Tootfinder

Quantum algorithm for linear matrix equations
Rolando D. Somma, Guang Hao Low, Dominic W. Berry, Ryan Babbush
https://arxiv.org/abs/2508.02822 https://arxi…

Quantum algorithm for linear matrix equations
We describe an efficient quantum algorithm for solving the linear matrix equation AX+XB=C, where A, B and C are given complex matrices and X is unknown. This is known as the Sylvester equation, a fundamental equation with applications in control theory and physics. Rather than encoding the solution in a quantum state in a fashion analogous to prior quantum linear algebra solvers, our approach constructs the solution matrix X in a block-encoding, rescaled by some factor. This allows us to obtain…

Even Faster Kernel Matrix Linear Algebra via Density Estimation
Rikhav Shah, Sandeep Silwal, Haike Xu
https://arxiv.org/abs/2510.02540 https://arxiv.org/pd…

Even Faster Kernel Matrix Linear Algebra via Density Estimation
This paper studies the use of kernel density estimation (KDE) for linear algebraic tasks involving the kernel matrix of a collection of $n$ data points in $\mathbb R^d$. In particular, we improve upon existing algorithms for computing the following up to $(1+\varepsilon)$ relative error: matrix-vector products, matrix-matrix products, the spectral norm, and sum of all entries. The runtimes of our algorithms depend on the dimension $d$, the number of points $n$, and the target error $\varepsilon…

MTQA:Matrix of Thought for Enhanced Reasoning in Complex Question Answering
Fengxiao Tang, Yufeng Li, Zongzong Wu, Ming Zhao
https://arxiv.org/abs/2509.03918 https://

MTQA:Matrix of Thought for Enhanced Reasoning in Complex Question Answering
Complex Question Answering (QA) is a fundamental and challenging task in NLP. While large language models (LLMs) exhibit impressive performance in QA, they suffer from significant performance degradation when facing complex and abstract QA tasks due to insufficient reasoning capabilities. Works such as Chain-of-Thought (CoT) and Tree-of-Thought (ToT) aim to enhance LLMs' reasoning abilities, but they face issues such as in-layer redundancy in tree structures and single paths in chain structures…

Cap amplitudes in random matrix models
Kazumi Okuyama
https://arxiv.org/abs/2509.03930 https://arxiv.org/pdf/2509.03930

Cap amplitudes in random matrix models
For general one-matrix models in the large $N$ limit, we introduce the cap amplitude $ψ(b)$ as the expansion coefficient of the 1-form $ydx$ on the spectral curve. We find that the dilaton equation for the discrete volume $N_{g,n}$ of the moduli space of genus-$g$ Riemann surfaces with $n$ boundaries is interpreted as gluing the cap amplitude along one of the boundaries. In this process, one of the boundaries is capped and the number of boundaries decreases by one. In a similar manner, the gen…

Sparsity and Total Variation Constrained Multilayer Linear Unmixing for Hyperspectral Imagery
Gang Yang
https://arxiv.org/abs/2508.03403 https://arxiv.org/…

Sparsity and Total Variation Constrained Multilayer Linear Unmixing for Hyperspectral Imagery
Hyperspectral unmixing aims at estimating material signatures (known as endmembers) and the corresponding proportions (referred to abundances), which is a critical preprocessing step in various hyperspectral imagery applications. This study develops a novel approach called sparsity and total variation (TV) constrained multilayer linear unmixing (STVMLU) for hyperspectral imagery. Specifically, based on a multilayer matrix factorization model, to improve the accuracy of unmixing, a TV constraint…

Solving Zero-Sum Games with Fewer Matrix-Vector Products
Ishani Karmarkar, Liam O'Carroll, Aaron Sidford
https://arxiv.org/abs/2509.04426 https://arxiv…

Solving Zero-Sum Games with Fewer Matrix-Vector Products
In this paper we consider the problem of computing an $ε$-approximate Nash Equilibrium of a zero-sum game in a payoff matrix $A \in \mathbb{R}^{m \times n}$ with $O(1)$-bounded entries given access to a matrix-vector product oracle for $A$ and its transpose $A^\top$. We provide a deterministic algorithm that solves the problem using $\tilde{O}(ε^{-8/9})$-oracle queries, where $\tilde{O}(\cdot)$ hides factors polylogarithmic in $m$, $n$, and $ε^{-1}$. Our result improves upon the state-of-the…

Messenger: Hauptserver von Matrix down
Nach einem Datenbankfehler ist Matrix.org offline. Das Einspielen des Backups ist in Arbeit, eigene Instanzen sind nicht betroffen.
https://www.heise.de/news/Messen…

Board Game Arena: A Framework and Benchmark for Assessing Large Language Models via Strategic Play
Lucia Cipolina-Kun, Marianna Nezhurina, Jenia Jitsev
https://arxiv.org/abs/2508.03368

Board Game Arena: A Framework and Benchmark for Assessing Large Language Models via Strategic Play
The Board Game Arena library provides a framework for evaluating the decision making abilities of large language models (LLMs) through strategic board games implemented in Google OpenSpiel library. The framework enables systematic comparisons between LLM based agents and other agents (random, human, reinforcement learning agents, etc.) in various game scenarios by wrapping multiple board and matrix games and supporting different agent types. It integrates API access to models via LiteLLM, local…

On-shell Matrix Elements of the EMT Trace in Gauge Theories and Heavy Quark Masses
Long Chen, Zhe Li, Marco Niggetiedt
https://arxiv.org/abs/2509.03580 https://

On-shell Matrix Elements of the EMT Trace in Gauge Theories and Heavy Quark Masses
We present a novel diagrammatic proof of the identity between the forward matrix element of the energy-momentum-tensor (EMT) trace operator over a single particle's on-shell state and its perturbative pole mass to any loop orders in perturbative gauge theories (with gauge bosons and fermions), without appealing to any pre-laid operator renormalization conditions or Ward identities. The proof is based on the equation of mass-dimensional analysis in dimensional regularization, the topological pro…

Computability of dimension groups
Maria Sabitova
https://arxiv.org/abs/2509.04350 https://arxiv.org/pdf/2509.04350

Computability of dimension groups
We investigate the computability of the isomorphism set $\operatorname{Iso}(G_A,G_B)$ between $G_A$ and $G_B$, where $G_A$ is a subgroup of $\mathbb{Q}^n$ generated by columns of integer powers of a non-singular $n \times n$-matrix $A$ with integer entries. Assuming that the characteristic polynomial of $A$ is irreducible -- and under an additional condition when $n$ is not prime -- we prove that $\operatorname{Iso}(G_A,G_B)$ is computable; that is, there exists an algorithm that determines the…

Sensor placement for sparse force reconstruction
Jeunghoon Lee
https://arxiv.org/abs/2509.03825 https://arxiv.org/pdf/2509.03825

Sensor placement for sparse force reconstruction
The present study proposes a Gram-matrix-based sensor placement strategy for sparse force reconstruction in the frequency domain. A modal decomposition of the Gram matrix reveals that its structure is dominated by a few modes near the target frequency, and that each modal contribution reflects the spatial correlation of the corresponding mode shape. This suggests that placing sensors near nodal regions where spatial correlation is low can reduce coherence in the frequency response function (FRF…

Distributed Non-Uniform Scaling Control of Multi-Agent Formation via Matrix-Valued Constraints
Tao He, Gangshan Jing
https://arxiv.org/abs/2508.02289 https://

Distributed Non-Uniform Scaling Control of Multi-Agent Formation via Matrix-Valued Constraints
Distributed formation maneuver control refers to the problem of maneuvering a group of agents to change their formation shape by adjusting the motions of partial agents, where the controller of each agent only requires local information measured from its neighbors. Although this problem has been extensively investigated, existing approaches are mostly limited to uniform scaling transformations. This article proposes a new type of local matrix-valued constraints, via which non-uniform scaling co…

Fast Gaussian process inference by exact Mat\'ern kernel decomposition
Nicolas Langren\'e, Xavier Warin, Pierre Gruet
https://arxiv.org/abs/2508.01864 https://

Fast Gaussian process inference by exact Matérn kernel decomposition
To speed up Gaussian process inference, a number of fast kernel matrix-vector multiplication (MVM) approximation algorithms have been proposed over the years. In this paper, we establish an exact fast kernel MVM algorithm based on exact kernel decomposition into weighted empirical cumulative distribution functions, compatible with a class of kernels which includes multivariate Matérn kernels with half-integer smoothness parameter. This algorithm uses a divide-and-conquer approach, during which…

Replaced article(s) found for math.AT. https://arxiv.org/list/math.AT/new
[1/1]:
- Expected Complexity of Persistence Barcode Computation via Matrix Reduction
Barbara Giunti, Guillaume Houry, Michael Kerber, Matthias S\"ols

Distributed Source Coding for Compressing Vector-Linear Functions
Xuan Guang, Xiufang Sun, Ruze Zhang
https://arxiv.org/abs/2508.02996 https://arxiv.org/pd…

Distributed Source Coding for Compressing Vector-Linear Functions
Inspired by mobile satellite communication systems and the important and prevalent applications of computational tasks, we consider a distributed source coding model for compressing vector-linear functions, which consists of multiple sources, multiple encoders and a decoder linked to all the encoders. Each encoder has access to a certain subset of the sources and the decoder is required to compute with zero error a vector-linear function of the source information, which corresponds to a matrix …

New conjectures on the inertia of graphs
Saieed Akbari, Clive Elphick, Hitesh Kumar, Shivaramakrishna Pragada, Quanyu Tang
https://arxiv.org/abs/2508.01163 https://

New conjectures on the inertia of graphs
Let $G$ be a graph with adjacency matrix $A(G)$. We conjecture that \[2n^+(G) \le n^-(G)(n^-(G) + 1),\] where $n^+(G)$ and $n^-(G)$ denote the number of positive and negative eigenvalues of $A(G)$, respectively. This conjecture generalizes to all graphs the well-known absolute bound for strongly regular graphs. The conjecture also relates to a question posed by Torgašev. We prove the conjecture for special graph families, including line graphs and planar graphs, and provide examples where the …

Replaced article(s) found for math-ph. https://arxiv.org/list/math-ph/new
[1/2]:
- A class of 2 X 2 correlated random-matrix models with Brody spacing distribution
Jamal Sakhr

Pointed Racks and Their Applications to Braid Theory
Angel Apollos, Jose Ceniceros
https://arxiv.org/abs/2508.03013 https://arxiv.org/pdf/2508.03013…

Pointed Racks and Their Applications to Braid Theory
We define a new algebraic structure called a \emph{pointed rack} and use it to construct ambient isotopy invariants of $ n $-braids. We first introduce an integer-valued invariant of braids using pointed racks. This is then strengthened by defining a matrix-valued invariant using racks. Moreover, our invariant determines the rack coloring invariant previously defined for the closure of the braid. Finally, we include examples of braids that are distinguished by these new invariants.

Khintchine-type theorems for weighted uniform inhomogeneous approximations via transference principle
Vasiliy Neckrasov
https://arxiv.org/abs/2508.01912 https://

Khintchine-type theorems for weighted uniform inhomogeneous approximations via transference principle
In [Compositio Math. 155 (2019)] Kleinbock and Wadleigh proved a "zero-one law" for uniform inhomogeneous Diophantine approximations. We generalize this statement with arbitrary weight functions and establish a new and simple proof of this statement, based on transference principle. We also give a complete description of the sets of $g$-Dirichlet pairs with a fixed matrix in this setup from Lebesgue measure point of view. As an application, we consider the set of badly approximable matrices and…

Datenbank kaputt: Der Hauptserver von Matrix.org ist offline https://www.golem.de/news/datenbank-kaputt-der-hauptserver-von-matrix-org-ist-offline-2509-199737.html

Datenbank kaputt: Der Hauptserver von Matrix.org ist offline - Golem.de
Zahlreiche Anwender können den Chatdienst von Matrix.org derzeit nicht nutzen. Die Organisation hat Probleme mit der Datenbank des Hauptservers.

A matrix preconditioning framework for physics-informed neural networks based on adjoint method
Jiahao Song, Wenbo Cao, Weiwei Zhang
https://arxiv.org/abs/2508.03421 https://

A matrix preconditioning framework for physics-informed neural networks based on adjoint method
Physics-informed neural networks (PINNs) have recently emerged as a popular approach for solving forward and inverse problems involving partial differential equations (PDEs). Compared to fully connected neural networks, PINNs based on convolutional neural networks offer advantages in the hard enforcement of boundary conditions and in reducing the computational cost of partial derivatives. However, the latter still struggles with slow convergence and even failure in some scenarios. In this study…

Quantum thermalization and the route to ergodicity
Amichay Vardi, Doron Cohen
https://arxiv.org/abs/2508.00949 https://arxiv.org/pdf/2508.00949

Quantum thermalization and the route to ergodicity
We consider a minimal model for quantum thermalization of coupled chaotic subsystems. The route towards ergodicity is explored as a function of the coupling strength. The results are contrasted with the predictions of standard Random Matrix Theory (RMT) and the Eigenstates Thermalization Hypothesis (ETH). We highlight a coupling regime of disparity between the spectral statistics that indicates chaos, and ergodicity measures that indicate lack of ETH thermalization. The analysis involves a revi…

A One-Particle Density Matrix Framework for Mode-Shell Correspondence: Characterizing Topology in Higher-Order Topological Insulators
Miguel F. Mart\'inez, Lucien Jezequel, Jens H. Bardarson, Thomas Klein Kvorning, Julia D. Hannukainen
https://arxiv.org/abs/2509.03632

A One-Particle Density Matrix Framework for Mode-Shell Correspondence: Characterizing Topology in Higher-Order Topological Insulators
We present a framework for characterizing higher-order topological phases directly from the one-particle density matrix, without any reference to an underlying Hamiltonian. Our approach extends the mode-shell correspondence, originally formulated for single-particle Hamiltonians, to Gaussian states subject to chiral constraints. In this correspondence, the mode index counts topological boundary modes, while the shell index quantifies the bulk topology in a surrounding region, providing a bulk-b…

Robust fuzzy clustering with cellwise outliers
Giorgia Zaccaria, Lorenzo Benzakour, Luis A. Garc\'ia-Escudero, Francesca Greselin, Agust\'in Mayo-\'Iscar
https://arxiv.org/abs/2508.03310

Robust fuzzy clustering with cellwise outliers
Fuzzy clustering is a technique for identifying subgroups in heterogeneous populations by quantifying unit membership degrees. The magnitude of the latter depends on the desired level of fuzzification, based on the purpose of the analysis. We combine the advantages of fuzzy clustering with a robust approach able to detecting cellwise outliers, i.e., anomalous cells in a data matrix. The proposed methodology is formulated within a probabilistic framework and estimated via an Expectation-Maximiza…

Optimal Quantum $(r,\delta)$-Locally Repairable Codes From Matrix-Product Codes
Meng Cao, Kun Zhou
https://arxiv.org/abs/2508.03597 https://arxiv.org/pdf/2…

Optimal Quantum $(r,δ)$-Locally Repairable Codes From Matrix-Product Codes
This paper studies optimal quantum $(r,δ)$-LRCs from matrix-product (MP) codes. We establish a necessary and sufficient condition for an MP code to be an optimal $(r,δ)$-LRC. Based on this, we present a characterization for optimal quantum $(r,δ)$-LRCs from MP codes with nested constituent codes, and also study optimal quantum $(r,δ)$-LRCs constructed from MP codes with non-nested constituent codes. Through Hermitian dual-containing and Euclidean dual-containing MP codes, we present five in…

Crosslisted article(s) found for cs.MS. https://arxiv.org/list/cs.MS/new
[1/1]:
- On the energy efficiency of sparse matrix computations on multi-GPU clusters
Massimo Bernaschi, Alessandro Celestini, Pasqua D'Ambra, Giorgio Richelli

I wished I could disagree with this post but sadly I cannot. I had high hopes for Matrix and still use it but boy is it not fixing the core and conceptual issues.
https://shkspr.mobi/blog/2025/07/im-never-going-back-to-matrix/

I'm never going back to Matrix
I should love Matrix. It is a decentralised, privacy preserving, multi-platform chat tool. Goodbye Slack and your ridiculous free limits. Adiós Discord and your weird gamification. Suck it IRC with your obscure syntax and faint stench of BO. WhatsApp and Telegram can stick their heads in a bucket of lukewarm sick and sing sea shanties! Let's join the future! The problem is - Matrix is shit. Not …

Topolow: Force-Directed Euclidean Embedding of Dissimilarity Data with Robustness Against Non-Metricity and Sparsity
Omid Arhami, Pejman Rohani
https://arxiv.org/abs/2508.01733 …

Topolow: Force-Directed Euclidean Embedding of Dissimilarity Data with Robustness Against Non-Metricity and Sparsity
The problem of embedding a set of objects into a low-dimensional Euclidean space based on a matrix of pairwise dissimilarities is fundamental in data analysis, machine learning, and statistics. However, the assumptions of many standard analytical methods are violated when the input dissimilarities fail to satisfy metric or Euclidean axioms. We present the mathematical and statistical foundations of Topolow, a physics-inspired, gradient-free optimization framework for such embedding problems. To…

Macaulay representation of the prolongation matrix and the SOS conjecture
Zhiwei Wang, Chenlong Yue, Xiangyu Zhou
https://arxiv.org/abs/2509.04314 https://…

Macaulay representation of the prolongation matrix and the SOS conjecture
Let $z \in \mathbb{C}^n$, and let $A(z,\bar{z})$ be a real valued diagonal bihomogeneous Hermitian polynomial such that $A(z,\bar{z})\|z\|^2$ is a sum of squares, where $\|z\|$ denotes the Euclidean norm of $z$. In this paper, we provide an estimate for the rank of the sum of squares $A(z,\bar{z})\|z\|^2$ when $A(z,\bar{z})$ is not semipositive definite. As a consequence, we confirm the SOS conjecture proposed by Ebenfelt for $2 \leq n \leq 6$ when $A(z,\bar{z})$ i…

Towards Faster Feasible Matrix Multiplication by Trilinear Aggregation
Oded Schwartz, Eyal Zwecher
https://arxiv.org/abs/2508.01748 https://arxiv.org/pdf/2…

Towards Faster Feasible Matrix Multiplication by Trilinear Aggregation
Matrix multiplication is a fundamental kernel in high performance computing. Many algorithms for fast matrix multiplication can only be applied to enormous matrices ($n>10^{100}$) and thus cannot be used in practice. Of all algorithms applicable to feasible input, Pan's $O(n^{2.773372})$ algorithm (1982) is asymptotically the fastest. We obtain an $O(n^{2.773203})$ algorithm applicable to the same input sizes as Pan's algorithm. This algorithm is the fastest matrix multiplication algorithm with…

Multi-Community Spectral Clustering for Geometric Graphs
Luiz Emilio Allem, Konstantin Avrachenkov, Carlos Hoppen, Hariprasad Manjunath, Lucas Siviero Sibemberg
https://arxiv.org/abs/2508.00893

Multi-Community Spectral Clustering for Geometric Graphs
In this paper, we consider the soft geometric block model (SGBM) with a fixed number $k \geq 2$ of homogeneous communities in the dense regime, and we introduce a spectral clustering algorithm for community recovery on graphs generated by this model. Given such a graph, the algorithm produces an embedding into $\mathbb{R}^{k-1}$ using the eigenvectors associated with the $k-1$ eigenvalues of the adjacency matrix of the graph that are closest to a value determined by the parameters of the model.…

Upper bound of transient growth in accelerating and decelerating wall-driven flows using the Lyapunov method
Zhengyang Wei, Weichen Zhao, Chang Liu
https://arxiv.org/abs/2508.01410

Upper bound of transient growth in accelerating and decelerating wall-driven flows using the Lyapunov method
This work analyzes accelerating and decelerating wall-driven flows by quantifying the upper bound of transient energy growth using a Lyapunov-type approach. By formulating the linearized Navier-Stokes equations as a linear time-varying system and constructing a time-dependent Lyapunov function, we obtain a rigorous upper bound on transient energy growth by solving linear matrix inequalities (LMI). The LMI approach can obtain the upper bound of transient energy growth that closely matches transi…

Estimation of Algebraic Sets: Extending PCA Beyond Linearity
Alberto Gonz\'alez-Sanz, Gilles Mordant, \'Alvaro Samperio, Bodhisattva Sen
https://arxiv.org/abs/2508.01976

Estimation of Algebraic Sets: Extending PCA Beyond Linearity
An algebraic set is defined as the zero locus of a system of real polynomial equations. In this paper we address the problem of recovering an unknown algebraic set $\mathcal{A}$ from noisy observations of latent points lying on $\mathcal{A}$ -- a task that extends principal component analysis, which corresponds to the purely linear case. Our procedure consists of three steps: (i) constructing the {\it moment matrix} from the Vandermonde matrix associated with the data set and the degree of the …

Low-rank matrix and tensor approximations: advancing efficiency of machine-learning interatomic potentials
Igor Vorotnikov, Fedor Romashov, Nikita Rybin, Maxim Rakhuba, Ivan S. Novikov
https://arxiv.org/abs/2509.04440

Low-rank matrix and tensor approximations: advancing efficiency of machine-learning interatomic potentials
Machine-learning interatomic potentials (MLIPs) have become a mainstay in computationally-guided materials science, surpassing traditional force fields due to their flexible functional form and superior accuracy in reproducing physical properties of materials. This flexibility is achieved through mathematically-rigorous basis sets that describe interatomic interactions within a local atomic environment. The number of parameters in these basis sets influences both the size of the training datase…

#Matrix 2024: Can not decrypt this message
#Matrix 2025: Can not find this message
Progress.

Character tables are ideal Perron similarities
David Z. Gershnik, Alexander J. Lewis, Pietro Paparella
https://arxiv.org/abs/2508.02830 https://arxiv.org/p…

Character tables are ideal Perron similarities
An invertible matrix is called a Perron similarity if it diagonalizes an irreducible, nonnegative matrix. Each Perron similarity gives a nontrivial polyhedral cone, called the spectracone, and polytope, called the spectratope, of realizable spectra (thought of as vectors in complex Euclidean space). A Perron similarity is called ideal if its spectratope coincides with the conical hulls of its rows. Identifying ideal Perron similarities is of great interest in the pursuit of the longstanding non…

Sparse Gabor representations of metaplectic operators: controlled exponential decay and Schr\"odinger confinement
Elena Cordero, Gianluca Giacchi, Edoardo Pucci, Salvatore Ivan Trapasso
https://arxiv.org/abs/2508.02226

Sparse Gabor representations of metaplectic operators: controlled exponential decay and Schrödinger confinement
Motivated by the phase space analysis of Schrödinger evolution operators, in this paper we investigate how metaplectic operators are approximately diagonalized along the corresponding symplectic flows by exponentially localized Gabor wave packets. Quantitative bounds for the matrix coefficients arising in the Gabor wave packet decomposition of such operators are established, revealing precise exponential decay rates together with subtler dispersive and spreading phenomena. To this aim, we pres…

From Motifs to L\'evy Flights: Modeling Urban Mobility in Bogot\'a's Public Transport System
Juan F. Alay\'on-Mart\'inez, Alejandro P. Riascos
https://arxiv.org/abs/2510.02621

From Motifs to Lévy Flights: Modeling Urban Mobility in Bogotá's Public Transport System
In this paper, we study two years of access card validation records from Bogotá's multimodal public transport system, comprising over 2.3 billion trips across bus rapid transit, feeder buses, dual-service buses, and an aerial cable network. By reconstructing user trajectories as motifs, we identify recurrent mobility patterns that extend beyond simple round trips, enabling the construction of an integrated origin-destination (OD) matrix covering 2,828 urban zones. Similarity analysis using the…

The exact distribution of the conditional likelihood-ratio test in instrumental variables regression
Malte Londschien
https://arxiv.org/abs/2509.04144 https://

The exact distribution of the conditional likelihood-ratio test in instrumental variables regression
We derive the exact asymptotic distribution of the conditional likelihood-ratio test in instrumental variables regression under weak instrument asymptotics and for multiple endogenous variables. The distribution is conditional on all eigenvalues of the concentration matrix, rather than only the smallest eigenvalue as in an existing asymptotic upper bound. This exact characterization leads to a substantially more powerful test if there are differently identified endogenous variables. We provide …

Bulk asymptotics of the Gaussian $\beta$-ensemble characteristic polynomial
Gaultier Lambert, Elliot Paquette
https://arxiv.org/abs/2508.01458 https://arxi…

Bulk asymptotics of the Gaussian $β$-ensemble characteristic polynomial
The Gaussian $β$-ensemble (G$β$E) is a fundamental model in random matrix theory. In this paper, we provide a comprehensive asymptotic description of the characteristic polynomial of the G$β$E anywhere in the bulk of the spectrum that simultaneously captures both local-scale fluctuations (governed by the Sine-$β$ point process) and global/mesoscopic log-correlated Gaussian structure, which is accurate down to vanishing errors as $N\to\infty$. As immediate corollaries, we obtain several im…

Collisional decoherence in a BEC double-well accelerometer
Kateryna Korshynska, Sebastian Ulbricht
https://arxiv.org/abs/2508.01090 https://arxiv.org/pdf/2…

Collisional decoherence in a BEC double-well accelerometer
BEC-based quantum sensors offer a huge, yet not fully explored potential in gravimetry and accelerometry. In this paper, we study a possible setup for such a device, which is a weakly interacting Bose gas trapped in a double-well potential. In such a trap, the gas is known to exhibit Josephson oscillations, which rely on the coherence between the potential wells. Applying the density matrix approach, we consider transitions between the coherent, partially incoherent, and fully incoherent states…

Cholesky decomposition for symmetric matrices, Riemannian geometry, and random matrices
Apoorva Khare, Prateek Kumar Vishwakarma
https://arxiv.org/abs/2508.02715 https://…

Cholesky decomposition for symmetric matrices, Riemannian geometry, and random matrices
For each $n \geq 1$ and sign pattern $ε\in \{ \pm 1 \}^n$, we introduce a cone of real symmetric matrices $LPM_n(ε)$: those with leading principal $k \times k$ minors of signs $ε_k$. These cones are pairwise disjoint and their union $LPM_n$ is a dense cone in all symmetric matrices; they subsume positive and negative definite matrices, and symmetric (P-,) N-, PN-, almost P-, and almost N- matrices. We show that each $LPM_n$ matrix $A$ admits an uncountable family of Cholesky-type factorizati…

Transport in Single Quantum Dots: A Review from Linear Response to Nonlinear Regimes
Gustavo Diniz, Silvio Quintino, Vivian V. Fran\c{c}a
https://arxiv.org/abs/2508.01376 https:…

Transport in Single Quantum Dots: A Review from Linear Response to Nonlinear Regimes
Quantum dots are versatile systems for exploring quantum transport, electron correlations, and many-body phenomena such as the Kondo effect. While equilibrium properties are well understood through methods like the numerical renormalization group and density matrix renormalization group, nonequilibrium transport remains a major theoretical challenge. From the experimental point of view, recent advances in nanofabrication and measurement techniques have enabled the investigation of far-from-equi…

A Highly Scalable TDMA for GPUs and Its Application to Flow Solver Optimization
Seungchan Kim, Jihoo Kim, Sanghyun Ha, Donghyun You
https://arxiv.org/abs/2509.03933 https://

A Highly Scalable TDMA for GPUs and Its Application to Flow Solver Optimization
A tridiagonal matrix algorithm (TDMA), Pipelined-TDMA, is developed for multi-GPU systems to resolve the scalability bottlenecks caused by the sequential structure of conventional divide-and-conquer TDMA. The proposed method pipelines multiple tridiagonal systems, overlapping communication with computation and executing GPU kernels concurrently to hide non-scalable stages behind scalable compute stages. To maximize performance, the batch size is optimized to strike a balance between GPU occupan…

Direct Evaluation of CP Phase of CKM matrix, General Perturbative Expansion and Relations with Unitarity Triangles
Masaki J. S. Yang
https://arxiv.org/abs/2508.02058 https://

Direct Evaluation of CP Phase of CKM matrix, General Perturbative Expansion and Relations with Unitarity Triangles
In this letter, using a rephasing invariant formula $δ= \arg [ { V_{ud} V_{us} V_{c b} V_{tb} / V_{ub} \det V_{\rm CKM} }]$, we evaluate the CP phase $δ$ of the CKM matrix $V_{\rm CKM}$ perturbatively for small quark mixing angles $s_{ij}^{u,d}$ with associated phases $ρ_{ij}^{u,d}$. Consequently, we derived a relation $δ\simeq \arg [Δs_{12} Δs_{23} / ( Δs_{13} - s^u_{12} e^{-i ρ^u_{12}} Δs_{23} )]$ with $Δs_{ij} \equiv s^d_{ij} e^{-i ρ^d_{ij}} - s^u_{ij} e^{-i ρ^u_{ij}}$. Such a …

Recognizing flag varieties and reductive groups
I. Grojnowski, N. I. Shepherd-Barron
https://arxiv.org/abs/2509.03504 https://arxiv.org/pdf/2509.03504

Recognizing flag varieties and reductive groups
Fix a flat and projective morphism $X\rightarrowΣ$ of schemes. We show, first, that any set of $\mathbb{P}^1$-fibrations on $X$ defines a set of simple roots, a set of simple coroots and a Cartan matrix $C$. Second, $X$ is an étale $F$-bundle over some projective $Σ$-scheme, where $F$ is the flag variety of the adjoint Chevalley group over the integers defined by $C$. In particular, if the simple roots generate the Néron--Severi group of $X$ relative to $Σ$ and $X$ is cohomologically flat …

Inequalities for Optimization of Classification Algorithms: A Perspective Motivated by Diagnostic Testing
Paul N. Patrone, Anthony J. Kearsley
https://arxiv.org/abs/2508.01065 h…

Inequalities for Optimization of Classification Algorithms: A Perspective Motivated by Diagnostic Testing
Motivated by canonical problems in medical diagnostics, we propose and study properties of an objective function that uniformly bounds uncertainties in quantities of interest extracted from classifiers and related data analysis tools. We begin by adopting a set-theoretic perspective to show how two main tasks in diagnostics -- classification and prevalence estimation -- can be recast in terms of a variation on the confusion (or error) matrix ${\boldsymbol {\rm P}}$ typically considered in super…

Controllability of finite-dimensional linear fractional systems under uncertain parameters
Idriss Boutaayamou, Fouad Et-Tahri, Lahcen Maniar
https://arxiv.org/abs/2508.02420 htt…

Controllability of finite-dimensional linear fractional systems under uncertain parameters
This paper investigates the controllability of finite-dimensional linear fractional systems involving an uncertain parameter. We establish new results on the simultaneous and average controllability. In particular, we show that average controllability can be characterized by the so-called average Kalman rank condition and the average Gramian matrix. Moreover, using the average Gramian matrix, we design an open-loop control with minimal energy. These results can be seen as a natural generalizati…

Moment problems and bounds for matrix-valued smeared spectral functions
Ryan Abbott, William I. Jay, Patrick R. Oare
https://arxiv.org/abs/2508.01377 https://

Moment problems and bounds for matrix-valued smeared spectral functions
Numerical analytic continuation arises frequently in lattice field theory, particularly in spectroscopy problems. This work shows the equivalence of common spectroscopic problems to certain classes of moment problems that have been studied thoroughly in the mathematical literature. Mathematical results due to Kovalishina enable rigorous bounds on smeared matrix-valued spectral functions, which are implemented numerically for the first time. The required input is a positive-definite matrix of Eu…

Replaced article(s) found for cs.IT. https://arxiv.org/list/cs.IT/new
[1/1]:
- Optimal quantum locally recoverable codes from matrix-product construction
Carlos Galindo, Fernando Hernando, Carlos Munuera, Diego Ruano

The asymptotic rank of adjacency matrices of weighted configuration models over arbitrary fields
Remco van der Hofstad, Noela M\"uller, Haodong Zhu
https://arxiv.org/abs/2508.02813

The asymptotic rank of adjacency matrices of weighted configuration models over arbitrary fields
We study the asymptotic rank of adjacency matrices of a large class of edge-weighted configuration models. Here, the weight of a (multi-)edge can be any fixed non-zero element from an arbitrary field, as long as it is independent of the (multi-)graph. Our main result demonstrates that the asymptotic behavior of the normalized rank of the adjacency matrix neither depends on the fixed edge-weights, nor on which field they are chosen from. Our approach relies on a novel adaptation of the component…

Stabilizer R\'enyi Entropy for Translation-Invariant Matrix Product States
Lei-Yi-Nan Liu, Su Yi, Jian Cui
https://arxiv.org/abs/2508.03534 https://arx…

Stabilizer Rényi Entropy for Translation-Invariant Matrix Product States
Magic, capturing the deviation of a quantum state from the stabilizer formalism, is a key resource underpinning the quantum advantage. The recently introduced stabilizer Rényi entropy (SRE) offers a tractable measure of magic, avoiding the complexity of conventional methods. We study SRE in translation-invariant matrix product states (MPS), deriving exact expressions for representative states and introducing a numerically stable algorithm, named bond-DMRG, to compute the SRE density in infinit…

Robust MIMO Semantic Communication with Imperfect CSI via Knowledge Distillation
Mingze Gong, Shuoyao Wang, Shijian Gao, Jia Yan, Suzhi Bi
https://arxiv.org/abs/2509.04005 https…

Robust MIMO Semantic Communication with Imperfect CSI via Knowledge Distillation
Semantic communication (SemComm) has emerged as a new communication paradigm. To enhance efficiency, multiple-input-multiple-output (MIMO) technology has been further integrated into SemComm systems. However, existing MIMO SemComm systems assume perfect channel matrix estimation for channel-adaptive joint source-channel coding, which is impractical due to hardware and pilot overhead constraints. In this paper, we propose a semantic image transmission system with channel matrix and channel noise…

Inverse Monoid Topological Quantum Field Theories and Open-Closed Grand Canonical Symmetric Orbifolds
Jan Troost
https://arxiv.org/abs/2510.02782 https://a…

Inverse Monoid Topological Quantum Field Theories and Open-Closed Grand Canonical Symmetric Orbifolds
We present an open-closed topological quantum field theory for inverse monoids which generalizes the theory of principle fiber bundles with finite gauge group over Riemann surfaces with boundary. The theory is constructed using the isomorphism between the semisimple inverse monoid algebra and a matrix algebra which lies at the heart of monoid structure and representation theory. An example that we study in detail is the Ivanov-Kerov monoid of partial permutations. We review motivations from str…

thrown together a quick little discord server for #FediMobi, so if you're into the #fediverse and old mobile devices come on in! also bridged to matrix at #fedimobi:chat.bluepixelcomputing.com…

Solving Sudoku Using Oscillatory Neural Networks
Stefan Porfir, Bram F. Haverkort, Federico Sbravati, Aida Todri-Sanial
https://arxiv.org/abs/2508.02250 https://

Solving Sudoku Using Oscillatory Neural Networks
This paper explores the application of Oscillatory Neural Networks (ONNs) to solving Sudoku puzzles, presenting a biologically inspired approach based on phase synchronization. Each cell is represented by an oscillator whose phase encodes a digit, and the synchronization is governed by the Kuramoto model. The system dynamically evolves towards a valid solution by having the puzzle constraints encoded into the weight matrix of the network, and through a proposed novel phase mapping of the Sudoku…

Tensor Dynamic Mode Decomposition
Ziqin He, Mengqi Hu, Yifei Lou, Can Chen
https://arxiv.org/abs/2508.02627 https://arxiv.org/pdf/2508.02627

Tensor Dynamic Mode Decomposition
Dynamic mode decomposition (DMD) has become a powerful data-driven method for analyzing the spatiotemporal dynamics of complex, high-dimensional systems. However, conventional DMD methods are limited to matrix-based formulations, which might be inefficient or inadequate for modeling inherently multidimensional data including images, videos, and higher-order networks. In this letter, we propose tensor dynamic mode decomposition (TDMD), a novel extension of DMD to third-order tensors based on the…

Universal vector and matrix optimal transport
Boris Khesin, Klas Modin
https://arxiv.org/abs/2510.02039 https://arxiv.org/pdf/2510.02039

Universal vector and matrix optimal transport
In this paper we propose a gauge-theoretic approach to the problems of optimal mass transport for vector and matrix densities. This resolves both the issues of positivity and action transitivity constraints. Bures-type metrics on the corresponding semi-direct product groups of diffeomorphisms and gauge transformations are related to Wasserstein-type metrics on vector half-densities and matrix densities via Riemannian submersions. We also describe their relation to Poisson geometry and demonstra…

Randomized biorthogonalization through a two-sided Gram-Schmidt process
Laura Grigori, Lorenzo Piccinini, Igor Simunec
https://arxiv.org/abs/2509.04386 https://

Randomized biorthogonalization through a two-sided Gram-Schmidt process
We propose and analyze a randomized two-sided Gram-Schmidt process for the biorthogonalization of two given matrices $X, Y \in\mathbb{R}^{n\times m}$. The algorithm aims to find two matrices $Q, P \in\mathbb{R}^{n\times m}$ such that ${\rm range}(X) = {\rm range}(Q)$, ${\rm range}(Y) = {\rm range}(P)$ and $(ΩQ)^T ΩP = I$, where $Ω\in\mathbb{R}^{s \times n}$ is a sketching matrix satisfying an oblivious subspace $\varepsilon$-embedding property; in other words, the biorthogonality condition o…

The Non-commutative Spaces of Higher-Order Networks of Bach's Solo Violin Compositions: Dimension, Curvature, and Distance through the Spectral Triplet
Sara Najem, Dima Mrad
https://arxiv.org/abs/2509.04311

The Non-commutative Spaces of Higher-Order Networks of Bach's Solo Violin Compositions: Dimension, Curvature, and Distance through the Spectral Triplet
Our work is concerned with simplicial complexes that describe higher-order interactions in real complex systems. This description allows to go beyond the pairwise node-to-node representation that simple networks provide and to capture a hierarchy of interactions of different orders. The prime contribution of this work is the introduction of geometric measures for these simplicial complexes. We do so by noting the non-commutativity of the algebra associated with their matrix representations and …

Excitonic description of singlet fission beyond dimer model : a matrix product state approach
Supriyo Santra, Amartya Bose, Debashree Ghosh
https://arxiv.org/abs/2509.03966 http…

Excitonic description of singlet fission beyond dimer model : a matrix product state approach
The importance of singlet fission as a fundamental process with a variety of implications in energy harvesting cannot be overstated. The challenge is in characterizing the energy states of these large singlet fission molecular aggregates that participate in the process. Large dimensionality and essential multi-configuration nature of the electronic states of interest combine to make accurate ab initio calculations prohibitively difficult. We present a spin-resolved tight-binding excitonic model…

Arbitrary matrix coefficient assignment for block matrix linear control systems by static output feedback
Vasilii Zaitsev, Inna Kim
https://arxiv.org/abs/2509.03040 https://

Arbitrary matrix coefficient assignment for block matrix linear control systems by static output feedback
This work has introduced a generalized formulation of the problem of eigenvalue spectrum assignment for block matrix systems. In this problem, it is required to construct a feedback that provides that the matrix of the closed-loop system is similar to a block companion matrix with arbitrary predetermined block matrix coefficients. Sufficient conditions for the resolvability of this problem by linear static output feedback are obtained when the coefficients of the system have a special form, nam…

Singular values of sparse random rectangular matrices: Emergence of outliers at criticality
Ioana Dumitriu, Hai-Xiao Wang, Zhichao Wang, Yizhe Zhu
https://arxiv.org/abs/2508.01456

Singular values of sparse random rectangular matrices: Emergence of outliers at criticality
Consider the random bipartite Erdős-Rényi graph $\mathbb{G}(n, m, p)$, where each edge with one vertex in $V_{1}=[n]$ and the other vertex in $V_{2} =[m]$ is connected with probability $p$, and $n=\lfloor γm\rfloor$ for a constant aspect ratio $γ\geq 1$. It is well known that the empirical spectral measure of its centered and normalized adjacency matrix converges to the Marčenko-Pastur (MP) distribution. However, largest and smallest singular values may not converge to the right and left e…

Quadratic relations for ninth variations of Schur functions and application to Schur multiple zeta functions
Wataru Takeda, Yoshinori Yamasaki
https://arxiv.org/abs/2508.03150 h…

Quadratic relations for ninth variations of Schur functions and application to Schur multiple zeta functions
Macdonald's ninth variation of Schur functions is a broad generalization of the classical Schur function and its variants, defined via the Jacobi-Trudi determinant formula. In this paper, we establish various algebraic relations for $S^{(r)}_{λ/μ}(X)$, a class of the ninth variation introduced by Nakagawa, Noumi, Shirakawa, and Yamada, by combining the Jacobi-Trudi formula with determinant formulas such as the Desnanot-Jacobi adjoint matrix theorem and the Plücker relations, which generalize…

Flavour Invariants of Multi Higgs Models
Jo\~ao C. Belas, Jo\~ao P. Silva
https://arxiv.org/abs/2510.02465 https://arxiv.org/pdf/2510.02465

Flavour Invariants of Multi Higgs Models
In this work, a systematic way of analyzing the N Higgs Doublet Models flavor sector will be developed. We introduce a complete set of mixing matrices describing the rotation between certain suitably defined bases, akin to the Cabibbo-Kobayashi-Maskawa matrix, which describes the relation between the up-quark and down-quark mass bases. We point out the crucial importance played by the charged Higgs basis. It is also introduced for the first time a complete set of weak basis transformation invar…

Complexity of Bernstein--Vazirani algorithm in the presence of noise
Muhammad Faizan, Muhammad Faryad
https://arxiv.org/abs/2508.01884 https://arxiv.org/pd…

Complexity of Bernstein--Vazirani algorithm in the presence of noise
We analytically investigated the robustness of the Bernstein--Vazirani algorithm in the presence of depolarizing noise using the density matrix formalism. We derive exact expressions for the algorithm's success probability as a function of the depolarizing error rate $\boldsymbol{p}$ and number of qubits $\boldsymbol{n}$. The analysis reveals how performance degrades with increasing system size under realistic noise conditions. Furthermore, it was seen that scaling up quantum systems without si…

Simple harmonic oscillators from non-semisimple walled Brauer algebras
Sanjaye Ramgoolam, Micha{\l} Studzi\'nski
https://arxiv.org/abs/2509.04234 https://

Simple harmonic oscillators from non-semisimple walled Brauer algebras
Walled Brauer algebras $B_N ( m , n ) $ illuminate the combinatorics of mixed tensor representations of $U(N)$, with $m$ copies of the fundamental and $n$ copies of the anti-fundamental representation. They lie at the intersection of research in representation theory, AdS/CFT and quantum information theory. They have been used to study of correlators in multi-matrix models motivated by brane-anti-brane physics in AdS/CFT. They have been applied in computing and optimising fidelities of port-bas…

Crosslisted article(s) found for cs.DS. https://arxiv.org/list/cs.DS/new
[1/1]:
- Solving Zero-Sum Games with Fewer Matrix-Vector Products
Ishani Karmarkar, Liam O'Carroll, Aaron Sidford

Two-Timescale Sum-Rate Maximization for Movable Antenna Enhanced Systems
Xintai Chen, Biqian Feng, Yongpeng Wu, Derrick Wing Kwan Ng, Robert Schober
https://arxiv.org/abs/2509.04062

Two-Timescale Sum-Rate Maximization for Movable Antenna Enhanced Systems
This paper studies a novel movable antenna (MA)-enhanced multiuser multiple-input multiple-output downlink system designed to improve wireless communication performance. We aim to maximize the average achievable sum rate through two-timescale optimization exploiting instantaneous channel state information at the receiver (I-CSIR) for receive antenna position vector (APV) design and statistical channel state information at the transmitter (S-CSIT) for transmit APV and covariance matrix design. W…

Joint Frequency-Space Sparse Reconstruction for DOA Estimation under Coherent Sources and Amplitude-Phase Errors
Yutong Chen, Cong Zhou, Changsheng You, Shuo Shi
https://arxiv.org/abs/2509.03983

Joint Frequency-Space Sparse Reconstruction for DOA Estimation under Coherent Sources and Amplitude-Phase Errors
In this letter, we propose a joint frequency-space sparse reconstruction method for direction-of-arrival (DOA) estimation, which effectively addresses the issues arising from the existence of coherent sources and array amplitude-phase errors. Specifically, by using an auxiliary source with known angles, we first construct the real steering vectors (RSVs) based on the spectral peaks of received signals in the frequency domain, which serve as a complete basis matrix for compensation for amplitude…

Network connectivity analysis via shortest paths
Silvia Noschese, Lothar Reichel
https://arxiv.org/abs/2509.03230 https://arxiv.org/pdf/2509.03230

Network connectivity analysis via shortest paths
Complex systems of interacting components often can be modeled by a simple graph $\mathcal{G}$ that consists of a set of $n$ nodes and a set of $m$ edges. Such a graph can be represented by an adjacency matrix $A\in\R^{n\times n}$, whose $(ij)$th entry is one if there is an edge pointing from node $i$ to node $j$, and is zero otherwise. The matrix $A$ and its positive integer powers reveal important properties of the graph and allow the construction of the path length matrix $L$ for the graph. …

A Randomized GMsFEM with Data-Driven Predictors for Parametric Flow Problems in Multiscale Heterogeneous Media
Wing Tat Leung, Qiuqi Li, Songwei Liu
https://arxiv.org/abs/2508.01666

A Randomized GMsFEM with Data-Driven Predictors for Parametric Flow Problems in Multiscale Heterogeneous Media
In this paper, we propose a randomized generalized multiscale finite element method (Randomized GMsFEM) for flow problems with parameterized inputs and high-contrast heterogeneous media. The method employs a data-driven predictor to construct multiscale basis functions in two stages: offline and online. In the offline stage, a snapshot space is generated via spectral decompositions, and a reduced matrix is obtained using SVD to predict eigenfunctions. In the online stage, these eigenfunctions a…

Reduce-Rank Matrix Integer-Valued Autoregressive Model
Kaiyan Cui, Tianyun Guo, Suping Wang
https://arxiv.org/abs/2509.03338 https://arxiv.org/pdf/2509.033…

Reduce-Rank Matrix Integer-Valued Autoregressive Model
Integer-valued time series are widely present in many fields, such as finance, economics, disease transmission, and traffic flow. With data dimensions surging, the traditional multivariate generalized integer autoregressive (MGINAR) model faces parameter overload, poor interpretability, and structural information loss. Matrix integer-valued autoregression (MINAR) model captures row-column cross-correlations and reduces the number of parameters to be estimated. However, further growth in dimensi…

Second-order renormalized Hamiltonian of Yukawa theory
Kamil Serafin, Carter M. Gustin, Peter J. Love
https://arxiv.org/abs/2508.02972 https://arxiv.org/pd…

Second-order renormalized Hamiltonian of Yukawa theory
Using the renormalization group procedure for effective particles (RGPEP) we calculate the effective Hamiltonians in the theory of a fermion field coupled to a scalar field via the Yukawa interaction. The theory is renormalized by the addition of counterterms. Necessary counterterms are determined by computing matrix elements of the effective Hamiltonian. All calculations are performed up to the second order in the expansion in powers of the coupling constant. Renormalized effective Hamiltonian…

A new kind of $A_{\p}$-matrix for mixed graphs
Piyush Sharma, Ravinder Kumar
https://arxiv.org/abs/2509.02326 https://arxiv.org/pdf/2509.02326

A new kind of $A_{\p}$-matrix for mixed graphs
Nikiforov\cite{nikiforov2017merging} introduced the concept of the $A_{\p}$-matrix as a convex linear combination of a graph's adjacency matrix and its diagonal matrix of vertex degrees. In this paper, we introduce a new variant of the $A_{\p}$-matrix, which is a linear combination of the Hermitian adjacency matrix of the second kind, $H^{\om}$, and the degree-diagonal matrix. This study provides new insights into the $A_{\p}$-matrix as a Hermitian matrix, leading to novel bounds in spectral gr…

Quantum Dynamics and Information Measures in PT and Anti-PT-Symmetric Systems
Amir Ahmadi, Roozbeh H. Asgari, Javad T. Firouzjaee
https://arxiv.org/abs/2508.03169 https://

Quantum Dynamics and Information Measures in PT and Anti-PT-Symmetric Systems
In this study, we investigate qubit dynamics under PT and Anti-PT-symmetric non-Hermitian Hamiltonians, focusing on phase evolution, decoherence, quantum speed limits (QSL), and Rényi entanglement entropies. Using similarity transformations and Dyson maps, we analyze the reduced density matrix evolution in bosonic environments. Anti-PT-symmetric systems show enhanced robustness against decoherence, with slower entropy growth and longer coherence times compared to PT-symmetric counterparts. QSL…

Equivalent of Multivariate Polynomial Matrix
Jinwang Liu, Tao Wu, Jiancheng Guan, Ying Kang
https://arxiv.org/abs/2509.02574 https://arxiv.org/pdf/2509.025…

Equivalent of Multivariate Polynomial Matrix
The equivalence of multidimensional systems is closely related to the reduction of multivariate polynomial matrices, with the Smith normal form of matrices playing a key role. So far, the problem of reducing multivariate polynomial matrices into Smith normal form has not been fully solved. This article investigates the Smith normal form of quasi weakly linear multivariate polynomial matrices. Breaking through previous limitations, providing sufficient and necessary conditions.

Moment-SOS hierarchies for arrow-type polynomial matrix inequalities with applications to structural optimization
Marouan Handa, Marek Tyburec, Giovanni Fantuzzi, Victor Magron, Michal Ko\v{c}vara
https://arxiv.org/abs/2509.02849

Moment-SOS hierarchies for arrow-type polynomial matrix inequalities with applications to structural optimization
The Arrow Decomposition (AD) technique, initially introduced in [Mathematical Programming 190(1-2) (2021), pp 105-134], demonstrated superior scalability over the classical chordal decomposition in the context of Linear Matrix Inequalities (LMIs) if the matrix in question satisfied suitable assumptions. The primary objective of this paper is to extend the AD method to address Polynomial Optimization Problems (POPs) involving large-scale Polynomial Matrix Inequalities (PMIs), with the solution f…

Non-Asymptotic Analysis of Data Augmentation for Precision Matrix Estimation
Lucas Morisset, Adrien Hardy, Alain Durmus
https://arxiv.org/abs/2510.02119 https://

Non-Asymptotic Analysis of Data Augmentation for Precision Matrix Estimation
This paper addresses the problem of inverse covariance (also known as precision matrix) estimation in high-dimensional settings. Specifically, we focus on two classes of estimators: linear shrinkage estimators with a target proportional to the identity matrix, and estimators derived from data augmentation (DA). Here, DA refers to the common practice of enriching a dataset with artificial samples--typically generated via a generative model or through random transformations of the original data--…

Prospects for toponium formation at the LHC in the single-lepton mode
Benjamin Fuks, Kaoru Hagiwara, Kai Ma, L\'eandre Munoz-Aillaud, Ya-Juan Zheng
https://arxiv.org/abs/2509.03596

Prospects for toponium formation at the LHC in the single-lepton mode
We investigate the formation of toponium in the single-leptonic final state at the LHC. Our study builds on our recently proposed framework that incorporates the associated non-perturbative effects into Monte Carlo simulations through the Green's function of the non-relativistic QCD Hamiltonian and the re-weighting of hard-scattering matrix elements. This allows us to perform a phenomenological analysis that demonstrates that a statistically significant excess from toponium formation could alre…

A logical implication between two conjectures on matrix permanents
L\'eo Pioge, Kamil K. Pietrasz, Benoit Seron, Leonardo Novo, Nicolas J. Cerf
https://arxiv.org/abs/2508.00111

A logical implication between two conjectures on matrix permanents
We prove a logical implication between two old conjectures stated by Bapat and Sunder about the permanent of positive semidefinite matrices. Although Drury has recently disproved both conjectures, this logical implication yields a non-trivial link between two seemingly unrelated conditions that a positive semidefinite matrix may fulfill. As a corollary, the classes of matrices that are known to obey the first conjecture are then immediately proven to obey the second one. Conversely, we uncover …

Some Maker-Breaker games on hypergraphs
Patrick Bennett, Alan Frieze, Wesley Pegden
https://arxiv.org/abs/2509.02788 https://arxiv.org/pdf/2509.02788

Some Maker-Breaker games on hypergraphs
We consider some biased Maker-Breaker games. Starting with the complete $k$-uniform hypergraph on $n$ vertices, at each turn Maker claims one edge, and then Breaker claims $b$ edges. Maker's goal is to obtain a set of edges having some increasing property. We consider the case where Maker's desired property is minimum degree $m$, or having a full-rank incidence matrix, or having a Berge Hamilton cycle or having a perfect matching or a Hamilton $\ell$-cycle.

A Limit on the Total Lepton Number in the Universe from BBN and the CMB
Valerie Domcke, Miguel Escudero, Mario Fernandez Navarro, Stefan Sandner
https://arxiv.org/abs/2510.02438

A Limit on the Total Lepton Number in the Universe from BBN and the CMB
At temperatures below the QCD phase transition, any substantial lepton number in the Universe can only be present within the neutrino sector. In this work, we systematically explore the impact of a non-vanishing lepton number on Big Bang Nucleosynthesis (BBN) and the Cosmic Microwave Background (CMB). Relying on our recently developed framework based on momentum averaged quantum kinetic equations for the neutrino density matrix, we solve the full BBN reaction network to obtain the abundances of…

Multi-instantons in 2d string theory
Sergei Alexandrov, Rishabh Kaushik
https://arxiv.org/abs/2509.03293 https://arxiv.org/pdf/2509.03293

Multi-instantons in 2d string theory
Instanton contributions in 2d string theory are known to include subtle numerical factors $ζ_n$ closely related to a contour prescription in multi-instanton string amplitudes. Both ingredients appear to be ambiguous due to a degeneracy between $(1,n)$-ZZ instantons and $n$ (1,1)-ZZ instantons in the linear dilaton background. We resolve this ambiguity using insights from the dual matrix quantum mechanics where the multipliers $ζ_n$ can be derived from an integral representation of the scatter…

Understanding and Improving the Shampoo Optimizer via Kullback-Leibler Minimization
Wu Lin, Scott C. Lowe, Felix Dangel, Runa Eschenhagen, Zikun Xu, Roger B. Grosse
https://arxiv.org/abs/2509.03378

Understanding and Improving the Shampoo Optimizer via Kullback-Leibler Minimization
As an adaptive method, Shampoo employs a structured second-moment estimation, and its effectiveness has attracted growing attention. Prior work has primarily analyzed its estimation scheme through the Frobenius norm. Motivated by the natural connection between the second moment and a covariance matrix, we propose studying Shampoo's estimation as covariance estimation through the lens of Kullback-Leibler (KL) minimization. This alternative perspective reveals a previously hidden limitation, moti…

Spacetime Wavelet Method for Linear Boundary-Value Problems in Sylvester Matrix Equation Form
Cody D. Cochran, Karel Matous
https://arxiv.org/abs/2509.02720 https://

Spacetime Wavelet Method for Linear Boundary-Value Problems in Sylvester Matrix Equation Form
We present a high-order spacetime numerical method for discretizing and solving linear initial-boundary value problems using wavelet-based techniques with user-prescribed error estimates. The spacetime wavelet discretization yields a system of algebraic equations resulting in a Sylvester matrix equation. We solve this system with a Global Generalized Minimal Residual (GMRES) method in conjunction with a wavelet-based recursive algorithm to improve convergence. We perform rigorous verification s…

Statistical Mechanics of Random Mixed State Ensembles with Fixed Energy
Harry J. D. Miller
https://arxiv.org/abs/2508.00809 https://arxiv.org/pdf/2508.0080…

Statistical Mechanics of Random Mixed State Ensembles with Fixed Energy
Mixed state ensembles such as the Bures-Hall and Hilbert-Schmidt measure are probability distributions that characterise the statistical properties of random density matrices and can be used to determine the typical features of mixed quantum states. Here we extend this framework by considering the properties of random states with fixed average energy, and the ensemble-averaged density matrix is derived under this additional physical constraint. This gives rise to a type of microcanonical ensemb…

Generalized Golub-Kahan bidiagonalization for generalized saddle point systems
Na-Na Wang, Ji-Cheng Li
https://arxiv.org/abs/2509.02936 https://arxiv.org/p…

Generalized Golub-Kahan bidiagonalization for generalized saddle point systems
We consider the iterative solution of generalized saddle point systems. When the right bottom block is zero, Arioli [SIAM J. Matrix Anal. Appl., 34 (2013), pp. 571--592] proposed a CRAIG algorithm based on generalized Golub-Kahan Bidiagonalization (GKB) for the augmented systems with the leading block being symmetric and positive definite (SPD), and then Dumitrasc et al. [SIAM J. Matrix Anal. Appl., 46 (2025), pp. 370--392] extended the GKB for the case where the symmetry condition of the leadi…

On the Characteristic polynomial of ABS Matrix and ABS-Energy of Some Graphs
Sharad Barde, Ganesh Mundhe, Mayur Kshirsagar, A. N. Bhavale
https://arxiv.org/abs/2509.02155 https:…

On the Characteristic polynomial of ABS Matrix and ABS-Energy of Some Graphs
For a graph $G$ with $n$ vertices and $m$ edges, Lin \textit{et al.} \cite{Lin} define the \textit{atom--bond sum-connectivity} ($ABS$) matrix of $G$ such that the $(i,j)^{\text{th}}$ entry is \[ \sqrt{1 - \frac{2}{d_i + d_j}} \] if vertex $v_i$ is adjacent to the vertex $v_j$, and $0$ otherwise. In this article, we determine the characteristic polynomial of the $ABS$ matrix for certain specific classes of graphs. Furthermore, we compute the $ABS$ eigenvalues and the $ABS$ energy for these clas…

Bootstrapping supersymmetric (matrix) quantum mechanics
Samuel Laliberte, Brian McPeak
https://arxiv.org/abs/2510.01356 https://arxiv.org/pdf/2510.01356

Bootstrapping supersymmetric (matrix) quantum mechanics
We apply the quantum-mechanics bootstrap to supersymmetric quantum mechanics (SUSY QM) and to its matrix relative, the Marinari-Parisi model, which is conjectured to describe the worldvolume of unstable $D0$ branes. Using positivity of moment matrices together with Heisenberg, gauge, and (zero-temperature) thermal constraints, we obtain rigorous bounds on ground-state data. In the cases where SUSY is spontaneously broken, we find bounds that apply to the lowest-energy normalizable eigenstate. …

DeMuon: A Decentralized Muon for Matrix Optimization over Graphs
Chuan He, Shuyi Ren, Jingwei Mao, Erik G. Larsson
https://arxiv.org/abs/2510.01377 https://

DeMuon: A Decentralized Muon for Matrix Optimization over Graphs
In this paper, we propose DeMuon, a method for decentralized matrix optimization over a given communication topology. DeMuon incorporates matrix orthogonalization via Newton-Schulz iterations-a technique inherited from its centralized predecessor, Muon-and employs gradient tracking to mitigate heterogeneity among local functions. Under heavy-tailed noise conditions and additional mild assumptions, we establish the iteration complexity of DeMuon for reaching an approximate stochastic stationary …

Zeroing Diagonals, Conjugate Hollowization, and Characterizing Nondefinite Operators
David R. Nicholus
https://arxiv.org/abs/2508.00096 https://arxiv.org/p…

Zeroing Diagonals, Conjugate Hollowization, and Characterizing Nondefinite Operators
We prove the conjecture by Damm and Fassbender that, for any pair $L,M$ of real traceless matrices, there exists an orthogonal $V$ such that $V^{-1} L \, V$ is hollow and $V M V^{-1}$ is almost hollow, where a matrix is hollow if and only if its main diagonal consists only of 0s, and a traceless matrix is almost hollow if and only if all its main diagonal elements are 0 except, at most, the last two. The claim is a corollary to our considerably more general theorem, as well as another corolla…

Degree-similar graphs and cospectral graphs
Yi-Zheng Fan, Ruo-Jie Xing, Yi-Liu Zhang, Wei Wang
https://arxiv.org/abs/2509.01520 https://arxiv.org/pdf/2509.…

Degree-similar graphs and cospectral graphs
Let $G$ be a graph with adjacency matrix $A(G)$ and degree matrix $D(G)$, and let $L_μ(G):=A(G)-μD(G)$. Two graphs $G_1$ and $G_2$ are called \emph{degree-similar} if there exists an invertible matrix $M$ such that $M^{-1} A(G_1) M =A(G_2)$ and $M^{-1} D(G_1) M =D(G_2)$. In this paper, we address three problems concerning degree-similar graphs proposed by Godsil and Sun. First, we present a new characterization of degree-similar graphs using degree partition, from which we derive methods and …

Entanglement Complexity in Many-body Systems from Positivity Scaling Laws
Anna O. Schouten, David A. Mazziotti
https://arxiv.org/abs/2509.02944 https://arx…

Entanglement Complexity in Many-body Systems from Positivity Scaling Laws
Area laws describe how entanglement entropy scales and thus provide important necessary conditions for efficient quantum many-body simulation, but they do not, by themselves, yield a direct measure of computational complexity. Here we introduce a complementary framework based on $p$-particle positivity conditions from reduced density matrix (RDM) theory. These conditions form a hierarchy of $N$-representability constraints for an RDM to correspond to a valid $N$-particle quantum system, becomin…

On Error Bounds for Rank-Constrained Affine Matrix Sets
Ruoning Chen, Defeng Sun, Liping Zhang
https://arxiv.org/abs/2510.01709 https://arxiv.org/pdf/2510.…

On Error Bounds for Rank-Constrained Affine Matrix Sets
Rank-constrained matrix problems appear frequently across science and engineering. The convergence analysis of iterative algorithms developed for these problems often hinges on local error bounds, which correlate the distance to the feasible set with a measure of how much the constraints are violated. Foundational results in semi-algebraic geometry guarantee that such bounds exist, yet the associated exponents are generally not explicitly determined. This paper establishes a local Hölderian er…

Non-SOS Positivstellens\"atze for semi-algebraic sets defined by polynomial matrix inequalities
Feng Guo
https://arxiv.org/abs/2509.01159 https://arxi…

Non-SOS Positivstellensätze for semi-algebraic sets defined by polynomial matrix inequalities
This paper establishes new Positivstellensätze for polynomials that are positive on sets defined by polynomial matrix inequalities (PMIs). We extend the classical Handelman and Krivine-Stengle theorems from the scalar inequality setting to the matrix context, deriving explicit certificate forms that do not rely on sums-of-squares (SOS). Specifically, we show that under certain conditions, any polynomial positive on a PMI-defined semialgebraic set admits a representation using Kronecker powers …

Fast and Accurate SVD-Type Updating in Streaming Data
Johannes J. Brust, Michael A. Saunders
https://arxiv.org/abs/2509.02840 https://arxiv.org/pdf/2509.02…

Fast and Accurate SVD-Type Updating in Streaming Data
For a datastream, the change over a short interval is often of low rank. For high throughput information arranged in matrix format, recomputing an optimal SVD approximation after each step is typically prohibitive. Instead, incremental and truncated updating strategies are used, which may not scale for large truncation ranks. Therefore, we propose a set of efficient new algorithms that update a bidiagonal factorization, and which are similarly accurate as the SVD methods. In particular, we deve…

Picking NPA constraints from a randomly sampled quantum moment matrix
G. Viola, A. Chaturvedi
https://arxiv.org/abs/2509.02309 https://arxiv.org/pdf/2509.0…

Picking NPA constraints from a randomly sampled quantum moment matrix
We describe a simple and flexible method for implementing semi-definite programming relaxations for bounding the set of quantum correlations. The method relies on obtaining equality constraints from randomly sampled moment matrices and hence allows the user to easily access the set of quantum behavior in diverse operational scenarios.

Efficient QR-based Column Subset Selection through Randomized Sparse Embeddings
Israa Fakih, Laura Grigori
https://arxiv.org/abs/2509.03198 https://arxiv.o…

Efficient QR-based Column Subset Selection through Randomized Sparse Embeddings
In this paper, we introduce an efficient algorithm for column subset selection that combines the column-pivoted QR factorization with sparse subspace embeddings. The proposed method, SE-QRSC, is particularly effective for wide matrices with significantly more columns than rows. Starting from a matrix $A$, the algorithm selects $k$ columns from the sketched matrix $B = A Ω^T$, where $Ω$ is a sparse subspace embedding of $\mathrm{range}(A^T)$. The sparsity structure of $Ω$ is then exploited to…

Quantum Fisher information matrices from R\'enyi relative entropies
Mark M. Wilde
https://arxiv.org/abs/2510.02218 https://arxiv.org/pdf/2510.02218

Quantum Fisher information matrices from Rényi relative entropies
Quantum generalizations of the Fisher information are important in quantum information science, with applications in high energy and condensed matter physics and in quantum estimation theory, machine learning, and optimization. One can derive a quantum generalization of the Fisher information matrix in a natural way as the Hessian matrix arising in a Taylor expansion of a smooth divergence. Such an approach is appealing for quantum information theorists, given the ubiquity of divergences in qua…