establish the uniqueness of the associated Lagrange multiplier f…

Analysis of a fast fully discrete finite element method for fractional viscoelastic wave propagation
Hao Yuan, Xiaoping Xie
https://arxiv.org/abs/2507.11822

Analysis of a fast fully discrete finite element method for fractional viscoelastic wave propagation
This paper is devoted to a numerical analysis of a fractional viscoelastic wave propagation model that generalizes the fractional Maxwell model and the fractional Zener model. First, we convert the model problem into a velocity type integro-differential equation and establish existence, uniqueness and regularity of its solution. Then we consider a conforming linear/bilinear/trilinear finite element semi-discrete scheme and a fast scheme of backward Euler full discretization with a sum-of-expone…

Solving Distance-Based Optimization Problems Using Optical Hardware
Guangyao Li, Richard Zhipeng Wang, Natalia G. Berloff
https://arxiv.org/abs/2507.11378 …

Solving Distance-Based Optimization Problems Using Optical Hardware
We present a practical approach to solving distance-based optimization problems using optical computing hardware. The objective is to minimize an energy function defined as the weighted sum of squared differences between measured distances and the squared Euclidean distances of point coordinates. By representing coordinates as complex numbers, we map the optimization problem onto optical fields, enabling its solution through either the canonical transformation (CT) method or the gain-based bifu…

Rings Whose Units Have Identity Plus Quasi-Nilpotent Square
Shahram Najafi, Ahmad Moussavi, Peter Danchev
https://arxiv.org/abs/2509.11319 https://arxiv.or…

Rings Whose Units Have Identity Plus Quasi-Nilpotent Square
In this paper, we investigate the structural and characterizing properties of the so-called {\it 2-UQ rings}, that are rings such that the square of every unit is the sum of an idempotent and a quasi-nilpotent element that commute with each other. We establish some fundamental connections between 2-UQ rings and relevant widely classes of rings including 2-UJ, 2-UU and tripotent rings. Our novel results include: (1) complete characterizations of 2-UQ group rings, showing that they force underlyi…

A Poisson representation of the positive sojourn time of L\'evy processes
Helmut H. Pitters
https://arxiv.org/abs/2509.11776 https://arxiv.org/pdf/2509…

A Poisson representation of the positive sojourn time of Lévy processes
We study the distribution of the positive sojourn time $$ A_t:= \int_0^t \mathbf 1\{ X_s>0 \}ds $$ of an arbitrary Lévy process $X:= (X_t)_{t\geq 0}$. For an exponential random variable $E^{(q)}$ of rate $q>0$ independent of $X$ we show the representation in law \begin{align*} A_{E^{(q)}} =_d \sum_{T\in Π} T \end{align*} as the sum of points of a Poisson process $Π$ with intensity given explicitely in terms of the positivity $t\mapsto \mathbb P\{X_t>0\}$. This representation raises some fu…

Most incompatible measurements and sum-of-squares optimisation
S\'ebastien Designolle
https://arxiv.org/abs/2509.10381 https://arxiv.org/pdf/2509.10381…

Most incompatible measurements and sum-of-squares optimisation
Measurement incompatibility, or joint measurability, is a cornerstone of quantum theory and a useful resource. For finite-dimensional systems, quantifying this resource and establishing universal bounds valid for all measurements is a long-standing problem. In this work, we exhibit analytical universal parent measurements giving access to bounds that beat the state of the art. In particular, we can show that, for relevant robustnesses, sets of anticommuting observables give rise to the most inc…

Leading order asymptotics for non-local energies and the Read-Shockley law
Peter J. Grabner, Florian Theil
https://arxiv.org/abs/2509.12041 https://arxiv.o…

Leading order asymptotics for non-local energies and the Read-Shockley law
We study an energy minimization problem $\sum_{i \neq j} W(z_i - z_j)$ for $N$ points $\left\{z_1, \dots, z_N\right\}$ with applications in dislocation theory. The $N$ points lie in the two-dimensional domain $\mathbb{R} \times [-π, π]$, %who are trying to minimize their interaction energy where where the kernel $W$ is derived from the Volterra potential $V(x,y) = \frac{x^2}{x^2+y^2}-\frac12\log(x^2+y^2)$. We prove that the minimum energy is given by $- N \log{N} +\mathcal{O}(N)$. This lowe…

Compact representation and long-time extrapolation of real-time data for quantum systems
Andre Erpenbeck, Yuanran Zhu, Yang Yu, Lei Zhang, Richard Gerum, Olga Goulko, Chao Yang, Guy Cohen, Emanuel Gull
https://arxiv.org/abs/2506.13760

Compact representation and long-time extrapolation of real-time data for quantum systems
Representing real-time data as a sum of complex exponentials provides a compact form that enables both denoising and extrapolation. As a fully data-driven method, the Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithm is agnostic to the underlying physical equations, making it broadly applicable to various observables and experimental or numerical setups. In this work, we consider applications of the ESPRIT algorithm primarily to extend real-time dynamical d…

Physics-Informed Linear Model (PILM): Analytical Representations and Application to Crustal Strain Rate Estimation
Tomohisa Okazaki
https://arxiv.org/abs/2507.12218

Physics-Informed Linear Model (PILM): Analytical Representations and Application to Crustal Strain Rate Estimation
Many physical systems are described by partial differential equations (PDEs), and solving these equations and estimating their coefficients or boundary conditions (BCs) from observational data play a crucial role in understanding the associated phenomena. Recently, a machine learning approach known as physics-informed neural network, which solves PDEs using neural networks by minimizing the sum of residuals from the PDEs, BCs, and data, has gained significant attention in the scientific communi…

On the number of triangles in $K_4$-free graphs
Jialin He, Jie Ma, Yan Wang, Chunlei Zu
https://arxiv.org/abs/2509.12100 https://arxiv.org/pdf/2509.12100…

On the number of triangles in $K_4$-free graphs
Erdős asked whether for any $n$-vertex graph $G$, the parameter $p^*(G)=\min \sum_{i\ge 1} (|V(G_i)|-1)$ is at most $\lfloor n^2/4\rfloor$, where the minimum is taken over all edge decompositions of $G$ into edge-disjoint cliques $G_i$. In a restricted case (also conjectured independently by Erdős), Győri and Keszegh [Combinatorica, 37(6) (2017), 1113--1124] proved that $p^*(G)\leq \lfloor n^2/4\rfloor$ for all $K_4$-free graphs $G$. Motivated by their proof approach, they conjectu…

Pricing energy spread options with variance gamma-driven Ornstein-Uhlenbeck dynamics
Tim Leung, Kevin Lu
https://arxiv.org/abs/2507.11480 https://

Pricing energy spread options with variance gamma-driven Ornstein-Uhlenbeck dynamics
We consider the pricing of energy spread options for spot prices following an exponential Ornstein-Uhlenbeck process driven by a sum of independent multivariate variance gamma processes. Within this class of mean-reverting, infinite activity price processes, the Esscher transform is used to obtain an equivalent martingale measure. We focus on the weak variance alpha-gamma process and show that it is not closed under the Esscher transform. By deriving an analytic expression for the cumulant gene…

A New Framework for the Sum of Squared $\kappa$-$\mu$ RVs with Application to Sub-THz Systems
Gustavo Rodrigues de Lima Tejerina, Italo Atzeni
https://arxiv.org/abs/2508.06242 h…

A New Framework for the Sum of Squared $κ$-$μ$ RVs with Application to Sub-THz Systems
In this paper, we adopt the $κ$-$μ$ model to characterize the propagation in the sub-THz band. We develop a new exact representation of the sum of squared independent and identically distributed $κ$-$μ$ random variables, which can be used to express the power of the received signal in multi-antenna systems. Unlike existing ones, the proposed analytical framework is remarkably tractable and computationally efficient, and thus can be conveniently employed to analyze systems with massive anten…

WZW Partition Functions from Supersymmetric Localization
Boan Zhao
https://arxiv.org/abs/2507.11673 https://arxiv.org/pdf/2507.11673

WZW Partition Functions from Supersymmetric Localization
We prove a conjecture of Murthy and Witten which expresses modular invariant WZW partition functions as lattice sums. We show that when the sum is over the root lattice of SU(N), the result correctly reproduces the diagonal modular invariants of SU(N)_k whenever N > 2 and N + k is even. Beyond these cases, the proposition is not always true and we provide a counterexample when k >> N > 2 and k + N is odd. This proof generalizes the proof by Murthy and Witten for the SU(2) case. We then move ont…

Replaced article(s) found for eess.AS. https://arxiv.org/list/eess.AS/new
[1/1]:
- The Whole Is Bigger Than the Sum of Its Parts: Modeling Individual Annotators to Capture Emotiona...
James Tavernor, Yara El-Tawil, Emily Mower Provost

Imma be rich! Thanks Elon!

An elementary proof of existence and uniqueness of stationary distributions for irreducible Markov chains
Rinaldo B. Schinazi
https://arxiv.org/abs/2506.13662

An elementary proof of existence and uniqueness of stationary distributions for irreducible Markov chains
Consider an $n\times n$ matrix $P$ with the following properties. All entries in $P$ are positive or $0$, the sum of each row is 1 and for all $i$ and $j$ in $\{1,\dots,n\}$ there exists a natural number $k$ such that the $(i,j)$ entry of the matrix $P^k$ is strictly positive. Then, there exists a unique row vector $v$ with only strictly positive entries, whose sum of entries is 1 and such that $vP=P$. We present a proof of this well-known result that uses only basic algebra and the Bolzano-Wei…

Way More Than the Sum of Their Parts: From Statistical to Structural Mixtures
James P. Crutchfield
https://arxiv.org/abs/2507.07343 https://

Way More Than the Sum of Their Parts: From Statistical to Structural Mixtures
We show that mixtures comprised of multicomponent systems typically are much more structurally complex than the sum of their parts; sometimes, infinitely more complex. We contrast this with the more familiar notion of statistical mixtures, demonstrating how statistical mixtures miss key aspects of emergent hierarchical organization. This leads us to identify a new kind of structural complexity inherent in multicomponent systems and to draw out broad consequences for system ergodicity.

Sublinear-Time Algorithms for Diagonally Dominant Systems and Applications to the Friedkin-Johnsen Model
Weiming Feng, Zelin Li, Pan Peng
https://arxiv.org/abs/2509.13112 https:…

Sublinear-Time Algorithms for Diagonally Dominant Systems and Applications to the Friedkin-Johnsen Model
We study sublinear-time algorithms for solving linear systems $Sz = b$, where $S$ is a diagonally dominant matrix, i.e., $|S_{ii}| \geq δ+ \sum_{j \ne i} |S_{ij}|$ for all $i \in [n]$, for some $δ\geq 0$. We present randomized algorithms that, for any $u \in [n]$, return an estimate $z_u$ of $z^*_u$ with additive error $\varepsilon$ or $\varepsilon \lVert z^*\rVert_\infty$, where $z^*$ is some solution to $Sz^* = b$, and the algorithm only needs to read a small portion of …

Query Answering under Volume-Based Diversity Functions
Marcelo Arenas, Timo Camillo Merkl, Reinhard Pichler, Cristian Riveros
https://arxiv.org/abs/2509.11929 https://

Query Answering under Volume-Based Diversity Functions
When query evaluation produces too many tuples, a new approach in query answering is to retrieve a diverse subset of them. The standard approach for measuring the diversity of a set of tuples is to use a distance function between tuples, which measures the dissimilarity between them, to then aggregate the pairwise distances of the set into a score (e.g., by using sum or min aggregation). However, as we will point out in this work, the resulting diversity measures may display some unintuitive be…

Bicriteria Polygon Aggregation with Arbitrary Shapes
Lotte Blank, David Eppstein, Jan-Henrik Haunert, Herman Haverkort, Benedikt Kolbe, Philip Mayer, Petra Mutzel, Alexander Naumann, Jonas Sauer
https://arxiv.org/abs/2507.11212

Bicriteria Polygon Aggregation with Arbitrary Shapes
We study the problem of aggregating polygons by covering them with disjoint representative regions, thereby inducing a clustering of the polygons. Our objective is to minimize a weighted sum of the total area and the total perimeter of the regions. This problem has applications in cartographic map generalization and urban analytics. Here, the polygons represent building footprints and the clusters may represent urban areas. Previous approaches forced the boundaries of the regions to come from a…

$U$-spin sum rules for two-body decays of bottom baryons
Si-Jia Wen, Wei-Chen Fu, Di Wang
https://arxiv.org/abs/2508.09763 https://arxiv.org/pdf/2508.09763…

$U$-spin sum rules for two-body decays of bottom baryons
$U$-spin symmetry, which reflects the symmetry between the down-type $d$ and $s$ quarks, is a powerful tool for analyzing heavy hadron weak decays. Motivated by recent experimental achievements in the bottom baryon sector, we study the $U$-spin sum rules for bottom baryon decays. The effective Hamiltonian for $b$ quark decay is zero under the $U$-spin lowering operators $U_-^n$, permitting us to derive $U$-spin sum rules involving only the $b\to d$ transition or $b\to s$ transition. Moreover, a…

On the sum of the angles between three vectors
Iosif Pinelis
https://arxiv.org/abs/2508.04759 https://arxiv.org/pdf/2508.04759

On the sum of the angles between three vectors
For any three nonzero vectors $a,b,c$ in $\mathbb R^2$, we obtain a necessary and sufficient condition for the sum of the three pairwise angles between these vectors to equal $2π$. As an easy consequence of this, a proof of Euclid's theorem that the sum of the interior angles of any triangle is $π$ is provided. So, the main result of this note can be considered a generalization of Euclid's theorem. To a large extent, the consideration is reduced almost immediately to a choice for the sum of t…

On the Bit Size of Sum-of-Squares Proofs for Symmetric Formulations
Alex Bortolotti, Monaldo Mastrolilli, Marilena Palomba, Luis Felipe Vargas
https://arxiv.org/abs/2509.06928 h…

On the Bit Size of Sum-of-Squares Proofs for Symmetric Formulations
The Sum-of-Squares (SoS) hierarchy is a powerful framework for polynomial optimization and proof complexity, offering tight semidefinite relaxations that capture many classical algorithms. Despite its broad applicability, several works have revealed fundamental limitations to SoS automatability. (i) While low-degree SoS proofs are often desirable for tractability, recent works have revealed they may require coefficients of prohibitively large bit size, rendering them computationally infeasible.…

Lattice paths and the Geode
Ira M. Gessel
https://arxiv.org/abs/2507.09405 https://arxiv.org/pdf/2507.09405

Lattice paths and the Geode
Let $t_1,t_2,\dots$ be variables, and let $S$ be the formal power series in the variables $t_1, t_2,\dots$ satisfying $S=1+\sum_{i=1}^\infty t_n S^n.$ Let $S_1 =\sum_{n=1}^\infty t_n$. Wildberger and Rubine recently showed that there is a formal power series $G$ in the $t_i$, which they called the Geode, satisfying $S=1+GS_1$. In this paper we discuss some of the properties of the Geode and of the related series $H=G/S$, which satisfies $S=1/(1-HS_1)$. We show that \begin{equation*} G=\biggl(1-…

Turnpike properties for zero-sum stochastic linear quadratic differential games of Markovian regime switching system
Xun Li, Fan Wu, Xin Zhang
https://arxiv.org/abs/2509.09358 h…

Turnpike properties for zero-sum stochastic linear quadratic differential games of Markovian regime switching system
This paper investigates the long-time behavior of zero-sum stochastic linear-quadratic (SLQ) differential games within Markov regime-switching diffusion systems and establishes the turnpike property of the optimal triple. By verifying the convergence of the associated coupled differential Riccati equations (CDREs) along with their convergence rate, we show that, for a sufficiently large time horizon, the equilibrium strategy in the finite-horizon problem can be closely approximated by that of t…

Samsung agrees to acquire Seattle-based Xealth, which helps healthcare providers manage digital health tools and has raised over $50M, for an undisclosed sum (Taylor Soper/GeekWire)
https://www.geekwire.com/2025/samsung-acquiring…

On a Restriction Problem of Hickman and Wright for the Parabola in $\mathbb{Z}/N\mathbb{Z}$ for Squarefree $N$
Nathaniel Kingsbury-Neuschotz
https://arxiv.org/abs/2509.09885 htt…

On a Restriction Problem of Hickman and Wright for the Parabola in $\mathbb{Z}/N\mathbb{Z}$ for Squarefree $N$
Hickman and Wright proved an $L^2$ restriction estimate for the parabola $Σ$ in $\mathbb{Z}/N\mathbb{Z}$ of the form $$\left(\frac{1}{|Σ|}\sum\limits_{m\inΣ}|\widehat{f}(m)|^2 \right)^{\frac{1}{2}}\leq C_εN^ε\cdot N^{-1}\left(\sum\limits_{x\in (\mathbb{Z}/N\mathbb{Z})^2}|f(x)|^\frac{6}{5}\right)^\frac{5}{6}$$ for all functions $f:(\mathbb{Z}/N\mathbb{Z})^2\rightarrow \mathbb{C}$ and any $ε>0$, and that this bound is sharp when $N$ has a large square facto…

Linear Equations for Solving Partial Latin Squares and Sudokus
Ralf P\"oppel
https://arxiv.org/abs/2509.10472 https://arxiv.org/pdf/2509.10472

Linear Equations for Solving Partial Latin Squares and Sudokus
For Latin squares the units (rows and columns) have fixed sum. The same holds for rows, columns, and blocks in Sudokus. Summing the elements of a unit yields a linear equation, and the set of all such equations forms a system of linear equations that models the relations of the variables in Latin squares and Sudoku puzzles. Every completed Latin square or Sudoku satisfies this system, enabling analysis and completion of partially filled puzzles. The linear system provides necessary but not suff…

On Levi operators between normed and vector lattices
Eduard Emelyanov
https://arxiv.org/abs/2506.12578 https://arxiv.org/pdf/2506.125…

On Levi operators between normed and vector lattices
The notion of Levi operator is an operator abstraction of the Levy property of a norm. Various aspects of Levi operators have been studied recently by several authors. The present paper is devoted to Levi operators from a normed lattice to a vector lattice. It is proved that every finite rank operator is a Levi operator. An example is given showing that the sum of a positive rank one operator and a positive compact Levi operator need not to be a Levi operator. We prove that every quasi Levi ope…

An algorithm for the Product-Sum Equality
Hlib Husarov, Eberhard Mayerhofer
https://arxiv.org/abs/2508.09647 https://arxiv.org/pdf/2508.09647

An algorithm for the Product-Sum Equality
We propose a recursive algorithm for identifying all finite sequences of positive integers whose product equals their sum. Our method uses solutions of strictly shorter length that are iteratively extended in pursuit of a valid solution. The algorithm is efficient, with a time complexity similar to the quick sort algorithm.

Restricted Jacobi permutations
Alyssa G. Henke, Kyle R. Hoffman, Derek H. Stephens, Yongwei Yuan, Yan Zhuang
https://arxiv.org/abs/2509.11494 https://arxiv…

Restricted Jacobi permutations
Jacobi permutations, introduced by Viennot in the context of Jacobi elliptic functions, are counted by the Euler numbers $E_{n}$ appearing in the series expansion $\sec x+\tan x=\sum_{n=0}^{\infty}E_{n}x^{n}/n!$. We conduct a systematic study of pattern avoidance in Jacobi permutations, achieving a complete enumeration of Jacobi permutations avoiding a prescribed set of length 3 patterns. In the case of a single pattern restriction, we obtain refined enumerations with respect to several permuta…

Convergent Q-Learning for Infinite-Horizon General-Sum Markov Games through Behavioral Economics
Yizhou Zhang, Eric Mazumdar
https://arxiv.org/abs/2508.08669 https://

Convergent Q-Learning for Infinite-Horizon General-Sum Markov Games through Behavioral Economics
Risk-aversion and bounded rationality are two key characteristics of human decision-making. Risk-averse quantal-response equilibrium (RQE) is a solution concept that incorporates these features, providing a more realistic depiction of human decision making in various strategic environments compared to a Nash equilibrium. Furthermore a class of RQE has recently been shown in arXiv:2406.14156 to be universally computationally tractable in all finite-horizon Markov games, allowing for the developm…

Diffraction-Unlimited Tip-Enhanced Sum-Frequency Vibrational Nanoscopy
Shota Takahashi, Koichi Kumagai, Atsunori Sakurai, Tatsuto Mochizuki, Tomonori Hirano, Akihiro Morita, Toshiki Sugimoto
https://arxiv.org/abs/2509.09179

Diffraction-Unlimited Tip-Enhanced Sum-Frequency Vibrational Nanoscopy
Sum-frequency generation (SFG) is a powerful second-order nonlinear spectroscopic technique that provides detailed insights into molecular structures and absolute orientations at surfaces and interfaces. However, conventional SFG based on far-field schemes suffers from the diffraction limit of light, which inherently averages spectroscopic information over micrometer-scale regions and obscures nanoscale structural inhomogeneity. Here, we overcome this fundamental limitation by leveraging a high…

Rephasing Invariant Formula for the CP Phase in the Kobayashi-Maskawa Parametrization and the Exact Sum Rule with the Unitarity Triangle $\delta_{\rm PDG} \delta_{\rm KM} = \pi - \alpha \gamma$
Masaki J. S. Yang
https://arxiv.org/abs/2508.10249

Rephasing Invariant Formula for the CP Phase in the Kobayashi-Maskawa Parametrization and the Exact Sum Rule with the Unitarity Triangle $δ_{\rm PDG} + δ_{\rm KM} = π- α+ γ$
In this letter, we obtain a rephasing invariant formula for the CP phase in the Kobayashi--Maskawa parameterization $δ_{\rm KM} = \arg [ - { V_{ud} \det V_{\rm CKM} / V_{us} V_{ub} V_{cd} V_{td}} ]$. General perturbative expansion of the formula and observed value $δ_{\rm KM} \simeq π/2$ reveal that the phase difference of the 1-2 mixings $e^{i (ρ_{12}^{d} - ρ_{12}^{u})}$ is close to maximal for sufficiently small 1-3 quark mixings $s_{13}^{u,d}$. Moreover, by combining this result with an…

Invariants for sum-rank metric codes
Paolo Santonastaso, Ferdinando Zullo
https://arxiv.org/abs/2507.04158 https://arxiv.org/pdf/2507…

Invariants for sum-rank metric codes
The code equivalence problem is central in coding theory and cryptography. While classical invariants are effective for Hamming and rank metrics, the sum-rank metric, which unifies both, introduces new challenges. This paper introduces new invariants for sum-rank metric codes: generalised idealisers, the centraliser, the center, and a refined notion of linearity. These lead to the definition of nuclear parameters, inspired by those used in division algebra theory, where they are crucial for pro…

Stably exotic 4-manifolds
Daniel Kasprowski, Mark Powell
https://arxiv.org/abs/2508.10499 https://arxiv.org/pdf/2508.10499…

Stably exotic 4-manifolds
A pair of closed, smooth $4$-manifolds $M$ and $M'$ are stably exotic if they are stably homeomorphic but not stably diffeomorphic, where stabilisation refers to connected sum with copies of $S^2 \times S^2$. Orientable stable exotica do not exist by a result of Gompf, but Kreck showed that nonorientable examples are plentiful. We investigate which values of the fundamental group $π$ and the first and second Stiefel-Whitney classes $w_1$ and $w_2$ admit stably exotic pairs, providing a complet…

Enhancing Sum Capacity via Quantum and No-Signaling Cooperation Between Transmitters
Seung-Hyun Nam, Hyun-Young Park, Jiyoung Yun, Ashutosh Rai, Si-Hyeon Lee, Joonwoo Bae
https://arxiv.org/abs/2509.08219

Enhancing Sum Capacity via Quantum and No-Signaling Cooperation Between Transmitters
We consider a communication scenario over a discrete memoryless interference channel or multiple access channel without feedback, where transmitters exploit classical, quantum, or no-signaling cooperation. In this scenario, several previous works have shown that the sum capacities of channels involving pseudo-telepathy games can be enhanced by quantum or no-signaling cooperation. However, a full characterization of which channels admit such an improvement remains open. By focusing on the common…

Self-reverse labelings of distance magic graphs
Petr Kov\'a\v{r}, Ksenija Rozman, Primo\v{z} \v{S}parl
https://arxiv.org/abs/2507.11226 https://…

Self-reverse labelings of distance magic graphs
A graph is distance magic if it admits a bijective labeling of its vertices by integers from $1$ up to the order of the graph in such a way that the sum of the labels of all the neighbors of a vertex is independent of a given vertex. We introduce the concept of a self-reverse distance magic labeling of a regular graph which allows for a more compact description of the graph and the labeling in terms of the corresponding quotient graph. We show that the members of several known infinite families…

Lower bounds for mask polynomials with many cyclotomic divisors
Gergely Kiss, Izabella {\L}aba, Caleb Marshall, G\'abor Somlai
https://arxiv.org/abs/2507.11672

Lower bounds for mask polynomials with many cyclotomic divisors
Given a nonempty set $A \subset \mathbb{N}\cup\{0\}$, define the mask polynomial $A(X)=\sum_{a\in A} X^a$. Suppose that there are $s_1,\dots,s_k\in\nn\setminus\{1\}$ such that the cyclotomic polynomials $Φ_{s_1},\dots,Φ_{s_k}$ divide $A(X)$. What is the smallest possible size of $A$? For $k=1$, this was answered by Lam and Leung in 2000. Less is known about the case when $k\geq 2$; in particular, one may ask whether (similarly to the $k=1$ case) the optimal configurations have a simple ``fibe…

On the First Non-Universal Term in Random Polynomial Real Zeros
Phuc Lam, Oanh Nguyen
https://arxiv.org/abs/2509.12170 https://arxiv.org/pdf/2509.12170

On the First Non-Universal Term in Random Polynomial Real Zeros
Let $P_n(x) = \sum_{k=0}^{n} ξ_k x^k$ be a Kac random polynomial, where the coefficients $ξ_k$ are i.i.d.\ copies of a given random variable $ξ$. Based on numerical experiments, it has been conjectured that if $ξ$ has mean zero, unit variance, and a finite $(2+\varepsilon_0)$-moment for some $\varepsilon_0>0$, then \[ \mathbb{E}[N_{\mathbb{R}}(P_n)] \;=\; \frac{2}π \log n + C_ξ + o_n(1), \] where $N_{\mathbb{R}}(P_n)$ denotes the number of real roots of $P_n$, and $C_ξ$ is an absol…

Descent problem for certificate of non-negativity on semi-algebraic sets
Manoj K. Keshari, Debapriya Ojha, Niladri Sekhar Patra
https://arxiv.org/abs/2508.07060 https://

Descent problem for certificate of non-negativity on semi-algebraic sets
Let $F$ be a subfield of $\mathbb R$ and let $K$ be a basic closed semi-algebraic set in $\mathbb R$ with $\partial K\subset F$. Let $\mathcal N$ be the natural choice of generators of $K$. We show that if $f\in F[x]$ is $\geq 0$ on $K$, then $f$ can be written as $$f=\sum_{e\in\{0,1\}^s } a_eσ_e g^e $$ where $a_e\in F_{\geq 0}$, $σ_e\in \sum F[x]^2$ and $g^{e}=g_1^{e_1} \cdots g_s^{e_s}$. In other words, the preordering $T_{\mathcal N}$ of $F[x]$ is saturated. In case $F=\mathbb R$, this res…

Local uniqueness and non-degeneracy of blowup solutions for regular Liouville systems
Zetao Cheng, Haoyu Li, Lei Zhang
https://arxiv.org/abs/2509.09781 https://

Local uniqueness and non-degeneracy of blowup solutions for regular Liouville systems
We study the following Liouville system defined on a compact Riemann surface $M$, \begin{equation} -Δu_i=\sum_{j=1}^n a_{ij}ρ_j\Big(\frac{h_j e^{u_j}}{\int_Ωh_j e^{u_j}}-1\Big)\mbox{ in }M\mbox{ for }i=1,\cdots,n,\nonumber \end{equation} where the coefficient matrix $A=(a_{ij})_{n\times n}$ is nonnegative, $h_1, \ldots, h_n$ are positive smooth functions, and $ρ_1, \ldots, ρ_n$ are positive constants. For the blowup solutions, we establish their uniqueness and non-degeneracy based on nat…

Exact Sum Rules and Zeta Generating Formulas from the ODE/IM correspondence
Syo Kamata
https://arxiv.org/abs/2508.06366 https://arxiv.org/pdf/2508.06366

Exact Sum Rules and Zeta Generating Formulas from the ODE/IM correspondence
We formulate exact sum rules (ESRs) and zeta generating formulas (ZGFs) for quantum mechanics defined by the ${\cal PT}$-symmetric potential $V_{\cal PT}(x) = x^{2K} (ix)^\varepsilon$ with $K,\varepsilon \in \mathbb{N}$, as well as the Hermitian potential $V_{\cal H}(x) = x^{2 K}$ with $K \in {\mathbb N} + 1$, based on the fusion relations of the $A_{2M-1}$ T-system in the framework of the ODE/IM correspondence. In this setup, the fusion relations on the integrable model (IM) side correspond to…

$\Xi_c \to \Xi$ Semileptonic Decays: An LCSR View on the Experiment-Lattice Tension
T. M. Aliev, S. Bilmis, M. Savci
https://arxiv.org/abs/2509.10181 https://

$Ξ_c \to Ξ$ Semileptonic Decays: An LCSR View on the Experiment-Lattice Tension
We present a light-cone QCD sum rule analysis of the semileptonic decays of $Ξ_c$ baryons, focusing on the channels $Ξ_c^0 \to Ξ^- \ell^+ ν_\ell$, and $Ξ_c^+ \to Ξ^0 \ell^+ ν_\ell$. The transition form factors are calculated within the light-cone QCD sum rules framework, using the distribution amplitudes of the heavy $Ξ_c$ baryons. The obtained form factors are then used to compute the differential and total decay widths, as well as the branching fractions. Our numerical results for the…

Log-Concavity and Log-Convexity of Restricted Infinite Products
Krystian Gajdzica, Bernhard Heim, Markus Neuhauser
https://arxiv.org/abs/2509.11246 https://

Log-Concavity and Log-Convexity of Restricted Infinite Products
In this paper we provide a classification on the sign distribution of $Δ_{E,\ell}(n):= p_{E,\ell }(n)^2 - p_{E,\ell }(n-1) \, p_{E,\ell }(n+1)$, where \begin{equation*} \sum_{n =0}^{\infty} p_{E,\ell }(n) \, q^n := \prod_{n \in S} \left(1 - q^n \right)^{-f_{\ell}(n)},\quad (\ell \in \mathbb{N}, f_1\equiv 1). \end{equation*} We take the product over $1\in S \subset \mathbb{N}$ and denote the complement by $E$, the set of exceptions. In the case of $\ell=1$ and $E$ the multiples of $k$, $p_{E,…

Improved Average Bounds for an Inequality of Alladi, Erd\"os, and Vaaler
Cooper O'Kuhn
https://arxiv.org/abs/2509.12570 https://arxiv.org/pdf/2509…

Improved Average Bounds for an Inequality of Alladi, Erdös, and Vaaler
We prove an averaged version of a claim suspected to be true by Alladi, Erdös, and Vaaler. Qualitatively, the result states that a divisor sum of a multiplicative function, which obeys certain size constraints, derives most of its value from its "small" divisors.

Sparsifying Sums of Positive Semidefinite Matrices
Arpon Basu, Pravesh K. Kothari, Yang P. Liu, Raghu Meka
https://arxiv.org/abs/2508.08169 https://arxiv.o…

Sparsifying Sums of Positive Semidefinite Matrices
In this paper, we revisit spectral sparsification for sums of arbitrary positive semidefinite (PSD) matrices. Concretely, for any collection of PSD matrices $\mathcal{A} = \{A_1, A_2, \ldots, A_r\} \subset \mathbb{R}^{n \times n}$, given any subset $T \subseteq [r]$, our goal is to find sparse weights $μ\in \mathbb{R}_{\geq 0}^r$ such that $(1 - ε) \sum_{i \in T} A_i \preceq \sum_{i \in T} μ_i A_i \preceq (1 + ε) \sum_{i \in T} A_i.$ This generalizes spectral sparsification of graphs which …

On the Diminished Sombor Index of Fixed-Order Molecular Graphs With Cyclomatic Number at Least 3
Abdulaziz Mutlaq Alotaibi, Abdulaziz M. Alanazi, Taher S. Hassan, Akbar Ali
https://arxiv.org/abs/2509.12294

On the Diminished Sombor Index of Fixed-Order Molecular Graphs With Cyclomatic Number at Least 3
For a graph $G$ with edge set $E$, let $d(u)$ denote the degree of a vertex $u$ in $G$. The diminished Sombor (DSO) index of $G$ is defined as $DSO(G)=\sum_{uv\in E}\sqrt{(d(u))^2+(d(v))^2}(d(u)+d(v))^{-1}$. The cyclomatic number of a graph is the smallest number of edges whose removal makes the graph acyclic. A connected graph of maximum degree at most $4$ is known as a molecular graph. The primary motivation of the present study comes from a conjecture concerning the minimum DSO index of fixe…

First determination of $V_{cs,cd}$ from inclusive $D$ meson decays
Kang-Kang Shao, Hai-Long Feng, Xue-Yin Liu, Qin Qin, Liang Sun, Fu-Sheng Yu
https://arxiv.org/abs/2509.11404 h…

First determination of $V_{cs,cd}$ from inclusive $D$ meson decays
We report the first determination of the Cabibbo-Kobayashi-Maskawa matrix elements $|V_{cs}|$ and $|V_{cd}|$ from a global fit to data from inclusive and sum-of-exclusive charm decays. Simultaneously, the heavy quark expansion parameters are determined, and they are in good agreement with results from the literature, validating the robustness of this work. With the current precision, our determined value for $|V_{cs}|$ is consistent with the world-average value ext…

Functional central limit theorem for dependent models with finite memory
V\'ictor Hugo V\'azquez Guevara, Manuel Gonz\'alez-Navarrete
https://arxiv.org/abs/2506.12145 …

Functional central limit theorem for dependent models with finite memory
We provide complementary results for a family of models with dependence on their previous $k$-sum. Using a martingale-based approach, we establish a functional central limit theorem and analyze the limiting behavior of the center of mass. Additionally, we explore the connection between our findings and the study of certain reinforced random walks in the literature

On a family of sums of powers of the floor function and their links with generalized Dedekind sums
Steven Brown
https://arxiv.org/abs/2507.11666 https://…

On a family of sums of powers of the floor function and their links with generalized Dedekind sums
In this paper we are concerned with a family of sums involving the floor function. With $r$ a non negative integer and $n$ and $m$ positive integers we consider the sums \begin{equation*}\mathbf{S}_{r}\left(n,m\right)=\sum_{k=1}^{n-1}{\left\lfloor \frac{km}{n}\right\rfloor}^r\end{equation*} While a formula for $\mathbf{S}_1$ is well known, we provide closed-form formulas for $\mathbf{S}_2$ and $\mathbf{S}_3$ as well as the reciprocity laws they satisfy. Additionally, one can find a closed-form …

One-weight codes in the sum-rank metric
Usman Mushrraf, Ferdinando Zullo
https://arxiv.org/abs/2508.04262 https://arxiv.org/pdf/2508.04262

One-weight codes in the sum-rank metric
One-weight codes, in which all nonzero codewords share the same weight, form a highly structured class of linear codes with deep connections to finite geometry. While their classification is well understood in the Hamming and rank metrics - being equivalent to (direct sums of) simplex codes - the sum-rank metric presents a far more intricate landscape. In this work, we explore the geometry of one-weight sum-rank metric codes, focusing on three distinct classes. First, we introduce and classify …

Meeting a Challenge raised by Ekhad and Zeilberger related to Stern's Triangle
Jinlong Tang, Guoce Xin
https://arxiv.org/abs/2506.13375 https://…

Meeting a Challenge raised by Ekhad and Zeilberger related to Stern's Triangle
This paper resolves an open problem raised by Ekhad and Zeilberger for computing $ω(10000)$, which is related to Stern's triangle. While $ν(n)$, defined as the sum of squared coefficients in $\prod_{i=0}^{n-1} (1 + x^{2^i} + x^{2^{i+1}})$, admits a rational generating function, the analogous function $ω(n)$ for $\prod_{i=0}^{n-1} (1 + x^{2^i+1} + x^{2^{i+1}+1})$ presents substantial computational difficulties due to its complex structure. We develop a method integrating constant term techn…

On the verification of a Nicolas inequality
Orlando Galdames-Bravo
https://arxiv.org/abs/2509.11182 https://arxiv.org/pdf/2509.11182

On the verification of a Nicolas inequality
Nicolas inequality we deal can be written as \begin{equation}\label{Nicineq} e^γ\log\log N_x < \dfrac{N_x}{φ(N_x)}\,, \end{equation} where $x\ge 2$, $N_x$ denotes the product of the primes less or equal than $x$, $γ$ is the Euler constant and $φ$ is the Euler totient function. We show that there is a large $x_0>0$ such that this inequality fails infinitely often for integers $x\ge x_0$. To this aim we analyze the sign of the Big-o function in the Mertens estimate for the sum of reciprocals …

The $\eta$-$\eta'$ mixing and its application in the $B^ /D^ /D_s^ \to\eta^{(\prime)}\ell^ \nu_\ell$ decays
Yu-Jie Zhang, Xing-Gang Wu, Dan-Dan Hu, Long Zeng
https://arxiv.org/abs/2506.13214

The $η$-$η'$ mixing and its application in the $B^+/D^+/D_s^+\toη^{(\prime)}\ell^+ ν_\ell$ decays
In this paper, we take into account the intrinsic charm and gluonic contents into the $η-η^\prime$ mixing scheme and formulate the tetramixing $η-η^\prime-G-η_c$ to study the mixing properties of $η^{(\prime)}$ mesons. Using the newly derived mixing parameters, we calculate the transition form factors (TFFs) of $B^+/D^+/D_s^+\toη^{(\prime)}$ within the QCD light-cone sum rules up to next-to-leading order QCD corrections and twist-4 contributions. Using the extrapolated TFFs, we then calc…

Space-time fractional stochastic partial differential equations driven by L\'evy white noise
Yuhui Guo, Jiang-Lun Wu
https://arxiv.org/abs/2506.12834 h…

Space-time fractional stochastic partial differential equations driven by Lévy white noise
This paper is concerned with the following space-time fractional stochastic nonlinear partial differential equation \begin{equation*} \left(\partial_t^β+\fracν{2}\left(-Δ\right)^{α/ 2}\right) u=I_{t}^γ\Big[ f(t,x,u)-\sum_{i=1}^{d} \frac{\partial}{\partial x_i} q_i(t,x,u)+ σ(t,x,u) F_{t,x}\Big] \end{equation*} for a random field $u(t,x):[0,\infty)\times\mathbb{R}^d \mapsto\mathbb{R}$, where $α>0, β\in(0,2), γ\ge0, ν>0, F_{t,x}$ is a Lévy space-time white noise, $I_{t}^γ$ stands for…

Spanning subgraphs and spectral radius in graphs
Sizhong Zhou
https://arxiv.org/abs/2507.11078 https://arxiv.org/pdf/2507.11078

Spanning subgraphs and spectral radius in graphs
A spanning tree $T$ of a connected graph $G$ is a subgraph of $G$ that is a tree covers all vertices of $G$. The leaf distance of $T$ is defined as the minimum of distances between any two leaves of $T$. A fractional matching of a graph $G$ is a function $h$ assigning every edge a real number in $[0,1]$ so that $\sum\limits_{e\in E_G(v)}{h(e)}\leq1$ for any $v\in V(G)$, where $E_G(v)$ denotes the set of edges incident with $v$ in $G$. A fractional matching of $G$ is called a fractional perfect …

On the Squared Distance Matrix of a Starlike Block Graph
Joyentanuj Das, Sumit Mohanty
https://arxiv.org/abs/2509.10854 https://arxiv.org/pdf/2509.10854

On the Squared Distance Matrix of a Starlike Block Graph
Let $D(G)$ be the distance matrix of a simple connected graph $G$. The Hadamard product $D(G)~\circ~ D(G)$ is called the squared distance matrix of $G$, and is denoted by $Δ(G)$. A simple connected graph is called a starlike block graph if it has a central cut vertex, and each of its blocks is a complete graph. Let $ \mathcal{S}(n_1, n_2, \ldots, n_b)$ be the starlike block graph with blocks $K_{n_1+1}, K_{n_2+1}, \ldots, K_{n_b+1} $ on $n=1 + \sum_{i=1}^b n_i$ vertices. In this article, we co…

Point process convergence of extremes in $K$-symmetric exclusion
Michael Conroy, Adri\'an Gonz\'alez Casanova, Sunder Sethuraman
https://arxiv.org/abs/2506.12632

Point process convergence of extremes in $K$-symmetric exclusion
We consider the behavior of extremal particles in $K$-symmetric exclusion on $\mathbb{Z}$ when the process starts from certain infinite-particle step configurations where there are no particles to the right of a maximal one. In such a system, the occupancy of a site is limited to at most $K \geq 1$. Let $X^{(0)}_t\geq X^{(1)}_t\geq \cdots$ denote the order statistics of the particles in the system. We show that the point process $\sum_{m=0}^\infty δ_{v_t(X_{t/K}^{(m)})}$ converges in distribut…

$b \to c$ semileptonic sum rule: Current status and prospects
Motoi Endo, Syuhei Iguro, Satoshi Mishima, Ryoutaro Watanabe
https://arxiv.org/abs/2508.06322 https://

$b \to c$ semileptonic sum rule: Current status and prospects
The $b \to c$ semileptonic sum rules provide relations between the decay rates of $B \to D^{(*)} τ\barν$ and $Λ_b \to Λ_c τ\barν$. Starting from the heavy quark and zero-recoil limits, we revisit the derivation of the sum rule for total decay rates. We then examine deviations from the limits and investigate corrections arising from realistic hadron masses and higher-order contributions to form factors, taking account of uncertainties. We show that these corrections are negligible compared…

Existence and Uniqueness Property On a Generalized Ledin-Brousseau Sum
Ivan Hadinata
https://arxiv.org/abs/2507.03813 https://arxiv.o…

Existence and Uniqueness Property On a Generalized Ledin-Brousseau Sum
In this paper, we present the existence and uniqueness property on a finite sum involving a polynomial and a homogeneous linear recurrence sequence. This finite sum is of the form $\sum_{k=1}^n P(k)s_{hk+r}$ where $n$ is a positive integer, $P(x)$ is a polynomial in $\mathbb C[x]$, $h$ and $r$ are some integers, and $(s_k)_{k\in\mathbb Z}$ is a homogeneous linear recurrence sequence of degree $m\geq 2$ with some constraints.

Large values of Dirichlet polynomials with multiplicative coefficients
Zikang Dong, Yutong Song, Weijia Wang, Hao Zhang, Shengbo Zhao
https://arxiv.org/abs/2509.09771 https://…

Large values of Dirichlet polynomials with multiplicative coefficients
In this paper, we investigate large values of Dirichlet polynomials with multiplicative coefficients $\sum_{n\le N}f(n)n^{it}$, where $1\ll t\le T$ for large $T$. We prove an improved Omega result in the region $\exp((\log T)^{\frac12+\varepsilon})\le N\le\sqrt T$, where $T$ is large. We also show an Omega result when $\log N$ is around $\sqrt{\log T\log_2T}$.

Doubly heavy spin-$\frac {3}{2} $ baryons spectrum in the ground and excited states
M. Shekari Tousi, K. Azizi
https://arxiv.org/abs/2508.10328 https://arx…

Doubly heavy spin-$\frac {3}{2} $ baryons spectrum in the ground and excited states
This study employs QCD sum rules to predict the masses and residues of spin-$\frac {3}{2} $ doubly heavy baryons including two heavy quarks (c and/or b) and one light quark, specifically focusing on $ Ξ_{cc}^*$, $ Ξ_{bc}^*$, $ Ξ_{bb}^*$, $ Ω_{cc}^*$, $ Ω_{bc}^*$ and $ Ω_{bb}^*$. Our study provides results for the ground state ($1S$), first orbital excitation ($1P$), and the first radial excitation ($2S$), within a consistent theoretical framework. In addition to mass spectra, we provide r…

Regular sets in Cayley sum graphs on generalized dicyclic groups
Meiqi Peng, Yuefeng Yang, Wenying Zhu
https://arxiv.org/abs/2507.07736 https://

Regular sets in Cayley sum graphs on generalized dicyclic groups
For a graph $Γ=(V(Γ),E(Γ))$, a subset $C$ of $V(Γ)$ is called an $(α,β)$-regular set in $Γ$, if every vertex of $C$ is adjacent to exactly $α$ vertices of $C$ and every vertex of $V(Γ)\setminus C$ is adjacent to exactly $β$ vertices of $C$. In particular, if $C$ is an $(α,β)$-regular set in some Cayley sum graph of a finite group $G$ with connection set $S$, then $C$ is called an $(α,β)$-regular set of $G$. In this paper, we consider a generalized dicyclic group $G$ and for each s…

On the correlations between character sums of division polynomials under shifts
Subham Bhakta, Igor E. Shparlinski
https://arxiv.org/abs/2507.09271 https:/…

On the correlations between character sums of division polynomials under shifts
Let $E$ be an elliptic curve over the finite field $\mathbb{F}_p$, and $P \in E(\mathbb{F}_p)$ be an $\mathbb{F}_p$-rational point. We study the sums \[ S_{χ,P}(N,h) = \sum_{n=1}^N χ(ψ_n(P)) χ(ψ_{n+h}(P)), \] where $ψ_n(P)$ denotes the $n$-th division polynomial evaluated at $P$, and $χ$ is a multiplicative character of $\mathbb{F}_p^{*}$. We estimate $S_{χ,P}(N,h)$ on average over $h$ over a rather short interval $h \in [1, H]$. We also obtain a multidimensional generalisation of this …

Further constructions of square integer relative Heffter arrays
Diane Donovan, Sarah Lawson, James Lefevre
https://arxiv.org/abs/2509.09907 https://arxiv.o…

Further constructions of square integer relative Heffter arrays
A square integer relative Heffter array is an $n \times n$ array whose rows and columns sum to zero, each row and each column has exactly $k$ entries and either $x$ or $-x$ appears in the array for every $x \in \mathbb{Z}_{2nk+t}\setminus J$, where $J$ is a subgroup of size $t$. There are many open problems regarding the existence of these arrays. In this paper we construct two new infinite families of these arrays with the additional property that they are strippable. These constructions compl…

Mass spectrum of the $\Omega\bar{\Omega}$ states
Bing-Dong Wan, Jun-Hao Zhang, Yan Zhang
https://arxiv.org/abs/2508.10763 https://arxiv.org/pdf/2508.10763

Mass spectrum of the $Ω\barΩ$ states
In this study, we investigate the mass spectrum of the $Ω\barΩ$ states with quantum numbers $J^{PC}=0^{-+}$, $1^{--}$, $0^{++}$, and $1^{++}$ within the framework of QCD sum rules. Employing suitably constructed interpolating currents, the analyses are carried out with the operator product expansion (OPE) including condensate contributions up to dimension $12$. Our results indicate the existence of four possible baryonium states with masses $m_{0^{-+}}=(3.22\pm0.07)$ GeV, $m_{1^{--}}=(3.28\pm…

On certain root number $1$ cases of the cube sum problem
Shamik Das, Somnath Jha
https://arxiv.org/abs/2508.05361 https://arxiv.org/pdf/2508.05361

On certain root number $1$ cases of the cube sum problem
We consider certain families of integers $n$ determined by some congruence condition, such that the global root number of the elliptic curve $E_{-432n^2}: Y^2=X^3-432n^2$ is $1$ for every $n$, however a given $n$ may or may not be a sum of two rational cubes. We give explicit criteria in terms of the $2$-parts and $3$-parts of the ideal class groups of certain cubic number fields to determine whether such an $n$ is a cube sum. In particular, we study integers $n$ divisible by $3$ such that the …

On the sum-of-squares function
Vitalii V. Iudelevich
https://arxiv.org/abs/2508.02701 https://arxiv.org/pdf/2508.02701

On the sum-of-squares function
In this paper, we derive the following asymptotic formula $$ \mathop{{\sum}'}_{n\leqslant x}\dfrac{r(n)}{r(n+1)} = {x}{(\ln x)^{-3/4}}(c+o(1)),\ \ x \to +\infty,$$ where $r(n)$ is the number of representations of $n$ as a sum of two squares, $c$ is a positive constant, and the prime indicates summation over those $n$ for which $r(n+1)\neq 0$.

Special restricted partition functions for the stable sheaf cohomology on flag varieties
Mircea Cimpoeas
https://arxiv.org/abs/2509.09418 https://arxiv.org…

Special restricted partition functions for the stable sheaf cohomology on flag varieties
Let $\mathbf a:=(a_1,\ldots,a_r)$ be a sequence of positive integers, $d\geq 2$ and $j\geq 1$, some integers. We study the functions $p_{\mathbf a,d}(n):=$ the number of integer solutions $(x_1,\dots,x_r)$ of $\sum_{i=1}^r a_ix_i=n$, with $x_i\geq 0$ and $x_i \equiv 0,1(\bmod\;d)$, for all $1\leq i\leq r$, and $p_{\mathbf a,d}(n;j):=$ the number of $(x_1,\ldots,x_r)$ as above which satisfy also the condition $\sum_{i=1}^r \left(x_i-(d-2)\left\lfloor \frac{x_i}{d} \right\rfloor\right) =j$. We …