Tootfinder

Infinite matrix product states for $(1 1)$-dimensional gauge theories
Ross Dempsey, Anna-Maria E. Gl\"uck, Silviu S. Pufu, Benjamin T. S{\o}gaard
https://arxiv.org/abs/2508.16363

Infinite matrix product states for $(1+1)$-dimensional gauge theories
We present a matrix product operator construction that allows us to represent the lattice Hamiltonians of (abelian or non-abelian) gauge theories in a local and manifestly translation-invariant form. In particular, we use symmetric matrix product states and introduce link-enhanced matrix product operators (LEMPOs) that can act on both the physical and virtual spaces of the matrix product states. This construction allows us to study Hamiltonian lattice gauge theories on infinite lattices. As exa…

Towards automated generation of fast and accurate algorithms for recursive matrix multiplication
Jean-Guillaume Dumas (CASC), Cl\'ement Pernet (CASC), Alexandre Sedoglavic (CRIStAL)
https://arxiv.org/abs/2506.19405

Towards automated generation of fast and accurate algorithms for recursive matrix multiplication
We propose a strategy for the generation of fast and accurate versions of non-commutative recursive matrix multiplication algorithms. To generate these algorithms, we consider matrix and tensor norm bounds governing the stability and accuracy of numerical matrix multiplication. We start by a unification on known max-norm bounds on matrix multiplication stability and then extend them to further norms and more generally to recursive bilinear algorithms and the alternative basis matrix multiplicat…

Exact Matrix Seriation through Mathematical Optimization: Stress and Effectiveness-Based Models
V\'ictor Blanco, Alfredo Mar\'in, Justo Puerto
https://arxiv.org/abs/2506.19821

Exact Matrix Seriation through Mathematical Optimization: Stress and Effectiveness-Based Models
Matrix seriation, the problem of permuting the rows and columns of a matrix to uncover latent structure, is a fundamental technique in data science, particularly in the visualization and analysis of relational data. Applications span clustering, anomaly detection, and beyond. In this work, we present a unified framework grounded in mathematical optimization to address matrix seriation from a rigorous, model-based perspective. Our approach leverages combinatorial and mixed-integer optimization t…

1995: M-Theory
1997: Matrix string theory
1999: The Matrix (development began 1994)
#stringtheory #mtheory #thematrix

Modeling the uncertainty on the covariance matrix for probabilistic forecast reconciliation
Chiara Carrara, Lorenzo Zambon, Dario Azzimonti, Giorgio Corani
https://arxiv.org/abs/2506.19554

Modeling the uncertainty on the covariance matrix for probabilistic forecast reconciliation
In forecast reconciliation, the covariance matrix of the base forecasts errors plays a crucial role. Typically, this matrix is estimated, and then treated as known. In contrast, we propose a Bayesian reconciliation model that explicitly accounts for the uncertainty in the covariance matrix. We choose an Inverse-Wishart prior, which leads to a multivariate-t reconciled predictive distribution and allows a completely analytical derivation. Empirical experiments demonstrate that this approach impr…

Israel is accelerating its efforts to cement its permanent control over the West Bank
through a number of sweeping legal and institutional changes,
according to a new report from Adalah, The Legal Center for Arab Minority Rights in Israel.
The 87-page report, 
"Legal Structures of Distinction, Separation, and Territorial Domination", describes the ways in which the Netanyahu government is rapidly building on a long-standing legal matrix that further threatens…

Israel is changing the legal system governing the West Bank to accelerate annexation: report
Netanyahu’s government is building on a long-standing legal matrix to accelerate Israel’s de facto annexation in the West Bank

Asus' ROG Matrix Platinum GeForce RTX 5090 erinnert an Radeon HD 4870
Asus will die schnellste GeForce RTX 5090 auflegen. Die ROG Matrix Platinum erinnert an alte Modelle wie die Radeon HD 4870.
htt…

A High-Dimensional Statistical Theory for Convex and Nonconvex Matrix Sensing
Joshua Agterberg, Ren\'e Vidal
https://arxiv.org/abs/2506.20659 https://

A High-Dimensional Statistical Theory for Convex and Nonconvex Matrix Sensing
The problem of matrix sensing, or trace regression, is a problem wherein one wishes to estimate a low-rank matrix from linear measurements perturbed with noise. A number of existing works have studied both convex and nonconvex approaches to this problem, establishing minimax error rates when the number of measurements is sufficiently large relative to the rank and dimension of the low-rank matrix, though a precise comparison of these procedures still remains unexplored. In this work we provide …

Online Algorithms for Recovery of Low-Rank Parameter Matrix in Non-stationary Stochastic Systems
Yanxin Fu, Junbao Zhou, Yu Hu, Wenxiao Zhao
https://arxiv.org/abs/2506.19299

Online Algorithms for Recovery of Low-Rank Parameter Matrix in Non-stationary Stochastic Systems
This paper presents a two-stage online algorithm for recovery of low-rank parameter matrix in non-stationary stochastic systems. The first stage applies the recursive least squares (RLS) estimator combined with its singular value decomposition to estimate the unknown parameter matrix within the system, leveraging RLS for adaptability and SVD to reveal low-rank structure. The second stage introduces a weighted nuclear norm regularization criterion function, where adaptive weights derived from th…

New Hardness Results for Low-Rank Matrix Completion
Dror Chawin, Ishay Haviv
https://arxiv.org/abs/2506.18440 https://arxiv.org/pdf/2…

New Hardness Results for Low-Rank Matrix Completion
The low-rank matrix completion problem asks whether a given real matrix with missing values can be completed so that the resulting matrix has low rank or is close to a low-rank matrix. The completed matrix is often required to satisfy additional structural constraints, such as positive semi-definiteness or a bounded infinity norm. The problem arises in various research fields, including machine learning, statistics, and theoretical computer science, and has broad real-world applications. This…

Heuristic Bounded Prime Gaps via a Chaotic Multidimensional Sieve and Random Matrix Theory
Milad Ghadimi
https://arxiv.org/abs/2507.17986 https://arxiv.org…

Heuristic Bounded Prime Gaps via a Chaotic Multidimensional Sieve and Random Matrix Theory
We present the Enhanced Multidimensional Chaotic Heuristic Sieve (EMCHS), a novel probabilistic framework that integrates chaotic perturbations and random matrix theory (RMT) to suggest improved bounds on prime gaps. Building upon the foundational sieves of Goldston-Pintz-Yildirim and Maynard, EMCHS heuristically suggests unconditional gaps of at most 180 and conditional gaps of at most 8 under a partial Elliott-Halberstam conjecture (EHC) with delta = 0.3. These heuristic suggestions surpass M…

Ich würde gern Matrix (das offene Kommunikationsprotokoll für Echtzeitkommunikation, nicht den Film) mögen, aber der Reifegrad der Clients macht es einem echt nicht leicht.

Changing the discrete spectrum of the half-line matrix Schr\"odinger operator
Tuncay Aktosun, Ricardo Weder
https://arxiv.org/abs/2506.17882 https://

Changing the discrete spectrum of the half-line matrix Schrödinger operator
We consider the matrix-valued Schrödinger operator on the half line with the general selfadjoint boundary condition. When the discrete spectrum is changed without changing the continuous spectrum, we present a review of the transformations of the relevant quantities including the regular solution, the Jost solution, the Jost matrix, the scattering matrix, and the boundary matrices used to describe the selfadjoint boundary condition. The changes in the discrete spectrum are considered when an e…

ZORMS-LfD: Learning from Demonstrations with Zeroth-Order Random Matrix Search
Olivia Dry, Timothy L. Molloy, Wanxin Jin, Iman Shames
https://arxiv.org/abs/2507.17096

ZORMS-LfD: Learning from Demonstrations with Zeroth-Order Random Matrix Search
We propose Zeroth-Order Random Matrix Search for Learning from Demonstrations (ZORMS-LfD). ZORMS-LfD enables the costs, constraints, and dynamics of constrained optimal control problems, in both continuous and discrete time, to be learned from expert demonstrations without requiring smoothness of the learning-loss landscape. In contrast, existing state-of-the-art first-order methods require the existence and computation of gradients of the costs, constraints, dynamics, and learning loss with re…

Rowmotion and Echelonmotion
Colin Defant, Yuhan Jiang, Rene Marczinzik, Adrien Segovia, David E Speyer, Hugh Thomas, Nathan Williams
https://arxiv.org/abs/2507.18230 https://

Rowmotion and Echelonmotion
Given a linear extension $σ$ of a finite poset $R$, we consider the permutation matrix indexing the Schubert cell containing the Cartan matrix of $R$ with respect to $σ$. This yields a bijection $\mathrm{Ech}_σ\colon R\to R$ that we call echelonmotion; it is the inverse of the Coxeter permutation studied by Klász, Marczinzik, and Thomas. Those authors proved that echelonmotion agrees with rowmotion when $R$ is a distributive lattice. We generalize this result to semidistributive lattices. I…

Dynamics of Cu$_2$O Rydberg excitons -- real density matrix approach
Karol Karpinski, Gerard Czajkowski
https://arxiv.org/abs/2506.19336 https://

Dynamics of Cu$_2$O Rydberg excitons -- real density matrix approach
Basing on recent reliable measurements of the life- and coherence time of Cu$_2$O Rydberg excitons, we present an analytical method which enables to describe the experimental results. The real-density matrix approach (RDMA) is applied to describe two-photon absorption in Cu$_2$O through the excitonic response to the exciting fields. This approach produces an analytical expression for the emission intensity time evolution, and can be used to explain trends in reported experimental data. Our appr…

Fermionic S-matrix and cosmological correlators: T-violation at O(H)
Aman Goyal, Aneek Jana, Swapnanil Mandal, Aninda Sinha
https://arxiv.org/abs/2506.19950

Fermionic S-matrix and cosmological correlators: T-violation at O(H)
We study the Bunch-Davies (BD) and Unruh-de Witt (UdW) de Sitter S-matrices in the presence of spin-$1/2$ fermions. Building on recent work, this enables us to correlate the de Sitter S-matrix with cosmological correlators. We consider a finite-time version of the UdW S-matrix to study $O(H)$ corrections to some typical particle physics processes such as beta decay. Owing to the lack of time-reversal symmetry in the expanding Poincaré patch, we find signatures of intrinsic T-violation in polar…

A matrix-valued measure associated to the derivatives of a function of generalised bounded deformation
Gianni Dal Maso, Davide Donati
https://arxiv.org/abs/2506.19978

A matrix-valued measure associated to the derivatives of a function of generalised bounded deformation
We associate to every function $u\in GBD(Ω)$ a measure $μ_u$ with values in the space of symmetric matrices, which generalises the distributional symmetric gradient $Eu$ defined for functions of bounded deformation. We show that this measure $μ_u$ admits a decomposition as the sum of three mutually singular matrix-valued measures $μ^a_u$, $μ^c_u$, and $μ^j_u$, the absolutely continuous part, the Cantor part, and the jump part, as in the case of $BD(Ω)$ functions. We then characterise the…

I can't... every time someone shows the ChatGPT logo, I first recognize the Element (Matrix app) logo. Same green tone in the background and a white, swirly shape on top.

Analytic formulation of Leptogenesis with neutrino oscillation data employing the general parametrization for neutrino mass matrix
Nobuchika Okada, Digesh Raut
https://arxiv.org/abs/2506.20580

Analytic formulation of Leptogenesis with neutrino oscillation data employing the general parametrization for neutrino mass matrix
The observed neutrino oscillations and baryon asymmetry, unexplained by the Standard Model (SM), can both be accounted for by extending the SM to include Majorana right-handed neutrinos (RHNs). Tiny neutrino masses naturally arise through the Type-I seesaw mechanism, which involves lepton number violation. Meanwhile, the baryon asymmetry can be generated via leptogenesis, where the out-of-equilibrium decay of RHNs produces a lepton asymmetry that is partially converted into a baryon asymmetry t…

Precision Matrix Regularization in Sufficient Dimension Reduction for Improved Quadratic Discriminant Classification
Derik T. Boonstra, Rakheon Kim, Dean M. Young
https://arxiv.org/abs/2506.19192

Precision Matrix Regularization in Sufficient Dimension Reduction for Improved Quadratic Discriminant Classification
Sufficient dimension reduction (SDR) methods, which often rely on class precision matrices, are widely used in supervised statistical classification problems. However, when class-specific sample sizes are small relative to the original feature-space dimension, precision matrix estimation becomes unstable and, as a result, increases the variability of the linear dimension reduction (LDR) matrix. Ultimately, this fact causes suboptimal supervised classification. To address this problem, we develo…

The Alpha Group Dynamic Mapping
Cleber Souza Corr\^ea, Thiago Braido Nogueira de Melo
https://arxiv.org/abs/2507.18303 https://arxiv.org/pdf/2507.18303

The Alpha Group Dynamic Mapping
This paper investigates the dynamical behavior of a system of ordinary differential equations (ODEs) governed by a matrix that represents the division in the algebra of the Alpha group. As the system evolves, the matrix induces topological transitions in geometric spaces, controlled by a rotational parameter. Numerical simulations are performed using a fourth-order Runge-Kutta method implemented in Python. The results reveal the emergence of topological nodes, the existence of critical points a…

Fundamental limits of distributed covariance matrix estimation via a conditional strong data processing inequality
Mohammad Reza Rahmani, Mohammad Hossein Yassaee, Mohammad Reza Aref
https://arxiv.org/abs/2507.16953

Fundamental limits of distributed covariance matrix estimation via a conditional strong data processing inequality
Estimating high-dimensional covariance matrices is a key task across many fields. This paper explores the theoretical limits of distributed covariance estimation in a feature-split setting, where communication between agents is constrained. Specifically, we study a scenario in which multiple agents each observe different components of i.i.d. samples drawn from a sub-Gaussian random vector. A central server seeks to estimate the complete covariance matrix using a limited number of bits communica…

Die strukturellen Voraussetzungen zur #CO2-Reduktion liegen bei politischen Maßnahmen. Das Pariser #Klimaabkommen lässt grüßen.
Die Verantwortung kann man nicht auf Bürger delegieren. Aber wer will, kann durch individuelles Verhalten einen kleinen Beitrag leisten. Ich habe aus einer Studie …

Orthogonal eigenvectors and singular vectors of tensors
Alvaro Ribot, Anna Seigal, Piotr Zwiernik
https://arxiv.org/abs/2506.19009 https://

Orthogonal eigenvectors and singular vectors of tensors
The spectral theorem says that a real symmetric matrix has an orthogonal basis of eigenvectors and that, for a matrix with distinct eigenvalues, the basis is unique (up to signs). In this paper, we study the symmetric tensors with an orthogonal basis of eigenvectors and show that, for a generic such tensor, the orthogonal basis is unique. This resolves a conjecture by Mesters and Zwiernik. We also study the non-symmetric setting. The singular value decomposition says that a real matrix has an o…

Hmm - as a frequent advocate for #Matrix and #Element, this is food for thought: https://マリウス.com/giving-up-on-element-

Geometry of Yang-Baxter matrix equations over finite fields
Yin Chen, Shaoping Zhu
https://arxiv.org/abs/2506.17893 https://arxiv.org…

Geometry of Yang-Baxter matrix equations over finite fields
Let $A$ be a $2\times 2$ matrix over a finite field and consider the Yang-Baxter matrix equation $XAX=AXA$ with respect to $A$. We use a method of computational ideal theory to explore the geometric structure of the affine variety of all solutions to this equation. In particular, we exhibit all solutions explicitly and determine cardinality formulas for these varieties.

A Complete Loss Landscape Analysis of Regularized Deep Matrix Factorization
Po Chen, Rujun Jiang, Peng Wang
https://arxiv.org/abs/2506.20344 https://

A Complete Loss Landscape Analysis of Regularized Deep Matrix Factorization
Despite its wide range of applications across various domains, the optimization foundations of deep matrix factorization (DMF) remain largely open. In this work, we aim to fill this gap by conducting a comprehensive study of the loss landscape of the regularized DMF problem. Toward this goal, we first provide a closed-form expression of all critical points. Building on this, we establish precise conditions under which a critical point is a local minimizer, a global minimizer, a strict saddle po…

The exact recovery with sub-exponential measurement matrix
Dai Guozheng Diao Tiankun
https://arxiv.org/abs/2506.17965 https://arxiv.o…

The exact recovery with sub-exponential measurement matrix
Let $A$ be an $m \times n$ random matrix, where each entry is an i.i.d.sub-exponential random variable with mean 0 and variance $\frac{1}{m^2}$. We demonstrate that, with high probability, the sub-exponential matrix $A$ can be used for the exact reconstruction of $s$-sparse vectors via $\ell_1$-minimization, provided that $m \ge C_1 s \log\left(\frac{C_2 n}{s}\right)$. This improves upon the existing results by Adamczak et al.

The structure of non-Fricke Monstrous Lie algebras
Daniel Tan
https://arxiv.org/abs/2507.17854 https://arxiv.org/pdf/2507.17854

The structure of non-Fricke Monstrous Lie algebras
We consider Borcherds algebras with no real roots and the property that all zeroes in the Borcherds Cartan matrix occur in a single diagonal zero block. It follows that all other entries of the matrix are negative. We give a structure theorem for these Borcherds algebras, decomposing them into free, Heisenberg and abelian subalgebras. We show that a class of such Borcherds algebras are the Monstrous Lie algebras associated to non-Fricke elements of the Monster finite simple group. This new pers…

Microscopic field theories of the quantum skyrmion Hall effect
Vinay Patil, Archi Banerjee, Ashley M. Cook
https://arxiv.org/abs/2508.16547 https://arxiv.o…

Microscopic field theories of the quantum skyrmion Hall effect
We construct effective field theories of the quantum skyrmion Hall effect from matrix Chern-Simons theory for $N$ electrons, corresponding to matrix dimension $N$. We first consider a quantum Hall droplet within finite $N$ matrix Chern-Simons theory. Taking into account the differential geometry of the matrix Chern-Simons droplet for a partially-filled fuzzy two-sphere, we first generalize the quantization procedure by replacing the Poisson bracket, a classical Lie derivative, with a quantum co…

Replaced article(s) found for cs.AI. https://arxiv.org/list/cs.AI/new
[4/5]:
- Unified Sparse-Matrix Representations for Diverse Neural Architectures
Yuzhou Zhu
h…

Bayesian Variable Selection in Multivariate Regression Under Collinearity in the Design Matrix
Joyee Ghosh, Xun Li
https://arxiv.org/abs/2507.17975 https://

Bayesian Variable Selection in Multivariate Regression Under Collinearity in the Design Matrix
We consider the problem of variable selection in Bayesian multivariate linear regression models, involving multiple response and predictor variables, under multivariate normal errors. In the absence of a known covariance structure, specifying a model with a non-diagonal covariance matrix is appealing. Modeling dependency in the random errors through a non-diagonal covariance matrix is generally expected to lead to improved estimation of the regression coefficients. In this article, we highlight…

Transfer-matrix approach to the Blume-Capel model on the triangular lattice
Dimitrios Mataragkas, Alexandros Vasilopoulos, Nikolaos G. Fytas, Dong-Hee Kim
https://arxiv.org/abs/2506.16483

Transfer-matrix approach to the Blume-Capel model on the triangular lattice
We investigate the spin-$1$ Blume-Capel model on an infinite strip of the triangular lattice using the transfer-matrix method combined with a sparse-matrix factorization technique. Through finite-size scaling analysis of numerically exact spectra for strip widths up to $L = 19$, we accurately locate the tricritical point improving upon recent Monte Carlo estimates. In the first-order regime, we observe exponential scaling of the spectral gap, reflecting the linear growth of interfacial tension …

A matrix criterion and algorithmic approach for the Peterson hit problem: Part I
Dang Vo Phuc
https://arxiv.org/abs/2506.18392 https://

A matrix criterion and algorithmic approach for the Peterson hit problem: Part I
The Peterson hit problem in algebraic topology is to explicitly determine the dimension of the quotient space $Q\mathcal P_k = \mathbb F_2\otimes_{\mathcal A}\mathcal P_k$ in positive degrees, where $\mathcal{P}_k$ denotes the polynomial algebra in $k$ variables over the field $\mathbb{F}_2$, considered as an unstable module over the Steenrod algebra $\mathcal{A}$. Current approaches to this problem still rely heavily on manual computations, which are highly prone to errors due to the intricate…

Bayesian Non-Negative Matrix Factorization with Correlated Mutation Type Probabilities for Mutational Signatures
Iris Lang, Jenna Landy, Giovanni Parmigiani
https://arxiv.org/abs/2506.15855

Bayesian Non-Negative Matrix Factorization with Correlated Mutation Type Probabilities for Mutational Signatures
Somatic mutations, or alterations in DNA of a somatic cell, are key markers of cancer. In recent years, mutational signature analysis has become a prominent field of study within cancer research, commonly with Nonnegative Matrix Factorization (NMF) and Bayesian NMF. However, current methods assume independence across mutation types in the signatures matrix. This paper expands upon current Bayesian NMF methodologies by proposing novel methods that account for the dependencies between the mutatio…

Dissipation-Driven Topological Phase Transition in Quantum Open Systems Independent of system Hamiltonian
Tian-Shu Deng, Fan Yang
https://arxiv.org/abs/2508.16275 https://

Dissipation-Driven Topological Phase Transition in Quantum Open Systems Independent of system Hamiltonian
We investigate dissipation-driven topological phase transitions in one-dimensional quantum open systems governed by the Lindblad equation with linear dissipation operators, which ensure the density matrix retains its Gaussian form throughout the dynamics. By employing the modular Hamiltonian framework, we rigorously demonstrate that the $\rm{Z}_2$ topological invariant characterizing steady states in one-dimensional class D systems is exclusively dependent on the dissipation operators, rather t…

Robust estimation of a Markov chain transition matrix from multiple sample paths
Lasse Leskel\"a, Maximilien Dreveton
https://arxiv.org/abs/2506.20325

Robust estimation of a Markov chain transition matrix from multiple sample paths
Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and stationary distribution from observed sample paths is a core statistical challenge, particularly when multiple independent trajectories are available. While classical theory typically assumes identical chains with known stationary distributions, real-world data…

Enhanced Robotic Navigation in Deformable Environments using Learning from Demonstration and Dynamic Modulation
Lingyun Chen, Xinrui Zhao, Marcos P. S. Campanha, Alexander Wegener, Abdeldjallil Naceri, Abdalla Swikir, Sami Haddadin
https://arxiv.org/abs/2506.20376

Enhanced Robotic Navigation in Deformable Environments using Learning from Demonstration and Dynamic Modulation
This paper presents a novel approach for robot navigation in environments containing deformable obstacles. By integrating Learning from Demonstration (LfD) with Dynamical Systems (DS), we enable adaptive and efficient navigation in complex environments where obstacles consist of both soft and hard regions. We introduce a dynamic modulation matrix within the DS framework, allowing the system to distinguish between traversable soft regions and impassable hard areas in real-time, ensuring safe and…

dot matrix printer head cut in half (source: https://en.wikipedia.org/wiki/Dot_matrix_printing#/media/File:Tally_Genicom_T2240_print_head_assembly_-_cross_section.jpg)

On a conjecture concerning the extensions of a reciprocal matrix
Ros\'ario Fernandes
https://arxiv.org/abs/2507.16593 https://arx…

On a conjecture concerning the extensions of a reciprocal matrix
Let $A$ be a reciprocal matrix of order $n$ and $w$ be its Perron eigenvector. To infer the efficiency of $w$ for $A$, based on the principle of Pareto optimal decisions, we study the strong connectivity of a certain digraph associated with $A$ and $w$. A reciprocal matrix $B$ of order $n+1$ is an extension of $A$ if the matrix $A$ is obtained from $B$ by removing its last row and column. We prove that there is no extension of a reciprocal matrix whose digraph associated with the extension and …

Communication-Efficient Publication of Sparse Vectors under Differential Privacy
Quentin Hillebrand, Vorapong Suppakitpaisarn, Tetsuo Shibuya
https://arxiv.org/abs/2506.20234

Communication-Efficient Publication of Sparse Vectors under Differential Privacy
In this work, we propose a differentially private algorithm for publishing matrices aggregated from sparse vectors. These matrices include social network adjacency matrices, user-item interaction matrices in recommendation systems, and single nucleotide polymorphisms (SNPs) in DNA data. Traditionally, differential privacy in vector collection relies on randomized response, but this approach incurs high communication costs. Specifically, for a matrix with $N$ users, $n$ columns, and $m$ nonzero …

Harmonious Color Pairings: Insights from Human Preference and Natural Hue Statistics
Ortensia Forni, Alexandre Darmon, Michael Benzaquen
https://arxiv.org/abs/2508.15777 https:/…

Harmonious Color Pairings: Insights from Human Preference and Natural Hue Statistics
While color harmony has long been studied in art and design, a clear consensus remains elusive, as most models are grounded in qualitative insights or limited datasets. In this work, we present a quantitative, data-driven study of color pairing preferences using controlled hue-based palettes in the HSL color space. Participants evaluated combinations of thirteen distinct hues, enabling us to construct a preference matrix and define a combinability index for each color. Our results reveal that p…

ARSAR-Net: Adaptively Regularized SAR Imaging Network via Non-matrix-inversion ADMM
Shiping Fu, Yufan Chen, Zhe Zhang, Xiaolan Qiu, Qixiang Ye
https://arxiv.org/abs/2506.18324

ARSAR-Net: Adaptively Regularized SAR Imaging Network via Non-matrix-inversion ADMM
Deep unfolding networks have constituted an emerging method for synthetic aperture radar (SAR) imaging. However, baseline unfolding networks, when unfolded from the alternating direction method of multipliers (ADMM), lack generalization capability across scenes as the regularizers are empirically designed. In this study, we introduce a learnable regularizer to the unfolding network and create an adaptively regularized SAR imaging network (ARSAR-Net), which pursues generalization capability acro…

Two classes of NMDS codes from Roth-Lempel codes
Zhonghao Liang, Qunying Liao
https://arxiv.org/abs/2506.19346 https://arxiv.org/pdf/…

Two classes of NMDS codes from Roth-Lempel codes
Since near maximum distance separable (NMDS) codes have good algebraic properties and excellent error-correcting capabilities, they have been widely used in various fields such as communication systems, data storage, quantum codes, and so on. In this paper, basing on the generator matrix of Roth-Lempel codes, we present two classes of NMDS codes which generalize Han's and Zheng's constructions in 2023 and 2025, respectively. And we also completely determine their weight distributions.

The Generalized Matrix Separation Problem: Algorithms
Xuemei Chen, Owen Deen
https://arxiv.org/abs/2507.17069 https://arxiv.org/pdf/2507.17069

The Generalized Matrix Separation Problem: Algorithms
When given a generalized matrix separation problem, which aims to recover a low rank matrix $L_0$ and a sparse matrix $S_0$ from $M_0=L_0+HS_0$, the work \cite{CW25} proposes a novel convex optimization problem whose objective function is the sum of the $\ell_1$-norm and nuclear norm. In this paper we detail the iterative algorithms and its associated computations for solving this convex optimization problem. We present various efficient implementation strategies, with attention to practical ca…

Accelerating Correlated Wave Function Calculations with Hierarchical Matrix Compression of the Two-Electron Integrals
Hongji Gao, Xiangmin Jiao, Benjamin G. Levine
https://arxiv.org/abs/2506.16576

Accelerating Correlated Wave Function Calculations with Hierarchical Matrix Compression of the Two-Electron Integrals
Leveraging matrix sparsity has proven a fruitful strategy for accelerating quantum chemical calculations. Here we present the hierarchical SOS-MP2 algorithm, which uses hierarchical matrix ($\mathcal{H}^{2}$) compression of the electron repulsion integral (ERI) tensor to reduce both time and space complexity. This approach is based on the atomic orbital Laplace transform MP2 calculations, leveraging the data sparsity of the ERI tensor and the element-wise sparsity of the energy-weighted density…

Replaced article(s) found for cs.CE. https://arxiv.org/list/cs.CE/new
[1/1]:
- Generalized Scattering Matrix Synthesis: Independent Region Decomposition for Hybrid Antenna--Sca...
Chenbo Shi, Shichen Liang, Jin Pan, Xin Gu, Le Zuo

Our new corporate owners' IT rules have changed the #retentionpolicy on Microsoft #Teams. Instead of years, now two months.
I relish screams of "oh no the IMPORTANT FILE is gone!" - I kept telling people `Teams/Slack/Discord/Matrix is NOT a document repository! Stop storing important shit i…

Approximating Submodular Matroid-Constrained Partitioning
Krist\'of B\'erczi, Karthekeyan Chandrasekaran, Tam\'as Kir\'aly, Daniel P. Szabo
https://arxiv.org/abs/2506.19507

Approximating Submodular Matroid-Constrained Partitioning
The submodular partitioning problem asks to minimize, over all partitions P of a ground set V, the sum of a given submodular function f over the parts of P. The problem has seen considerable work in approximability, as it encompasses multiterminal cuts on graphs, k-cuts on hypergraphs, and elementary linear algebra problems such as matrix multiway partitioning. This research has been divided between the fixed terminal setting, where we are given a set of terminals that must be separated by P, a…

Einige der zuletzt hier besonders häufig geteilten #News:
Matrix statt MJP, ZBP & Co: Ist bald Schluss mit dem staatlichen Postfach-Chaos?

Universal Frequency Correlations and Recurrence Statistics of Complex Impedance Matrices
Nadav Shaibe, Jared Erb, Thomas M. Antonsen, Steven M. Anlage
https://arxiv.org/abs/2508.16563

Universal Frequency Correlations and Recurrence Statistics of Complex Impedance Matrices
Linear electromagnetic wave scattering systems can be characterized by an impedance matrix that relates the voltages and currents at the ports of the system. When the system size becomes greater than the wavelength of the fields involved, the impedance matrix becomes a complicated function of the details of the system, in which case a statistical model, such as the Random Coupling Model (RCM) becomes useful. The statistics of the elements of the RCM impedance matrix depend on the excitation fre…

On the minimum number of Toeplitz factors of a matrix
Ignacio Garc\'ia-Marco, Irene M\'arquez-Corbella, Daniel Seco
https://arxiv.org/abs/2506.16432

On the minimum number of Toeplitz factors of a matrix
We disprove a conjecture by Ye and Lim, by showing that there are $3 \times 3$ complex matrices which can't be expressed as the product of two Toeplitz matrices of the same size. We also improve previous estimates by Ye and Lim on the minimum number of Toeplitz matrices needed to factor any $n \times n$ matrix, for low values of $n$.

Massive deformations of supersymmetric Yang-Mills matrix models
Adrien Martina
https://arxiv.org/abs/2507.17813 https://arxiv.org/pdf/2507.17813

Massive deformations of supersymmetric Yang-Mills matrix models
We systematically classify all supersymmetry-preserving mass deformations of SYM matrix models in all dimensions (D = 3, 4, 6, 10). In D = 10 the polarized IKKT model emerges as the only possible deformation. Moreover, in the particular case D = 4 we identify two massive, sign-problem-free models, making them attractive candidates for non-perturbative numerical studies.

Spectral approximation to fractional integral operator
Xiaolin Liu, Kuan Xu
https://arxiv.org/abs/2506.19332 https://arxiv.org/pdf/25…

Spectral approximation to fractional integral operator
We propose a fast and stable method for constructing matrix approximations to fractional integral operators applied to series in the Chebyshev fractional polynomials. This method utilizes a recurrence relation satisfied by the fractional integrals of mapped Chebyshev polynomials and significantly outperforms existing methods. Through numerical examples, we highlight the broad applicability of these matrix approximations, including the solution of boundary value problems for fractional integral …

Evaluation of the Transfer Matrix of a Plasma Ramp with Squared Cosine Shape via an Approximate Solution of the Mathieu Differential Equation
Stefano Romeo, Angelo Biagioni, Lucio Crincoli, Alessio Del Dotto, Massimo Ferrario, Anna Giribono, Gianmarco Parise, Andrea Renato Rossi, Gilles Jacopo Silvi, Cristina Vaccarezza
https://arxiv.org/a…

Evaluation of the Transfer Matrix of a Plasma Ramp with Squared Cosine Shape via an Approximate Solution of the Mathieu Differential Equation
The high longitudinal electric fields generated in plasma wakefields are very attractive for a new generation of high gradient plasma based accelerators. On the other hand, the strong transverse fields increase the demand for a proper matching device in order to avoid the spoiling of beam transverse quality. A solution can be provided by the use of a plasma ramp, a region at the plasma injection/extraction with smoothly increasing/decreasing plasma density. The transport of a beam inside a plas…

{\tt RapidGBM}: An Efficient Tool for Fermi-GBM Visibility Checking and Data Analysis with a Case Study of EP240617a
Yun Wang, Jia Ren, Lu-Yao Jiang, Hao Zhou, Yi-Han Iris Yin, Yi-Fang Liang, Zhi-Ping Jin, Yi-Zhong Fan, Da-Ming Wei, Wei Chen, Hui Sun, Jing-Wei Hu, Dong-Yue Li, Jun Yang, Wen-Da Zhang, Yuan Liu, Wei-Min Yuan, Xue-Feng Wu
https://

{\tt RapidGBM}: An Efficient Tool for Fermi-GBM Visibility Checking and Data Analysis with a Case Study of EP240617a
We have developed a lightweight tool {\tt RapidGBM}, featured by a web-based interface and capabilities of rapid calculation of Fermi-GBM visibilities and performing basic data analysis. It has two key features: (1) immediately check the visibility of Fermi-GBM for new transients, and (2) check the light curve and perform spectral analysis after the hourly TTE data is released. The visibility check and the response matrix generation required for spectral analysis can be achieved through the his…

Scalable Bayesian inference on high-dimensional multivariate linear regression
Xuan Cao, Kyoungjae Lee
https://arxiv.org/abs/2508.16446 https://arxiv.org/p…

Scalable Bayesian inference on high-dimensional multivariate linear regression
We consider jointly estimating the coefficient matrix and the error precision matrix in high-dimensional multivariate linear regression models. Bayesian methods in this context often face computational challenges, leading to previous approaches that either utilize a generalized likelihood without ensuring the positive definiteness of the precision matrix or rely on maximization algorithms targeting only the posterior mode, thus failing to address uncertainty. In this work, we propose two Bayesi…

The circular law for non-Hermitian random band matrices up to bandwidth $N^{1/2 c}$
Yi Han
https://arxiv.org/abs/2508.18143 https://arxiv.org/pdf/2508.1814…

The circular law for non-Hermitian random band matrices up to bandwidth $N^{1/2+c}$
We consider inhomogeneous square random matrices of size $N$ with independent entries of mean 0 and finite variance. We assume that the variance profile of this matrix is doubly stochastic and has a band-like structure with an appropriately defined bandwidth $W$. We prove that when the entries have a bounded density and a subgaussian tail, then the empirical spectral measure for the eigenvalues of the matrix converges to the circular law as $N$ tends to infinity whenever $W\geq N^{1/2+c}$ for a…

Eigenvalue estimates for the Coulombic one-particle density matrix and the kinetic energy density matrix
Alexander V. Sobolev
https://arxiv.org/abs/2506.16178

Eigenvalue estimates for the Coulombic one-particle density matrix and the kinetic energy density matrix
Consider a bound state (an eigenfunction) $ψ$ of an atom with $N$ electrons. We study the spectra of the one-particle density matrix $γ$ and of the one-particle kinetic energy density matrix $τ$ associated with $ψ$. The paper contains two results. First, we obtain the bounds $λ_k(γ)\le C_1 k^{-8/3}$ and $λ_k(τ)\le C_2 k^{-2}$ with some positive constants $C_1, C_2$ that depend explicitly on the eigenfunction $ψ$. The sharpness of these bounds is confirmed by the asymptotic results obta…

The Phases of Chaos
Tarek Anous, Diego M. Hofman
https://arxiv.org/abs/2506.20542 https://arxiv.org/pdf/2506.20542

The Phases of Chaos
We develop a novel physical picture to understand certain universal properties of the GUE matrix model which are typically ascribed to quantum chaos, i.e. the ramp and the plateau. We argue that these features should instead be associated with a pattern of spontaneous (or weak explicit) symmetry breaking. In this language, the GUE matrix model corresponds to an effective theory that describes the symmetry-broken phase, and where the Hermitian matrix of the GUE should be understood as a massive …

Weak unitary symmetries of open quantum dynamics: beyond quantum master equations
Calum A. Brown, Robert L. Jack, Katarzyna Macieszczak
https://arxiv.org/abs/2506.19814

Weak unitary symmetries of open quantum dynamics: beyond quantum master equations
We consider Markovian open quantum dynamics with weak unitary symmetries. Starting from the quantum master equation for the system alone, it is known that the joint dynamics of the system and its environment can be obtained by dilation, leading to a closed dynamics for a continuous matrix product state. Performing counting measurements on the environment gives rise to stochastic dynamics of quantum trajectories for the system, which when averaged yield back the quantum master equation. In this …

Interpretable Kernels
Patrick J. F. Groenen, Michael Greenacre
https://arxiv.org/abs/2508.15932 https://arxiv.org/pdf/2508.15932

Interpretable Kernels
The use of kernels for nonlinear prediction is widespread in machine learning. They have been popularized in support vector machines and used in kernel ridge regression, amongst others. Kernel methods share three aspects. First, instead of the original matrix of predictor variables or features, each observation is mapped into an enlarged feature space. Second, a ridge penalty term is used to shrink the coefficients on the features in the enlarged feature space. Third, the solution is not obtain…

11 can be reduced to 10
Abraham Berman, Eliyahu Levy
https://arxiv.org/abs/2506.19868 https://arxiv.org/pdf/2506.19868

11 can be reduced to 10
Laffey and Smigoc proved that for every 2x2 doubly nonnegative integer matrix A, icpr(A) is less than or equal to 11. We prove that 11 can be replaced by 10, and show that for many small matrices, even by 9.15

Multifold degeneracy points of quantum systems and singularities of matrix varieties
Gy\"orgy Frank, Andr\'as P\'alyi, Gerg\H{o} Pint\'er, D\'aniel Varjas
https://arxiv.org/abs/2507.17485

Multifold degeneracy points of quantum systems and singularities of matrix varieties
Parameter-dependent quantum systems often exhibit energy degeneracy points, whose comprehensive description naturally lead to the application of methods from singularity theory. A prime example is an electronic band structure where two energy levels coincide in a point of momentum space. It may happen, and this case is the focus of our work, that three or more levels coincide at a parameter point, called multifold degeneracy. Upon a generic perturbation, such a multifold degeneracy point is dis…

Matrix-Free Evaluation of High-Order Shifted Boundary Finite Element Operators
Micha{\l} Wichrowski
https://arxiv.org/abs/2507.17053 https://arxiv.org/pdf/…

Matrix-Free Evaluation of High-Order Shifted Boundary Finite Element Operators
This paper presents a matrix-free approach for implementing the shifted boundary method (SBM) in finite element analysis. The SBM is a versatile technique for solving partial differential equations on complex geometries by shifting boundary conditions to nearby surrogate boundaries. We focus on the efficient evaluation of shifted boundary operators using precomputed data and tensor-product structures. The proposed method avoids the explicit assembly of global matrices, achieving a computational…

Matrix-Weighted Campanato Spaces: Duality and Calder\'on--Zygmund Operators
Yiqun Chen, Dachun Yang, Wen Yuan
https://arxiv.org/abs/2508.15195 https://…

Matrix-Weighted Campanato Spaces: Duality and Calderón--Zygmund Operators
Let $p\in(0,\infty)$, $q\in[1,\infty)$, $s\in\mathbb Z_+$, and $W$ be an $A_p$-matrix weight, which in the scalar case is exactly a Muckenhoupt $A_{\max\{1,p\}}$ weight. In this article, by using the reducing operators of $W$, we introduce matrix-weighted Campanato spaces $\mathcal L_{p,q,s,W}$. When $p\in(0,1]$, applying the atomic and the finite atomic characterizations of the matrix-weighted Hardy space $H^p_W$, we prove that the dual space of $H^p_W$ is precisely $\mathcal L_{p,q,s,W}$, whi…

Validity of generalized Gibbs ensemble in a random matrix model with a global $\mathbb{Z}_2$-symmetry
Adway Kumar Das
https://arxiv.org/abs/2506.16176 http…

Validity of generalized Gibbs ensemble in a random matrix model with a global $\mathbb{Z}_2$-symmetry
$\mathbb{Z}_2$ symmetry is ubiquitous in quantum mechanical systems where it drives various phase transitions and emergent physics. To understand the role of $\mathbb{Z}_2$ symmetry in the thermalization of a local observable in a disordered system, we consider random symmetric centrosymmetric (SC) matrices where the exchange symmetry is conserved. Such a conservation law splits the Hilbert space into decoupled subspaces such that the energy spectrum of a SC matrix is a superposition of two pur…

Probing the Scotogenic Dirac Model with FIMP Dark Matter and $\Delta N_{\rm eff}$
Shu-Yuan Guo, Man-Yu Zhao
https://arxiv.org/abs/2508.16362 https://arxiv.…

Probing the Scotogenic Dirac Model with FIMP Dark Matter and $ΔN_{\rm eff}$
We study a feebly interacting massive particle realization of the Scotogenic Dirac Model in which the lightest neutral fermion $N_1$ serves as a dark matter candidate, produced via the freeze-in or super-WIMP mechanism. The model generates Dirac neutrino masses at one loop, resulting in a rank-2 mass matrix that predicts one nearly massless neutrino. We analyze the DM relic density for various next-to-lightest odd particles (NLOPs), finding that coannihilation effects and enhanced annihilation …

Recurrent neural network-based robust control systems with closed-loop regional incremental ISS and application to MPC design
Daniele Ravasio, Marcello Farina, Alessio La Bella, Andrea Ballarino
https://arxiv.org/abs/2506.20334

Recurrent neural network-based robust control systems with closed-loop regional incremental ISS and application to MPC design
This paper investigates the design of output-feedback schemes for systems described by a class of recurrent neural networks. We propose a procedure based on linear matrix inequalities for designing an observer and a static state-feedback controller. The algorithm leverages global and regional incremental input-to-state stability (incremental ISS) and enables the tracking of constant setpoints, ensuring robustness to disturbances and state estimation uncertainty. To address the potential limitat…

Replaced article(s) found for stat.ML. https://arxiv.org/list/stat.ML/new
[1/1]:
- Fundamental Limits of Matrix Sensing: Exact Asymptotics, Universality, and Applications
Yizhou Xu, Antoine Maillard, Lenka Zdeborov\'a, Florent Krzakala

Dynamics of colored-noise-driven stochastic Schr\"odinger equations
Pietro De Checchi, Federico Gallina, Barbara Fresch, Giulio G. Giusteri
https://arxiv.org/abs/2507.17864

Dynamics of colored-noise-driven stochastic Schrödinger equations
In this work, we study the effect of colored stochastic noise as a source of fluctuations in the dynamics of a two-level system, e.g. the states of a qubit system or two local sites in a transfer problem. We derive the stochastic Schrödinger equations (SSE) and related quantum master equations (QME) for the average density matrix for different stochastic potentials. We compare the case of memory and memoryless processes, which reflect different short-time behaviors and, in some cases, can lead…

Evaluation of a determinant involving Legendre symbols
Chen-Kai Ren, Zhi-Wei Sun
https://arxiv.org/abs/2507.18589 https://arxiv.org/pdf/2507.18589

Evaluation of a determinant involving Legendre symbols
Let $p>3$ be a prime, and let $(\frac{\cdot}p)$ be the Legendre symbol. Let $A_p(x)$ denote the matrix $[x+a_{ij}]_{1\leqslant i,j\leqslant (p-1)/2}$, where $$ a_{ij}=\begin{cases} (\frac{j}{p}) &\text{if} \ i=1, \$\frac{i+j}{p}) &\text{if} \ i>1. \end{cases}$$ In 2018 Z.-W. Sun conjectured that $\det A_p(0)=-2^{(p-3)/2}$ if $p\equiv 3 \pmod{4}$, which was later confirmed by G. Zaimi. In this paper we evaluate $\det A_p(x)$ completely.

Normal and Dynamical Typicality in a Random Matrix Model
L\'aszl\'o Erd\H{o}s, Joscha Henheik, Cornelia Vogel
https://arxiv.org/abs/2506.17177 http…

Normal and Dynamical Typicality in a Random Matrix Model
We prove normal typicality and dynamical typicality for a (centered) random block-band matrix model with block-dependent variances. A key feature of our model is that we achieve intermediate equilibration times, an aspect that has not been proven rigorously in any model before. Our proof builds on recently established concentration estimates for products of resolvents of Wigner type random matrices [arXiv:2403.10359] and an intricate analysis of the deterministic approximation.

On the edge reconstruction of the second immanantal polynomials of undirected graph and digraph
Tingzeng Wu
https://arxiv.org/abs/2507.14607 https://

On the edge reconstruction of the second immanantal polynomials of undirected graph and digraph
Let $M=(m_{ij})$ be an $n\times n$ matrix. The second immanant of matrix $M$ is defined by \begin{eqnarray*} d_{2}(M)=\sum_{σ\in S_{n}}χ_{2}(σ)\prod_{s=1}^{n}m_{sσ(s)}, \end{eqnarray*} where $χ_{2}$ is the irreducible character of $S_{n}$ corresponding to the partition $(2^{1},1^{n-2})$. The polynomial $d_{2}(xI-M)$ is called the second immanantal polynomial of matrix $M$. Denote by $D(G)$ (resp. $D(\overrightarrow{G})$) and $A(G)$ (resp. $A(\overrightarrow{G})$) the diagonal matrix of ver…

Further aspects of Supersymmetric Virasoro Minimal Strings
Clifford V. Johnson
https://arxiv.org/abs/2506.19000 https://arxiv.org/pdf…

Further aspects of Supersymmetric Virasoro Minimal Strings
A supersymmetric version of the Virasoro minimal string was defined some time ago using random matrix model techniques. Several of the special properties of the matrix model that were noted (accessible fully non-perturbatively) underlie features shared by both 0A and 0B versions of the theory. This paper develops the formalism much further, including showing how the 0A and 0B choices familiar in continuum approaches have a direct analogue in terms of building solutions of the appropriate string…

Monte Carlo studies of the emergent spacetime in the polarized IKKT model
Chien-Yu Chou, Jun Nishimura, Cheng-Tsung Wang
https://arxiv.org/abs/2507.18472 https://

Monte Carlo studies of the emergent spacetime in the polarized IKKT model
The IKKT matrix model has been investigated as a promising nonperturbative formulation of superstring theory. One of the recent developments concerning this model is the discovery of the dual supergravity solution corresponding to the model obtained after supersymmetry-preserving mass deformation, which is dubbed the polarized IKKT model. Here we perform Monte Carlo simulations of this model in the case of matrix size N = 2 for a wide range of the deformation parameter Omega. While we reproduce…

Efficient many-jet event generation with Flow Matching
Enrico Bothmann, Timo Jan{\ss}en, Max Knobbe, Bernhard Schmitzer, Fabian Sinz
https://arxiv.org/abs/2506.18987

Efficient many-jet event generation with Flow Matching
We apply for the first time the Flow Matching method to the problem of phase-space sampling for event generation in high-energy collider physics. By training the model to remap the random numbers used to generate the momenta and helicities of the scattering matrix elements as implemented in the portable partonic event generator Pepper, we find substantial efficiency improvements in the studied processes. We focus our study on the highest final-state multiplicities in Drell--Yan and top--antitop…

Noise-tolerant tomography of multimode linear optical interferometers with single photons
Yu. A. Biriukov, R. D. Morozov, I. V. Dyakonov, M. V. Rakhlin, A. I. Galimov, G. V. Klimko, S. V. Sorokin, I. V. Sedova, M. M. Kulagina, Yu. M. Zadiranov, A. A. Toropov, A. A. Korneev, S. P. Kulik, S. S. Straupe
https://arxiv.org/abs/2506.2…

Noise-tolerant tomography of multimode linear optical interferometers with single photons
Linear optical networks are fundamental to the advancement of quantum technologies, including quantum computing, communication, and sensing. The accurate characterization of these networks, described by unitary matrices, is crucial to their effective utilization and scalability. In this work, we present the method for reconstructing the transfer matrix of a linear optical interferometer based on the analysis of cross-correlation functions of photon counts between pairs of output modes. Our appr…

MDR-DeePC: Model-Inspired Distributionally Robust Data-Enabled Predictive Control
Shihao Li, Jiachen Li, Christopher Martin, Soovadeep Bakshi, Dongmei Chen
https://arxiv.org/abs/2506.19744

MDR-DeePC: Model-Inspired Distributionally Robust Data-Enabled Predictive Control
This paper presents a Model-Inspired Distributionally Robust Data-enabled Predictive Control (MDR-DeePC) framework for systems with partially known and uncertain dynamics. The proposed method integrates model-based equality constraints for known dynamics with a Hankel matrix-based representation of unknown dynamics. A distributionally robust optimization problem is formulated to account for parametric uncertainty and stochastic disturbances. Simulation results on a triple-mass-spring-damper sys…

Pattern formation Statistics on Fermat Quotients
Cristian Cobeli, Alexandru Zaharescu, Zhuo Zhang
https://arxiv.org/abs/2506.17684 https://

Pattern formation Statistics on Fermat Quotients
Despite their simple definition as $\mathfrak{q}_p(b):=\frac{b^{p-1}-1}{p} \pmod p$, for $0\le b \le p^2-1$ and $\gcd(b,p)=1$, and their regular arrangement in a $p\times(p-1)$ Fermat quotient matrix $\mathtt{FQM}(p)$ of integers from $[0,p-1]$, Fermat quotients modulo $p$ are well known for their overall lack of regularity. Here, we discuss this contrasting effect by proving that, on the one hand, any line of the matrix behaves like an analogue of a randomly distributed sequence of numbers, an…

Properties of the temporal transfer matrix in integrable Floquet circuits
Ilya Vilkoviskiy, Marirko Kirill
https://arxiv.org/abs/2508.13883 https://arxiv.o…

Properties of the temporal transfer matrix in integrable Floquet circuits
One possible approach to studying non-equilibrium dynamics is the so-called influence matrix (IM) formalism. The influence matrix can be viewed as a quantum state that encodes complete information about the non-equilibrium dynamics of a boundary degree of freedom. It has been shown that the IM is the unique stationary point of the temporal transfer matrix. This transfer matrix, however, is non-diagonalizable and exhibits a non-trivial Jordan block structure. In this article, we demonstrate that…

Carroll Geometry Meets De Sitter Space via Holography
Chris D. A. Blair, Niels A. Obers, Ziqi Yan
https://arxiv.org/abs/2506.19720 https://

Carroll Geometry Meets De Sitter Space via Holography
We explain how to relate the ideas of Carroll geometry, matrix theory on instantonic objects, and infinite boost limits of M-theory. Based on these new insights, we explore the implications for possible holographic constructions involving a de Sitter or flat space bulk. We show that Carroll-like geometry in a hypothetical de Sitter holography mirrors the recently realized important role played by Galilei-like geometry in matrix theory and the AdS/CFT correspondence. This also allows us to gener…

Chapter 7 Multi-Criteria Decision-Making: Reference-Type Methods
Zhiyuan Wang, Gade Pandu Rangaiah
https://arxiv.org/abs/2508.16087 https://arxiv.org/pdf/2…

Chapter 7 Multi-Criteria Decision-Making: Reference-Type Methods
This chapter describes selected reference-type multi-criteria decision-making (MCDM) methods that rank alternatives by comparing them with one or more reference solutions derived from an alternatives-criteria matrix (ACM). After explaining the idea of constructing positive ideal, negative ideal and/or average reference solutions, the chapter details the algorithmic steps of each method, illustrating them with a common ACM example. The 9 methods covered are: Technique for Order of Preference by …

Statistics-encoded tensor network approach in disordered quantum many-body spin chains
Hao Zhu, Ding-Zu Wang, Shi-Ju Ran, Guo-Feng Zhang
https://arxiv.org/abs/2508.16286 https:/…

Statistics-encoded tensor network approach in disordered quantum many-body spin chains
Simulating the dynamics of quantum many-body systems with disorder is a fundamental challenge. In this work, we propose a general approach -- the statistics-encoded tensor network (SeTN) -- to study such systems. By encoding disorder into an auxiliary layer and averaging separately, SeTN restores translational invariance, enabling a well-defined transfer matrix formulation. We derive a universal criterion, $n \gg α^2 t^2$, linking discretization $n$, disorder strength $α$, and evolution durat…

The Laplacian matrix of weighted threshold graphs
Yingyue Ke, Willem H. Haemers, Piet Van Mieghem
https://arxiv.org/abs/2506.16839 https://

The Laplacian matrix of weighted threshold graphs
Threshold graphs are generated from one node by repeatedly adding a node that links to all existing nodes or adding a node without links. In the weighted threshold graph, we add a new node in step $i$, which is linked to all existing nodes by a link of weight $w_i$. In this work, we consider the set ${\cal A}_N$ that contains all Laplacian matrices of weighted threshold graphs of order $N$. We show that ${\cal A}_N$ forms a commutative algebra. Using this, we find a common basis of eigenvectors…

Diophantine approximation on abelian varieties; a conjecture of M. Waldschmidt
Lior Fishman, David Lambert, Keith Merrill, David Simmons
https://arxiv.org/abs/2506.19060

Diophantine approximation on abelian varieties; a conjecture of M. Waldschmidt
Following the work of Waldschmidt, we investigate problems in Diophantine approximation on abelian varieties. First we show that a conjecture of Waldschmidt for a given simple abelian variety is equivalent to a well-known Diophantine condition holding for a certain matrix related to that variety. We then posit a related but weaker conjecture, and establish the upper bound direction of that conjecture in full generality. For rank 1 elliptic curves defined over a number field $K \subset \mathbb{R…

Fast Flexible LSQR with a Hybrid Variant for Efficient Large-Scale Regularization
Eva Miku\v{s}ov\'a, Iveta Hn\v{e}tynkov\'a
https://arxiv.org/abs/2506.19666

Fast Flexible LSQR with a Hybrid Variant for Efficient Large-Scale Regularization
A wide range of applications necessitates solving large-scale ill-posed problems contaminated by noise. Krylov subspace regularization methods are particularly advantageous in this context, as they rely solely on matrix-vector multiplication. Among the most widely used techniques are LSQR and CGLS, both of which can be extended with flexible preconditioning to enforce solution properties such as nonnegativity or sparsity. Flexible LSQR (FLSQR) can also be further combined with direct methods to…

Estimating the variance-covariance matrix of two-step estimates of latent variable models: A general simulation-based approach
Roberto Di Mari, Jouni Kuha
https://arxiv.org/abs/2507.16324

Estimating the variance-covariance matrix of two-step estimates of latent variable models: A general simulation-based approach
We propose a general procedure for estimating the variance-covariance matrix of two-step estimates of structural parameters in latent variable models. The method is partially simulation-based, in that it includes drawing simulated values of the measurement parameters of the model from their sampling distribution obtained from the first step of two-step estimation, and using them to quantify part of the variability in the parameter estimates from the second step. This is asymptotically equal wit…

An alternative interpretation of the Grioli gyroscope suspension points
Alexei A. Deriglazov
https://arxiv.org/abs/2506.19819 https://

An alternative interpretation of the Grioli gyroscope suspension points
We present a detailed analysis of all possible regular precessions of a heavy asymmetric body with a fixed point not coinciding with the center of mass. The calculations are done in terms of the rotation matrix, by writing the Euler-Poisson equations with all involved vectors parameterized in the Laboratory frame. It is shown that a regular precession is possible if the suspension point is chosen on the straight lines (lying in the principal plane) which are frontiers of the regions where, as t…

General Proximal Quasi-Newton Methods based on model functions for nonsmooth nonconvex problems
Xiaoxi Jia, Peter Ochs
https://arxiv.org/abs/2507.18363 https://

General Proximal Quasi-Newton Methods based on model functions for nonsmooth nonconvex problems
In this manuscript, we propose a general proximal quasi-Newton method tailored for nonconvex and nonsmooth optimization problems, where we do not require the sequence of the variable metric (or Hessian approximation) to be uniformly bounded as a prerequisite, instead, the variable metric is updated by a continuous matrix generator. From the respective of the algorithm, the objective function is approximated by the so-called local model function and subproblems aim to exploit the proximal point(…

Resource-Efficient Simulations of Particle Scattering on a Digital Quantum Computer
Yahui Chai, Joe Gibbs, Vincent R. Pascuzzi, Zo\"e Holmes, Stefan K\"uhn, Francesco Tacchino, Ivano Tavernelli
https://arxiv.org/abs/2507.17832

Resource-Efficient Simulations of Particle Scattering on a Digital Quantum Computer
We develop and demonstrate methods for simulating the scattering of particle wave packets in the interacting Thirring model on digital quantum computers, with hardware implementations on up to 80 qubits. We identify low-entanglement time slices of the scattering dynamics and exploit their efficient representation by tensor networks. Circuit compression based on matrix product state techniques yields on average a reduction by a factor of 3.2 in circuit depth compared to conventional approaches, …

Some short notes on oriented line graphs and related matrices
Cyriac Antony, Jacob Antony
https://arxiv.org/abs/2507.13821 https://ar…

Some short notes on oriented line graphs and related matrices
The notion of oriented line graphs is introduced by Kotani and Sunada, and they are closely related to Hashimato's non-backtracking matrix. It is known that for regular graphs $G$, the eigenvalues of the adjacency matrix of the oriented line graph $\vec{L}(G)$ of $G$ are the reciprocals of the poles of the Ihara zeta function of $G$. We determine the characteristic polynomial of the adjacency matrix of the underlying undirected graph of $\vec{L}(G)$ and the skew-symmetric adjacency matrix of $\…

A digital twin of atomic ensemble quantum memories
Elizabeth Robertson, Benjamin Maa{\ss}, Konrad Tschernig, Janik Wolters
https://arxiv.org/abs/2506.20403

A digital twin of atomic ensemble quantum memories
Accurate performance estimation of experimentally demonstrated quantum memories is key to understand the nuances in their deployment in photonic quantum networks. While several software packages allow for accessible quantum simulation, they often do not account for the loss and noise in physical devices. We present a framework for modeling ensemble-based atomic quantum memories using the quantum channel formalism. We provide a Kraus matrix representation of several experimentally implemented st…

How weak are weak factors? Uniform inference for signal strength in signal plus noise models
Anna Bykhovskaya, Vadim Gorin, Sasha Sodin
https://arxiv.org/abs/2507.18554 https://…

How weak are weak factors? Uniform inference for signal strength in signal plus noise models
The paper analyzes four classical signal-plus-noise models: the factor model, spiked sample covariance matrices, the sum of a Wigner matrix and a low-rank perturbation, and canonical correlation analysis with low-rank dependencies. The objective is to construct confidence intervals for the signal strength that are uniformly valid across all regimes - strong, weak, and critical signals. We demonstrate that traditional Gaussian approximations fail in the critical regime. Instead, we introduce a u…

Quantum Fisher information as a witness of non-Markovianity and criticality in the spin-boson model
Daniele Parlato, Grazia Di Bello, Fabrizio Pavan, Giulio De Filippis, Carmine Antonio Perroni
https://arxiv.org/abs/2508.16413

Quantum Fisher information as a witness of non-Markovianity and criticality in the spin-boson model
The quantum Fisher information, the quantum analogue of the classical Fisher information, is a central quantity in quantum metrology and quantum sensing because of its connection to parameter estimation and fidelity susceptibility. Using numerically exact methods applied to a paradigmatic open quantum system, the spin-boson model, we calculate both static and dynamical quantum Fisher information matrix elements with respect to spin-bath couplings and magnetic field strengths. As the spin-bath i…

Complex non-backtracking matrix for directed graphs
Keishi Sando, Hideitsu Hino
https://arxiv.org/abs/2507.12503 https://arxiv.org/pd…

Complex non-backtracking matrix for directed graphs
Graph representation matrices are essential tools in graph data analysis. Recently, Hermitian adjacency matrices have been proposed to investigate directed graph structures. Previous studies have demonstrated that these matrices can extract valuable information for clustering. In this paper, we propose the complex non-backtracking matrix that integrates the properties of the Hermitian adjacency matrix and the non-backtracking matrix. The proposed matrix has similar properties with the non-backt…

A Charge Constraint in BMN
Yoav Zigdon
https://arxiv.org/abs/2506.19924 https://arxiv.org/pdf/2506.19924

A Charge Constraint in BMN
I derive a new charge constraint that ties the four angular momenta in a $\frac{1}{16}$-BPS sector of the Berenstein, Maldacena, and Nastase (BMN) supersymmetric $U(N)$ matrix quantum mechanics. The result is related to the charge constraint of the $U(N)$, $\mathcal{N}=4$ Super-Yang-Mills (SYM) conformal field theory by identifying three SYM charges with three BMN angular momenta generating $SO(6)$, two equal SYM angular momenta with a BMN angular momentum of $SO(3)$, and scaling $N^2$ by $3$. …

Supersymmetry and integrability of the elliptic $\mathrm{AdS}_3 \times \mathrm{S}^3 \times \mathrm{T}^4$ superstring
Ben Hoare, Fiona K. Seibold
https://arxiv.org/abs/2507.18548

Supersymmetry and integrability of the elliptic $\mathrm{AdS}_3 \times \mathrm{S}^3 \times \mathrm{T}^4$ superstring
We construct a 1-parameter family of Ramond-Ramond fluxes supporting the elliptic $\mathrm{AdS}_3 \times \mathrm{S}^3 \times \mathrm{T}^4$ metric with constant dilaton and preserving 8 of the 16 supercharges of the undeformed background. On the supersymmetric locus, we compute the tree-level worldsheet S-matrix in uniform light-cone gauge up to quadratic order in fermions and find that it non-trivially satisfies the classical Yang-Baxter equation. Moreover, imposing classical integrability and …

Building multi-BTZ black holes through Riemann-Hilbert problem
Jun-ichi Sakamoto, Shinya Tomizawa
https://arxiv.org/abs/2506.19310 https://

Building multi-BTZ black holes through Riemann-Hilbert problem
We construct a recently found class of non-BPS black hole solutions with asymptotically $AdS_3\times S^3\times T^4$ in type IIB supergravity, consisting of multiple BTZ black holes localized on an $S^3$, within the group theoretical framework of Breitenlohner and Maison (BM). Starting with the multi-neutral black string solution as a seed, we solve the associated Riemann-Hilbert problem for the BM linear system. First, we determine the monodromy matrix corresponding to this seed solution by gen…