Tootfinder

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 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 …

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…

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…

Quantitative structure determination from experimental four-dimensional scanning transmission electron microscopy via the scattering matrix
Emmanuel W. C. Terzoudis-Lumsden, Alireza Sadri, Matthew Weyland, Laure Bourgeois, Stephanie M. Ribet, Georgios Varnavides, Colin Ophus, Timothy C. Petersen, Scott D. Findlay
https://arxiv.o…

Quantitative structure determination from experimental four-dimensional scanning transmission electron microscopy via the scattering matrix
Considerable inroads have recently been made on algorithms to determine the sample potential from four-dimensional scanning transmission electron microscopy data from thick samples where multiple scattering cannot be neglected. This paper further develops the scattering matrix approach to such structure determination. Through simulation, we demonstrate how this approach can be modified to better handle partial spatial coherence, unknown probe defocus, and information from the dark field region.…

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

On the PI-exponent of matrix algebras and algebras with generalized actions
Thiago Castilho de Mello, Felipe Yukihide Yasumura
https://arxiv.org/abs/2506.21257

On the PI-exponent of matrix algebras and algebras with generalized actions
We compute the PI-exponent of the matrix ring with coefficients in an associative algebra. As a consequence, we prove the following. Let $\mathcal{R}$ be a PI-algebra with a positive PI-exponent. If $M_n(\mathcal{R})$ and $M_m(\mathcal{R})$ satisfy the same set of polynomial identities then $n=m$. We provide examples where this result fails if either $\mathcal{R}$ is not PI or has zero exponent. We obtain the same statement for certain finite-dimensional algebras with generalized action over an…

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…

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…

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…

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…

Log entry: The Matrix project proceeds apace. Dr. Forbin is continuing his work on Colossus, while Dr. Ellis and Dr. Morris continue to prep Harold Benson and Mr. Anderson for surgery...
https://www.reut…

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…

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…

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

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 …

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…

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…

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…

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…

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…

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 …

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.

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…

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…

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 …

DECA: A Near-Core LLM Decompression Accelerator Supporting Out-of-Order Invocation
Gerasimos Gerogiannis (Intel Corporation,University of Illinois at Urbana-Champaign), Stijn Eyerman (Intel Corporation), Evangelos Georganas (Intel Labs), Wim Heirman (Intel Corporation), Josep Torrellas (University of Illinois at Urbana-Champaign)
https://

DECA: A Near-Core LLM Decompression Accelerator Supporting Out-of-Order Invocation
To alleviate the memory bandwidth bottleneck in Large Language Model (LLM) inference workloads, weight matrices are stored in memory in quantized and sparsified formats. Hence, before tiles of these matrices can be processed by in-core generalized matrix multiplication (GeMM) hardware engines, they need to be dequantized and de-sparsified. This is currently performed in software with vector operations. Unfortunately, this approach delivers only modest performance. Moreover, it is hard to unders…

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…

This https://arxiv.org/abs/2505.09918 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nli…

Classical integrable spin chains of Landau-Lifshitz type from R-matrix identities
We describe a family of 1+1 classical integrable space-discrete models of the Landau-Lifshitz type through the usage of ansatz for $U$-$V$ (Lax) pair with spectral parameter satisfying the semi-discrete Zakharov-Shabat equation. The ansatz for $U$-$V$ pair is based on $R$-matrices satisfying the associative Yang-Baxter equation and certain additional properties. Equations of motion are obtained using a set of $R$-matrix identities. In the continuous limit we reproduce the previously known famil…

{\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…

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…

Detectability and Parameter Estimation for Einstein Telescope Configurations with GWJulia
Andrea Begnoni, Stefano Anselmi, Mauro Pieroni, Alessandro Renzi, Angelo Ricciardone
https://arxiv.org/abs/2506.21530

Detectability and Parameter Estimation for Einstein Telescope Configurations with GWJulia
Future gravitational-wave (GW) detectors are expected to detect tens of thousands of compact binary coalescences (CBC) per year, depending also on the final detectors layout. For this reason, it is essential to have a fast, reliable tool for forecasting how different detector layouts will affect parameter estimation for these events. The Fisher Information Matrix (FIM) is a common tool for tackling this problem. In this paper, we present a new open source code GWJulia to perform FIM analysis of…

Strong convergence to operator-valued semicirculars
David Jekel, Yoonkyeong Lee, Brent Nelson, Jennifer Pi
https://arxiv.org/abs/2506.19940 https://…

Strong convergence to operator-valued semicirculars
We establish a framework for weak and strong convergence of matrix models to operator-valued semicircular systems parametrized by operator-valued covariance matrices $η= (η_{i,j})_{i,j \in I}$. Non-commutative polynomials are replaced by covariance polynomials that can involve iterated applications of $η_{i,j}$, leading to the notion of covariance laws. We give sufficient conditions for weak and strong convergence of general Gaussian random matrices and deterministic matrices to a $B$-valued…

Replaced article(s) found for cs.SC. https://arxiv.org/list/cs.SC/new
[1/1]:
- A matrix criterion and algorithmic approach for the Peterson hit problem: Part I
Dang Vo Phuc

Theoretical study of transition energies and matrix elements of the cadmium atom
Gleb Penyazkov, Yanmei Yu, Leonid V. Skripnikov, Shiqian Ding
https://arxiv.org/abs/2506.19963

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.

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…

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…

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…

Join Andrew Musselman and Trevor Grant as they present the latest developments in Mahout's new quantum compute layer, Qumat. They will provide an overview of the project, explain why Qumat was developed, and demonstrate its current capabilities. They will also present a demo of Qumat in action and conclude with calls to action for researchers and engineers who are interested in using and contributing to the project.
Learn more:

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 $n$.

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…

Boosting Binomial Exotic Option Pricing with Tensor Networks
Maarten van Damme, Rishi Sreedhar, Martin Ganahl
https://arxiv.org/abs/2505.17033 https://

Boosting Binomial Exotic Option Pricing with Tensor Networks
Pricing of exotic financial derivatives, such as Asian and multi-asset American basket options, poses significant challenges for standard numerical methods such as binomial trees or Monte Carlo methods. While the former often scales exponentially with the parameters of interest, the latter often requires expensive simulations to obtain sufficient statistical convergence. This work combines the binomial pricing method for options with tensor network techniques, specifically Matrix Product States…

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…

The CN matrix of a pure braid projection
Yuko Ozawa, Ayaka Shimizu, Yoshiro Yaguchi
https://arxiv.org/abs/2506.08659 https://arxiv.or…

The CN matrix of a pure braid projection
The CN matrix of an $n$-braid projection $B$ is an $n \times n$ matrix such that each $(i,j)$ entry indicates the number of crossings between $i^{th}$ and $j^{th}$ strands of $B$. In this paper, patterns of an $n \times n$ matrix to be a CN matrix are discussed and the CN matrix of a pure 6-braid projection is characterized. As an application, the OU matrix of a pure 6-braid diagram and the crossing matrix of a positive pure 6-braid are also characterized.

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.

Diffusion-Based Hypothesis Testing and Change-Point Detection
Sean Moushegian, Taposh Banerjee, Vahid Tarokh
https://arxiv.org/abs/2506.16089 https://

Diffusion-Based Hypothesis Testing and Change-Point Detection
Score-based methods have recently seen increasing popularity in modeling and generation. Methods have been constructed to perform hypothesis testing and change-point detection with score functions, but these methods are in general not as powerful as their likelihood-based peers. Recent works consider generalizing the score-based Fisher divergence into a diffusion-divergence by transforming score functions via multiplication with a matrix-valued function or a weight matrix. In this paper, we ext…

Relationship between unpredictability and intermittency in shell models of turbulence and experiments
Ewen Frog\'e (IMT Atlantique - MEE, ODYSSEY, Lab-STICC_OSE), Carlos Granero-Belinchon (ODYSSEY, IMT Atlantique - MEE, Lab-STICC_OSE), St\'ephane G. Roux (IMT Atlantique - MEE, Lab-STICC_MATRIX), Thierry Chonavel (IMT Atlantique - MEE, Lab-STICC_MATRIX), Nicolas B. Garnier

Relationship between unpredictability and intermittency in shell models of turbulence and experiments
We study the predictability of turbulent velocity signals using probabilistic analog-forecasting. Here, predictability is defined by the accuracy of forecasts and the associated uncertainties. We study the Gledzer-Ohkitani-Yamada (GOY) shell model of turbulence as well as experimental measurements from a fully developed turbulent flow. In both cases, we identify the extreme values of velocity at small scales as localized unpredictable events that lead to a loss of predictability: worse predicti…

Is Sparse Matrix Reordering Effective for Sparse Matrix-Vector Multiplication?
Omid Asudeh, Sina Mahdipour Saravani, Gerald Sabin, Fabrice Rastello, P Sadayappan
https://arxiv.org/abs/2506.10356

Is Sparse Matrix Reordering Effective for Sparse Matrix-Vector Multiplication?
This work evaluates the impact of sparse matrix reordering on the performance of sparse matrix-vector multiplication across different multicore CPU platforms. Reordering can significantly enhance performance by optimizing the non-zero element patterns to reduce total data movement and improve the load-balancing. We examine how these gains vary over different CPUs for different reordering strategies, focusing on both sequential and parallel execution. We address multiple aspects, including appro…

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.

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…

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…

SCET sum rules for $\Lambda_b \to \Lambda \ell^ \ell^-$, $\Lambda \gamma$ decays
Long-Shun Lu, Cai-Dian L\"u, Yue-Long Shen, Yan-Bing Wei
https://arxiv.org/abs/2506.21419

SCET sum rules for $Λ_b$ $\rightarrow$ $Λ\ell^+\ell^-$, $Λγ$ decays
We construct light-cone sum rules for various types of effective form factors in the $Λ_b \to Λ\ell^+\ell^-$ and $Λ_b \to Λγ$ decays by analyzing vacuum-to-$Λ_b$ (or $γ^\ast$-to-$Λ_b$) correlation functions with the light $Λ$-baryon interpolating current. These form factors, defined via hadronic matrix elements within soft-collinear effective theory (SCET), enter the next-to-leading-power QCD factorization formulas for large-recoil transitions. Implementing the perturbative matching fr…

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 nucl-th. https://arxiv.org/list/nucl-th/new
[1/1]:
- Benchmarking nuclear matrix elements of $0\nu\beta\beta$ decay with high-energy nuclear collisions
Yi Li, Xin Zhang, Giuliano Giacalone, Jiangming Yao

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 …

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.

Confined acoustic phonons in CsPbI3 nanocrystals explored by resonant Raman scattering on excitons
Carolin Harkort, Ina V. Kalitukha, Nataliia E. Kopteva, Mikhail O. Nestoklon, Serguei V. Goupalov, Lucien Saviot, Dennis Kudlacik, Dmitri R. Yakovlev, Elena V. Kolobkova, Maria S. Kuznetsova, Manfred Bayer
https://arxiv.org/abs/250…

Confined acoustic phonons in CsPbI3 nanocrystals explored by resonant Raman scattering on excitons
Optical properties of the lead halide perovskites nanocrystals are controlled by confined excitons and rich spectrum of confined acoustic and optical phonons. We study experimentally and theoretically the exciton-phonon interaction in CsPbI3 perovskite nanocrystals embedded in a glass matrix. Energies of phonon modes allowed by selection rules are detected by resonant Raman scattering for nanocrystals with sizes of 4-13 nm, covering exciton energies of 1.72-2.25 eV. While optical phonon energie…

Contrastive Matrix Completion with Denoising and Augmented Graph Views for Robust Recommendation
Narges Nemati, Mostafa Haghir Chehreghani
https://arxiv.org/abs/2506.10658

Contrastive Matrix Completion with Denoising and Augmented Graph Views for Robust Recommendation
Matrix completion is a widely adopted framework in recommender systems, as predicting the missing entries in the user-item rating matrix enables a comprehensive understanding of user preferences. However, current graph neural network (GNN)-based approaches are highly sensitive to noisy or irrelevant edges--due to their inherent message-passing mechanisms--and are prone to overfitting, which limits their generalizability. To overcome these challenges, we propose a novel method called Matrix Comp…

Generalized Hilbert operators acting from Hardy spaces to weighted Bergman spaces
Liyi Wang, Shanli Ye
https://arxiv.org/abs/2506.19338 https://

Generalized Hilbert operators acting from Hardy spaces to weighted Bergman spaces
Let $μ$ be a positive Borel measure on the interval $[0,1)$. For $α>0$, the generalized Hankel matrix $\mathcal{H}_{μ, α}=(μ_{n, k, α})_{n, k \geq 0}$ with entries $μ_{n, k, α}=\int_{[0,1)} \frac{Γ(n+α)}{n ! Γ(α)} t^{n+k} \mathrm{d}μ(t)$ induces formally the operator \begin{equation*} \mathcal{H}_{μ, α}(f)(z)=\sum_{n=0}^{\infty}\left(\sum_{k=0}^{\infty} μ_{n, k, α} a_k\right) z^n \end{equation*} on the space of all analytic function $f(z)=\sum_{k=0}^{\infty} a_{k} z^{k}$ in the…

Pivot probabilities and norm effects in Gaussian elimination for $\beta$-ensembles
Kenji Gunawan, John Peca-Medlin
https://arxiv.org/abs/2506.20470 https:/…

Pivot probabilities and norm effects in Gaussian elimination for $β$-ensembles
We analyze pivot probabilities in Gaussian elimination with partial pivoting (GEPP) for $2 \times 2$ random matrix ensembles. For GUE matrices, we resolve a previously reported discrepancy between theoretical predictions and empirical observations by deriving the exact pivot probability under standard LAPACK-style implementations. We further show that Dumitriu-Edelman tridiagonal $β$-ensembles agree with the earlier theoretical expectations. Finally, we propose an open question on pivot behavi…

from my link log —
faer: a general-purpose linear algebra library for Rust.
https://docs.rs/faer/
saved 2025-03-24 https://dotat.at/:/ILSBW.…

A Novel Compiler Transformation for Fast Sparse Matrix Multiplication in GPUs
Hossein Albakri, Kazem Cheshmi
https://arxiv.org/abs/2506.15174 https://

A Novel Compiler Transformation for Fast Sparse Matrix Multiplication in GPUs
Sparse data structures are commonly used in neural networks to reduce the memory footprint. These data structures are compact but cause irregularities such as random memory accesses, which prevent efficient use of the memory hierarchy. GPUs are a common platform for machine learning practitioners, but running compact data structures on these devices often leads to slow-downs due to inefficient use of computing and memory resources. This paper proposes a new compiler transformation, enumerate-an…

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…

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…

Matrix Invariants as Homotopy Invariants in Finite $T_0$-spaces
Pedro J. Chocano
https://arxiv.org/abs/2506.16861 https://arxiv.org/p…

Matrix Invariants as Homotopy Invariants in Finite $T_0$-spaces
We establish a bijection between the set of finite topological $T_0$-spaces (or partially ordered sets) and classes of square matrices. The absolute value of the determinant or the rank of these matrices are simple homotopy invariants for the corresponding topological spaces, and consequently, for finite simplicial complexes. We calculate these invariants for various families of topological spaces and explore other relationships and problems posed for finite posets within the context of these m…

Causal Inference for Latent Outcomes Learned with Factor Models
Jenna M. Landy, Dafne Zorzetto, Roberta De Vito, Giovanni Parmigiani
https://arxiv.org/abs/2506.20549

Causal Inference for Latent Outcomes Learned with Factor Models
In many fields$\unicode{x2013}$including genomics, epidemiology, natural language processing, social and behavioral sciences, and economics$\unicode{x2013}$it is increasingly important to address causal questions in the context of factor models or representation learning. In this work, we investigate causal effects on $\textit{latent outcomes}$ derived from high-dimensional observed data using nonnegative matrix factorization. To the best of our knowledge, this is the first study to formally ad…

Chiral-odd generalized parton distributions in the large-$N_{c}$ limit of QCD: Next-to-leading-order contributions
June-Young Kim
https://arxiv.org/abs/2506.21013

Chiral-odd generalized parton distributions in the large-$N_{c}$ limit of QCD: Next-to-leading-order contributions
We investigate the nucleon's chiral-odd generalized parton distribution functions (GPDs) in the large-$N_c$ limit of QCD. Extending previous work on the leading-order contribution in the $1/N_c$ expansion, we focus on the next-to-leading-order contributions and provide a complete set of flavor-singlet and flavor-non-singlet chiral-odd GPDs. This study includes the derivation of the spin-flavor structure of the baryon matrix element of the chiral-odd operator, the proof of the polynomiality prop…

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 $3$. …

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…

A generalization of Rao's theorem to graded $R$-subalgebras of $R[t]$
Diksha Garg, Anjan Gupta
https://arxiv.org/abs/2506.18836 https://

A generalization of Rao's theorem to graded $R$-subalgebras of $R[t]$
Let $R$ be a Noetherian local ring of Krull dimension $d$ such that $(d!)R = R$, and let $A$ be a graded $R$-subalgebra of the polynomial algebra $R[t]$. We prove that every unimodular row of length $d + 1$ over $A$ can be completed to an invertible matrix. This is a generalization of a classical result by Rao, who proved that in the same setting, every unimodular row of length $d + 1$ over $R[t]$ admits a completion to an invertible matrix.

On the Jordan-Chevalley-Dunford decomposition of operators in type $I$ Murray-von Neumann algebras
Soumyashant Nayak, Renu Shekhawat
https://arxiv.org/abs/2506.17227

On the Jordan-Chevalley-Dunford decomposition of operators in type $I$ Murray-von Neumann algebras
We show that, for $n \ge 3$, the mapping on $M_n(\mathbb{C})$ which sends a matrix to its diagonalizable part in its Jordan-Chevalley decomposition, is {\bf norm-unbounded} on any neighbourhood of the zero matrix. Let $X$ be a Stonean space, and $\mathcal{N}(X)$ denote the $*$-algebra of (unbounded) normal functions on $X$, containing $C(X)$ as a $*$-subalgebra. We show that every element of $M_n\big(\mathcal{N}(X)\big)$ has a unique Jordan-Chevalley decomposition. Furthermore, when $n \ge 3$ a…

Lookup Table-based Multiplication-free All-digital DNN Accelerator Featuring Self-Synchronous Pipeline Accumulation
Hiroto Tagata, Takashi Sato, Hiromitsu Awano
https://arxiv.org/abs/2506.16800

Lookup Table-based Multiplication-free All-digital DNN Accelerator Featuring Self-Synchronous Pipeline Accumulation
Deep neural networks (DNNs) have been widely applied in our society, yet reducing power consumption due to large-scale matrix computations remains a critical challenge. MADDNESS is a known approach to improving energy efficiency by substituting matrix multiplication with table lookup operations. Previous research has employed large analog computing circuits to convert inputs into LUT addresses, which presents challenges to area efficiency and computational accuracy. This paper proposes a novel …

Lexicographic products and lexicographic powers of graphs -- a walk matrix approach
Domingos M. Cardoso, Paula Carvalho, Helena Gomes, Sofia J. Pinheiro, Paula Rama
https://arxiv.org/abs/2506.12168

Lexicographic products and lexicographic powers of graphs -- a walk matrix approach
The characteristic polynomial and the spectrum of the lexicographic product of graphs $H[G]$, a specific instance of the generalized composition (also called $H$-join), are explicitly determined for arbitrary graphs $H$ and $G$, in terms of the eigenvalues of $G$ and an $H[G]$ associated matrix $\widetilde{\bf W}$, which relates $H$ with $G$. This study also establishes conditions under which a main eigenvalue of $G$ is a main or non-main eigenvalue of the matrix $\widetilde{\bf W}$, when the n…

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…

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 …

Random Matrix Theory for Deep Learning: Beyond Eigenvalues of Linear Models
Zhenyu Liao, Michael W. Mahoney
https://arxiv.org/abs/2506.13139 https://

Random Matrix Theory for Deep Learning: Beyond Eigenvalues of Linear Models
Modern Machine Learning (ML) and Deep Neural Networks (DNNs) often operate on high-dimensional data and rely on overparameterized models, where classical low-dimensional intuitions break down. In particular, the proportional regime where the data dimension, sample size, and number of model parameters are all large and comparable, gives rise to novel and sometimes counterintuitive behaviors. This paper extends traditional Random Matrix Theory (RMT) beyond eigenvalue-based analysis of linear mode…

Fast solution of a phase-field model of pitting corrosion
Gianluca Frasca-Caccia, Dajana Conte, Beatrice Paternoster
https://arxiv.org/abs/2506.18058 https…

Fast solution of a phase-field model of pitting corrosion
Excessive computational times represent a major challenge in the solution of corrosion models, limiting their practical applicability, e.g., as a support to predictive maintenance. In this paper, we propose an efficient strategy for solving a phase-field model for metal corrosion. Based on the Kronecker structure of the diffusion matrix in classical finite difference approximations on rectangular domains, time-stepping IMEX methods are efficiently solve in matrix form. However, when the domain …

Effect of Berry connection on attosecond transient absorption spectroscopy in gapped graphene
Jiayu Yan, Hongxuan Er, Wei Dang, Jiahuan Ren, Chao Chen, Dianxiang Ren, Fulong Dong
https://arxiv.org/abs/2506.19286

Effect of Berry connection on attosecond transient absorption spectroscopy in gapped graphene
We investigated the attosecond transient absorption spectroscopy (ATAS) in gapped graphene by numerically solving the four-band density-matrix equations. Our results reveal that, in contrast to graphene whose fishbone-shaped spectra primarily oscillates at twice the frequency of the pump laser, the ATAS of gapped graphene exhibits a first-order harmonic component induced by the Berry connection. To gain insight into this interesting results, we employ a simplified model that considers only the …

Lagrange multiplier expressions for matrix polynomial optimization and tight relaxations
Lei Huang, Jiawang Nie, Jiajia Wang, Lingling Xie
https://arxiv.org/abs/2506.12579

Lagrange multiplier expressions for matrix polynomial optimization and tight relaxations
This paper studies matrix constrained polynomial optimization. We investigate how to get explicit expressions for Lagrange multiplier matrices from the first order optimality conditions. The existence of these expressions can be shown under the nondegeneracy condition. Using Lagrange multiplier matrix expressions, we propose a strengthened Moment-SOS hierarchy for solving matrix polynomial optimization. Under some general assumptions, we show that this strengthened hierarchy is tight, or equiva…

Testing Separability of High-Dimensional Covariance Matrices
Bongjung Sung, Peter D. Hoff
https://arxiv.org/abs/2506.17463 https://ar…

Testing Separability of High-Dimensional Covariance Matrices
Due to their parsimony, separable covariance models have been popular in modeling matrix-variate data. However, the inference from such a model may be misleading if the population covariance matrix $Σ$ is actually non-separable, motivating the use of statistical tests of separability. Likelihood ratio tests have tractable null distributions and good power when the sample size $n$ is larger than the number of variables $p$, but are not well-defined otherwise. Other existing separability tests f…

A_infinity Action of Open N=2 Superstring Field Theory
Xianghang Zhang
https://arxiv.org/abs/2506.21247 https://arxiv.org/pdf/2506.21…

A_infinity Action of Open N=2 Superstring Field Theory
We formulate a string field theory for open N=2 strings with an A_infinity algebra structure. Starting from the BRST cohomology relative to the U(1) anti-ghost zero-mode, we generalize [arXiv:1312.2948] and constructed all interacting vertices recursively and without singularity. We also show that our string field theory reproduces the correct perturbative S-matrix.

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…

Solution Methods and Perturbation Analysis for the Equality-Constrained Total Least Squares Problem over Reduced Biquaternions
Neha Bhadala
https://arxiv.org/abs/2506.18319

Solution Methods and Perturbation Analysis for the Equality-Constrained Total Least Squares Problem over Reduced Biquaternions
This paper proposes a theoretical framework to address the reduced biquaternion equality-constrained total least squares (RBTLSE) problem. The objective is to find an approximate solution to the system $AX \approx B$, subject to linear constraints $CX = D$, while explicitly accounting for errors in both the coefficient matrix $A$ and the observation matrix $B$. We establish conditions under which real and complex solutions exist and develop corresponding solution methods using real and complex …

MATRIX HAWAII: PineAPPL interpolation grids with MATRIX
S. Devoto, T. Jezo, S. Kallweit, C. Schwan
https://arxiv.org/abs/2506.14486 https://

MATRIX HAWAII: PineAPPL interpolation grids with MATRIX
We present an interface between PineAPPL and Matrix, which allows fully differential cross sections to be calculated in the form of interpolation grids, accurate at next-to-next-to-leading order (NNLO) in QCD and next-to-leading order in electroweak (EW) theory. This interface is the first publicly available tool to calculate interpolation grids at NNLO QCD accuracy for a wide set of processes. Interpolation grids provide the functionality to compute predictions for arbitrary parton distributio…

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…

Mesoscale FEM Model of Concrete: Statistical Assessment of Inherent Stress Concentrations in Dependence on Phase Heterogeneity
Jan Ma\v{s}ek (Institute of Physics of Materials, Czech Academy of Sciences, Brno, Czech Republic, Institute of Structural Mechanics, Faculty of Civil Engineering, Brno University of Technology, Brno, Czech Republic), Petr Miarka (Institute of Physics of Materials, Czech Academy of Sciences, Brno, Czech Republic, Institute of Structural Mechanics, Faculty of Ci…

Mesoscale FEM Model of Concrete: Statistical Assessment of Inherent Stress Concentrations in Dependence on Phase Heterogeneity
Concrete heterogeneity originates from its production process, which involves bonding aggregates with a binder matrix. This study presents a mesoscale finite element model (MFEM) that offers detailed insights into the fracture process at the aggregate-cement matrix interface, focusing on one of concrete's key properties: its mechanical response. Unlike discrete models, which often average out critical stress concentrations within the mesostructure, the MFEM approach captures detailed stress dis…

On the Upper Bounds for the Matrix Spectral Norm
Alexey Naumov, Maxim Rakhuba, Denis Ryapolov, Sergey Samsonov
https://arxiv.org/abs/2506.15660 https://

On the Upper Bounds for the Matrix Spectral Norm
We consider the problem of estimating the spectral norm of a matrix using only matrix-vector products. We propose a new Counterbalance estimator that provides upper bounds on the norm and derive probabilistic guarantees on its underestimation. Compared to standard approaches such as the power method, the proposed estimator produces significantly tighter upper bounds in both synthetic and real-world settings. Our method is especially effective for matrices with fast-decaying spectra, such as tho…

Polynomial Eigenfunctions and Matrix Lyapunov Equations from Energy Balance Integrals
Netzer Moriya
https://arxiv.org/abs/2506.15288 https://

Polynomial Eigenfunctions and Matrix Lyapunov Equations from Energy Balance Integrals
We establish a unified theoretical framework that connects classical orthogonal polynomial systems to matrix Lyapunov equations through the fundamental physics of energy dissipation in stochastic dynamical systems. Starting from the energy balance principle in infinite-dimensional Hilbert spaces, we derive a master integral representation that naturally encompasses both spectral geometry and covariance dynamics. The theory reveals that established orthogonal polynomials (Zernike, Hermite, spher…

Matrix models as tau functions of the UC hierarchy of integrable equations. II
Chuanzhong Li, Andrei Mironov, Alexander Yu. Orlov
https://arxiv.org/abs/2506.12867

Matrix models as tau functions of the UC hierarchy of integrable equations. II
We present a family of matrix models such that their partition functions are tau functions of the universal character (UC) hierarchy. This develops one of the topics of our previous paper arXiv:2410.14823. We found new matrix models associated with the product of two spheres with embedded graphs via a gluing matrix. We also generalize these studies to multi-matrix models case, which corresponds to the multi-component UC hierarchy.

The Bott-Duffin drazin inverse and its application
Lu Zheng, Xiangyu Zhang, Kezheng Zuo, Jing Zhou
https://arxiv.org/abs/2506.16018 https://

The Bott-Duffin drazin inverse and its application
The paper introduce a new type of generalized inverse, called Bott-Duffin drazin inverse (or, in short, BDD-inverse) of a complex square matrix, and give some of its properties, characterizations and representations. Furthermore, We discuss the problem of the minimum P-norm solution of the constraint matrix equation by using the Bott-Duffin drazin inverse, and give Cramer s rule for this minimum P-norm solution.

A Random Matrix Theory of Pauli Tomography
Nathan Keenan, John Goold, Alex Nico-Katz
https://arxiv.org/abs/2506.12010 https://arxiv.o…

A Random Matrix Theory of Pauli Tomography
Quantum state tomography (QST), the process of reconstructing some unknown quantum state $\hatρ$ from repeated measurements on copies of said state, is a foundationally important task in the context of quantum computation and simulation. For this reason, a detailed characterization of the error $Δ\hatρ= \hatρ-\hatρ^\prime$ in a QST reconstruction $\hatρ^\prime$ is of clear importance to quantum theory and experiment. In this work, we develop a fully random matrix theory (RMT) treatment of…

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…

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…

This https://arxiv.org/abs/2411.15479 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Sparse Polynomial Matrix Optimization
A polynomial matrix inequality is a formula asserting that a polynomial matrix is positive semidefinite. Polynomial matrix optimization concerns minimizing the smallest eigenvalue of a symmetric polynomial matrix subject to a tuple of polynomial matrix inequalities. This work explores the use of sparsity methods in reducing the complexity of sum-of-squares based methods in verifying polynomial matrix inequalities or solving polynomial matrix optimization. In the unconstrained setting, Newton po…

Replaced article(s) found for math.RA. https://arxiv.org/list/math.RA/new
[1/1]:
- Rank-Preserving Index-Dependent Matrix Transformations: Applications to Clockwork and Deconstruct...
Aadarsh Singh

Analysis of Floating-Point Matrix Multiplication Computed via Integer Arithmetic
Ahmad Abdelfattah, Jack Dongarra, Massimiliano Fasi, Mantas Mikaitis, Fran\c{c}oise Tisseur
https://arxiv.org/abs/2506.11277

Analysis of Floating-Point Matrix Multiplication Computed via Integer Arithmetic
Ootomo, Ozaki, and Yokota [Int. J. High Perform. Comput. Appl., 38 (2024), p. 297-313] have proposed a strategy to recast a floating-point matrix multiplication in terms of integer matrix products. The factors A and B are split into integer slices, the product of these slices is computed exactly, and AB is approximated by accumulating these integer products in floating-point arithmetic. This technique is particularly well suited to mixed-precision matrix multiply-accumulate units with integer s…

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…