Tootfinder

This https://arxiv.org/abs/2401.17466 has been replaced.
link: https://scholar.google.com/scholar?q=a

DC electric field driven discretization of single-particle excitation spectra in a Mott insulator
We theoretically investigate the single-particle excitation spectra of a one-dimensional Hubbard model at half filling using an infinite matrix-product state and elucidate the discretized energy spectra emerging under the influence of a dc electric field. In a weak electric-field regime, we observe two kinds of spectral structures in the density of states. With increasing the electric-field strength, the discretized spectra, the period of which is proportional to the strength, become dominant, …

This https://arxiv.org/abs/2410.00023 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

Self-Tuning Spectral Clustering for Speaker Diarization
Spectral clustering has proven effective in grouping speech representations for speaker diarization tasks, although post-processing the affinity matrix remains difficult due to the need for careful tuning before constructing the Laplacian. In this study, we present a novel pruning algorithm to create a sparse affinity matrix called spectral clustering on p-neighborhood retained affinity matrix (SC-pNA). Our method improves on node-specific fixed neighbor selection by allowing a variable number …

This https://arxiv.org/abs/2506.03947 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Block Alpha-Circulant Preconditioners for All-at-Once Diffusion-Based Covariance Operators
Covariance matrices are central to data assimilation and inverse methods derived from statistical estimation theory. Previous work has considered the application of an all-at-once diffusion-based representation of a covariance matrix operator in order to exploit inherent parallellism in the underlying problem. In this paper, we provide practical methods to apply block $α$-circulant preconditioners to the all-at-once system for the case where the main diffusion operation matrix cannot be readil…

This https://arxiv.org/abs/2306.05306 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Vertex isoperimetry on signed graphs and spectra of non-bipartite Cayley and Cayley sum graphs
For a non-bipartite finite Cayley graph, we show the non-trivial eigenvalues of its normalized adjacency matrix lie in the interval $$\left[-1+\frac{ch_{out}^2}{d},1-\frac{Ch_{out}^2}{d}\right],$$ for some absolute constant $c$ and $C$, where $h_{out}$ stands for the outer vertex boundary isoperimetric constant. This improves upon recent obtained estimates aiming at a quantitative version of a result due to Breuillard, Green, Guralnick and Tao. We achieve this by extending the work of Bobkov, H…

Decidability of multiplicative matrix equations and related Diophantine problems
Sebastian Heintze, Armand Noubissie, Robert F. Tichy
https://arxiv.org/abs/2506.03932

Decidability of multiplicative matrix equations and related Diophantine problems
Some new decidability results for multiplicative matrix equations over algebraic number fields are established. In particular, special instances of the so-called knapsack problem are considered. The proofs are based on effective methods for Diophantine problems in finitely generated domains as presented in the recent book of Evertse and Györy. The focus lies on explicit bounds for the size of the solutions in terms of heights as well as on bounds for the number of solutions. This approach also…

This https://arxiv.org/abs/2504.00155 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hepp…

Monte Carlo phase space integration of multiparticle cross sections with carlomat_4.5
Multidimensional phase space integrals must be calculated in order to obtain predictions for total or differential cross sections, or to simulate unweighted events of multiparticle reactions. The corresponding matrix elements, already in the leading order, receive contributions typically from dozens of thousands of the Feynman diagrams, many of which often involve strong peaks due to denominators of some Feynman propagators approaching their minima. As the number of peaks exceeds by far the num…

Determinants of Random Unitary Pencils
Michael T. Jury, George Roman
https://arxiv.org/abs/2506.04400 https://arxiv.org/pdf/2506.0440…

Determinants of Random Unitary Pencils
We investigate determinants of random unitary pencils (with scalar or matrix coefficients), which generalize the characteristic polynomial of a single unitary matrix. In particular we examine moments of such determinants, obtained by integrating against the Haar measure on the unitary group. We obtain an exact formula in the case of scalar coefficients, and conjecture an asymptotic formula in the general case, and prove a special case of the conjecture.

This https://arxiv.org/abs/2305.17053 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Asymptotic initial value representation of the solutions of semi-classical systems presenting smooth codimension one crossings
This paper is devoted to the construction of approximations of the propagator associated with a semi-classical matrix-valued Schrödinger operator with symbol presenting smooth eigenvalues crossings. Inspired by the approach of the theoretical chemists Herman and Kluk who propagated continuous superpositions of Gaussian wave-packets for scalar equations, we consider frozen and thawed Gaussian initial value representations that incorporate classical transport and branching processes along a hopp…

Construction of the smallest Ree-Tits unital from the special linear group of degree two over the field with eight elements
Markus Johannes Stroppel
https://arxiv.org/abs/2506.02732

Construction of the smallest Ree-Tits unital from the special linear group of degree two over the field with eight elements
We construct the smallest Ree-Tits unital from a group of matrices that is isomorphic to the commutator group of the corresponding Ree group. The matrix description is used to determine configurations in the unital via explicit computations. Embeddings into larger Ree-Tits unitals are made explicit.

Strong stability of linear delay-difference equations
Felipe Gon\c{c}alves Netto, Yacine Chitour, Guilherme Mazanti
https://arxiv.org/abs/2506.05002 https:…

Strong stability of linear delay-difference equations
This paper considers linear delay-difference equations, that is, equations relating the state at a given time with its past values over a given bounded interval. After providing a well-posedness result and recalling Hale--Silkowski Criterion for strong stability in the case of equations with finitely many pointwise delays, we propose a generalization of the notion of strong stability to the more general class of linear delay-difference equations with an integral term defined by a matrix-valued …

Virtual Polarization Elements for Spatially Varying Jones Matrix Transformations on a Free-Space Plane
Mingyue Wang (Department of Physics, Xiamen University, Xiamen, China), Jiayuan Wang (Department of Physics, Xiamen University, Xiamen, China, Shenzhen Research Institute of Xiamen University, Shenzhen, China)
https://arxiv.org…

Virtual Polarization Elements for Spatially Varying Jones Matrix Transformations on a Free-Space Plane
Precise control over the spatial and polarization properties of light is foundational for advanced photonic systems, yet most conventional approaches are constrained to local, contact-based manipulation at physical interfaces. To overcome these constraints, here we introduce a fundamentally new framework for action-at-a-distance polarization control using virtual polarization elements (VPEs). VPEs apply prescribed local Jones matrix transformations between an input field at the modulation plane…

The ${}^9$Be photodisintegration cross section within Cluster Effective Field Theory
Ylenia Capitani, Elena Filandri, Chen Ji, Winfried Leidemann, Giuseppina Orlandini
https://arxiv.org/abs/2506.05040

The ${}^9$Be photodisintegration cross section within Cluster Effective Field Theory
A low-energy calculation of ${}^9$Be photodisintegration cross section is presented within an $ααn$ cluster approach. The $αn$ and $αα$ contact interactions are derived from cluster effective field theory. The two-body potentials defined in momentum space are regularized by a Gaussian cutoff. The associated low-energy constants are found by comparing the calculated low-energy T-matrix with its effective range expansion. A three-body state-dependent potential is also introduced in the model…

This https://arxiv.org/abs/2506.01294 has been replaced.
initial toot: https://mastoxiv.page/@ar…

Equation of State and First Principles Prediction of the Vibrational Matrix Shift of Solid Parahydrogen
We generate the equation of state (EOS) of solid parahydrogen using a path-integral Monte Carlo (PIMC) simulation based on a highly accurate first-principles adiabatic hindered rotor (AHR) potential energy curve for the \para dimer. The EOS curves for the fcc and hcp structures of solid parahydrogen near the equilibrium density show that the hcp structure is the more stable of the two, in agreement with experiment. To accurately reproduce the structural and energy properties of solid parahydrog…

This https://arxiv.org/abs/2309.03765 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csRO_…

Equivariant Symmetries for Inertial Navigation Systems
This paper investigates the problem of inertial navigation system (INS) filter design through the lens of symmetry. The extended Kalman filter (EKF) and its variants have been the staple of INS filtering for 50 years. However, recent advances in inertial navigation systems have exploited matrix Lie group structure to design stochastic filters and state observers that have been shown to display superior performance compared to classical solutions. In this work, we explore various symmetries of i…

This https://arxiv.org/abs/2401.16619 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Quantum algorithms for calculating determinant and inverse of matrix and solving linear algebraic systems
We propose quantum algorithms, purely quantum in nature, for calculating the determinant and inverse of an $(N-1)\times (N-1)$ matrix (depth is $O(N^2\log N)$) which is a simple modification of the algorithm for calculating the determinant of an $N\times N$ matrix (depth is $O(N\log^2 N)$. The basic idea is to encode each row of the matrix into a pure state of some quantum system. In addition, we use the representation of the elements of the inverse matrix in terms of algebraic complements. Thi…

This https://arxiv.org/abs/2505.24603 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLG_…

The Gaussian Mixing Mechanism: Renyi Differential Privacy via Gaussian Sketches
Gaussian sketching, which consists of pre-multiplying the data with a random Gaussian matrix, is a widely used technique for multiple problems in data science and machine learning, with applications spanning computationally efficient optimization, coded computing, and federated learning. This operation also provides differential privacy guarantees due to its inherent randomness. In this work, we revisit this operation through the lens of Renyi Differential Privacy (RDP), providing a refined pri…

This https://arxiv.org/abs/2503.21831 has been replaced.
initial toot: https://mastoxiv.page/@…

Thermodynamics of the XX spin chain in the QTM approach
The free energy density of the XX chain in magnetic field is obtained in two alternative ways within the Quantum Transfer Matrix approach. In both the cases the proofs are complete and self-consistent. All the intermediate constructions are presented explicitly in detail.

Matrix representations of the twisted virtual braid group and its extensions
Mohamad N. Nasser, Vaibhav Keshari, Madeti Prabhakar
https://arxiv.org/abs/2506.03806

Matrix representations of the twisted virtual braid group and its extensions
This paper classifies complex local representations of the twisted virtual braid group, $\mathrm{TVB}_2$, into $\mathrm{GL}_3(\mathbb{C})$. It shows that such representations fall into eight types, all of which are unfaithful and reducible to degree $2 \times 2$. Further reducibility to degree 1 is analyzed for specific types. The paper also examines complex homogeneous local representations of $\mathrm{TVB}_n$ into $\mathrm{GL}_{n+1}(\mathbb{C})$ for $n \geq 3$, identifying seven unfaithful ty…

On the rank of a random symmetric matrix in the large deviation regime
Yi Han
https://arxiv.org/abs/2506.01155 https://arxiv.org/pdf/…

On the rank of a random symmetric matrix in the large deviation regime
Let $A$ be an $n\times n$ random symmetric matrix with independent identically distributed subgaussian entries of unit variance. We prove the following large deviation inequality for the rank of $A$: for all $1\leq k\leq c\sqrt{n}$, $$\mathbb{P}(\operatorname{Rank}(A)\geq n-k)\geq 1-\exp(-c'kn),$$ for some fixed constants $c,c'>0$. A similar large deviation inequality is proven for the rank of the adjacency matrix of dense Erdos-Renyi graphs. This corank estimate enhances the recent breakthroug…

An Array Decomposition Method for Finite Arrays with Electrically Connected Elements for fast Toeplitz Solvers
Lucas {\AA}kerstedt, Harald Hultin, B. L. G. Jonsson
https://arxiv.org/abs/2506.04710

An Array Decomposition Method for Finite Arrays with Electrically Connected Elements for fast Toeplitz Solvers
A large part of the geometry of array antennas is often partially defined by finite translational symmetries. Applying the method of moments (MoM) with the RWG-like element on an appropriately structured mesh to these arrays results in an impedance matrix where the main part exhibits a multilevel block Toeplitz structure. This article introduces a memory-efficient construction method that effectively represents and reuses impedance calculations. The proposed method, applicable to electrically c…

This https://arxiv.org/abs/2505.23199 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Chaos in the holographic matrix models for meson and baryon
In recent years, the investigation of chaos has become a bridge connecting gravity theory and quantum field theory, especially within the framework of gauge-gravity duality. In this work, we study holographically the chaos in the matrix models for meson and baryon, which are derived from the $\mathrm{D4}/\mathrm{D6}/\overline{\mathrm{D6}}$ approach as a top-down holographic model for QCD. Since these matrix models can be simplified into coupled oscillator models with special parameters, we anal…

This https://arxiv.org/abs/2503.10569 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

Low-Rank Matrix Regression via Least-Angle Regression
Low-rank matrix regression is a fundamental problem in data science with various applications in systems and control. Nuclear norm regularization has been widely applied to solve this problem due to its convexity. However, it suffers from high computational complexity and the inability to directly specify the rank. This work introduces a novel framework for low-rank matrix regression that addresses both unstructured and Hankel matrices. By decomposing the low-rank matrix into rank-1 bases, the …

This https://arxiv.org/abs/2506.03074 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

GL-LowPopArt: A Nearly Instance-Wise Minimax Estimator for Generalized Low-Rank Trace Regression
We present `GL-LowPopArt`, a novel Catoni-style estimator for generalized low-rank trace regression. Building on `LowPopArt` (Jang et al., 2024), it employs a two-stage approach: nuclear norm regularization followed by matrix Catoni estimation. We establish state-of-the-art estimation error bounds, surpassing existing guarantees (Fan et al., 2019; Kang et al., 2022), and reveal a novel experimental design objective, $\mathrm{GL}(π)$. The key technical challenge is controlling bias from the non…

Latent Variable Autoregression with Exogenous Inputs
Daniil Bargman
https://arxiv.org/abs/2506.04488 https://arxiv.org/pdf/2506.04488…

Latent Variable Autoregression with Exogenous Inputs
This paper introduces a new least squares regression methodology called (C)LARX: a (constrained) latent variable autoregressive model with exogenous inputs. Two additional contributions are made as a side effect: First, a new matrix operator is introduced for matrices and vectors with blocks along one dimension; Second, a new latent variable regression (LVR) framework is proposed for economics and finance. The empirical section examines how well the stock market predicts real economic activity …

This https://arxiv.org/abs/2503.18154 has been replaced.
initial toot: https://mastoxiv.page/@…

Emergent supercounterfluid and quantum phase diagram of two-component interacting bosons in one-dimensional optical lattice
Motivated by a recent experiment that realizes nearest-neighbor dipolar couplings in an optical lattice [C. Lagoin, $\textit{et al.}$, Nature $\textbf{609}$, 485 (2022)], we study a one-dimensional version of the two-component extended Bose-Hubbard model via the density-matrix renormalization group method. By using the nearest-neighbor and on-site interaction parameters from the experiment, we start by mapping the quantum phase diagram in the hopping parameters $t_{A}\mbox{-}t_{B}$ plane with b…

This https://arxiv.org/abs/2503.22659 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

R-matrix valued Lax pair for elliptic Calogero-Inozemtsev system and associative Yang-Baxter equations of ${\rm BC}_n$ type
We consider the elliptic Calogero-Inozemtsev system of ${\rm BC}_n$ type with five arbitrary constants and propose $R$-matrix valued generalization for $2n\times 2n$ Takasaki's Lax pair. For this purpose we extend the Kirillov's ${\rm B}$-type associative Yang-Baxter equations to the similar relations depending on the spectral parameters and the Planck constants. General construction uses the elliptic Shibukawa-Ueno $R$-operator and the Komori-Hikami $K$-operators satisfying reflection equation…

This https://arxiv.org/abs/2505.20730 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIR_…

What LLMs Miss in Recommendations: Bridging the Gap with Retrieval-Augmented Collaborative Signals
User-item interactions contain rich collaborative signals that form the backbone of many successful recommender systems. While recent work has explored the use of large language models (LLMs) for recommendation, it remains unclear whether LLMs can effectively reason over this type of collaborative information. In this paper, we conduct a systematic comparison between LLMs and classical matrix factorization (MF) models to assess LLMs' ability to leverage user-item interaction data. We further in…

This https://arxiv.org/abs/2409.16757 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csNE_…

An Adaptive Re-evaluation Method for Evolution Strategy under Additive Noise
The Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES) is one of the most advanced algorithms in numerical black-box optimization. For noisy objective functions, several approaches were proposed to mitigate the noise, e.g., re-evaluations of the same solution or adapting the population size. In this paper, we devise a novel method to adaptively choose the optimal re-evaluation number for function values corrupted by additive Gaussian white noise. We derive a theoretical lower bound o…

This https://arxiv.org/abs/2501.03470 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Positivstellensätze for polynomial matrices with universal quantifiers
This paper investigates Positivstellensätze for polynomial matrices subject to universally quantified polynomial matrix inequality constraints. We first establish a matrix-valued Positivstellensatz under the Archimedean condition, incorporating universal quantifiers. For scalar-valued polynomial objectives, we further develop a sparse Positivstellensatz that leverages correlative sparsity patterns within these quantified constraints. Moving beyond the Archimedean framework, we then derive a se…

Violation of Luttinger's theorem in one-dimensional interacting fermions
Meng Gao, Yin Zhong
https://arxiv.org/abs/2506.04064 https://

Violation of Luttinger's theorem in one-dimensional interacting fermions
Using the density matrix renormalization group method, we systematically investigate the evolution of the Luttinger integral in the one-dimensional generalized t-V model as a function of filling and interaction strength, identifying three representative phases. In the weak-coupling regime, the zero-frequency Green's function shows a branch-cut structure at the Fermi momentum, and the Luttinger integral accurately reflects the particle density. As the interaction increases, the spectral weight n…

This https://arxiv.org/abs/2310.03798 has been replaced.
link: https://scholar.google.com/scholar?q=a

The Quantum Spectral Method: From Atomic Orbitals to Classical Self-Force
Can classical systems be described analytically at all orders in their interaction strength? For periodic and approximately periodic systems, the answer is yes, as we show in this work. Our analytical approach, which we call the \textit{Quantum Spectral Method}, is based on a novel application of Bohr's correspondence principle, obtaining non-perturbative classical dynamics as the classical limit of \textit{quantum matrix elements}. A major application of our method is the calculation of self-f…

Exploring the Non-uniqueness of Node Co-occurrence Matrices of Hypergraphs
Timothy LaRock, Renaud Lambiotte
https://arxiv.org/abs/2506.01479 https://

Exploring the Non-uniqueness of Node Co-occurrence Matrices of Hypergraphs
Hypergraphs extend traditional networks by capturing multi-way or group interactions. Given the complexity of hypergraph data and the wide range of methodology available for pairwise network analysis, hypergraph data is often projected onto a weighted and undirected network. The simplest of these projections, often referred to as a node co-occurrence matrix, is known to be non-unique, as distinct non-isomorphic hypergraphs can produce the same weighted adjacency matrix. This non-uniqueness rais…

Improving compiler support for SIMD offload using Arm Streaming SVE
Mohamed Husain Noor Mohamed, Adarsh Patil, Latchesar Ionkov, Eric Van Hensbergen
https://arxiv.org/abs/2506.02233

Improving compiler support for SIMD offload using Arm Streaming SVE
The wider adoption of tightly coupled core-adjacent accelerators, such as Arm Scalable Matrix Extension (SME), hinges on lowering software programming complexity. In this paper, we focus on enabling the use of SME architecture in Streaming Scalable Vector Extension (SSVE) mode for workloads written in C/C++. While current compilers optimize loops for all types of SIMD instructions, these techniques primarily target vector units within the core and falter when applied to disaggregated, core-adja…

Not every graph can be reconstructed from its boundary distance matrix
Jos\'e C\'aceres, Ignacio M. Pelayo
https://arxiv.org/abs/2506.02652 https:/…

Not every graph can be reconstructed from its boundary distance matrix
A vertex $v$ of a connected graph $G$ is said to be a boundary vertex of $G$ if for some other vertex $u$ of $G$, no neighbor of $v$ is further away from $u$ than $v$. The boundary $\partial(G)$ of $G$ is the set of all of its boundary vertices. The boundary distance matrix $\hat{D}_G$ of a graph $G=([n],E)$ is the square matrix of order $κ$, being $κ$ the order of $\partial(G)$, such that for every $i,j\in \partial(G)$, $[\hat{D}_G]_{ij}=d_G(i,j)$. In a recent paper [doi.org/10.7151/dmgt…

This https://arxiv.org/abs/2406.06819 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Classification of almost abelian Lie groups admitting left-invariant complex or symplectic structures
We classify the almost abelian Lie algebras $\mathfrak g_A=\mathbb R e_0 \ltimes_A \mathbb R^{2n-1}$ admitting complex or symplectic structures. The matrix $A\in M(2n-1,\mathbb R )$ encodes the adjoint action of $e_0$ on the abelian ideal $\mathbb R^{2n-1}$, and the existence of complex or symplectic structures on $\mathfrak g_A$ imposes restrictions on the Jordan normal form of $A$. The classification essentially reduces to the case when $A$ is nilpotent, so we start by considering this case. …

Testing for large-dimensional covariance matrix under differential privacy
Shiwei Sang, Yicheng Zeng, Xuehu Zhu, Shurong Zheng
https://arxiv.org/abs/2506.02410

Testing for large-dimensional covariance matrix under differential privacy
The increasing prevalence of high-dimensional data across various applications has raised significant privacy concerns in statistical inference. In this paper, we propose a differentially private integrated statistic for testing large-dimensional covariance structures, enabling accurate statistical insights while safeguarding privacy. First, we analyze the global sensitivity of sample eigenvalues for sub-Gaussian populations, where our method bypasses the commonly assumed boundedness of data co…

Atomic scale structure and dynamical properties of (TeO$_2$)$_{1-x}$-(Na$_2$O)$_{x}$ glasses through first-principles modeling and XRD measurements
Firas Shuaib, Assil Bouzid, Remi Piotrowski, Gaelle Delaizir, Pierre-Marie Geffroy, David Hamani, Raghvender Raghvender, Steve Dave Wansi Wendji, Carlo Massobrio, Mauro Boero, Guido Ori, Philippe Thomas, Olivier Masson

Atomic scale structure and dynamical properties of (TeO$_2$)$_{1-x}$-(Na$_2$O)$_{x}$ glasses through first-principles modeling and XRD measurements
We resort to first-principles molecular dynamics, in synergy with experiments, to study structural evolution and Na$^+$ cation diffusion inside (TeO$_2$)$_{1-x}$-(Na$_2$O)$_{x}$ (x = 0.10-0.40) glasses. Experimental and modeling results show a fair quantitative agreement in terms of total X-ray structure factors and pair distribution functions, thereby setting the ground for a comprehensive analysis of the glassy matrix evolution. We find that the structure of (TeO$_2$)$_{1-x}$-(Na$_2$O)$_{x}$ …

This https://arxiv.org/abs/2503.14315 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

Equiripple MIMO Beampattern Synthesis using Chebyshev Approximation
This letter presents a method for synthesizing equiripple MIMO transmit beampatterns using Chebyshev approximation. The MIMO beampattern is represented as a non-negative real-valued trigonometric polynomial where the $\ell^{\text{th}}$ order polynomial coefficient is the sum of the $\ell^{\text{th}}$ order diagonal of the waveform correlation matrix. The optimal coefficients for a given equiripple beampattern design is then posed as a Chebyshev approximation problem which is efficiently solved …

On local non-tangential growth of the resolvent of a banded Toeplitz operator
L. Golinskii, S. Kupin
https://arxiv.org/abs/2506.00584 https://

On local non-tangential growth of the resolvent of a banded Toeplitz operator
We study the growth of the resolvent of a Hardy--Toeplitz operator $T_b$ with a Laurent polynomial symbol (\emph{i.e., } the matrix $T_b$ is banded), at the neighborhood of a point $w_0\in\partial(σ(T_b))$ on the boundary of its spectrum. We show that such growth is inverse linear in some non-tangential domains at the vertex $w_0$, provided that $w_0$ does not belong to a certain finite set on the complex plane.

Algorithm for computing canonical bases and foldings of quantum groups
Toshiaki Shoji, Zhiping Zhou
https://arxiv.org/abs/2506.00793 https://

Algorithm for computing canonical bases and foldings of quantum groups
Let ${\mathbf U}_q^-$ be the negative half of a quantum group of finite type. Let $P$ be the transition matrix between the canonical basis and a PBW basis of ${\mathbf U}_q^-$. In the case ${\mathbf U}_q^-$ is symmetric, Antor gave a simple algorithm of computing $P$ by making use of monomial bases. By the folding theory, ${\mathbf U}_q^-$ (symmetric, with a certain automorphism) is related to a quantum group $\underline{\mathbf U}_q^-$ of non-symmetric type. In this paper, we extend the result…

Accelerating Randomized Algorithms for Low-Rank Matrix Approximation
Dandan Jiang, Bo Fu, Weiwei Xu
https://arxiv.org/abs/2506.03859 https://

Accelerating Randomized Algorithms for Low-Rank Matrix Approximation
Randomized algorithms are overwhelming methods for low-rank approximation that can alleviate the computational expenditure with great reliability compared to deterministic algorithms. A crucial thought is generating a standard Gaussian matrix $\mathbf{G}$ and subsequently obtaining the orthonormal basis of the range of $\mathbf{AG}$ for a given matrix $\mathbf{A}$. Recently, the \texttt{farPCA} algorithm offers a framework for randomized algorithms, but the dense Gaussian matrix remains computa…

This https://arxiv.org/abs/2505.23891 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

A microscopic Normal Matrix Model for $(A)dS_2$
We describe the duality between the gravitating $c=1$ (compact) Sine-Gordon model and a normal matrix model. From a two-dimensional quantum gravity perspective and due to the periodic nature of the potential, this model admits both anti-de Sitter and de-Sitter saddles, similarly to simpler models of Sine-Dilaton gravity, as well as more complicated interpolating "wineglass wormhole" geometries. From a string theory perspective the Euclidean de-Sitter (genus zero) saddles are related to the pres…

This https://arxiv.org/abs/2503.20117 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLG_…

Exact and Linear Convergence for Federated Learning under Arbitrary Client Participation is Attainable
This work tackles the fundamental challenges in Federated Learning (FL) posed by arbitrary client participation and data heterogeneity, prevalent characteristics in practical FL settings. It is well-established that popular FedAvg-style algorithms struggle with exact convergence and can suffer from slow convergence rates since a decaying learning rate is required to mitigate these scenarios. To address these issues, we introduce the concept of stochastic matrix and the corresponding time-varyin…

This https://arxiv.org/abs/2412.15969 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On cutoff via rigidity for high dimensional curved diffusions
We consider overdamped Lanvegin diffusions in Euclidean space, with curvature equal to the spectral gap. This includes the Ornstein-Uhlenbeck process as well as non Gaussian and non product extensions with convex interaction, such as the Dyson process from random matrix theory. We show that a cutoff phenomenon or abrupt convergence to equilibrium occurs in high-dimension, at a critical time equal to the logarithm of the dimension divided by twice the spectral gap. This cutoff holds for Wasserst…

Rapid yet accurate Tile-circuit and device modeling for Analog In-Memory Computing
J. Luquin, C. Mackin, S. Ambrogio, A. Chen, F. Baldi, G. Miralles, M. J. Rasch, J. B\"uchel, M. Lalwani, W. Ponghiran, P. Solomon, H. Tsai, G. W. Burr, P. Narayanan
https://arxiv.org/abs/2506.00004

Rapid yet accurate Tile-circuit and device modeling for Analog In-Memory Computing
Analog In-Memory Compute (AIMC) can improve the energy efficiency of Deep Learning by orders of magnitude. Yet analog-domain device and circuit non-idealities -- within the analog ``Tiles'' performing Matrix-Vector Multiply (MVM) operations -- can degrade neural-network task accuracy. We quantify the impact of low-level distortions and noise, and develop a mathematical model for Multiply-ACcumulate (MAC) operations mapped to analog tiles. Instantaneous-current IR-drop (the most significant circ…

Fast numerical generation of Lie closure
Yutaro Iiyama
https://arxiv.org/abs/2506.01120 https://arxiv.org/pdf/2506.01120

Fast numerical generation of Lie closure
Finding the Lie-algebraic closure of a handful of matrices has important applications in quantum computing and quantum control. For most realistic cases, the closure cannot be determined analytically, necessitating an explicit numerical construction. The standard construction algorithm makes repeated calls to a subroutine that determines whether a matrix is linearly independent from a potentially large set of matrices. Because the common implementation of this subroutine has a high complexity, …

Equivalence of Left- and Right-Invariant Extended Kalman Filters on Matrix Lie Groups
Finn G. Maurer, Erlend A. Basso, Henrik M. Schmidt-Didlaukies, Torleiv H. Bryne
https://arxiv.org/abs/2506.01514

Equivalence of Left- and Right-Invariant Extended Kalman Filters on Matrix Lie Groups
This paper derives the extended Kalman filter (EKF) for continuous-time systems on matrix Lie groups observed through discrete-time measurements. By modeling the system noise on the Lie algebra and adopting a Stratonovich interpretation for the stochastic differential equation (SDE), we ensure that solutions remain on the manifold. The derivation of the filter follows classical EKF principles, naturally integrating a necessary full-order covariance reset post-measurement update. A key contribut…

Equation of State and First Principles Prediction of the Vibrational Matrix Shift of Solid Parahydrogen
Alexander Ibrahim, Lecheng Wang, Tom Halverson, Robert J Le Roy, Pierre-Nicholas Roy
https://arxiv.org/abs/2506.01294

Equation of State and First Principles Prediction of the Vibrational Matrix Shift of Solid Parahydrogen
We generate the equation of state (EOS) of solid parahydrogen using a path-integral Monte Carlo (PIMC) simulation based on a highly accurate first-principles adiabatic hindered rotor (AHR) potential energy curve for the \para dimer. The EOS curves for the fcc and hcp structures of solid parahydrogen near the equilibrium density show that the hcp structure is the more stable of the two, in agreement with experiment. To accurately reproduce the structural and energy properties of solid parahydrog…

This https://arxiv.org/abs/2501.10745 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Changing the ranking in eigenvector centrality of a weighted graph by small perturbations
In this article, we consider eigenvector centrality for the nodes of a graph and study the robustness (and stability) of this popular centrality measure. For a given weighted graph ${\mathcal G}$ (both directed and undirected), we consider the associated weighted adjacency matrix $A$, which by definition is a non-negative matrix. The eigenvector centralities of the nodes of ${\mathcal G}$ are the entries of the Perron eigenvector of $A$, which is the (positive) eigenvector associated with the e…

Purcell Enhancement and Suppression in Laser Cooling of Yb$^{3 }$:YLF Nanocrystals in a Fabry-P\'erot Microcavity
Lucas Mendicino, Franco Mayo, Christian Schmiegelow, Augusto Roncaglia
https://arxiv.org/abs/2505.24083

Purcell Enhancement and Suppression in Laser Cooling of Yb$^{3+}$:YLF Nanocrystals in a Fabry-Pérot Microcavity
We investigate the improvement of anti-Stokes laser cooling of a Yb$^{3+}$:YLF nanocrystal in a Fabry-Pérot microcavity via the Purcell effect. Our analysis accounts for both the enhancement of emission lines resonant with the cavity transmission and the suppression of off-resonance emissions. Using a quantum-mechanical framework, we modeled the Yb$^{3+}$ ions in a YLiF$_4$ matrix and the laser system to calculate the minimum achievable temperature and cooling efficiency, incorporating cavity-…

$C^{1,\alpha}$ regularity of the solution for the obstacle problem for the linearized Monge-Amp\`ere operator
Meng Ji
https://arxiv.org/abs/2505.24410 http…

$C^{1,α}$ regularity of the solution for the obstacle problem for the linearized Monge-Ampère operator
In this paper, we study the regularity of the solution for the obstacle problem associated with the linearized Monge-Ampère operator: \begin{align*} \begin{cases} &u\geqφ\text{\quad in } Ω &L_{ w}u=\tr( W D^{2}u)\leq 0 \text{\quad in } Ω &L_{ w}u= 0 \text{\quad in } \{u>φ\} &u=0 \text{\quad on } \partialΩ, \end{cases} \end{align*} where $ W=(\det D^{2} w) D^{2} w^{-1}$ is the matrix of cofactor of $D^{2} w$, $w$ satisfies $λ\leq \det D^{2} w \leq Λ$ and $ w=0$ on $\partial �…

This https://arxiv.org/abs/2407.01227 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Non-intersecting paths and the determinant of the distance matrix of a tree
We present the first combinatorial proof of the Graham-Pollak Formula for the determinant of the distance matrix of a tree, via sign-reversing involutions and the Lindström-Gessel-Viennot Lemma. Our approach provides a cohesive and unified framework for the understanding of the existing generalizations and $q$-analogues of the Graham-Pollak Formula, and facilitates the derivation of a natural simultaneous generalizations for them.

Stable recovery of complex dictionary-sparse signals from phaseless measurements
Lianxing Xia, Haiye Huo
https://arxiv.org/abs/2506.03961 https://

Stable recovery of complex dictionary-sparse signals from phaseless measurements
Dictionary-sparse phase retrieval, which is also known as phase retrieval with redundant dictionary, aims to reconstruct an original dictionary-sparse signal from its measurements without phase information. It is proved that if the measurement matrix $A$ satisfies null space property (NSP)/strong dictionary restricted isometry property (S-DRIP), then the dictionary-sparse signal can be exactly/stably recovered from its magnitude-only measurements up to a global phase. However, the S-DRIP holds …

Application range of perfect spin hydrodynamics
Zbigniew Drogosz, Wojciech Florkowski, Valeriya Mykhaylova
https://arxiv.org/abs/2506.01537 https://…

Application range of perfect spin hydrodynamics
The application range of perfect spin hydrodynamics is studied in two cases: one based on the classical spin description and the other using a quantum spin density matrix (Wigner function). Different forms of the conditions connecting the components of the spin polarization tensor, particle mass, temperature, and hydrodynamic flow are introduced, and their mutual relations are explained. The results obtained are important for practical applications of spin hydrodynamics to model heavy-ion colli…

This https://arxiv.org/abs/2504.21223 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Surface Structure and Surface State of a Tight-Binding Model on a Diamond Lattice
Surface states of a tight-binding model with nearest-neighbor hopping on a diamond lattice of finite thickness are investigated. We consider systems with (001), (110), and (111) surfaces. Even if the surface direction is fixed, there is freedom to choose the surface structure due to the two-sublattice nature of a diamond lattice. The existence of surface states is governed by the topology of the matrix elements of the bulk Hamiltonian. In this sense, the existence of surface states is determine…

Test Gravitational-Wave Polarizations with Space-Based Detectors
Jun-Shuai Wang, Chang Liu, Ju Chen, Jibo He
https://arxiv.org/abs/2506.02909 https://

Test Gravitational-Wave Polarizations with Space-Based Detectors
In this work, we systematically investigate the capability of space-based gravitational wave detectors in constraining parameters of non-tensor polarization modes. Using Bayesian inference and Fisher Information Matrix methods, we analyze gravitational wave signals from the inspiral phase of supermassive binary black hole mergers. By starting with time-domain signals and applying Fourier transforms, we avoid the use of the stationary phase approximation. We found an asymmetry in the estimation …

This https://arxiv.org/abs/2002.10921 has been replaced.
link: https://scholar.google.com/scholar?q=a

A computer-friendly construction of the monster
Let $\mathbb{M}$ be the monster group which is the largest sporadic finite simple group, and has first been constructed in 1982 by Griess. In 1985, Conway has constructed a 196884-dimensional representation $ρ$ of $\mathbb{M}$ with matrix coefficients in $\mathbb{Z}[\frac{1}{2}]$. So these matrices may be reduced modulo any (not necessarily prime) odd number $p$, leading to representations of $\mathbb{M}$ in odd characteristic. The representation $ρ$ is based on representations of two maximal…

This https://arxiv.org/abs/2408.10868 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Inconsistency Removal of Reduced Bases in Parametric Model Order Reduction by Matrix Interpolation using Adaptive Sampling and Clustering
Parametric model order reduction by matrix interpolation allows for efficient prediction of the behavior of dynamic systems without requiring knowledge about the underlying parametric dependency. Within this approach, reduced models are first sampled and then made consistent with each other by transforming the underlying reduced bases. Finally, the transformed reduced operators can be interpolated to predict reduced models for queried parameter points. However, the accuracy of the predicted red…

This https://arxiv.org/abs/2506.02880 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the rate of convergence in the CLT for LSS of large-dimensional sample covariance matrices
This paper investigates the rate of convergence for the central limit theorem of linear spectral statistic (LSS) associated with large-dimensional sample covariance matrices. We consider matrices of the form ${\mathbf B}_n=\frac{1}{n}{\mathbf T}_p^{1/2}{\mathbf X}_n{\mathbf X}_n^*{\mathbf T}_p^{1/2},$ where ${\mathbf X}_n= (x_{i j} ) $ is a $p \times n$ matrix whose entries are independent and identically distributed (i.i.d.) real or complex variables, and ${\mathbf T} _p$ is a $p\times p$ nonr…

Stabilization of the Gradient Method for Solving Linear Algebraic Systems - A Method Related to the Normal Equation
Ibrahima Dione
https://arxiv.org/abs/2506.00702

Stabilization of the Gradient Method for Solving Linear Algebraic Systems - A Method Related to the Normal Equation
Although it is relatively easy to apply, the gradient method often displays a disappointingly slow rate of convergence. Its convergence is specially based on the structure of the matrix of the algebraic linear system, and on the choice of the stepsize defining the new iteration. We propose here a simple and robust stabilization of the gradient method, which no longer assumes a structure on the matrix (neither symmetric, nor positive definite) to converge, and which no longer requires an approac…

High-Dimensional Regularized Additive Matrix Autoregressive Model
Debika Ghosh, Samrat Roy, Nilanjana Chakraborty
https://arxiv.org/abs/2506.01403 https://…

High-Dimensional Regularized Additive Matrix Autoregressive Model
High-dimensional time series has diverse applications in econometrics and finance. Recent models for capturing temporal dependence have employed a bilinear representation for matrix time series, or the Tucker-decomposition based representation in case of tensor time series. A bilinear or Tucker-decomposition based temporal effect is difficult to interpret on many occasions, along with its computational complexity due to the non-convex nature of the underlying optimization problem. Moreover, the…

This https://arxiv.org/abs/2412.13320 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Density Matrix Renormalization Group simulations of the SU(N) Fermi-Hubbard chain implementing the full SU(N) symmetry via Semi-Standard Young Tableaux and Unitary Group Subduction Coefficients
We have developed an efficient method for performing density matrix renormalization group (DMRG) simulations of the SU(N) Fermi-Hubbard chain with open boundary conditions, fully leveraging the SU(N) symmetry of the problem. This method extends a previously developed approach for the SU(N) Heisenberg model and relies on the systematic use of the semi-standard Young tableaux (SSYT) basis in a DMRG algorithm `a la White. Specifically, the method aligns the site-by-site growth process of the infin…

This https://arxiv.org/abs/2504.06481 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Statistical Physics of the Polarised IKKT Matrix Model
The polarised IKKT matrix model is the worldpoint theory of $N$ D-instantons in a background three-form flux of magnitude $Ω$, and promises to be a highly tractable model of holography. The matrix integral can be viewed as a statistical physics partition function with inverse temperature $Ω^4$. At large $Ω$ the model is dominated by a matrix configuration corresponding to a 'polarised' spherical D1-brane. We show that at a critical value of $Ω^2 N$ the model undergoes a first order phase tr…

This https://arxiv.org/abs/2505.23633 has been replaced.
initial toot: https://mastoxiv.page/@…

Measuring topological invariants of even-dimensional non-Hermitian systems through quench dynamics
The accurate determination of non-Hermitian (NH) topological invariants plays a central role in the study of NH topological phases. In this work, we propose a general framework for directly measuring NH topological invariants in even-dimensional systems through quench dynamics. Our approach hinges on constructing an auxiliary Hermitian matrix topologically equivalent to the original NH Hamiltonian, enabling topological characterization via reduced-dimensional momentum subspaces called band inve…

The Schur multiplier norm and its dual norm
Erik Christensen
https://arxiv.org/abs/2505.24670 https://arxiv.org/pdf/2505.24670…

The Schur multiplier norm and its dual norm
We present a formula for the Schur multiplier norm of a complex self-adjoint matrix, and a formula for the norm, which is dual to the Schur multiplier norm, of a self-adjoint matrix. For a complex self-adjoint $n \times n $ matrix $X$ we show that its Schur multiplier norm is determined by $$ \|X\|_S = \min \{\, \|\mathrm{diag}(P)\|_\infty \, :\, - P \leq X \leq P \, \}.$$ The dual space of $( M_n(\bc), \|.\|_S)$ is $(M_n(\bc), \|.\|_{cbB}).$ For $X=X…

This https://arxiv.org/abs/2505.21924 has been replaced.
initial toot: https://mastoxiv.page/@ar…

Modified Transfer Matrix Method for the Extraction of Material Properties via Terahertz Time-Domain Spectroscopy
Terahertz Time-Domain Spectroscopy is a powerful technique for extracting the low-frequency optical properties of materials. However, the optical constants are difficult to determine directly from the experimental transfer function, such that various numerical approximations must be implemented to describe specific conditions. Here, we introduce a modified Transfer Matrix Method that uses a genetic algorithm for optimization to determine the refractive index of materials in the THz regime. We s…

VUSA: Virtually Upscaled Systolic Array Architecture to Exploit Unstructured Sparsity in AI Acceleration
Shereef Helal, Alberto Garcia-Ortiz, Lennart Bamberg
https://arxiv.org/abs/2506.01166

VUSA: Virtually Upscaled Systolic Array Architecture to Exploit Unstructured Sparsity in AI Acceleration
Leveraging high degrees of unstructured sparsity is a promising approach to enhance the efficiency of deep neural network DNN accelerators - particularly important for emerging Edge-AI applications. We introduce VUSA, a systolic-array architecture that virtually grows based on the present sparsity to perform larger matrix multiplications with the same number of physical multiply-accumulate MAC units. The proposed architecture achieves saving by 37% and 68% in area and power efficiency, respecti…

Universality of convergence rate of rightmost eigenvalue of complex IID random matrices
Yutao Ma, Xinchen Hu
https://arxiv.org/abs/2506.04560 https://

Universality of convergence rate of rightmost eigenvalue of complex IID random matrices
Let $X$ be an $n\times n$ matrix with independent and identically distributed (i.i.d.) entries $x_{ij} \stackrel{\text { d }}{=} n^{-1 / 2} ξ$ with $ξ$ being a complex random variable of mean zero and variance one. Let $\{σ_i\}_{1\le i\le n}$ be the eigenvalues of $X,$ and $R_n:=\max_i \Re σ_i$ and $Z_n$ be some scaled version of $R_n.$ It was proved that $Z_n$ converges weakly to the Gumbel distribution $Λ$ under certain moment conditions on $ξ.$ We further prove that for a complex rando…

Real and finite field versions of Chebotarev's theorem
Tarek Emmrich, Stefan Kunis
https://arxiv.org/abs/2506.02947 https://arxiv…

Real and finite field versions of Chebotarev's theorem
Chebotarev's theorem on roots of unity states that all minors of the Fourier matrix of prime size are non-vanishing. This result has been rediscovered several times and proved via different techniques. We follow the proof of Evans and Isaacs and generalize the original result to a real version and a version over finite fields. For the latter, we are able to remove an order condition between the characteristic of the field and the size of the matrix as well as decrease a sufficient lower bound o…

Understanding synchronization between quantum self-sustained oscillators through coherence generation
Mohit Kumar, Bijay Kumar Agarwalla
https://arxiv.org/abs/2506.01703

Understanding synchronization between quantum self-sustained oscillators through coherence generation
Understanding the origin of phase synchronization between quantum self-sustained oscillators has garnered significant interest in recent years. In this work, we study phase synchronization in three settings: between two continuous-variable oscillators, between two arbitrary quantum spins, and within a hybrid setup involving a spin and an oscillator. We derive a simple and general condition on the elements of the joint density matrix that must be satisfied for them to contribute to the relative …

This https://arxiv.org/abs/2503.15954 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Holographic deformations of matrix models
We study maximal supergravity in two dimensions, obtained from reduction of IIA supergravity on an $S^8$ sphere. The theory captures the low-lying fluctuations around the non-conformal D0-brane near-horizon geometry, dual to operators in the BFSS matrix model. Upon exciting some of the supergravity scalars, we construct half-supersymmetric domain wall solutions preserving $SO(p)\times SO(9-p)$ subgroups of the original $SO(9)$ symmetry. We determine their uplift to ten dimensions and the corres…

High-Speed Ultra-Energy-Efficient Memristor-Based Massive MIMO SIC Detector Circuit with Hybrid Analog-Digital Computing Architecture
Jia-Hui Bi, Shaoshi Yang, Sheng Chen, Ping Zhang
https://arxiv.org/abs/2506.03495

High-Speed Ultra-Energy-Efficient Memristor-Based Massive MIMO SIC Detector Circuit with Hybrid Analog-Digital Computing Architecture
The emerging memristor crossbar array based computing circuits exhibit computing speeds and energy efficiency far surpassing those of traditional digital processors. This type of circuits can complete high-dimensional matrix operations in an extremely short time through analog computing, making it naturally applicable to linear detection and maximum likelihood detection in massive multiple-input multiple-output (MIMO) systems. However, the challenge of employing memristor crossbar arrays to eff…

This https://arxiv.org/abs/2412.12533 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Multiparty Entanglement Microscopy of Quantum Ising models in 1d, 2d and 3d
Entanglement microscopy reveals the true quantum correlations among the microscopic building blocks of many-body systems [Nat. Commun. 16, 96 (2025)]. Using this approach, we study the multipartite entanglement of the quantum Ising model in 1d, 2d, and 3d. We first obtain the full reduced density matrix (tomography) of subregions that have at most 4 sites via quantum Monte Carlo, exact diagonalization, and the exact solution in 1d. We then analyze both bipartite and genuine multipartite entangl…

This https://arxiv.org/abs/2504.13693 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A microlocal Cauchy problem through a crossing point of Hamiltonian flows
In this paper, we consider $2\times 2$ matrix-valued pseudodifferential equations in which the two characteristic sets intersect with finite contact order. We show that the asymptotic behavior of its solution changes dramatically before and after the crossing point, and provide a precise asymptotic formula. This is a generalization of the previous results for matrix-valued Schrödinger operators and Landau-Zener models. The proof relies on a normal form reduction and a detailed analysis of a si…

On the rate of convergence in the CLT for LSS of large-dimensional sample covariance matrices
Jiang Cui, Jiang Hu, Zhidong Bai, Guorong Hu
https://arxiv.org/abs/2506.02880

On the rate of convergence in the CLT for LSS of large-dimensional sample covariance matrices
This paper investigates the rate of convergence for the central limit theorem of linear spectral statistic (LSS) associated with large-dimensional sample covariance matrices. We consider matrices of the form ${\mathbf B}_n=\frac{1}{n}{\mathbf T}_p^{1/2}{\mathbf X}_n{\mathbf X}_n^*{\mathbf T}_p^{1/2},$ where ${\mathbf X}_n= (x_{i j} ) $ is a $p \times n$ matrix whose entries are independent and identically distributed (i.i.d.) real or complex variables, and ${\mathbf T} _p$ is a $p\times p$ nonr…

This https://arxiv.org/abs/2504.20305 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Fast LDL factorization for dense and sparse symmetric matrices over an arbitrary field
While existing algorithms may be used to solve a linear system over a general field in matrix-multiplication time, the complexity of constructing a symmetric triangular factorization (LDL) has received relatively little formal study. The LDL factorization is a common tool for factorization of symmetric matrices, and, unlike orthogonal counterparts, generalizes to an arbitrary field. We provide algorithms for dense and sparse LDL nd LU factorization that aim to minimize complexity for factorizat…

Phase Transition of Topological Index driven by Dephasing
Thomas G. Kiely, Cenke Xu
https://arxiv.org/abs/2506.04102 https://arxiv.or…

Phase Transition of Topological Index driven by Dephasing
We study topological insulators under dephasing noise. With examples of both a $2d$ Chern insulator and a $3d$ topological insulator protected by time-reversal symmetry, we demonstrate that there is a phase transition at finite dephasing strength between phases with nontrivial and trivial topological indices. Here the topological index is defined through the correlation matrix. The transition can be diagnosed through the spectrum of the whole correlation matrix or of a local subsystem. Interest…

Rounding error analysis of randomized CholeskyQR2 for sparse matrices
Haoran Guan, Yuwei Fan
https://arxiv.org/abs/2506.04208 https://

Rounding error analysis of randomized CholeskyQR2 for sparse matrices
This work focuses on rounding error analysis of randomized CholeskyQR2 (RCholeskyQR2) for sparse matrices. We form RCholeskyQR2 with CholeskyQR2 and matrix sketching in order to accelerate CholeskyQR2 and improve its applicability by compressing the input matrix $X \in \mathbb{R}^{m\times n}$. In many real-world applications, the input matrix $X$ is always sparse. In this work, we follow the model of sparse matrices proposed in \cite{CSparse} and provide an improved rounding error analysis of R…

This https://arxiv.org/abs/2505.20262 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

On world-sheet S-matrix of NSR string in static gauge
As was shown in arXiv:1203.1054, expanding the Nambu action near the "long string" vacuum in the static gauge one finds that the one-loop 2 to 2 scattering amplitude of the $D-2=24$ transverse 2d fluctuations $X^i$ is given by a pure phase expression consistent with underlying integrability. Similar computation in the Green-Schwarz superstring was carried out in arXiv:2404.09658. Here we consider the case of the NSR string starting with its manifestly 2d covariant action given by $D$ scalar mul…

This https://arxiv.org/abs/2410.10946 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Equivalence checking of quantum circuits via intermediary matrix product operator
As quantum computing advances, the complexity of quantum circuits is rapidly increasing, driving the need for robust methods to aid in their design. Equivalence checking plays a vital role in identifying errors that may arise during compilation and optimization of these circuits and is a critical step in quantum circuit verification. In this work, we introduce a novel method based on Matrix Product Operators (MPOs) for determining the equivalence of quantum circuits. Our approach contracts tens…

Computing matrix $\varphi$-functions arising in exponential integrators
Awad H. Al-Mohy, Xiaobo Liu
https://arxiv.org/abs/2506.01193 https://

Computing matrix $φ$-functions arising in exponential integrators
A new scaling and recovering algorithm is proposed for simultaneously computing the matrix $φ$-functions that arise in exponential integrator methods for the numerical solution of certain first-order systems of ordinary differential equations (ODEs). The algorithm initially scales the input matrix down by a nonnegative integer power of two, then computes the $[m/m]$ diagonal Padé approximant to $φ_p$, where $p$ is the largest index of interest. The remaining $[m+p{-}j/m]$ Padé approximants …

This https://arxiv.org/abs/2501.09567 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Bridging conformal field theory and parton approaches to SU(n)_k chiral spin liquids
We employ the $\mathrm{SU}(n)_k$ Wess-Zumino-Witten (WZW) model in conformal field theory to construct lattice wave functions in both one and two dimensions. The spins on all lattice sites are chosen to transform under the $\mathrm{SU}(n)$ irreducible representation with a single row and $k$ boxes in the Young tableau. It is demonstrated that the wave functions can be reinterpreted as parton states, which enables efficient conversion to matrix product states such that many physical properties c…

S-algebra in Gauge Theory: Twistor, Spacetime and Holographic Perspectives
Adam Kmec, Lionel Mason, Romain Ruzziconi, Atul Sharma
https://arxiv.org/abs/2506.01888

S-algebra in Gauge Theory: Twistor, Spacetime and Holographic Perspectives
The celestial $S$-algebra arose from a reinterpretation of collinear limits of the Yang-Mills S-matrix as OPEs in celestial holography. It was subsequently represented via asymptotic charge aspects defined in the Yang-Mills radiative phase space defined at null infinity on the one hand, and via a twisted holography vertex algebra construction in twistor space on the other. Here we first identify it with the traditional symmetry algebra of self-dual Yang-Mills theory as an integrable system via …

This https://arxiv.org/abs/2504.08335 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Entropic bounds for conditionally Gaussian vectors and applications to neural networks
Using entropic inequalities from information theory, we provide new bounds on the total variation and 2-Wasserstein distances between a conditionally Gaussian law and a Gaussian law with invertible covariance matrix. We apply our results to quantify the speed of convergence to Gaussian of a randomly initialized fully connected neural network and its derivatives - evaluated in a finite number of inputs - when the initialization is Gaussian and the sizes of the inner layers diverge to infinity. O…

Leveraging machine learning features for linear optical interferometer control
Sergei S. Kuzmin, Ivan V. Dyakonov, Stanislav S. Straupe
https://arxiv.org/abs/2505.24032

Leveraging machine learning features for linear optical interferometer control
We have developed an algorithm that constructs a model of a reconfigurable optical interferometer, independent of specific architectural constraints. The programming of unitary transformations on the interferometer's optical modes relies on either an analytical method for deriving the unitary matrix from a set of phase shifts or an optimization routine when such decomposition is not available. Our algorithm employs a supervised learning approach, aligning the interferometer model with a trainin…

This https://arxiv.org/abs/2412.06551 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Deterministic and randomized LU-Householder CholeskyQR
In this work, we develop LU-Householder CholeskyQR (LHC) for QR factorization of tall-skinny matrices. Similar to LU-CholeskyQR \cite{LUChol}, LHC does not require a sufficient condition of $κ_{2}(X)$ for the input tall-skinny matrix $X \in \mathbb{R}^{m\times n}$. This characteristic ensures the algorithm's reliability in the real-world applications, which is different from other CholeskyQR-type algorithms. To address the issue of numerical breakdown in Cholesky factorization of LU-CholeskyQR…

This https://arxiv.org/abs/2504.10484 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Generalized Symmetries of Non-SUSY and Discrete Torsion String Backgrounds
String / M-theory backgrounds with degrees of freedom at a localized singularity provide a general template for generating strongly correlated systems decoupled from lower-dimensional gravity. There are by now several complementary procedures for extracting the associated generalized symmetry data from orbifolds of the form $\mathbb{R}^6 / Γ$, including methods based on the boundary topology of the asymptotic geometry, as well as the adjacency matrix for fermionic degrees of freedom in the qui…

{\guillemotleft}Anticommuting{\guillemotright} $\mathbb{Z}_2$ quantum spin liquids
Sumiran Pujari, Harsh Nigam
https://arxiv.org/abs/2506.03866 https://

«Anticommuting» $\mathbb{Z}_2$ quantum spin liquids
We discuss a class of lattice $S=\frac{1}{2}$ quantum Hamiltonians with bond-dependent Ising couplings with a mutually «anticommuting» algebra of extensively many local $\mathbb{Z}_2$ conserved charges that was introduced in [arXiv:2407.06236] including the nomenclature. This mutual algebra is reminiscent of the spin-$\frac{1}{2}$ Pauli matrix algebra but encoded in the structure of \emph{local conserved charges}. These models have finite residual entropy density in the ground state with a si…

Point Jacobi-type preconditioning and parameter tuning for Calderon-preconditioned Burton-Miller method in transmission problems
Keigo Tomoyasu, Hiroshi Isakari
https://arxiv.org/abs/2506.01440

Point Jacobi-type preconditioning and parameter tuning for Calderon-preconditioned Burton-Miller method in transmission problems
It was recently demonstrated that the boundary element method based on the Burton-Miller formulation (BM-BEM), widely used for solving exterior problems, can be adapted to solve transmission problems efficiently. This approach utilises Calderon's identities to improve the spectral properties of the underlying integral operator. Consequently, most eigenvalues of the squared BEM coefficient matrix, i.e. the collocation-discretised version of the operator, cluster at a few points in the complex pl…

This https://arxiv.org/abs/2501.03742 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Computing accurate eigenvalues using a mixed-precision Jacobi algorithm
We provide a rounding error analysis of a mixed-precision preconditioned Jacobi algorithm, which uses low precision to compute the preconditioner, applies it at high precision (amounting to two matrix-matrix multiplications) and solves the eigenproblem using the Jacobi algorithm at working precision. Our analysis yields meaningfully smaller relative forward error bounds for the computed eigenvalues compared with those of the Jacobi algorithm. We further prove that, after preconditioning, if the…

On the regularization property of Levenberg-Marquardt method with Singular Scaling for nonlinear inverse problems
Rafaela Filippozzi, Everton Boos, Douglas S. Gon\c{c}alves, Fermin S. V. Baz\'an
https://arxiv.org/abs/2506.00190

On the regularization property of Levenberg-Marquardt method with Singular Scaling for nonlinear inverse problems
Recently, in Applied Mathematics and Computation 474 (2024) 128688, a Levenberg-Marquardt method (LMM) with Singular Scaling was analyzed and successfully applied in parameter estimation problems in heat conduction where the use of a particular singular scaling matrix (semi-norm regularizer) provided approximate solutions of better quality than those of the classic LMM. Here we propose a regularization framework for the Levenberg-Marquardt method with Singular Scaling (LMMSS) applied to nonline…

This https://arxiv.org/abs/2504.13809 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A Fast Direct Solver for Boundary Integral Equations Using Quadrature By Expansion
We construct and analyze a hierarchical direct solver for linear systems arising from the discretization of boundary integral equations using the Quadrature by Expansion (QBX) method. Our scheme builds on the existing theory of Hierarchical Semi-Separable (HSS) matrix operators that contain low-rank off-diagonal submatrices. We use proxy-based approximations of the far-field interactions and the Interpolative Decomposition (ID) to construct compressed HSS operators that are used as fast direct …

Structured Column Subset Selection for Bayesian Optimal Experimental Design
Hugo D\'iaz, Arvind K. Saibaba, Srinivas Eswar, Vishwas Rao, Zichao Wendy Di
https://arxiv.org/abs/2506.00336

Structured Column Subset Selection for Bayesian Optimal Experimental Design
We consider optimal experimental design (OED) for Bayesian inverse problems, where the experimental design variables have a certain multiway structure. Given $d$ different experimental variables with $m_i$ choices per design variable $1 \le i\le d$, the goal is to select $k_i \le m_i$ experiments per design variable. Previous work has related OED to the column subset selection problem by mapping the design variables to the columns of a matrix $\mathbf{A}$. However, this approach is applicable o…

This https://arxiv.org/abs/2408.10370 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Convergence analysis of Levenberg-Marquardt method with Singular Scaling for nonzero residue nonlinear least-squares problems
Recently, a Levenberg-Marquardt method with Singular Scaling matrix, called LMMSS, was proposed and successfully applied in parameter estimation in heat conduction problems, where the choice of suitable singular scaling matrix resulted in better quality approximate solutions than those of the classical Levenberg-Marquardt. In this paper, we study convergence properties of LMMSS when applied to nonzero residual nonlinear least-squares problems. We show that the local convergence of the iterates …