Tootfinder

Characterizing $A_\sigma$-minimizer graphs: given order and independence number
Shuchao Li, Jiaqi Zhang
https://arxiv.org/abs/2508.09770 https://arxiv.org/…

Characterizing $A_σ$-minimizer graphs: given order and independence number
For a given graph \( G \), let \( A(G) \), \( Q(G) \), and \( D(G) \) denote the adjacency matrix, signless Laplacian matrix, and diagonal degree matrix of \( G \), respectively. The \( A_σ(G) \) matrix, proposed by Nikiforov, is defined as \( A_σ(G)=σD(G)+(1 - σ)A(G) \), where \( σ\in[0,1] \). This matrix captures the gradual transition from \( A(G) \) to \( Q(G) \). Let \( \mathcal{G}_{n,α} \) denote the family of all connected graphs with \( n \) vertices and independence number \( α\…

Relationship between a $\Phi^4$ matrix model and harmonic oscillator systems
Harald Grosse, Naoyuki Kanomata, Akifumi Sako, Raimar Wulkenhaar
https://arxiv.org/abs/2507.09454

Relationship between a $Φ^4$ matrix model and harmonic oscillator systems
A Hermitian $Φ^4$ matrix model with a Kontsevich-type kinetic term is studied. It was recently discovered that the partition function of this matrix model satisfies the Schrödinger equation of the $N$-body harmonic oscillator, and that eigenstates of the Virasoro operators can be derived from this partition function. We extend these results and obtain an explicit formula for such eigenstates in terms of the free energy. Furthermore, the Schrödinger equation for the $N$-body harmonic oscillat…

L-CLIPScore: a Lightweight Embedding-based Captioning Metric for Evaluating and Training
Li Li, Yingzhe Peng, Xu Yang, Ruoxi Cheng, Haiyang Xu, Ming Yan, Fei Huang
https://arxiv.org/abs/2507.08710

L-CLIPScore: a Lightweight Embedding-based Captioning Metric for Evaluating and Training
We propose a novel embedding-based captioning metric termed as L-CLIPScore that can be used for efficiently evaluating caption quality and training captioning model. L-CLIPScore is calculated from a lightweight CLIP (L-CLIP), which is a dual-encoder architecture compressed and distilled from CLIP. To compress, we apply two powerful techniques which are weight multiplexing and matrix decomposition for reducing the parameters of encoders and word embedding matrix, respectively. To distill, we des…

Matrix-Free Evaluation Strategies for Continuous and Discontinuous Galerkin Discretizations on Unstructured Tetrahedral Grids
Dominik Still, Niklas Fehn, Wolfgang A. Wall, Martin Kronbichler
https://arxiv.org/abs/2509.10226

Matrix-Free Evaluation Strategies for Continuous and Discontinuous Galerkin Discretizations on Unstructured Tetrahedral Grids
This study presents novel strategies for improving the node-level performance of matrix-free evaluation of continuous and discontinuous Galerkin spatial discretizations on unstructured tetrahedral grids. In our approach the underlying integrals of a generic finite-element operator are computed cell-by-cell through numerical quadrature using tabulated dense local matrices of shape functions, achieving high throughput for low to moderate-order polynomial degrees. By employing dense matrix-matrix …

On Conservative Matrix Fields: Continuous Asymptotics and Arithmetic
Shachar Weinbaum, Elyasheev Leibtag, Rotem Kalisch, Michael Shalyt, Ido Kaminer
https://arxiv.org/abs/2507.08138

On Conservative Matrix Fields: Continuous Asymptotics and Arithmetic
Ratios of D-finite sequences and their limits -- known as Apéry limits -- have driven much of the work on irrationality proofs since Apéry's 1979 breakthrough proof of the irrationality of $ζ(3)$. We extend ratios of D-finite sequences to a high-dimensional setting by introducing the Conservative Matrix Field (CMF). We demonstrate how classical Apéry limits are included by this object as special cases. A useful construction of CMFs is provided, drawing a connection to gauge transformations …

Spatio-Temporal Autoregressions for High Dimensional Matrix-Valued Time Series
Baojun Dou, Jing He, Sudhir Tiwari, Qiwei Yao
https://arxiv.org/abs/2508.10291 https://

Spatio-Temporal Autoregressions for High Dimensional Matrix-Valued Time Series
Motivated by predicting intraday trading volume curves, we consider two spatio-temporal autoregressive models for matrix time series, in which each column may represent daily trading volume curve of one asset, and each row captures synchronized 5-minute volume intervals across multiple assets. While traditional matrix time series focus mainly on temporal evolution, our approach incorporates both spatial and temporal dynamics, enabling simultaneous analysis of interactions across multiple dimens…

Neutrino oscillations and PMNS matrix in gauge-Higgs unification
Yutaka Hosotani
https://arxiv.org/abs/2507.08321 https://arxiv.org/p…

Neutrino oscillations and PMNS matrix in gauge-Higgs unification
In the $SO(5) \times U(1) \times SU(3)$ gauge-Higgs unification in the Randall-Sundrum (RS) warped space neutrino oscillations and the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix in the $W$ couplings originate from Majorana mass terms on the ultraviolet brane in the RS space. Tiny neutrino masses are generated by an inverse seesaw mechanism. The PMNS matrix in the normal ordering with $δ_{CP}=π$ naturally arises consistently with the NuFit-6.0 analysis of neutrino oscillation data.

Output-Sparse Matrix Multiplication Using Compressed Sensing
Huck Bennett, Karthik Gajulapalli, Alexander Golovnev, Evelyn Warton
https://arxiv.org/abs/2508.10250 https://

Output-Sparse Matrix Multiplication Using Compressed Sensing
We give two algorithms for output-sparse matrix multiplication (OSMM), the problem of multiplying two $n \times n$ matrices $A, B$ when their product $AB$ is promised to have at most $O(n^δ)$ many non-zero entries for a given value $δ\in [0, 2]$. We then show how to speed up these algorithms in the fully sparse setting, where the input matrices $A, B$ are themselves sparse. All of our algorithms work over arbitrary rings. Our first, deterministic algorithm for OSMM works via a two-pass redu…

Symbolic Feedforward Networks for Probabilistic Finite Automata: Exact Simulation and Learnability
Sahil Rajesh Dhayalkar
https://arxiv.org/abs/2509.10034 https://

Symbolic Feedforward Networks for Probabilistic Finite Automata: Exact Simulation and Learnability
We present a formal and constructive theory showing that probabilistic finite automata (PFAs) can be exactly simulated using symbolic feedforward neural networks. Our architecture represents state distributions as vectors and transitions as stochastic matrices, enabling probabilistic state propagation via matrix-vector products. This yields a parallel, interpretable, and differentiable simulation of PFA dynamics using soft updates-without recurrence. We formally characterize probabilistic subse…

Convergence and asymptotic freeness of missing data matrices
Kartick Adhikari, Dev Ahir
https://arxiv.org/abs/2508.10610 https://arxiv.org/pdf/2508.10610…

Convergence and asymptotic freeness of missing data matrices
We consider a random matrix of the form $D_n \odot X_n$ (known as a variance profile matrix), where $\odot$ denotes the Hadamard product of the two matrices, $D_n$ is a deterministic matrix, and $X_n$ is a random matrix. We call $D_n\odot X_n$ as a missing data matrix of $X_n$ when the entries of $D_n$ are either $0$ or $1$. This framework is commonly used in various applied fields, such as biology, neuroscience, and network data analysis. We study the convergence and asymptotic freeness of mis…

Complexity of mixed Schatten norms of quantum maps
Jan Kochanowski, Omar Fawzi, Cambyse Rouz\'e
https://arxiv.org/abs/2507.08358 https://

Complexity of mixed Schatten norms of quantum maps
We study the complexity of computing the mixed Schatten $\|Φ\|_{q\to p}$ norms of linear maps $Φ$ between matrix spaces. When $Φ$ is completely positive, we show that $\| Φ\|_{q \to p}$ can be computed efficiently when $q \geq p$. The regime $q \geq p$ is known as the non-hypercontractive regime and is also known to be easy for the mixed vector norms $\ell_{q} \to \ell_{p}$ [Boyd, 1974]. However, even for entanglement-breaking completely-positive trace-preserving maps $�…

On the Consistency and Performance of the Iterative Bayesian Update
Ehab ElSalamouny, Catuscia Palamidessi
https://arxiv.org/abs/2508.09980 https://arxiv.o…

On the Consistency and Performance of the Iterative Bayesian Update
For many social, scientific, and commercial purposes, it is often important to estimate the distribution of the users' data regarding a sensitive attribute, e.g., their ages, locations, etc. To allow this estimation while protecting the users' privacy, every user applies a local privacy protection mechanism that releases a noisy (sanitized) version of their original datum to the data collector; then the original distribution is estimated using one of the known methods, such as the matrix invers…

Hybrid Data-Driven Predictive Control for Robust and Reactive Exoskeleton Locomotion Synthesis
Kejun Li, Jeeseop Kim, Maxime Brunet, Marine P\'etriaux, Yisong Yue, Aaron D. Ames
https://arxiv.org/abs/2508.10269

Hybrid Data-Driven Predictive Control for Robust and Reactive Exoskeleton Locomotion Synthesis
Robust bipedal locomotion in exoskeletons requires the ability to dynamically react to changes in the environment in real time. This paper introduces the hybrid data-driven predictive control (HDDPC) framework, an extension of the data-enabled predictive control, that addresses these challenges by simultaneously planning foot contact schedules and continuous domain trajectories. The proposed framework utilizes a Hankel matrix-based representation to model system dynamics, incorporating step-to-…

Nonderogatory matrices as sums of $p$-potent and nilpotent matrices
Andrada Pojar
https://arxiv.org/abs/2508.10079 https://arxiv.org/pdf/2508.10079

Nonderogatory matrices as sums of $p$-potent and nilpotent matrices
We prove that every nonderogatory matrix $A$ over a field of positive odd characteristic $p,$ that is sum of a $p$-potent matrix and a nilpotent matrix, has a decomposition $A=E+V,$ such that $E^p=E,$ and $V^3=0.$

Indices of holomorphic foliations and the bifurcation conjecture
Maycol Falla Luza, Arturo Fern\'andez-P\'erez, David Mar\'in, Rudy Rosas
https://arxiv.org/abs/2508.10708

Indices of holomorphic foliations and the bifurcation conjecture
In this paper, we revisit local invariants (Gómez-Mont-Seade-Verjovsky, variation, Camacho-Sad and Baum-Bott indices) associated with singular holomorphic foliations on $(\mathbb{C}^2 , 0)$ and we provide semi-global formulas for them in terms of the reduction of singularities of the foliation. A key technical ingredient is the Cholesky-type factorization of the intersection matrix of the exceptional divisor, which allows for an explicit control of multiplicities and indices along the resoluti…

New Lower Bounds for the Minimum Singular Value in Matrix Selection
Zhiqiang Xu
https://arxiv.org/abs/2508.10452 https://arxiv.org/pdf/2508.10452

New Lower Bounds for the Minimum Singular Value in Matrix Selection
The objective of the matrix selection problem is to select a submatrix $A_{S}\in \mathbb{R}^{n\times k}$ from $A\in \mathbb{R}^{n\times m}$ such that its minimum singular value is maximized. In this paper, we employ the interlacing polynomial method to investigate this problem. This approach allows us to identify a submatrix $A_{S_0}\in \mathbb{R}^{n\times k}$ and establish a lower bound for its minimum singular value. Specifically, unlike common interlacing polynomial approaches that estimate …

Attention's forward pass and Frank-Wolfe
Albert Alcalde, Borjan Geshkovski, Dom\`enec Ruiz-Balet
https://arxiv.org/abs/2508.09628 https://arxiv.org/pdf…

Attention's forward pass and Frank-Wolfe
We study the hardmax limit of self-attention dynamics for token embeddings obtained in the zero-temperature ($β\to+\infty$) regime, and relate it to the finite-$β$ setting. In this limit, the update rule can be viewed as a Frank-Wolfe step for a quadratic objective over the convex hull of the current token embeddings. When the key-query matrix is negative semidefinite, the method linearly contracts all tokens to a single cluster at the origin. When it is positive semidefinite, extending the h…

Representation Theory of $UT_3(\mathbb{F}_3)$ and its Applications to Equivariant Decomposition in Neural Architectures
Bich Van Nguyen, Nguyen Cao Manh Thang
https://arxiv.org/abs/2507.08397

Representation Theory of $UT_3(\mathbb{F}_3)$ and its Applications to Equivariant Decomposition in Neural Architectures
In this paper we prove theorems characterizing the decomposition of equivariant feature spaces, filters and a structural preservation theorem for invariant subspace chains in group equivariant convolutional neural networks(G-CNN). Furthermore, we give explicit matrix forms for irreducible representations of $UT_3(\F_3)$-the unitriangular matrix groups over the field with three elements. These results provide a foundation for designing new G-CNN architectures via representations of $UT_3(\F_3)$ …

Counting Short Trajectories in Elementary Cellular Automata using the Transfer Matrix Method
C\'edric Koller, Barbora Hudcov\'a
https://arxiv.org/abs/2508.09768 https://…

Counting Short Trajectories in Elementary Cellular Automata using the Transfer Matrix Method
Elementary Cellular Automata (ECAs) exhibit diverse behaviours often categorized by Wolfram's qualitative classification. To provide a quantitative basis for understanding these behaviours, we investigate the global dynamics of such automata and we describe a method that allows us to compute the number of all configurations leading to short attractors in a limited number of time steps. This computation yields exact results in the thermodynamic limit (as the CA grid size grows to infinity), and …

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

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

Interfacially ordered phase states enable high-strength ductile eutectic Al alloys
Hemant Kumar, Praveen Kumar, Dierk Raabe, Baptiste Gault, Surendra Kumar Makineni
https://arxiv.org/abs/2507.08327

Interfacially ordered phase states enable high-strength ductile eutectic Al alloys
Lightweight, high-strength structural materials are component enablers in transportation and aerospace, improving carbon footprint and fuel efficiency. Aluminium (Al)-based eutectics have property combinations that qualify them for such applications. However, they are prone to catastrophic failure because of insufficient load transfer across the interfaces between the brittle eutectic phase and the ductile matrix. Here we present a general solution to this problem by engineering these interface…

OISMA: On-the-fly In-memory Stochastic Multiplication Architecture for Matrix-Multiplication Workloads
Shady Agwa, Yihan Pan, Georgios Papandroulidakis, Themis Prodromakis
https://arxiv.org/abs/2508.08822

OISMA: On-the-fly In-memory Stochastic Multiplication Architecture for Matrix-Multiplication Workloads
Artificial Intelligence models are currently driven by a significant up-scaling of their complexity, with massive matrix multiplication workloads representing the major computational bottleneck. In-memory computing architectures are proposed to avoid the Von Neumann bottleneck. However, both digital/binary-based and analogue in-memory computing architectures suffer from various limitations, which significantly degrade the performance and energy efficiency gains. This work proposes OISMA, a nove…

Gaussian Copula-Based Outage Performance Analysis of Fluid Antenna Systems: Channel Coefficient- or Envelope-Level Correlation Matrix?
Rui Xu, Yinghui Ye, Xiaoli Chu, Guangyue Lu, Farshad Rostami Ghadi, Kai-Kit Wong
https://arxiv.org/abs/2509.09411

Gaussian Copula-Based Outage Performance Analysis of Fluid Antenna Systems: Channel Coefficient- or Envelope-Level Correlation Matrix?
Gaussian copula has been employed to evaluate the outage performance of Fluid Antenna Systems (FAS), with the covariance matrix reflecting the dependence among multivariate normal random variables (RVs). While prior studies approximate this matrix using the channel coefficient correlation matrix from Jake's model, this work instead employs the channel envelope correlation matrix, motivated by the fact that the multivariate normal RVs are generated by transforming correlated channel envelopes. T…

Low-Frequency Scattering of TE and TM Waves by an Inhomogeneous Medium with Planar Symmetry
Farhang Loran, Ali Mostafazadeh
https://arxiv.org/abs/2509.10205 https://

Low-Frequency Scattering of TE and TM Waves by an Inhomogeneous Medium with Planar Symmetry
Stationary scattering of TE and TM waves propagating in an isotropic medium with planar symmetry is described by Bergmann's equation in one dimension. This is a generalization of Helmholtz equation which allows for developing transfer matrix methods to deal with the corresponding scattering problems. We use a dynamical formulation of stationary scattering to study the low-frequency scattering of these waves when the inhomogeneities of the medium causing the scattering are confined to a planar s…

Integral Cayley graphs over a nonabelian group of order $8n$
Bei Ye, Xiaogang Liu
https://arxiv.org/abs/2508.10653 https://arxiv.org/pdf/2508.10653

Integral Cayley graphs over a nonabelian group of order $8n$
A graph is called an integral graph when all eigenvalues of its adjacency matrix are integers. We study which Cayley graphs over a nonabelian group $$ T_{8n}=\left\langle a,b\mid a^{2n}=b^8=e,a^n=b^4,b^{-1}ab=a^{-1} \right \rangle $$ are integral graphs. Based on the group representation theory, we first give the irreducible matrix representations and characters of $T_{8n}$. Then we give necessary and sufficient conditions for which Cayley graphs over $T_{8n}$ are integral graphs. As applicatio…

Diagonal Isometric Form for Tensor Product States in Two Dimensions
Benjamin Sappler, Masataka Kawano, Michael P Zaletel, Frank Pollmann
https://arxiv.org/abs/2507.08080

Diagonal Isometric Form for Tensor Product States in Two Dimensions
Isometric tensor product states (isoTPS) generalize the isometric form of the one-dimensional matrix product states (MPS) to tensor networks in two and higher dimensions. Here, we introduce an alternative isometric form for isoTPS by incorporating auxiliary tensors to represent the orthogonality hypersurface. We implement the time evolving block decimation (TEBD) algorithm on this new isometric form and benchmark the method by computing ground states and the real time evolution of the transvers…

Exploiting repeated matrix block structures for more efficient CFD on modern supercomputers
Josep Plana-Riu, F. Xavier Trias, \`Adel Alsalti-Baldellou, Xavier \'Alvarez-Farr\'e, Guillem Colomer, Assensi Oliva
https://arxiv.org/abs/2508.06710

Exploiting repeated matrix block structures for more efficient CFD on modern supercomputers
Computational Fluid Dynamics (CFD) simulations are often constrained by the memory-bound nature of sparse matrix-vector operations, which eventually limits performance on modern high-performance computing (HPC) systems. This work introduces a novel approach to increase arithmetic intensity in CFD by leveraging repeated matrix block structures. The method transforms the conventional sparse matrix-vector product (SpMV) into a sparse matrix-matrix product (SpMM), enabling simultaneous processing o…

2-loop scattering on superstring and supermembrane in flat space
M. Beccaria, R. Roiban, A. A. Tseytlin
https://arxiv.org/abs/2507.09528 https://

2-loop scattering on superstring and supermembrane in flat space
We consider the S-matrix of transverse scalar excitations on an infinite $D=10$ GS superstring and $D=11$ supermembrane in flat target space. We compute the 4-particle scattering amplitude in the 2-loop approximation and demonstrate that, like in the Nambu string case, the $D=10$ GS string S-matrix does not contain non-trivial 2d UV divergences (UV pole not accompanied by terms with logarithms of momenta is an artifact of dimensional regularization). This is consistent with underlying integrabi…

Extraction of neutron-capture cross sections on $^{92}$Zr using the charge-exchange Oslo method
N. D. Pathirana, R. G. T. Zegers, B. Gao, A. Spyrou, A. C. Larsen, H. Berg, D. Bazin, H. L. Crawford, A. Gade, P. Gastis, T. Ginter, C. J. Guess, M. Guttormsen, S. Noji, B. Longfellow, J. Pereira, L. A. Riley, D. Weisshaar, J. C. Zamora
https://…

Extraction of neutron-capture cross sections on $^{92}$Zr using the charge-exchange Oslo method
The $^{93}$Nb($t$,$^{3}$He) reaction at 115 MeV/u was studied to demonstrate that nuclear level densities and $γ$-ray strength functions can be extracted from charge-exchange reactions at intermediate energies using the Oslo technique. The matrix of excitation energy in $^{93}$Zr, reconstructed from the ($t$,$^{3}$He) reaction, versus the energy of $γ$ rays emitted by the excited $^{93}$Zr nuclei, was obtained in an experiment with the S800 Spectrograph operated in coincidence with the GRETIN…

A 240 Elements Matrix Probe with Aberration Mask for 4D Carotid Artery Computational Ultrasound Imaging
Yuyang Hu, Michael Brown, Didem Dogan, Mah\'e Bulot, Maxime Cheppe, Guillaume Ferin, Geert Leus, Antonius F. W. van der Steen, Pieter Kruizinga, Johannes G. Bosch
https://arxiv.org/abs/2508.10527…

A 240 Elements Matrix Probe with Aberration Mask for 4D Carotid Artery Computational Ultrasound Imaging
Three-dimensional (3D) ultrasound provides enhanced visualization of the carotid artery (CA) anatomy and volumetric flow, offering improved accuracy for cardiovascular diagnosis and monitoring. However, fully populated matrix transducers with large apertures are complex and costly to implement. Computational ultrasound imaging (cUSi) offers a promising alternative by enabling simplified hardware design through model-based reconstruction and spatial field encoding. In this work, we present a 3D …

Edge Reconstruction in a Quantum Spin Hall Insulator
Rahul Soni, Matthias Thamm, Gonzalo Alvarez, Bernd Rosenow, Adrian Del Maestro
https://arxiv.org/abs/2508.10726 https://

Edge Reconstruction in a Quantum Spin Hall Insulator
We study interaction-driven edge reconstruction in a quantum spin Hall insulator described by the Bernevig-Hughes-Zhang model with Kanamori-Hubbard interactions using the real-space density matrix renormalization group method in both the grand-canonical and canonical ensembles. For a two-dimensional cylinder with a smooth edge, we identify discrete particle-number transitions that lead to a spin-polarized edge state stabilized by an emergent ferromagnetic exchange interaction. The reconstructio…

Quantum Algorithms for Projection-Free Sparse Convex Optimization
Jianhao He, John C. S. Lui
https://arxiv.org/abs/2507.08543 https://

Quantum Algorithms for Projection-Free Sparse Convex Optimization
This paper considers the projection-free sparse convex optimization problem for the vector domain and the matrix domain, which covers a large number of important applications in machine learning and data science. For the vector domain $\mathcal{D} \subset \mathbb{R}^d$, we propose two quantum algorithms for sparse constraints that finds a $\varepsilon$-optimal solution with the query complexity of $O(\sqrt{d}/\varepsilon)$ and $O(1/\varepsilon)$ by using the function value oracle, reducing a fa…

Ehrenfest Dynamics with Spontaneous Localization
Anderson A. Tomaz, Rafael S. Mattos, Saikat Mukherjee, Mario Barbatti
https://arxiv.org/abs/2508.09526 https://

Ehrenfest Dynamics with Spontaneous Localization
We propose Ehrenfest Dynamics with Spontaneous Localization (SLED), a decoherence-corrected extension of Ehrenfest dynamics based on the Gisin-Percival quantum-state diffusion (QSD) equation. In SLED, the electronic wavefunction evolves stochastically in the adiabatic energy basis, producing trajectory-level localization. The trajectory ensemble reproduces a Lindblad-type propagation of the reduced electronic density matrix. This approach ensures linearity, trace preservation, and complete posi…

From Revolution to Ruin: An Empirical Analysis Yemen's State Collapse
Riste Ichev, Rok Spruk
https://arxiv.org/abs/2507.08512 https://

From Revolution to Ruin: An Empirical Analysis Yemen's State Collapse
We assess the broad repercussions of Yemen's 2011 revolution and subsequent civil war on its macroeconomic trajectories, human development, and quality of governance by constructing counterfactual benchmarks using a balanced panel of 37 developing countries over 1990-2022. Drawing on matrix-completion estimators with alternative shrinkage regimes and a LASSO-augmented synthetic-control method, we generate Yemen's hypothetical no-conflict paths for key macroeconomic aggregates, demographic and h…

Algebraic approach to a $d$-dimensional matrix Hamiltonian with so($d 1)$ symmetry
Christiane Quesne
https://arxiv.org/abs/2508.07949 https://arxiv.org/pdf…

Algebraic approach to a $d$-dimensional matrix Hamiltonian with so($d+1)$ symmetry
A novel spin-extended so($d+1$,1) algebra is introduced and shown to provide an interesting framework for discussing the properties of a $d$-dimensional matrix Hamiltonian with spin 1/2 and so($d+1$) symmetry. With some $d+2$ additional operators, spanning a basis of an so($d+1$,1) irreducible representation, the so($d+1$,1) generators provide a very easy way for deriving the integrals of motion of the matrix Hamiltonian in Sturm representation. Such integrals of motion are then transformed int…

Mathematical and numerical study of symmetry and positivity of the tensor-valued spring constant defined from P1-FEM for two- and three-dimensional linear elasticity
Oussama Ounissi, Masato Kimura, Hirofumi Notsu
https://arxiv.org/abs/2509.10335

Mathematical and numerical study of symmetry and positivity of the tensor-valued spring constant defined from P1-FEM for two- and three-dimensional linear elasticity
In this study, we consider a spring-block system that approximates a $d$-dimensional linear elastic body, where $d=2$ or $d=3$. We derive a $d\times d$ matrix as the spring constant using the P1 finite element method with a triangular mesh for the linear elasticity equations. We mathematically analyze the symmetry and positive-definiteness of the spring constant. Even if we assume full symmetry of the elasticity tensor, the symmetry of the matrix obtained as the spring constant is not trivial. …

The pure $Y=X^{d}$ truncated moment problem
Lawrence Fialkow, Alja\v{z} Zalar
https://arxiv.org/abs/2508.10375 https://arxiv.org/pdf/2508.10375

The pure $Y=X^{d}$ truncated moment problem
Let $β\equivβ^{(2n)}$ be a real bivariate sequence of degree $2n$. We study the existence of representing measures for $β$ supported in the planar curve $y=x^{d}$ in the case where the associated moment matrix $M_{n}(β)$ is $(y-x^{d})$-pure. In Section 2 we provide a general necessary and sufficient condition for representing measures in terms of positive semidefiniteness and recursive generation of the associated core matrix. In particular, if the core matrix is positive definite, then the…

Matrix-valued bispectral discrete orthogonal polynomials
I. Bono Parisi
https://arxiv.org/abs/2509.08909 https://arxiv.org/pdf/2509.08909

Matrix-valued bispectral discrete orthogonal polynomials
We develop a unified construction of matrix-valued orthogonal polynomials associated with discrete weights, yielding bispectral sequences as eigenfunctions of second-order difference operators. This general framework extends the discrete families in the classical Askey scheme to the matrix setting by producing explicit matrix analogues of the Krawtchouk, Hahn, Meixner, and Charlier polynomials. In particular, we provide the first matrix extensions of the Krawtchouk and Hahn polynomials, filling…

Cohen-Lenstra flag universality for random matrix products
Yifeng Huang, Hoi H. Nguyen, Roger Van Peski
https://arxiv.org/abs/2508.10127 https://arxiv.org/…

Cohen-Lenstra flag universality for random matrix products
For $n \times n$ random integer matrices $M_1,\ldots,M_k$, the cokernels of the partial products $\mathrm{cok}(M_1 \cdots M_i), 1 \leq i \leq k$ naturally define a random flag of abelian $p$-groups. We prove that as $n \to \infty$, this flag converges universally, for any nondegenerate entry distribution, to the Cohen-Lenstra type measure which weights each flag inversely proportional to the size of its automorphism group. As a corollary, we prove universality of certain formulas for the limiti…

Low-rank Momentum Factorization for Memory Efficient Training
Pouria Mahdavinia, Mehrdad Mahdavi
https://arxiv.org/abs/2507.08091 https://arxiv.org/pdf/2507.08091 https://arxiv.org/html/2507.08091
arXiv:2507.08091v1 Announce Type: new
Abstract: Fine-tuning large foundation models presents significant memory challenges due to stateful optimizers like AdamW, often requiring several times more GPU memory than inference. While memory-efficient methods like parameter-efficient fine-tuning (e.g., LoRA) and optimizer state compression exist, recent approaches like GaLore bridge these by using low-rank gradient projections and subspace moment accumulation. However, such methods may struggle with fixed subspaces or computationally costly offline resampling (e.g., requiring full-matrix SVDs). We propose Momentum Factorized SGD (MoFaSGD), which maintains a dynamically updated low-rank SVD representation of the first-order momentum, closely approximating its full-rank counterpart throughout training. This factorization enables a memory-efficient fine-tuning method that adaptively updates the optimization subspace at each iteration. Crucially, MoFaSGD leverages the computed low-rank momentum factors to perform efficient spectrally normalized updates, offering an alternative to subspace moment accumulation. We establish theoretical convergence guarantees for MoFaSGD, proving it achieves an optimal rate for non-convex stochastic optimization under standard assumptions. Empirically, we demonstrate MoFaSGD's effectiveness on large language model alignment benchmarks, achieving a competitive trade-off between memory reduction (comparable to LoRA) and performance compared to state-of-the-art low-rank optimization methods. Our implementation is available at https://github.com/pmahdavi/MoFaSGD.
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Boolean Rank via Monomial Ideals
Juliann Geraci, Alexander B. Kunin, Alexandra Seceleanu
https://arxiv.org/abs/2509.09570 https://arxiv.org/pdf/2509.09570

Boolean Rank via Monomial Ideals
Boolean matrix factorization (BMF) has many applications in data mining, bioinformatics, and network analysis. The goal of BMF is to decompose a given binary matrix as the Boolean product of two smaller binary matrices, revealing underlying structure in the data. When interpreting a binary matrix as the adjacency matrix of a bipartite graph, BMF is equivalent to the NP-hard biclique cover problem. By approaching this problem through the lens of commutative algebra, we utilize algebraic struct…

A New Method of Deriving Doppler Velocities for Solar Orbiter SPICE
J. E. Plowman, D. M. Hassler, M. E. Molnar, A. K. Shrivastav, T. Varesano, F. Auch\`ere, A. Fludra, T. A. Kucera, T. J. Wang, Y. Zhu
https://arxiv.org/abs/2508.09121

A New Method of Deriving Doppler Velocities for Solar Orbiter SPICE
This paper presents a follow-up to previous work on correcting PSF-induced Doppler artifacts in observations by the SPICE spectrograph on Solar Orbiter. In a previous paper, we demonstrated correction of these artifacts in the $y-λ$ plane with PSF Regularization, treating the forward problem with a method based on large sparse matrix inversion. It has since been found that similar apparent artifacts are also present in the $x-λ$ direction, i.e., across adjacent slit positions. This is difficu…

Pascal's Matrix, Point Counting on Elliptic Curves and Prolate Spheroidal Functions
W. Riley Casper
https://arxiv.org/abs/2508.08494 https://arxiv.org/…

Pascal's Matrix, Point Counting on Elliptic Curves and Prolate Spheroidal Functions
The eigenvectors of the $(N+1)\times (N+1)$ symmetric Pascal matrix $T_N$ are analogs of prolate spheroidal wave functions in the discrete setting. The generating functions of the eigenvectors of $T_N$ are prolate spheroidal functions in the sense that they are simultaneously eigenfunctions of a third-order differential operator and an integral operator over the critical line $\{z\in\mathbb{C}: \text{Re}(z) = 1/2\}$. For even, positive integers $N$, we obtain an explicit formula for the generat…

Spirals, vortices, and helicity entanglements in dynamical Sauter-Schwinger pair creation
M. M. Majczak, K. Krajewska, A. Bechler, J. Z. Kami\'nski
https://arxiv.org/abs/2507.08720

Spirals, vortices, and helicity entanglements in dynamical Sauter-Schwinger pair creation
We study helicity correlations of electron-positron pairs created by a homogeneous time-dependent electric field in the Sauter-Schwinger scenario. Our analysis is based on solving the Dirac equation with the Feynman or anti-Feynman boundary conditions, which is equivalent to the scattering matrix approach widely used in high energy physics. Most importantly, both these methods allow to fully account for the helicity (or, more generally, spin) correlations of created particles. The influence of …

Total/dual correlation/coherence, redundancy/synergy, complexity, and O-information for real and complex valued multivariate data
Roberto D. Pascual-Marqui, Kieko Kochi, Toshihiko Kinoshita
https://arxiv.org/abs/2507.08773

Total/dual correlation/coherence, redundancy/synergy, complexity, and O-information for real and complex valued multivariate data
Firstly, assuming Gaussianity, equations for the following information theory measures are presented: total correlation/coherence (TC), dual total correlation/coherence (DTC), O-information, TSE complexity, and the redundancy-synergy index (RSI). Since these measures are functions of the covariance matrix "S" and its inverse "S^-1", the associated Wishart and inverse-Wishart distributions are of note. The DTC is shown here to be the Kullback-Leibler (KL) divergence for the inverse-Wishart pair …

Matrix-Driven Instant Review: Confident Detection and Reconstruction of LLM Plagiarism on PC
Ruichong Zhang
https://arxiv.org/abs/2508.06309 https://arxiv.…

Matrix-Driven Instant Review: Confident Detection and Reconstruction of LLM Plagiarism on PC
In recent years, concerns about intellectual property (IP) in large language models (LLMs) have grown significantly. Plagiarizing other LLMs (through direct weight copying, upcycling, pruning, or continual pretraining) and claiming authorship without properly attributing to the original license, is a serious misconduct that can lead to significant financial and reputational harm to the original developers. However, existing methods for detecting LLM plagiarism fall short in key areas. They fail…

Replaced article(s) found for nucl-th. https://arxiv.org/list/nucl-th/new
[1/1]:
- Effects of perturbation for transition operator of double-${\beta}$ decay on nuclear matrix eleme...
J. Terasaki, O. Civitarese

Replaced article(s) found for quant-ph. https://arxiv.org/list/quant-ph/new
[2/3]:
- Efficient mutual magic and magic capacity with matrix product states
Poetri Sonya Tarabunga, Tobias Haug

Deformation of semi-circle law for the correlated time series and Phase transition
Masato Hisakado, Takuya Kaneko
https://arxiv.org/abs/2508.07192 https://…

Deformation of semi-circle law for the correlated time series and Phase transition
We study the eigenvalue of the Wigner random matrix, which is created from a time series with temporal correlation. We observe the deformation of the semi-circle law which is similar to the eigenvalue distribution of the Wigner-Lèvy matrix. The distribution has a longer tail and a higher peak than the semi-circle law. In the absence of correlation, the eigenvalue distribution of the Wigner random matrix is known as the semi-circle law in the large $N$ limit. When there is a temporal correlatio…

High-Performance and Power-Efficient Emulation of Matrix Multiplication using INT8 Matrix Engines
Yuki Uchino, Katsuhisa Ozaki, Toshiyuki Imamura
https://arxiv.org/abs/2508.03984

High-Performance and Power-Efficient Emulation of Matrix Multiplication using INT8 Matrix Engines
Recent architectures integrate high-performance and power-efficient matrix engines. These engines demonstrate remarkable performance in low-precision matrix multiplication, which is crucial in deep learning. Several techniques have been proposed to emulate single- and double-precision general matrix-matrix multiplication (SGEMM and DGEMM, respectively) by leveraging such low-precision matrix engines. In this study, we present emulation methods that significantly outperforms conventional approac…

Crosslisted article(s) found for math.CO. https://arxiv.org/list/math.CO/new
[1/1]:
- Cohen-Lenstra flag universality for random matrix products
Yifeng Huang, Hoi H. Nguyen, Roger Van Peski

Companion matrices as sums of $p$-potent and nilpotent matrices
Andrada Pojar
https://arxiv.org/abs/2508.09276 https://arxiv.org/pdf/2508.09276

Companion matrices as sums of $p$-potent and nilpotent matrices
We prove that, over a field $\mathbb{F}$ of odd characteristic $p$, a companion matrix $C$ is the sum of $E$ and $N$, with $E$ $p$-potent (i.e. $E^p = E$,) and $N$ nilpotent, if and only if the trace of $C$ is an integer multiple of unity of $\mathbb{F}$.

Entropy Measures for Transition Matrices in Random Systems
Zhaohui Chen, Rene Meyer, Zhuo-Yu Xian
https://arxiv.org/abs/2508.09261 https://arxiv.org/pdf/25…

Entropy Measures for Transition Matrices in Random Systems
A transition matrix can be constructed through the partial contraction of two given quantum states. We analyze and compare four different definitions of entropy for transition matrices, including (modified) pseudo entropy, SVD entropy, and ABB entropy. We examine the probabilistic interpretation of each entropy measure and show that only the distillation interpretation of ABB entropy corresponds to the joint success probability of distilling entanglement between the two quantum states used to c…

Replaced article(s) found for cond-mat.mes-hall. https://arxiv.org/list/cond-mat.mes-hall/new
[1/1]:
- Density Matrix Renormalization Group Study of Domain Wall Qubits
Guanxiong Qu, Ji Zou, Daniel Loss, Tomoki Hirosawa

A Globally Optimal Analytic Solution for Semi-Nonnegative Matrix Factorization with Nonnegative or Mixed Inputs
Lu Chenggang
https://arxiv.org/abs/2508.07134 https://

A Globally Optimal Analytic Solution for Semi-Nonnegative Matrix Factorization with Nonnegative or Mixed Inputs
Semi-Nonnegative Matrix Factorization (semi-NMF) extends classical Nonnegative Matrix Factorization (NMF) by allowing the basis matrix to contain both positive and negative entries, making it suitable for decomposing data with mixed signs. However, most existing semi-NMF algorithms are iterative, non-convex, and prone to local minima. In this paper, we propose a novel method that yields a globally optimal solution to the semi-NMF problem under the Frobenius norm, through an orthogonal decomposi…

QB Ground State Energy Estimation Benchmark
Nicole Bellonzi, Joshua T. Cantin, Mohammad Reza Jangrouei, Alexander Kunitsa, Jason Necaise, Nam Nguyen, John Penuel, Maxwell D. Radin, Jhonathan Romero Fontalvo, Rashmi Sundareswara, Linjun Wang, Thomas Watts, Yanbing Zhou, Michael C. Garrett, Adam Holmes, Artur F. Izmaylov, Matthew Otten
https://

QB Ground State Energy Estimation Benchmark
Ground State Energy Estimation (GSEE) is a central problem in quantum chemistry and condensed matter physics, demanding efficient algorithms to solve complex electronic structure calculations. This work introduces a structured benchmarking framework for evaluating the performance of both classical and quantum solvers on diverse GSEE problem instances. We assess three prominent methods -- Semistochastic Heat-Bath Configuration Interaction (SHCI), Density Matrix Renormalization Group (DMRG), and …

Per-antenna power constraints: constructing Pareto-optimal precoders with cubic complexity under non-negligible noise conditions
Sergey Petrov, Samson Lasaulce, Merouane Debbah
https://arxiv.org/abs/2508.09646

Per-antenna power constraints: constructing Pareto-optimal precoders with cubic complexity under non-negligible noise conditions
Precoding matrix construction is a key element of the wireless signal processing using the multiple-input and multiple-output model. It is established that the problem of global throughput optimization under per-antenna power constraints belongs, in general, to the class of monotonic optimization problems, and is unsolvable in real-time. The most widely used real-time baseline is the suboptimal solution of Zero-Forcing, which achieves a cubic complexity by discarding the background noise coeffi…

Solvable Models of Heat Transport in Quantum Mechanics
R Loganayagam, Prithvi Narayan, Swathi T S
https://arxiv.org/abs/2508.09253 https://arxiv.org/pdf/25…

Solvable Models of Heat Transport in Quantum Mechanics
We investigate solvable models of heat transport between a pair of quantum mechanical systems initialized at two different temperatures. At time $t=0$, a weak interaction is switched on between the systems, and we study the resulting energy transport. Focusing on the heat current as the primary observable, we analyze both the transient dynamics and the long-time behavior of the system. We demonstrate that simple toy models - including Random Matrix Theory like models ({\it RMT models}) and Schw…

$m$-nil-clean nonderogatory matrices
Andrada Pojar
https://arxiv.org/abs/2508.10081 https://arxiv.org/pdf/2508.10081

$m$-nil-clean nonderogatory matrices
We prove that if $\mathbb{F}$ is a field of positive odd characteristic $p,$ and $m,$ and $n$ are positive integers such that $m\geq2,$ and $n\leq p,$ every $n\times n$ nonderogatory matrix $A\in \mathbb{M}_n(\mathbb{F})$ which is sum of $m$ idempotents and a nilpotent, has a decomposition $A=E_1+E_2+\dots+E_m+V,$ such that $E_i^2=E_i,$ for every $i\in \{1,\dots,m\},$ and $V^{[\frac{p-2}{m}]+2}=0.$

Entanglement certification from moments of positive maps
Qing-Hua Zhang, Xiaoyu Ma, Shao-Ming Fei
https://arxiv.org/abs/2508.09766 https://arxiv.org/pdf/25…

Entanglement certification from moments of positive maps
Entanglement certification is crucial in physical experiments, particularly when only partial knowledge of the quantum state is available. In this context, we present an entanglement criterion based on positive but not completely positive maps, which eliminates the need to identify eigenvalues of the output state. Notably, the Faddeev-LeVerrier algorithm establishes a relationship between the coefficients of characteristic polynomials and the moments of a matrix. This enables the existence of n…

Computing standard canonical forms of regular linear time varying DAEs via a preliminary stage
Diana Est\'evez Schwarz, Ren\'e Lamour, Roswitha M\"arz
https://arxiv.org/abs/2508.08921

Computing standard canonical forms of regular linear time varying DAEs via a preliminary stage
For regular linear time-invariant DAEs the corresponding matrix pencil is regular and the computation of a standard canonical form is well-understood. Although the investigation of linear DAEs with time-varying coefficients is more complex, it is analogously related to the examination of pairs of time-dependent matrix functions. We show how the computation of a standard canonical form (SCF) for linear time-varying DAEs becomes possible if a suitable block structure of the pair of matrix funct…

Evaluation of bound-state $\beta^-$-decay half-lives of fully ionized atoms
Priyanka Choudhary, Chong Qi
https://arxiv.org/abs/2507.08199 https://

Evaluation of bound-state $β^-$-decay half-lives of fully ionized atoms
Bound-state $β^-$-decay is a rare radioactive process where the created electron is trapped in an atomic orbital instead of being emitted. It can be observed in highly ionized atoms in particular when normal beta decay is energetically forbidden, but bound-state decay is still possible. In this work we present a systematic theoretical study on the bound-state $β^-$-decay of fully ionized atoms where key nuclear inputs include the nuclear matrix elements (expressed through $ft$ values) and the…

Photonic Matrix Multiplication Circuit Based on Double Racetrack Resonator Building Blocks
Hussein Talib, Phillip D. Sewell, Ana Vukovic, Sendy Phang
https://arxiv.org/abs/2509.09445

Photonic Matrix Multiplication Circuit Based on Double Racetrack Resonator Building Blocks
This paper presents a novel design framework for photonic matrix multiplication based on programmable photonic integrated circuits using double racetrack (DRT) resonators as building blocks. Here, we analytically demonstrate that the transfer function of the DRT resonator building block resembles that conventional building blocks, such as directional couplers and MZI, making it suitable for building programmable circuits that handle complex matrix calculations. Using this new DRT resonators bui…

On exotic matrix exponential sums and Bessel-Speh functions
Elad Zelingher
https://arxiv.org/abs/2507.06394 https://arxiv.org/pdf/250…

On exotic matrix exponential sums and Bessel-Speh functions
We define the notions of non-abelian exotic Gauss sums and of exotic matrix Kloosterman sums, the latter one generalizing the notions of Katz's exotic Kloosterman sums and of twisted matrix Kloosterman sums. Using Kondo's Gauss sum and results about Shintani lifts, we reduce non-abelian exotic Gauss sums to products of classical (exotic) Gauss sums. Using Macdonald's characteristic maps, we generalize our previous result and show that exotic matrix Kloosterman sums can be expressed as products …

A tensor-based dynamic mode decomposition based on the $\star_{\boldsymbol{M}}$-product
Arvind K. Saibaba, Misha E. Kilmer, Khalil Hall-Hooper, Fan Tian, Alex Mize
https://arxiv.org/abs/2508.10126

A tensor-based dynamic mode decomposition based on the $\star_{\boldsymbol{M}}$-product
Dynamic mode decomposition (DMD) is a data-driven method for estimating the dynamics of a discrete dynamical system. This paper proposes a tensor-based approach to DMD for applications in which the states can be viewed as tensors. Specifically, we use the $\star_{\boldsymbol{M}}$-product framework for tensor decompositions which we demonstrate offers excellent compression compared to matrix-based methods and can be implemented in a computationally efficient manner. We show how the proposed appr…

Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications
Weiyuan Gong, Tongyang Li, Xinzhao Wang, Zhiyu Zhang
https://arxiv.org/abs/2509.08911 https://

Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications
The Matrix Multiplicative Weight Update (MMWU) is a seminal online learning algorithm with numerous applications. Applied to the matrix version of the Learning from Expert Advice (LEA) problem on the $d$-dimensional spectraplex, it is well known that MMWU achieves the minimax-optimal regret bound of $O(\sqrt{T\log d})$, where $T$ is the time horizon. In this paper, we present an improved algorithm achieving the instance-optimal regret bound of $O(\sqrt{T\cdot S(X||d^{-1}I_d)})$, where…

A Matrix Decomposition Method for Odd-Type Gaussian Normal Basis Multiplication
Kittiphon Phalakarn, Athasit Surarerks
https://arxiv.org/abs/2508.07541 https://

A Matrix Decomposition Method for Odd-Type Gaussian Normal Basis Multiplication
Normal basis is used in many applications because of the efficiency of the implementation. However, most space complexity reduction techniques for binary field multiplier are applicable for only optimal normal basis or Gaussian normal basis of even type. There are 187 binary fields GF(2^k) for k from 2 to 1,000 that use odd-type Gaussian normal basis. This paper presents a method to reduce the space complexity of odd-type Gaussian normal basis multipliers over binary field GF(2^k). The idea is …

Random Modulation: Achieving Asymptotic Replica Optimality over Arbitrary Norm-Bounded and Spectrally Convergent Channel Matrices
Lei Liu, Yuhao Chi, Shunqi Huang
https://arxiv.org/abs/2508.08099

Random Modulation: Achieving Asymptotic Replica Optimality over Arbitrary Norm-Bounded and Spectrally Convergent Channel Matrices
This paper introduces a random modulation technique that is decoupled from the channel matrix, allowing it to be applied to arbitrary norm-bounded and spectrally convergent channel matrices. The proposed random modulation constructs an equivalent dense and random channel matrix, ensuring that the signals undergo sufficient statistical channel fading. It also guarantees the asymptotic replica maximum a posteriori (MAP) bit-error rate (BER) optimality of approximate message passing (AMP)-type det…

Does block size matter in randomized block Krylov low-rank approximation?
Tyler Chen, Ethan N. Epperly, Raphael A. Meyer, Christopher Musco, Akash Rao
https://arxiv.org/abs/2508.06486

Does block size matter in randomized block Krylov low-rank approximation?
We study the problem of computing a rank-$k$ approximation of a matrix using randomized block Krylov iteration. Prior work has shown that, for block size $b = 1$ or $b = k$, a $(1 + \varepsilon)$-factor approximation to the best rank-$k$ approximation can be obtained after $\tilde O(k/\sqrt{\varepsilon})$ matrix-vector products with the target matrix. On the other hand, when $b$ is between $1$ and $k$, the best known bound on the number of matrix-vector products scales with $b(k-b)$, which coul…

Replaced article(s) found for hep-ph. https://arxiv.org/list/hep-ph/new
[1/2]:
- Neutrino mixing matrix in terms of neutrino mass matrix and its Frobenius covariants
M. I. Krivoruchenko, F. \v{S}imkovic

A Novel Theoretical Approach on Micro-Nano Robotic Networks Based on Density Matrices and Swarm Quantum Mechanics
Maria Mannone, Mahathi Anand, Peppino Fazio, Abdalla Swikir
https://arxiv.org/abs/2509.08002

A Novel Theoretical Approach on Micro-Nano Robotic Networks Based on Density Matrices and Swarm Quantum Mechanics
In a robotic swarm, parameters such as position and proximity to the target can be described in terms of probability amplitudes. This idea led to recent studies on a quantum approach to the definition of the swarm, including a block-matrix representation. Here, we propose an advancement of the idea, defining a swarm as a mixed quantum state, to be described with a density matrix, whose size does not change with the number of robots. We end the article with some directions for future research.

The Strong Singular Value Property for Matrices
Caleb Cheung, Bryan Shader
https://arxiv.org/abs/2507.08313 https://arxiv.org/pdf/250…

The Strong Singular Value Property for Matrices
A new property, the strong singular value property, is introduced, developed, and utilized to study the problem of which lists of nonnegative real numbers occur as the singular values of a matrix with a prescribed zero-nonzero pattern.

Diminished Sombor matrix, spectral radius, and energy of the graphs
F. Movahedi
https://arxiv.org/abs/2508.06531 https://arxiv.org/pdf/2508.06531

Diminished Sombor matrix, spectral radius, and energy of the graphs
Consider a simple graph $G$ with vertex set $V = \{v_1, v_2, \ldots, v_n\}$ and edge set $E$. The diminished Sombor matrix $M_{DS}(G)$ is constructed such that its $(i, j)$ entry is $\frac{\sqrt{d_i^2+d_j^2}}{d_i+d_j}$ if vertices $v_iv_j \in E$, and $0$ otherwise, where $d_i$ represents the degree of vertex $v_i$. In this paper, we establish sharp bounds for the spectral radius, and energy of the Sombor matrix of graphs and identify the graphs that attain these extremal values.

Ab initio lattice study of neutron-alpha scattering with chiral forces at N3LO
Serdar Elhatisari, Fabian Hildenbrand, Ulf-G. Mei{\ss}ner
https://arxiv.org/abs/2507.08495

Ab initio lattice study of neutron-alpha scattering with chiral forces at N3LO
We present the first ab initio lattice calculation of neutron-alpha ($n$-$α$) scattering using nuclear lattice effective field theory (NLEFT) with chiral interactions at next-to-next-to-next-to-leading order (N3LO). Building on the high-fidelity chiral Hamiltonian introduced in Ref. [1], we compute scattering phase shifts in the $S$- and $P$-wave channels using the Lüscher finite-volume method. Our results demonstrate excellent agreement with empirical $R$-matrix phase shifts in the $^2S_{1/2…

Replaced article(s) found for math.RA. https://arxiv.org/list/math.RA/new
[1/1]:
- Classification of Jordan multiplicative maps on matrix algebras
Ilja Gogi\'c, Mateo Toma\v{s}evi\'c

Non-trivial Bifocal and Optical Vortex Generation of DNG Materials Unveiled by Generalized Transfer Matrix Method and Matrix Fourier Optics
Yifeng Qin
https://arxiv.org/abs/2509.09150

Non-trivial Bifocal and Optical Vortex Generation of DNG Materials Unveiled by Generalized Transfer Matrix Method and Matrix Fourier Optics
The investigation and analysis of exotic physical phenomena facilitated by metamaterials have emerged as a compelling area of interest in physics, material science, and engineering. However, there remains a lack of suitable theoretical tools for scrutinizing light-matter interactions in metamedia, particularly those involving distinct constitutive tensors, such as polarization cross-coupling or non-reciprocal propagation induced by bianisotropy. In this research, we apply the generalized transf…

Liouville CFT, Matrix Models and constrained WZW
Babak Haghighat
https://arxiv.org/abs/2508.06901 https://arxiv.org/pdf/2508.06901

Liouville CFT, Matrix Models and constrained WZW
In this paper we study matrix model realizations of Liouville conformal blocks with degenerate and irregular operators. The corresponding matrix model is Hermitian with a $β$-deformed measure and the degree of the potential corresponds to the degree of the irregular operator in the CFT conformal block. We then show how such matrix integrals can be obtained from an $SL(2,\mathbb{C})$ WZW model with a conformal constraint giving rise to Liouville theory. The corresponding conformal blocks satisf…

Efficient adaptive randomized algorithms for fixed-threshold low-rank matrix approximation
Qiaohua Liu, Yuejuan Yu
https://arxiv.org/abs/2508.07553 https://

Efficient adaptive randomized algorithms for fixed-threshold low-rank matrix approximation
The low-rank matrix approximation problems within a threshold are widely applied in information retrieval, image processing, background estimation of the video sequence problems and so on. This paper presents an adaptive randomized rank-revealing algorithm of the data matrix $A$, in which the basis matrix $Q$ of the approximate range space is adaptively built block by block, through a recursive deflation procedure on $A$. Detailed analysis of randomized projection schemes are provided to analyz…

Quantum Circuit Complexity of Matrix-Product Unitaries
Georgios Styliaris, Rahul Trivedi, J. Ignacio Cirac
https://arxiv.org/abs/2508.08160 https://arxiv.o…

Quantum Circuit Complexity of Matrix-Product Unitaries
Matrix-product unitaries (MPUs) are many-body unitary operators that, as a consequence of their tensor-network structure, preserve the entanglement area law in 1D systems. However, it is unknown how to implement an MPU as a quantum circuit since the individual tensors describing the MPU are not unitary. In this paper, we show that a large class of MPUs can be implemented with a polynomial-depth quantum circuit. For an $N$-site MPU built from a repeated bulk tensor with open boundary, we explici…

Supersymmetric M2-Brane Matrix Model with Restricted Volume-Preserving Deformations: Lorentz Covariance and BPS Spectrum
So Katagiri
https://arxiv.org/abs/2508.07259 https://

Supersymmetric M2-Brane Matrix Model with Restricted Volume-Preserving Deformations: Lorentz Covariance and BPS Spectrum
We present a novel supersymmetric Lorentz-covariant matrix model for M2-branes in M-theory, constructed via the framework of Restricted Volume-Preserving Deformations (RVPD) which is a residual symmetry from gauge-fixed volume-preserving diffeomorphisms. The model reformulates the supermembrane action entirely in terms of Nambu brackets, whose decomposition into Poisson brackets allows for a consistent matrix regularization that preserves both the Fundamental Identity and Lorentz covariance. Un…

Value bounds and Convergence Analysis for Averages of LRP attributions
Alexander Binder, Nastaran Takmil-Homayouni, Urun Dogan
https://arxiv.org/abs/2509.08963 https://

Value bounds and Convergence Analysis for Averages of LRP attributions
We analyze numerical properties of Layer-wise relevance propagation (LRP)-type attribution methods by representing them as a product of modified gradient matrices. This representation creates an analogy to matrix multiplications of Jacobi-matrices which arise from the chain rule of differentiation. In order to shed light on the distribution of attribution values, we derive upper bounds for singular values. Furthermore we derive component-wise bounds for attribution map values. As a main result,…

Tomography-assisted noisy quantum circuit simulator using matrix product density operators
Wei-guo Ma, Yun-Hao Shi, Kai Xu, Heng Fan
https://arxiv.org/abs/2508.07610 https://

Tomography-assisted noisy quantum circuit simulator using matrix product density operators
In recent years, efficient quantum circuit simulations incorporating ideal noise assumptions have relied on tensor network simulators, particularly leveraging the matrix product density operator (MPDO) framework. However, experiments on real noisy intermediate-scale quantum (NISQ) devices often involve complex noise profiles, encompassing uncontrollable elements and instrument-specific effects such as crosstalk. To address these challenges, we employ quantum process tomography (QPT) techniques …

Hierarchical Tucker Low-Rank Matrices: Construction and Matrix-Vector Multiplication
Yingzhou Li, Jingyu Liu
https://arxiv.org/abs/2508.05958 https://arxiv…

Hierarchical Tucker Low-Rank Matrices: Construction and Matrix-Vector Multiplication
In this paper, a hierarchical Tucker low-rank (HTLR) matrix is proposed to approximate non-oscillatory kernel functions in linear complexity. The HTLR matrix is based on the hierarchical matrix, with the low-rank blocks replaced by Tucker low-rank blocks. Using high-dimensional interpolation as well as tensor contractions, algorithms for the construction and matrix-vector multiplication of HTLR matrices are proposed admitting linear and quasi-linear complexities respectively. Numerical experime…

Replaced article(s) found for hep-th. https://arxiv.org/list/hep-th/new
[1/1]:
- A Matrix Model Proposal for Quantum Gravity and the Quantum Mechanics of Black Holes
Chong-Sun Chu

Work statistics of sudden Quantum quenches: A random matrix theory perspective on Gaussianity and its deviations
Miguel Tierz
https://arxiv.org/abs/2509.09640 https://

Work statistics of sudden Quantum quenches: A random matrix theory perspective on Gaussianity and its deviations
We show that, for sudden quenches, the work distribution reduces to the statistics of traces of powers of Haar unitaries, which are random unitary matrices drawn uniformly from the unitary group. For translation-invariant quadratic fermionic chains with interactions extending to $m$ neighbors and periodic boundary conditions, the Loschmidt amplitude admits a unitary matrix-model / Toeplitz representation, which yields a work variable of the form $W=\sum_{r\le m} a_r\,\mathrm{Re}\,\mathrm{Tr}\,U…

CR tournaments
Jing Zeng, Lihua You, Xinghui Zhao
https://arxiv.org/abs/2508.07332 https://arxiv.org/pdf/2508.07332…

CR tournaments
The determinant of a tournament $T$ is defined as the determinant of the skew-adjacency matrix of $T$. For a positive odd integer $k$, let $\mathcal{D}_k$ be the set of tournaments whose all subtournaments have determinant at most $k^2$. Some existing results show that, for $k \in \{1,3,5\}$, a tournament $T \in \mathcal{D}_k \backslash \mathcal{D}_{k-2}$ ($T \in \mathcal{D}_1$ when $k=1$) if and only if $T$ is switching equivalent to a transitive blowup of $L_{k+1}$, where $L_{k+1}$ is a tourn…

Replaced article(s) found for quant-ph. https://arxiv.org/list/quant-ph/new
[4/4]:
- Nonequilibrium Phase Transitions in Large $N$ Matrix Quantum Mechanics
Minjae Cho

Rational minimax approximation of matrix-valued functions
Lei-Hong Zhang, Ya-Nan Zhang, Chenkun Zhang, Shanheng Han
https://arxiv.org/abs/2508.06378 https://

Rational minimax approximation of matrix-valued functions
In this paper, we present a rigorous framework for rational minimax approximation of matrix-valued functions that generalizes classical scalar approximation theory. Given sampled data $\{(x_\ell, {F}(x_\ell))\}_{\ell=1}^m$ where ${F}:\mathbb{C} \to \mathbb{C}^{s \times t}$ is a matrix-valued function, we study the problem of finding a matrix-valued rational approximant ${R}(x) = {P}(x)/q(x)$ (with ${P}:\mathbb{C} \to \mathbb{C}^{s \times t}$ a matrix-valued polynomial and $q(x)$ a nonzero scala…

The distance spectrum of the line graph of the crown graph
S. Morteza Mirafzal
https://arxiv.org/abs/2508.07202 https://arxiv.org/pdf/2508.07202

The distance spectrum of the line graph of the crown graph
The distance eigenvalues of a connected graph $G$ are the eigenvalues of its distance matrix $D(G)$. A graph is called distance integral if all of its distance eigenvalues are integers. Let $n \geq 3$ be an integer. The crown graph $Cr(n)$ is a graph obtained from the complete bipartite graph $K_{n,n}$ by removing a perfect matching. Let $L(Cr(n))$ denote the line graph of the crown graph $Cr(n)$. Using the equitable partition method, the set of distinct distance eigenvalues of the graph $L(Cr(…

Extended JT supergravity and random matrix models: The power of the string equation
Clifford V. Johnson, Maciej Kolanowski
https://arxiv.org/abs/2507.07185

Extended JT supergravity and random matrix models: The power of the string equation
A number of supersymmetric Jackiw-Teitelboim (JT) gravity theories are known to be described (in the Euclidean path integral formulation) by double-scaled random matrix models. Such matrix models can be characterized using a certain ``string equation''. It was shown recently that in extended supergravity, when the number of BPS states scales as ${\rm e}^{S_0}$, where $S_0$ is the extremal entropy, a special ansatz for the leading order solution of the string equation yields the supergravity spe…

A brief introduction to matrix hydrodynamics
Klas Modin, Milo Viviani
https://arxiv.org/abs/2508.07088 https://arxiv.org/pdf/2508.07088

A brief introduction to matrix hydrodynamics
This survey gives a basic demonstration of matrix hydrodynamics; the field pioneered by V. Zeitlin, where 2-D incompressible fluids are spatially discretized via quantization theory.

Orthogonal Latin Squares of Order Ten with Two Relations: A SAT Investigation
Curtis Bright, Amadou Keita, Brett Stevens
https://arxiv.org/abs/2509.09633 https://

Orthogonal Latin Squares of Order Ten with Two Relations: A SAT Investigation
A $k$-net($n$) is a combinatorial design equivalent to $k-2$ mutually orthogonal Latin squares of order $n$. A relation in a net is a linear dependency over $\mathbb{F}_2$ in the incidence matrix of the net. A computational enumeration of all orthogonal pairs of Latin squares of order 10 whose corresponding nets have at least two nontrivial relations was achieved by Delisle in 2010 and verified by an independent search of Myrvold. In this paper, we confirm the correctness of their exhaustive en…

Information Transport in Classic-Quantum Hybrid System
Julian Rapp, Radhika H. Joshi, Alwin van Steensel, Yuli V. Nazarov, Mohammad H. Ansari
https://arxiv.org/abs/2508.07870 ht…

Information Transport in Classic-Quantum Hybrid System
Many important quantities in quantum information science, such as entropy and entanglement, are non-linear functions of the density matrix and cannot be expressed as operator observables. Standard open-system approaches evolve only a single copy of the density matrix, making it impossible to track the dynamics of such quantities. A formalism proposed by some of the present authors addressed this challenge by evolving multiple virtual replicas, but was limited to the weak-coupling regime. Here, …

Weighted Proper Orthogonal Decomposition for High-Dimensional Optimization
Sebastiaan P. C. van Schie, Boris Kramer, John T. Hwang
https://arxiv.org/abs/2508.09084 https://

Weighted Proper Orthogonal Decomposition for High-Dimensional Optimization
While proper orthogonal decomposition (POD) is widely used for model reduction, its standard form does not take into account any parametric model structure. Extensions to POD have been proposed to address this, but these either require large amounts of solution data, lack online adaptivity, or have limited approximation accuracy. We circumvent these limitations by instead assigning weights to the snapshot matrix columns, and updating these whenever the model is evaluated at a new point in the p…

Thermodynamic coprocessor for linear operations with input-size-independent calculation time based on open quantum system
I. V. Vovchenko, A. A. Zyablovsky, A. A. Pukhov, E. S. Andrianov
https://arxiv.org/abs/2509.09382

Thermodynamic coprocessor for linear operations with input-size-independent calculation time based on open quantum system
Linear operations, e.g., vector-matrix or vector-vector multiplications, are core operations of modern neural networks. To diminish computational time, these operations are implemented by parallel computations using different coprocessors. In this work we show that open quantum system consisting of bosonic modes and interacting with bosonic reservoirs can be used as analog coprocessor implementing multiple vector-matrix multiplications with stochastic matrices in parallel. Input vectors are enc…

Effects of One-particle Reduced Density Matrix Optimization in Variational Quantum Eigensolvers
Amanda Marques de Lima, Erico Souza Teixeira, Eivson Darlivam Rodrigues de Aguiar Silva, Ricardo Luiz Longo
https://arxiv.org/abs/2507.07667

Effects of One-particle Reduced Density Matrix Optimization in Variational Quantum Eigensolvers
The variational quantum eigensolver (VQE) is a promising method for simulating molecular systems on near-term quantum computers. This approach employs energy estimation; however, other relevant molecular properties can be extracted from the one-particle reduced density matrix (1-RDM) generated by VQE. The accuracy of these properties strongly depends on the reliability and convergence of the 1-RDM, which is not guaranteed by energy-only optimization. Thus, we investigate the effect of optimizin…

Error Analysis of Krylov Subspace approximation Based on IDR($s$) Method for Matrix Function Bilinear Forms
Qian Qian Xue, Xiao Qiang Yue, Xian-Ming Gu
https://arxiv.org/abs/2509.08563

Error Analysis of Krylov Subspace approximation Based on IDR($s$) Method for Matrix Function Bilinear Forms
The bilinear form u^\top f(A) v of matrix functions appears in many application problems, where u, v \in R^n\), A \in R^{n * n}\), and f(z) is a given analytic function.The IDR(s) method effectively reduces computational complexity and storage requirements by introducing dimension reduction techniques, while maintaining the numerical stability of the algorithm. This paper studies the numerical algorithm and posterior error estimation for the matrix function bilinear form u^{\top} f(A) v based o…

Scalable Quantum State Preparation for Encoding Genomic Data with Matrix Product States
Floyd M. Creevey, Hitham T. Hassan, James McCafferty, Lloyd C. L. Hollenberg, Sergii Strelchuk
https://arxiv.org/abs/2508.06184

Scalable Quantum State Preparation for Encoding Genomic Data with Matrix Product States
As quantum computing hardware advances, the need for algorithms that facilitate the loading of classical data into the quantum states of these devices has become increasingly important. This study presents a method for producing scalable quantum circuits to encode genomic data using the Matrix Product State (MPS) formalism. The method is illustrated by encoding the genome of the bacteriophage $ΦX174$ into a 15-qubit state, and analysing the trade-offs between MPS bond dimension, reconstruction…

Robust Lindbladian Estimation for Quantum Dynamics
Yinchen Liu, James R. Seddon, Tamara Kohler, Emilio Onorati, Toby S. Cubitt
https://arxiv.org/abs/2507.07912

Robust Lindbladian Estimation for Quantum Dynamics
We revisit the problem of fitting Lindbladian models to the outputs of quantum process tomography. A sequence of prior theoretical works approached the problem by considering whether there exists a Lindbladian generator close to a matrix logarithm of the tomographically estimated transfer matrix. This technique must take into account the non-uniqueness of the matrix logarithm, so that in general multiple branches of the logarithm must be checked. In contrast, all practical demonstrations of Lin…

Density matrix analysis of systems influenced by periodic Hamiltonians
Soham Sen, Manjari Dutta, Sunandan Gangopadhyay
https://arxiv.org/abs/2507.06355 htt…

Density matrix analysis of systems influenced by periodic Hamiltonians
In this work, we consider simple systems that are influenced by Hamiltonians with time periodicity. Our analysis is mainly focussed on the density matrix approach and aims to solve the Liouville equation of motion from which one can extract the state of the system when the system is in a pure state. We start our analysis with the standard Rabi-oscillation problem. We consider a density matrix corresponding to the entire model system and solve the Liouville equation of motion. We have then made …