Tootfinder

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 …

General Relativity in IIB Matrix Model
Pei-Ming Ho, Hikaru Kawai, Harold C. Steinacker
https://arxiv.org/abs/2509.06646 https://arxiv.org/pdf/2509.06646

General Relativity in IIB Matrix Model
The matrix models are non-perturbative formulations of string theory, from which many believe that spacetime arises. The matrix fluctuations around the spacetime thus created should represent both matter and gravitational fields. In this paper, we discuss how the gravitational field emerges from the IIB matrix model. In particular, we consider how diffeomorphism invariance arises and how unitarity is guaranteed in this theory. Specifically, we consider matrices as bilocal fields and discuss how…

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 …

FACT: the Features At Convergence Theorem for neural networks
Enric Boix-Adsera, Neil Mallinar, James B. Simon, Mikhail Belkin
https://arxiv.org/abs/2507.05644

FACT: the Features At Convergence Theorem for neural networks
A central challenge in deep learning theory is to understand how neural networks learn and represent features. To this end, we prove the Features at Convergence Theorem (FACT), which gives a self-consistency equation that neural network weights satisfy at convergence when trained with nonzero weight decay. For each weight matrix $W$, this equation relates the "feature matrix" $W^\top W$ to the set of input vectors passed into the matrix during forward propagation and the loss gradients passed t…

Subgraph Counting under Edge Local Differential Privacy Based on Noisy Adjacency Matrix
Jintao Guo, Ying Zhou, Chao Li, Guixun Luo
https://arxiv.org/abs/2507.06508

Subgraph Counting under Edge Local Differential Privacy Based on Noisy Adjacency Matrix
When analyzing connection patterns within graphs, subgraph counting serves as an effective and fundamental approach. Edge-local differential privacy (edge-LDP) and shuffle model have been employed to achieve subgraph counting under a privacy-preserving situation. Existing algorithms are plagued by high time complexity, excessive download costs, low accuracy, or dependence on trusted third parties. To address the aforementioned challenges, we propose the Noisy Adjacency Matrix (NAM), which combi…

Spatial weights matrix selection and model averaging for multivariate spatial autoregressive models
Xin Miao, Fang Fang, Xuening Zhu, Hansheng Wang
https://arxiv.org/abs/2509.06005

Spatial weights matrix selection and model averaging for multivariate spatial autoregressive models
In this paper, we focus on the model specification problem in multivariate spatial econometric models when a candidate set for the spatial weights matrix is available. We propose a model selection method for the multivariate spatial autoregressive model, when the true spatial weights matrix may not be in the candidates. We show that the selected estimator is asymptotically optimal in the sense of minimizing the squared loss. If the candidate set contains the true spatial weights matrix, the met…

Variable Matrix-Weighted Besov Spaces
Dachun Yang, Wen Yuan, Zongze Zeng
https://arxiv.org/abs/2509.07786 https://arxiv.org/pdf/2509.07786

Variable Matrix-Weighted Besov Spaces
In this article, applying matrix ${\mathcal A}_{p(\cdot),\infty}$ weights introduced in our previous work, we introduce the matrix-weighted variable Besov space via the matrix weight $W$ or the reducing operators ${\mathbb{A}}$ of order $p(\cdot)$ for $W$, Then we show that, defined either by the matrix weight $W$ or the reducing operators ${\mathbb{A}}$ of order $p(\cdot)$ for $W$, the matrix-weighted variable Besov spaces (respectively, the matrix-weighted variable Besov sequence spaces) are …

Dilepton angular distributions in the color-dipole $S$-matrix framework
Yan B. Bandeira, Victor P. Goncalves, Wolfgang Sch\"afer
https://arxiv.org/abs/2507.06207

Dilepton angular distributions in the color-dipole $S$-matrix framework
The dilepton production at forward rapidities in hadronic collisions at the LHC energies is considered and the helicity density matrix elements of gauge bosons that enter the Drell--Yan angular coefficients associated with the gauge boson decay ($G = γ^*, Z^0, W$) are derived using the color-dipole $S$ - matrix framework. We show results for $pp$ collisions at $\sqrt{s} = 14$ TeV for the nonvanishing helicity density matrix elements in the rapidity range of $2.0 \le y \le 4.0$ of the gauge bos…

Distributed Optimization of Finite Condition Number for Laplacian Matrix in Multi-Agent Systems
Yicheng Xu, Faryar Jabbari
https://arxiv.org/abs/2507.06440

Distributed Optimization of Finite Condition Number for Laplacian Matrix in Multi-Agent Systems
This paper addresses the distributed optimization of the finite condition number of the Laplacian matrix in multi-agent systems. The finite condition number, defined as the ratio of the largest to the second smallest eigenvalue of the Laplacian matrix, plays an important role in determining the convergence rate and performance of consensus algorithms, especially in discrete-time implementations. We propose a fully distributed algorithm by regulating the node weights. The approach leverages max …

Prescribed-Time Event-Triggered Control for Matrix-Scaled Networks
Sunny K P, Rakesh R Warier
https://arxiv.org/abs/2509.07703 https://arxiv.org/pdf/2509.0…

Prescribed-Time Event-Triggered Control for Matrix-Scaled Networks
This article proposes a distributed control method for matrix-scaled multi-agent networks aimed at achieving convergence within a user-defined time frame. The control law of each individual agent relies only on information from neighboring agents and is updated at discrete intervals determined by state-dependent triggering functions, reducing the frequency of agent interactions. To this end, first, the controller is augmented with a time-varying gain. Then, the dynamics of the closed-loop syste…

heise | Android-Smartphone: Nothing Phone (3) mit Dot-Matrix-Display im Test
Nothing schlägt mit dem Phone (3) den Weg in die Smartphone-Oberklasse ein. Aus den blinkenden LEDs wurde ein zweites Display.

Walk Matrix-Based Upper Bounds on Generalized Cospectral Mates
Muhammad Raza, Mudassir Shabbir, Waseem Abbas
https://arxiv.org/abs/2507.06927 https://

Walk Matrix-Based Upper Bounds on Generalized Cospectral Mates
The problem of characterizing graphs determined by their spectrum (DS) or generalized spectrum (DGS) has been a longstanding topic of interest in spectral graph theory, originating from questions in chemistry and mathematical physics. While previous studies primarily focus on identifying whether a graph is DGS, we address a related yet distinct question: how many non-isomorphic generalized cospectral mates a graph can have? Building upon recent advances that connect this question to the propert…

Crosslisted article(s) found for stat.ML. https://arxiv.org/list/stat.ML/new
[1/1]:
- Nonnegative matrix factorization and the principle of the common cause
E. Khalafyan, A. E. Allahverdyan, A. Hovhannisyan

Beyond Diagonal IRS Aided OFDM: Rate Maximization under Frequency-Dependent Reflection
Ye Yuan, Shuowen Zhang
https://arxiv.org/abs/2509.06378 https://arxi…

Beyond Diagonal IRS Aided OFDM: Rate Maximization under Frequency-Dependent Reflection
This paper studies a broadband orthogonal frequency division multiplexing (OFDM) system aided by a beyond diagonal intelligent reflecting surface (BD-IRS), where inter-connections exist among different elements such that the reflection matrix can exhibit a beyond diagonal structure. Under practical circuit structures, the reflection matrix of the BD-IRS is generally dependent on the circuit parameters (e.g., capacitance matrix for all tunable capacitors) as well as the operating frequency, whic…

Lissajous Varieties
Francesco Maria Mascarin, Simon Telen
https://arxiv.org/abs/2509.06844 https://arxiv.org/pdf/2509.06844

Lissajous Varieties
This paper studies affine algebraic varieties parametrized by sine and cosine functions, generalizing algebraic Lissajous figures in the plane. We show that, up to a combinatorial factor, the degree of these varieties equals the volume of a polytope. We deduce defining equations from rank constraints on a matrix with polynomial entries. We discuss applications of Lissajous varieties in dynamical systems, in particular the Kuramoto model. This leads us to study connections with convex optimizati…

Matrix-variate integer-valued autoregressive processes
Nuo Xu, Kai Yang, Fukang Zhu
https://arxiv.org/abs/2509.07347 https://arxiv.org/pdf/2509.07347

Matrix-variate integer-valued autoregressive processes
In the fields of sociology and economics, the modeling of matrix-variate integervalued time series is urgent. However, no prior studies have addressed the modeling of such data. To address this topic, this paper proposes a novel matrix-variate integer-valued autoregressive model. The key techniques lie in defining two leftand right-matricial thinning operators. The probabilistic and statistical properties of the proposed model are investigated. Furthermore, two estimation methods are developed:…

Site Basis Excitation Ansatz for Matrix Product States
Steven R. White
https://arxiv.org/abs/2509.06241 https://arxiv.org/pdf/2509.06241

Site Basis Excitation Ansatz for Matrix Product States
We introduce a simple and efficient variation of the tangent-space excitation ansatz used to compute elementary excitation spectra of one-dimensional quantum lattice systems using matrix product states (MPS). A small basis for the excitation tensors is formed based on a single diagonalization analogous to a single site DMRG step but for multiple states. Once overlap and Hamiltonian matrix elements are found, obtaining the excitation for any momentum only requires diagonalization of a tiny matri…

Hybrid restricted master problem for Boolean matrix factorisation
Ellen Visscher, Michael Forbes, Christopher Yau
https://arxiv.org/abs/2509.06192 https://…

Hybrid restricted master problem for Boolean matrix factorisation
We present bfact, a Python package for performing accurate low-rank Boolean matrix factorisation (BMF). bfact uses a hybrid combinatorial optimisation approach based on a priori candidate factors generated from clustering algorithms. It selects the best disjoint factors before performing either a second combinatorial or heuristic algorithm to recover the BMF. We show that bfact does particularly well at estimating the true rank of matrices in simulated settings. In real benchmarks, using a coll…

Singularity of biased discrete random matrix
Zeyan Song
https://arxiv.org/abs/2509.06408 https://arxiv.org/pdf/2509.06408

Singularity of biased discrete random matrix
Let A be an $n \times n$ random matrix whose entries are i.i.d. copies of a discrete random variable $ξ$. In this paper, we determine the probability that $A$ is singular when the distribution of $ξ$ is extremely biased.

Finite biorthogonal M matrix polynomials
Esra G\"Uldo\u{G}An Lekes\.Iz
https://arxiv.org/abs/2509.05817 https://arxiv.org/pdf/2509.05817

Finite biorthogonal M matrix polynomials
This paper provides a finite pair of biorthogonal matrix polynomials and their finite biorthogonality, several recurrence relations, matrix differential equation, generating function and integral representation.

HYLU: Hybrid Parallel Sparse LU Factorization
Xiaoming Chen
https://arxiv.org/abs/2509.07690 https://arxiv.org/pdf/2509.07690

HYLU: Hybrid Parallel Sparse LU Factorization
This article introduces HYLU, a hybrid parallel LU factorization-based general-purpose solver designed for efficiently solving sparse linear systems (Ax=b) on multi-core shared-memory architectures. The key technical feature of HYLU is the integration of hybrid numerical kernels so that it can adapt to various sparsity patterns of coefficient matrices. Tests on 34 sparse matrices from SuiteSparse Matrix Collection reveal that HYLU outperforms Intel MKL PARDISO in the numerical factorization pha…

Strategic Alignment Patterns in National AI Policies
Mohammad Hossein Azin, Hessam Zandhessami
https://arxiv.org/abs/2507.05400 https://

Strategic Alignment Patterns in National AI Policies
This paper introduces a novel visual mapping methodology for assessing strategic alignment in national artificial intelligence policies. The proliferation of AI strategies across countries has created an urgent need for analytical frameworks that can evaluate policy coherence between strategic objectives, foresight methods, and implementation instruments. Drawing on data from the OECD AI Policy Observatory, we analyze 15-20 national AI strategies using a combination of matrix-based visualizatio…

Replaced article(s) found for cs.CE. https://arxiv.org/list/cs.CE/new
[1/1]:
- The Software Landscape for the Density Matrix Renormalization Group
Per Sehlstedt, Jan Brandejs, Paolo Bientinesi, Lars Karlsson

Spectral Methods in Complex Systems
Francesco Caravelli
https://arxiv.org/abs/2509.05793 https://arxiv.org/pdf/2509.05793

Spectral Methods in Complex Systems
These notes offer a unified introduction to spectral methods for the study of complex systems. They are intended as an operative manual rather than a theorem-proof textbook: the emphasis is on tools, identities, and perspectives that can be readily applied across disciplines. Beginning with a compendium of matrix identities and inversion techniques, the text develops the connections between spectra, dynamics, and structure in finite-dimensional systems. Applications range from dynamical stabili…

Feature Understanding and Sparsity Enhancement via 2-Layered kernel machines (2L-FUSE)
Fabiana Camattari, Sabrina Guastavino, Francesco Marchetti, Emma Perracchione
https://arxiv.org/abs/2509.07806

Feature Understanding and Sparsity Enhancement via 2-Layered kernel machines (2L-FUSE)
We propose a novel sparsity enhancement strategy for regression tasks, based on learning a data-adaptive kernel metric, i.e., a shape matrix, through 2-Layered kernel machines. The resulting shape matrix, which defines a Mahalanobis-type deformation of the input space, is then factorized via an eigen-decomposition, allowing us to identify the most informative directions in the space of features. This data-driven approach provides a flexible, interpretable and accurate feature reduction scheme. …

Exactly solvable inhomogeneous XY spin chain
Pierre-Antoine Bernard, Nicolas Cramp\'e, Quentin Labriet, Lucia Morey, Luc Vinet
https://arxiv.org/abs/2507.06331

Exactly solvable inhomogeneous XY spin chain
Analytical expressions for the eigenvalues of certain inhomogeneous XY spin chains are computed. These models are rewritten in terms of free-fermion models using a well-known Jordan-Wigner transformation. Finding the spectrum of such models amounts to diagonalizing a matrix whose size is equal to the number of sites in the chain. This is achieved by recognizing and exploiting contiguity relations satisfied by specific orthogonal polynomials.

Jordan Derivation On Generalized Triangular Matrix Rings
Peter Danchev, Ayda Fatehi, Masoome Zahiri, Saeede Zahiri
https://arxiv.org/abs/2507.06871 https:/…

Jordan Derivation On Generalized Triangular Matrix Rings
In this note, we prove that any Jordan derivation on the generalized matrix ring $T_n(R,M)$ is a derivation. This extends some well-known results of this branch due to Brešar et al. in the cited literature.

Near-Threshold Voltage Massive MIMO Computing
Mikael Rinkinen, Mehdi Safarpour, Shahriar Shahabuddin, Olli Silven, Lauri Koskinen
https://arxiv.org/abs/2509.06651 https://

Near-Threshold Voltage Massive MIMO Computing
Massive MIMO systems have the potential to significantly enhance spectral efficiency, yet their widespread integration is hindered by the high power consumption of the underlying computations. This paper explores the applicability and effectiveness of Algorithm-Based Fault Tolerance (ABFT) for massive MIMO signal processing to tackle the reliability challenge of Near Threshold Computing (NTC). We propose modifying matrix arithmetic Newton iteration MIMO algorithm to seamlessly integrate ABFT to…

Replaced article(s) found for math.HO. https://arxiv.org/list/math.HO/new
[1/1]:
- Coval description of the boundary of a numerical range and the secondary values of a matrix
Petr Blaschke

Phases in WLZZ Matrix Models
A. Mironov, A. Oreshina, A. Popolitov
https://arxiv.org/abs/2507.05406 https://arxiv.org/pdf/2507.05406

Phases in WLZZ Matrix Models
We discuss the space of solutions to the Ward identities associated with the WLZZ models. We mostly concentrate on the case of these models described by a two-matrix model with the cubic potential in one of the matrices. We study how this space of solutions can be described by the freedom in choosing integration contours in the matrix integral.

Analytical Template for the 4-Point Correlation Function Covariance Beyond the Gaussian Random Field ${\rm I}$: 1-Loop Corrections involving Second-Order Densities
William Ortol\'a Leonard, Zachary Slepian
https://arxiv.org/abs/2509.05419

Analytical Template for the 4-Point Correlation Function Covariance Beyond the Gaussian Random Field ${\rm I}$: 1-Loop Corrections involving Second-Order Densities
Analytical templates for the covariance matrix of the 4-Point Correlation Function (4PCF) have been developed in the past assuming a Gaussian Random Field (GRF). In this work, we present the first non-Gaussian calculation of the 4PCF covariance, incorporating 1-loop corrections using the second-order density contrast. Furthermore, we introduce a non-trivial galaxy bias scheme at second order. To simplify the calculation, we decompose the covariance into five distinct structures, and then exploi…

Diagonal Frobenius Number via Gomory's Relaxation and Discrepancy
Dmitry Gribanov, Dmitry Malyshev, Panos Pardalos
https://arxiv.org/abs/2509.05629 https://

Diagonal Frobenius Number via Gomory's Relaxation and Discrepancy
For a matrix $A \in Z^{k \times n}$ of rank $k$, the diagonal Frobenius number $F_{\text{diag}}(A)$ is defined as the minimum $t \in Z_{\geq 1}$, such that, for any $b \in \text{span}_{Z}(A)$, the condition \begin{equation*} \exists x \in R_{\geq 0}^n,\, x \geq t \cdot 1 \colon \quad b = A x \end{equation*} implies that \begin{equation*} \exists z \in Z_{\geq 0}^n \colon\quad b = A z. \end{equation*} In this work, we show that \begin{equation*} F_{\text{diag}}(A) = Δ+ O(\log k), \end{e…

Matrix-product entanglement characterizing the optimality of state-preparation quantum circuits
Shuo Qi, Wen-Jun Li, Gang Su, Shi-Ju Ran
https://arxiv.org/abs/2507.05989

Matrix-product entanglement characterizing the optimality of state-preparation quantum circuits
Multipartite entanglement offers a powerful framework for understanding the complex collective phenomena in quantum many-body systems that are often beyond the description of conventional bipartite entanglement measures. Here, we propose a class of multipartite entanglement measures that incorporate the matrix product state (MPS) representation, enabling the characterization of the optimality of quantum circuits for state preparation. These measures are defined as the minimal distances from a t…

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…

Construction of Exceptional Points in Time-Modulated High-Contrast Elastic Media
Yixian Gao, Shuguan Ji, Shangling Song
https://arxiv.org/abs/2509.05561 https://

Construction of Exceptional Points in Time-Modulated High-Contrast Elastic Media
Spatially periodic elastic metamaterials, comprising hard inclusions within a soft matrix in $d$-dimensional space ($d\geq 2$), exhibit a rich spectrum of physical phenomena. This paper investigates such a model and presents the following contributions. First, we analyze the system's subwavelength quasi-frequencies under static conditions, establishing their functional dependence on the high-contrast parameter. This analysis enables the determination of the subwavelength quasi-frequency range. …

Theoretical Learning Performance of Graph Neural Networks: The Impact of Jumping Connections and Layer-wise Sparsification
Jiawei Sun, Hongkang Li, Meng Wang
https://arxiv.org/abs/2507.05533

Theoretical Learning Performance of Graph Neural Networks: The Impact of Jumping Connections and Layer-wise Sparsification
Jumping connections enable Graph Convolutional Networks (GCNs) to overcome over-smoothing, while graph sparsification reduces computational demands by selecting a sub-matrix of the graph adjacency matrix during neighborhood aggregation. Learning GCNs with graph sparsification has shown empirical success across various applications, but a theoretical understanding of the generalization guarantees remains limited, with existing analyses ignoring either graph sparsification or jumping connections.…

On the Schur Stability of Some Image Reconstruction Operators
Debraj Banerjee, Kunal Narayan Chaudhury
https://arxiv.org/abs/2509.06715 https://arxiv.org/p…

On the Schur Stability of Some Image Reconstruction Operators
We investigate an open problem arising in iterative image reconstruction. In its general form, the problem is to determine the stability of the parametric family of operators $P(t) = W (I-t B)$ and $R(t) = I-W + (I+tB)^{-1} (2W-I)$, where $W$ is a stochastic matrix and $B$ is a nonzero, nonnegative matrix. We prove that if $W$ is primitive, then there exists $T > 0$ such that the spectral radii $\varrho(P(t))$ and $\varrho(R(t))$ are strictly less than $1$ for all $0 < t < T$. The proof combine…

Marginal sets in semigroups and semirings
I. Buchinskiy, M. Kotov, A. Ponmaheshkumar, R. Perumal
https://arxiv.org/abs/2509.06562 https://arxiv.org/pdf/250…

Marginal sets in semigroups and semirings
In 2019, V. A. Roman'kov introduced the concept of marginal sets for groups. He developed a theory of marginal sets and demonstrated how these sets can be applied to improve some key exchange schemes. In this paper, we extend his ideas and introduce the concept of marginal sets for semigroups and semirings. For tropical matrix semigroups and semirings, we describe how some marginal sets can be constructed. We apply marginal sets to improve some key exchange schemes over semigroups.

Me IRL
https://piefed.blahaj.zone/post/278694

cintestinalis: Tadpole larva brain (C. intestinalis)
Entire connectivity matrix for the complete brain of a larva of Ciona intestinalis. Each directed edge represents a synaptic connection from pre-synaptic cell i to post-synaptic cell j (may not be a neuron). Edge weights represent the cumulative depth of presynaptic contacts in µm.
This network has 205 nodes and 2903 edges.
Tags: Biological, Connectome, Weighted

Real-space understanding of electron-phonon coupling in superconducting hydrides
Trinidad Novoa, Raffaello Bianco, Julia Contreras-Garc\'ia, Ion Errea
https://arxiv.org/abs/2507.06749

Real-space understanding of electron-phonon coupling in superconducting hydrides
Electron-phonon coupling is at the origin of conventional superconductivity, enabling the pairing of electrons into Cooper pairs. The electron-phonon matrix elements depend on the electronic eigenstates and, in the standard linear approximation, on the first derivative of the potential felt by the electrons with respect to ionic perturbations. Here, we focus on the derivatives of the potential with a twofold aim: to assess their contribution to the overall coupling and to analyze the limitation…

Finite projective planes meet spectral gaps
Yuhan Guo, Dong Zhang
https://arxiv.org/abs/2509.06247 https://arxiv.org/pdf/2509.06247

Finite projective planes meet spectral gaps
We show that for any connected graph $G$ with maximum degree $d\ge3$, the spectral gap from $0$ with respect to the adjacency matrix is at most $\sqrt{d-1}$. We further show that the upper bound $\sqrt{d-1}$ is achieved if and only if $G$ is the incidence graph of a finite projective plane of order $d-1$; and for other cases, the upper bound can be improved to $\sqrt{d-2}$. A similar yet more subtle phenomenon involving the normalized Laplacian is also investigated, in which we work on graphs…

"The precision of our analysis notwithstanding, the sad truth is that the future looks bleak and insurrectional, particularly for those in the USA. As these words hit the web, the SCOTUS has effectively abolished universal injunctions to presidential power, thereby kicking off the democracy overrule process we predicted exactly three years ago in this magazine–needless to say, a prediction we would have loved to get wrong."

Addition Automata and Attractors of Digit Systems Corresponding to Expanding Rational Matrices
Anjelo Gabriel R. Cruz, Manuel Joseph C. Loquias, J\"org M. Thuswaldner
https://arxiv.org/abs/2507.06158

Addition Automata and Attractors of Digit Systems Corresponding to Expanding Rational Matrices
Let $A$ be an expanding $2 \times 2$ matrix with rational entries and $\mathbb{Z}^2[A]$ be the smallest $A$-invariant $\mathbb{Z}$-module containing $\mathbb{Z}^2$. Let $\mathcal{D}$ be a finite subset of $\mathbb{Z}^2[A]$ which is a complete residue system of $\mathbb{Z}^2[A]/A\mathbb{Z}^2[A]$. The pair $(A,\mathcal{D})$ is called a {\em digit system} with {\em base} $A$ and {\em digit set} $\mathcal{D}$. It is well known that every vector $x \in \mathbb{Z}^2[A]$ can be written uniquely in the…

If you want to participate in the upcoming #NixOS steering committee election but haven't reached the required 25 commits mark in #nixpkgs yet, feel free to send some PRs to me for review. Also available for some 1:1 chats in Matrix or Discord to get any issues quickly sorted, so your PRs ca…

Learning from one graph: transductive learning guarantees via the geometry of small random worlds
Nils Detering, Luca Galimberti, Anastasis Kratsios, Giulia Livieri, A. Martina Neuman
https://arxiv.org/abs/2509.06894

Learning from one graph: transductive learning guarantees via the geometry of small random worlds
Since their introduction by Kipf and Welling in $2017$, a primary use of graph convolutional networks is transductive node classification, where missing labels are inferred within a single observed graph and its feature matrix. Despite the widespread use of the network model, the statistical foundations of transductive learning remain limited, as standard inference frameworks typically rely on multiple independent samples rather than a single graph. In this work, we address these gaps by develo…

Chapter 8 Multi-Criteria Decision-Making: Aggregation-Type Methods
Zhiyuan Wang, Gade Pandu Rangaiah
https://arxiv.org/abs/2509.06388 https://arxiv.org/pdf…

Chapter 8 Multi-Criteria Decision-Making: Aggregation-Type Methods
This chapter describes selected aggregation-type multi-criteria decision-making (MCDM) methods that convert an alternatives-criteria matrix (ACM) into a single performance score per alternative through additive, multiplicative or hybrid manipulations, for ranking the alternatives. The 8 methods are: Simple Additive Weighting (SAW), Multiplicative Exponent Weighting (MEW), Analytic Hierarchy Process (AHP), Analytic Network Process (ANP), Complex Proportional Assessment (COPRAS), Multi-Objective …

Gravitational form factors of pion in a nonlocal quark model
Vladimir Voronin
https://arxiv.org/abs/2507.06025 https://arxiv.org/pdf/…

Gravitational form factors of pion in a nonlocal quark model
Interaction with external gravitational field is introduced into a nonlocal quark model using the equivalence principle. This allows to define the energy-momentum tensor in flat space and evaluate its hadronic matrix element with external pions. It is found that bubble diagrams give a significant contribution to the corresponding gravitational form factors.

The Small Phase Condition is Necessary for Symmetric Systems
Xiaokan Yang, Wei Chen, Li Qiu
https://arxiv.org/abs/2507.06617 https://…

The Small Phase Condition is Necessary for Symmetric Systems
In this paper, we show that the small phase condition is both sufficient and necessary to ensure the feedback stability when the interconnected systems are symmetric. Such symmetric systems arise in diverse applications. The key lies in that, for a complex symmetric and semi-sectorial matrix, the transformation matrix in its generalized sectorial decomposition can be taken to be real. Such a result fills the gap of phase based necessary condition for the feedback stability of symmetric systems,…

A direct PinT algorithm for higher-order nonlinear equations
Shun-Zhi Zhong, Yong-Liang Zhao
https://arxiv.org/abs/2507.05743 https://

A direct PinT algorithm for higher-order nonlinear equations
This paper mainly studies a direct time-parallel algorithm for solving time-dependent differential equations of order 1 to 3. Different from the traditional time-stepping approach, we directly solve the all-at-once system from higher-order evolution equations by diagonalization the time discretization matrix $B$. Based on the connection between the characteristic equation and Chebyshev polynomials, we give explicit formulas for the eigenvector matrix $V$ of $B$ and its inverse $V^{-1}$ , and pr…

Entrywise transforms preserving matrix positivity and non-positivity
Dominique Guillot, Himanshu Gupta, Prateek Kumar Vishwakarma, Chi Hoi Yip
https://arxiv.org/abs/2507.06076

Entrywise transforms preserving matrix positivity and non-positivity
We characterize real and complex functions which, when applied entrywise to square matrices, yield a positive definite matrix if and only if the original matrix is positive definite. We refer to these transformations as sign preservers. Compared to classical work on entrywise preservers of Schoenberg and others, we completely resolve this problem in the harder fixed dimensional setting, extending a similar recent classification of sign preservers obtained for matrices over finite fields. When t…

Universal quantum control over bosonic network
Zhu-yao Jin, Jun Jing
https://arxiv.org/abs/2509.06560 https://arxiv.org/pdf/2509.06560

Universal quantum control over bosonic network
Perfect transfer of unknown states across distinct nodes is fundamental in the construction of bosonic quantum networks. We here develop a general theory to control an $N$-node bosonic network governed by the time-dependent Hamiltonian, as the universal quantum control theory for continuous-variable systems. In particular, we can activate nonadiabatic passages superposed of initial and target modes by the commutation condition for the Hamiltonian's coefficient matrix in the representation of ti…

Spectral test of reducibility for Matrix tuples
Michael Stessin, Rongwei Yang
https://arxiv.org/abs/2509.05836 https://arxiv.org/pdf/2509.05836

Spectral test of reducibility for Matrix tuples
If a tuple of matrices has a common invariant subspace, its projective joint spectrum has an algebraic component. In general, the converse is not true, and there might be algebraic components in the projective joint spectrum without corresponding common invariant subspaces. In this paper we give necessary and sufficient conditions for the occurrence of such correspondence.

Invertibility for non-Hermitian random band matrices with sublinear bandwidth and discrete entries
Yi Han
https://arxiv.org/abs/2507.05417 https://

Invertibility for non-Hermitian random band matrices with sublinear bandwidth and discrete entries
A well-known result in random matrix theory, proven by Kahn, Komlós and Szemerédi in 1995, states that a square random matrix with i.i.d. uniform $\{\pm 1\}$ entries is invertible with probability $1-\exp(-Ω(n))$. As a natural generalization of the model and motivated by the Anderson localization-delocalization transition in mathematical physics, we consider the invertibility of a class of random band matrices with independent entries where the bandwidth $d_n$ scales like $n^α$, for some $�…

A simpler probe of the quantum Mpemba effect in closed systems
Filiberto Ares, Colin Rylands, Pasquale Calabrese
https://arxiv.org/abs/2507.05946 https://

A simpler probe of the quantum Mpemba effect in closed systems
We study the local relaxation of closed quantum systems through the relative entropy between the reduced density matrix and its long time limit. We show, using analytic arguments combined with numerical checks, that this relative entropy can be very well approximated by an entropy difference, affording a significant computational advantage. We go on to relate this to the entanglement asymmetry of the subsystem with respect to time translation invariance. In doing this, we obtain a simple probe …

Analytical Template for the 4-Point Correlation Function Covariance Beyond the Gaussian Random Field ${\rm II}$: 1-Loop Corrections with Third-Order Densities
William Ortol\'a Leonard, Zachary Slepian
https://arxiv.org/abs/2509.05422

Analytical Template for the 4-Point Correlation Function Covariance Beyond the Gaussian Random Field ${\rm II}$: 1-Loop Corrections with Third-Order Densities
Analytical templates for the 4-Point Correlation Function (4PCF) covariance matrix have been developed in the past assuming a Gaussian Random Field (GRF). In this work, we present the second part of the beyond GRF calculation of the 4PCF covariance, incorporating 1-loop corrections stemming from the third-order density contrast. Furthermore, we introduce a non-trivial galaxy biasing scheme at third order. To simplify the calculation, we decompose the covariance into three distinct structures an…

The slice decomposition of planar hypermaps
Marie Albenque, J\'er\'emie Bouttier
https://arxiv.org/abs/2509.06850 https://arxiv.org/pdf/2509.06850

The slice decomposition of planar hypermaps
The slice decomposition is a bijective method for enumerating planar maps (graphs embedded in the sphere) with control over face degrees. In this paper, we extend the slice decomposition to the richer setting of hypermaps, naturally interpreted as properly face-bicolored maps, where the degrees of faces of each color can be controlled separately. This setting is closely related with the two-matrix model and the Ising model on random maps, which have been intensively studied in theoretical physi…

Simple polynomial equations over (mxm)-matrices
Vitalij A. Chatyrko, Alexandre Karassev
https://arxiv.org/abs/2507.07085 https://arxi…

Simple polynomial equations over (mxm)-matrices
Let $m$ be any integer $\geq 3$. We consider the polynomial equation $$X^n + a_{n-1}\cdot X^{n-1} + \dots + a_1 \cdot X + a_0 \cdot I = O,$$ over $(m \times m)$-matrices $X$ with the real entries, where $I$ is the identity matrix, $O$ is the null matrix, $a_i \in \mathbb R$ for each $i$ and $n \geq 1$. We discuss its solution set $S$ supplied with the natural Euclidean topology. In particular, we describe the solution set $S$ for $m=3$ and calculate its dimension.

Complex moments of the derivative of the Riemann zeta function
Christopher Hughes, Andrew Pearce-Crump
https://arxiv.org/abs/2509.07788 https://arxiv.org/p…

Complex moments of the derivative of the Riemann zeta function
We conjecture results about the complex moments of the derivative of the Riemann zeta function, evaluated at the non-trivial zeros of the Riemann zeta function. We do this via two different random matrix computations. In the first, we find an exact formula for the complex moments of the derivative of the characteristic polynomials of unitary matrices averaged over Haar measure using Selberg's integral. In the second, we consider the hybrid approach for zeta, first proposed by Gonek, Hughes and …

Network signflip parallel analysis for selecting the embedding dimension
David Hong, Joshua Cape
https://arxiv.org/abs/2509.05722 https://arxiv.org/pdf/250…

Network signflip parallel analysis for selecting the embedding dimension
This paper investigates the problem of selecting the embedding dimension for large heterogeneous networks that have weakly distinguishable community structure. For a broad family of embeddings based on normalized adjacency matrices, we introduce a novel spectral method that compares the eigenvalues of the normalized adjacency matrix to those obtained after randomly signflipping its entries. The proposed method, called network signflip parallel analysis (NetFlipPA), is interpretable, simple to i…

The $L^p$ regularity problem for parabolic operators with transversally independent coefficients
Martin Dindo\v{s}, Jill Pipher, Martin Ulmer
https://arxiv.org/abs/2509.06627 ht…

The $L^p$ regularity problem for parabolic operators with transversally independent coefficients
In this paper, we fully resolve the question of whether the Regularity problem for the parabolic PDE $\partial_tu - \mbox{div}(A\nabla u)=0$ on the domain $\mathbb R^{n+1}_+\times\mathbb R$ is solvable for some $p\in (1,\infty)$ under the assumption that the matrix $A$ is elliptic, has bounded and measurable coefficients and its coefficients are independent of the spatial variable $x_{n+1}$ (which is transversal to the boundary). We prove that for some $p_0>1$ the Regularity problem is solvable…

Replaced article(s) found for hep-th. https://arxiv.org/list/hep-th/new
[2/3]:
- Non-Perturbative $S$-matrix Renormalization
Laurent Freidel, Jos\'e Padua-Arg\"uelles, Susanne Schander, Marc Schiffer

Multivariate regression with missing response data for modelling regional DNA methylation QTLs
Shomoita Alam, Yixiao Zeng, Sasha Bernatsky, Marie Hudson, In\'es Colmegna, David A. Stephens, Celia M. T. Greenwood, Archer Y. Yang
https://arxiv.org/abs/2507.05990

Multivariate regression with missing response data for modelling regional DNA methylation QTLs
Identifying genetic regulators of DNA methylation (mQTLs) with multivariate models enhances statistical power, but is challenged by missing data from bisulfite sequencing. Standard imputation-based methods can introduce bias, limiting reliable inference. We propose \texttt{missoNet}, a novel convex estimation framework that jointly estimates regression coefficients and the precision matrix from data with missing responses. By using unbiased surrogate estimators, our three-stage procedure avoids…

Confinement, deconfinement, and bound states in the spin-$1$ and spin-$3/2$ generalizations of the Majumdar--Ghosh chain
Aman Sharma, Mithilesh Nayak, Natalia Chepiga, Henrik M. R{\o}nnow, Fr\'ed\'eric Mila
https://arxiv.org/abs/2509.06720

Confinement, deconfinement, and bound states in the spin-$1$ and spin-$3/2$ generalizations of the Majumdar--Ghosh chain
We investigate the nature of low-energy excitations in a spin chain with antiferrmomagnetic nearest-neighbor $J_1$, next-nearest-neighbor $J_2$, and three-site $J_3$ interactions using the time-dependent density matrix renormalization group and the single mode approximation techniques. In the absence of the $J_2$ interaction, we identify clear distinctions in the spectral functions in the fully dimerized phase across the exactly dimerized line for different magnitudes of the spins. In contrast …

Learnable quantum spectral filters for hybrid graph neural networks
Ammar Daskin
https://arxiv.org/abs/2507.05640 https://arxiv.org/p…

Learnable quantum spectral filters for hybrid graph neural networks
In this paper, we describe a parameterized quantum circuit that can be considered as convolutional and pooling layers for graph neural networks. The circuit incorporates the parameterized quantum Fourier circuit where the qubit connections for the controlled gates derived from the Laplacian operator. Specifically, we show that the eigenspace of the Laplacian operator of a graph can be approximated by using QFT based circuit whose connections are determined from the adjacency matrix. For an $N\t…

Replaced article(s) found for hep-ph. https://arxiv.org/list/hep-ph/new
[1/2]:
- Analytic structure of the MNS matrix with diagonal reflection symmetries
Masaki J. S. Yang

cintestinalis: Tadpole larva brain (C. intestinalis)
Entire connectivity matrix for the complete brain of a larva of Ciona intestinalis. Each directed edge represents a synaptic connection from pre-synaptic cell i to post-synaptic cell j (may not be a neuron). Edge weights represent the cumulative depth of presynaptic contacts in µm.
This network has 205 nodes and 2903 edges.
Tags: Biological, Connectome, Weighted

On subcodes of the generalized Reed-Solomon codes
Yu Ning
https://arxiv.org/abs/2507.04689 https://arxiv.org/pdf/2507.04689

On subcodes of the generalized Reed-Solomon codes
In this paper, we study a class of subcodes of codimension $1$ in the $[n,k+1]_q$ generalized Reed-Solomon (GRS) codes, whose generator matrix is derived by removing the row of degree $k-r$ from the generator matrix of the $[n,k+1]_q$ GRS codes, where $1 \le r \le k-1$. We show equivalent characterizations for this class of subcodes of the GRS codes being self-dual or near-MDS, which extends the results for $r=1$ in the literature. Along with these characterizations, families of self-dual near-…

Bohr-Sommerfeld Quantization Rules for 1-D Semiclassical Pseudo-Differential Operator: the Method of Microlocal Wronskian and Gram Matrix
Abdelwaheb Ifa
https://arxiv.org/abs/2508.05586

Bohr-Sommerfeld Quantization Rules for 1-D Semiclassical Pseudo-Differential Operator: the Method of Microlocal Wronskian and Gram Matrix
In this paper, we revisit the well known Bohr-Sommerfeld quantization rule (BS) of order 2 for a self-adjoint 1-D semiclassical pseudo-differential operator, within the algebraic and microlocal framework of B. Helffer and J. Sjöstrand. BS holds precisely when the Gram matrix consisting of scalar products of certain WKB solutions with respect to the "flux norm" is not invertible. This condition is obtained using the microlocal Wronskian and does not rely on traditional matching techniques. It i…

Spectra of high-dimensional sparse random geometric graphs
Yifan Cao, Yizhe Zhu
https://arxiv.org/abs/2507.06556 https://arxiv.org/pd…

Spectra of high-dimensional sparse random geometric graphs
We analyze the spectral properties of the high-dimensional random geometric graph $ G(n, d, p)$, formed by sampling $n$ i.i.d vectors $\{v_i\}_{i=1}^{n}$ uniformly on a $d$-dimensional unit sphere and connecting each pair $\{i,j\}$ whenever $\langle v_i, v_j \rangle \geq τ$ so that $p=\mathbb P(\langle v_i,v_j\rangle \geq τ)$. This model defines a nonlinear random matrix ensemble with dependent entries. We show that if $d =ω( np\log^{2}(1/p))$ and $np\to\infty$, the limiting spectral distrib…

Golden Ratio Growth and Phase Transitions in Chromatic Counts of Circular Chord Graphs
Rogelio N. Lopez-Bonilla, Julian Allagan, Shawn M. Langley, Angel J. Clinton
https://arxiv.org/abs/2509.05845

Golden Ratio Growth and Phase Transitions in Chromatic Counts of Circular Chord Graphs
We study generalized circular chord graphs $\mathcal C^{(k)}_n$, formed from a cycle $C_n$ by adding fixed-offset chords of length $k$ and, for even $n$, diameters. Using transfer matrix methods, we derive exact formulas for 3-colorings when $k=3$: for odd $n$, we obtain \[ P(\mathcal{C}_n^{(3)},3) = L_n + 2\cos\left(\frac{2πn}{3}\right) + 2s_n + 2 \] where $L_n$ is the Lucas sequence and $(s_n)$ satisfies $s_{n+3} = -s_{n+2} - s_n$, yielding golden-ratio asymptotic growth $φ^n + O(ρ^n)$ alo…

Depth-Aware Initialization for Stable and Efficient Neural Network Training
Vijay Pandey
https://arxiv.org/abs/2509.05018 https://arxiv.org/pdf/2509.05018

Depth-Aware Initialization for Stable and Efficient Neural Network Training
In past few years, various initialization schemes have been proposed. These schemes are glorot initialization, He initialization, initialization using orthogonal matrix, random walk method for initialization. Some of these methods stress on keeping unit variance of activation and gradient propagation through the network layer. Few of these methods are independent of the depth information while some methods has considered the total network depth for better initialization. In this paper, comprehe…

Geometric Invariants of Quantum Metrology
Christopher Wilson, John Drew Wilson, Luke Coffman, Shah Saad Alam, Murray J. Holland
https://arxiv.org/abs/2507.06128

Geometric Invariants of Quantum Metrology
We establish a previously unexplored conservation law for the Quantum Fisher Information Matrix (QFIM) expressed as follows; when the QFIM is constructed from a set of observables closed under commutation, i.e., a Lie algebra, the spectrum of the QFIM is invariant under unitary dynamics generated by these same operators. Each Lie algebra therefore endows any quantum state with a fixed "budget" of metrological sensitivity -- an intrinsic resource that we show, like optical squeezing in interfero…

Matrices over finite fields of odd characteristic as sums of diagonalizable and square-zero matrices
Peter Danchev, Esther Garc\'ia, Miguel G\'omez Lozano
https://arxiv.org/abs/2507.05762

Matrices over finite fields of odd characteristic as sums of diagonalizable and square-zero matrices
Let $\mathbb{F}$ be a finite field of odd characteristic. When $|\mathbb{F}|\ge 5$, we prove that every matrix $A$ admits a decomposition into $D+M$ where $D$ is diagonalizable and $M^2=0$. For $\mathbb{F}=\mathbb{F}_3$, we show that such decomposition is possible for non-derogatory matrices of order at least 5, and more generally, for matrices whose first invariant factor is not a non-zero trace irreducible polynomial of degree 3; we also establish that matrices consisting of direct …

FASTColor -- Full-color Amplitude Surrogate Toolkit for QCD
Javier Mari\~no Villadamigo, Rikkert Frederix, Tilman Plehn, Timea Vitos, Ramon Winterhalder
https://arxiv.org/abs/2509.07068

FASTColor -- Full-color Amplitude Surrogate Toolkit for QCD
High-multiplicity events remain a bottleneck for LHC simulations due to their computational cost. We present a ML-surrogate approach to accelerate matrix element reweighting from leading-color (LC) to full-color (FC) accuracy, building on recent advancements in LC event generation. Comparing a variety of modern network architectures for representative QCD processes, we achieve speed-up of around a factor two over the current LC-to-FC baseline. We also show how transformers learn and exploit und…

LINE: Public-key encryption
Gennady Khalimov, Yevgen Kotukh
https://arxiv.org/abs/2507.04501 https://arxiv.org/pdf/2507.04501

LINE: Public-key encryption
We propose a public key encryption cryptosystem based on solutions of linear equation systems with predefinition of input parameters through shared secret computation for factorizable substitutions. The existence of multiple equivalent solutions for an underdetermined system of linear equations determines the impossibility of its resolution by a cryptanalyst in polynomial time. The completion of input parameters of the equation system is implemented through secret homomorphic matrix transformat…

Graph Estimation Based on Neighborhood Selection for Matrix-variate Data
Minsub Shin, Johan Lim, Seongoh Park
https://arxiv.org/abs/2507.04711 https://

Graph Estimation Based on Neighborhood Selection for Matrix-variate Data
Undirected graphical models are powerful tools for uncovering complex relationships among high-dimensional variables. This paper aims to fully recover the structure of an undirected graphical model when the data naturally take matrix form, such as temporal multivariate data. As conventional vector-variate analyses have clear limitations in handling such matrix-structured data, several approaches have been proposed, mostly relying on the likelihood of the Gaussian distribution with a separable…

Interaction-enhanced quantum to classical crossover temperature in a Luttinger liquid
Yen-Wen Lu, Michael Mulligan
https://arxiv.org/abs/2507.05356 https:/…

Interaction-enhanced quantum to classical crossover temperature in a Luttinger liquid
We study electrical and thermal transport in a one-dimensional Luttinger liquid coupled to a three-dimensional acoustic phonon in both the ``clean" (umklapp scattering) and ``dirty" (disorder scattering) limits using the memory matrix formalism. By explicitly incorporating the Debye cutoff on phonon frequencies, we consider the low and high temperature transport regimes. We find the crossover temperature separating these two regimes to be interaction-dependent, with repulsive interactions incre…

cintestinalis: Tadpole larva brain (C. intestinalis)
Entire connectivity matrix for the complete brain of a larva of Ciona intestinalis. Each directed edge represents a synaptic connection from pre-synaptic cell i to post-synaptic cell j (may not be a neuron). Edge weights represent the cumulative depth of presynaptic contacts in µm.
This network has 205 nodes and 2903 edges.
Tags: Biological, Connectome, Weighted

Provably data-driven projection method for quadratic programming
Anh Tuan Nguyen, Viet Anh Nguyen
https://arxiv.org/abs/2509.04524 https://arxiv.org/pdf/25…

Provably data-driven projection method for quadratic programming
Projection methods aim to reduce the dimensionality of the optimization instance, thereby improving the scalability of high-dimensional problems. Recently, Sakaue and Oki proposed a data-driven approach for linear programs (LPs), where the projection matrix is learned from observed problem instances drawn from an application-specific distribution of problems. We analyze the generalization guarantee for the data-driven projection matrix learning for convex quadratic programs (QPs). Unlike in LPs…

Replaced article(s) found for stat.ML. https://arxiv.org/list/stat.ML/new
[1/3]:
- Non-negative matrix factorization algorithms generally improve topic model fits
Peter Carbonetto, Abhishek Sarkar, Zihao Wang, Matthew Stephens

H-Toeplitz operators on Fock space
Thokchom Sonamani Singh, M. Premjit Singh, Oinam Nilbir Singh, Khumballambam Priyobarta Singh
https://arxiv.org/abs/2507.06532

H-Toeplitz operators on Fock space
This paper explores H-Toeplitz operators on the Fock space, unifying aspects of Toeplitz and Hankel operators while introducing novel structural properties. We derive explicit matrix representations for these operators with respect to the orthonormal basis of monomials, analyze their commutativity, and establish compactness criteria. Key results include the characterization of commuting H-Toeplitz operators with harmonic symbols and the proof that non-zero H-Toeplitz operators cannot be Hilbert…

The Ubiquitous Sparse Matrix-Matrix Products
Ayd{\i}n Bulu\c{c}
https://arxiv.org/abs/2508.04077 https://arxiv.org/pdf/2508.04077

The Ubiquitous Sparse Matrix-Matrix Products
Multiplication of a sparse matrix with another (dense or sparse) matrix is a fundamental operation that captures the computational patterns of many data science applications, including but not limited to graph algorithms, sparsely connected neural networks, graph neural networks, clustering, and many-to-many comparisons of biological sequencing data. In many application scenarios, the matrix multiplication takes places on an arbitrary algebraic semiring where the scalar operations are overloa…

Replaced article(s) found for math.PR. https://arxiv.org/list/math.PR/new
[1/1]:
- Liouville quantum gravity from random matrix dynamics
Paul Bourgade, Hugo Falconet

On the Normalization of Confusion Matrices: Methods and Geometric Interpretations
Johan Erbani, Pierre-Edouard Portier, Elod Egyed-Zsigmond, Sonia Ben Mokhtar, Diana Nurbakova
https://arxiv.org/abs/2509.04959

On the Normalization of Confusion Matrices: Methods and Geometric Interpretations
The confusion matrix is a standard tool for evaluating classifiers by providing insights into class-level errors. In heterogeneous settings, its values are shaped by two main factors: class similarity -- how easily the model confuses two classes -- and distribution bias, arising from skewed distributions in the training and test sets. However, confusion matrix values reflect a mix of both factors, making it difficult to disentangle their individual contributions. To address this, we introduce b…

What's my phase again? Computing the vacuum-to-vacuum amplitude of quadratic bosonic evolution
Nicol\'as Quesada
https://arxiv.org/abs/2507.06154 h…

What's my phase again? Computing the vacuum-to-vacuum amplitude of quadratic bosonic evolution
Quadratic bosonic Hamiltonians and their associated unitary transformations form a fundamental class of operations in quantum optics, modeling key processes such as squeezing, displacement, and beam-splitting. Their Heisenberg-picture dynamics simplifies to linear (or possibly affine) transformations on quadrature operators, enabling efficient analysis and decomposition into optical gate sets using matrix operations. However, this formalism discards a phase, which, while often neglected, is ess…

Nonequilibrium Phase Transitions in Large $N$ Matrix Quantum Mechanics
Minjae Cho
https://arxiv.org/abs/2508.04764 https://arxiv.org/pdf/2508.04764

Nonequilibrium Phase Transitions in Large $N$ Matrix Quantum Mechanics
It is believed that the theory of quantum gravity describing our universe is unitary. Nonetheless, if we only have access to a subsystem, its dynamics is described by nonequilibrium physics. Motivated by this, we investigate the planar limit of large $N$ one-matrix quantum mechanics obeying the Lindblad master equation with dissipative jump terms, focusing on the existence, uniqueness, and properties of steady states. After showing that Lindblad dissipation is absent in the gauged model at larg…

Flavor Enhanced Chromomagnetic Dipole Moment in the Bestest Little Higgs Framework
T. Cisneros-P\'erez, A. Ramirez-Morales, R. Gamboa-Goni, C. Ortiz
https://arxiv.org/abs/2509.05560

Flavor Enhanced Chromomagnetic Dipole Moment in the Bestest Little Higgs Framework
We investigate the anomalous Chromomagnetic Dipole Moment (CMDM), $\hatμ_t^{\mathrm{BLHM}}$, of the top quark within the Bestest Little Higgs Model (BLHM). Our study incorporates novel interactions arising from the extended CKM matrix in the BLHM and explores a broad region of the experimentally allowed parameter space, yielding CMDM values on the order of $10^{-3}$. This result represents an improvement over previous CMDM calculations within the BLHM and makes it competitive with other beyond…

Controlling quantum entanglement with classical non-separable light
R. F. Barros, A. L. S. Santos Junior, A. Z. Khoury, R. Fickler
https://arxiv.org/abs/2507.06462

Controlling quantum entanglement with classical non-separable light
Here we investigate the quantum frequency conversion of entangled photons driven by a classically non-separable laser beam. We show that the frequency conversion dynamics is described by a quantum channel that stems from the classical drive field through the channel-state duality - the quantum channel is dual to the classical coherence matrix of the drive field. This implies that the evolution of entanglement in the conversion process is bound by the classical non-separability of the drive fiel…

On the T-linear resistivity of cuprates: theory
Charu Dhiman, Raman Sharma, Navinder Singh
https://arxiv.org/abs/2507.06725 https://a…

On the T-linear resistivity of cuprates: theory
By partitioning the electronic system of the optimally doped cuprates in two electronic components: (1) mobile electrons on oxygen sub-lattice; and (2) localized spins on copper sub-lattice, and considering the scattering of mobile electrons (on oxygen sub-lattice) via generation of paramagnons in the localized sub-system (copper spins), we ask what should be the electron-paramagnon coupling matrix element $M_q$ so that T-linear resistivity results. This 'reverse engineering approach' leads to …

An exact solution of planar QCD by a complex matrix ensemble
Alexander Migdal
https://arxiv.org/abs/2507.05096 https://arxiv.org/pdf/…

An exact solution of planar QCD by a complex matrix ensemble
We construct an exact solution to the planar QCD loop equation in four-dimensional Euclidean space using a novel matrix-valued momentum loop formalism. Central to this construction is a new loop calculus, where functional derivatives act on the loop velocity $\dot C(θ)$. This framework yields finite, well-defined expressions for point and area derivatives in loop space and highlights the role of the loop-space Bianchi identity in ensuring consistency with gauge theory. The Wilson loop is rep…

Energy loss baseline for light hadrons in oxygen-oxygen collisions at $\sqrt{s_\mathrm{NN}}=5.36\,\text{TeV}$
Aleksas Mazeliauskas
https://arxiv.org/abs/2509.07008 https://

Energy loss baseline for light hadrons in oxygen-oxygen collisions at $\sqrt{s_\mathrm{NN}}=5.36\,\text{TeV}$
I present predictions for inclusive charged hadron spectra in minimum-bias proton-proton and oxygen-oxygen collisions at a centre-of-mass energy of $\sqrt{s_\mathrm{NN}} = 5.36\,\text{TeV}$, assuming no final-state interactions. Using next-to-leading order perturbative QCD matrix elements, along with state-of-the-art (nuclear) parton distribution and fragmentation functions, I establish a baseline for the nuclear modification factor $R^h_\text{AA}$ in oxygen-oxygen collisions in the absence of …

Large-scale Efficient Molecule Geometry Optimization with Hybrid Quantum-Classical Computing
Yajie Hao, Qiming Ding, Xiaoting Wang, Xiao Yuan
https://arxiv.org/abs/2509.07460 ht…

Large-scale Efficient Molecule Geometry Optimization with Hybrid Quantum-Classical Computing
Accurately and efficiently predicting the equilibrium geometries of large molecules remains a central challenge in quantum computational chemistry, even with hybrid quantum-classical algorithms. Two major obstacles hinder progress: the large number of qubits required and the prohibitive cost of conventional nested optimization. In this work, we introduce a co-optimization framework that combines Density Matrix Embedding Theory (DMET) with Variational Quantum Eigensolver (VQE) to address these l…

Two-dimensional fractional Brownian motion: Analysis in time and frequency domains
Micha{\l} Balcerek, Adrian Pacheco-Pozo, Agnieszka Wy{\l}oma\'nska, Krzysztof Burnecki, Diego Krapf
https://arxiv.org/abs/2509.07537

Two-dimensional fractional Brownian motion: Analysis in time and frequency domains
This article introduces a novel construction of the two-dimensional fractional Brownian motion (2D fBm) with dependent components. Unlike similar models discussed in the literature, our approach uniquely accommodates the full range of model parameters and explicitly incorporates cross-dependencies and anisotropic scaling through a matrix-valued Hurst operator. We thoroughly analyze the theoretical properties of the proposed causal and well-balanced 2D fBm versions, deriving their auto- and cros…

Topological Holography for Mixed-State Phases and Phase Transitions
Ran Luo, Yi-Nan Wang, Zhen Bi
https://arxiv.org/abs/2507.06218 https://

Topological Holography for Mixed-State Phases and Phase Transitions
We extend the symmetry topological field theory (SymTFT) framework to open quantum systems. Using canonical purification, we embed mixed states into a doubled (2+1)-dimensional topological order and employ the slab construction to study (1+1)-dimensional mixed-state phases through condensable algebras in the doubled SymTFT. Hermiticity and positivity of the density matrix impose additional constraints on allowable anyon condensations, enabling a systematic classification of mixed-state phases -…

Classical Neural Networks on Quantum Devices via Tensor Network Disentanglers: A Case Study in Image Classification
Borja Aizpurua, Sukhbinder Singh, Rom\'an Or\'us
https://arxiv.org/abs/2509.06653

Classical Neural Networks on Quantum Devices via Tensor Network Disentanglers: A Case Study in Image Classification
We address the problem of implementing bottleneck layers from classical pre-trained neural networks on a quantum computer, with the goal of achieving quantum advantage on near-term devices. Our approach begins with a compression step in which the target linear layer is represented as an effective matrix product operator (MPO) without degrading model performance. The MPO is then further disentangled into a more compact form. This enables a hybrid classical-quantum execution scheme, where the dis…

Neural Posterior Unfolding
Fernando Torales Acosta, Jay Chan, Krish Desai, Vinicius Mikuni, Benjamin Nachman, Jingjing Pan, Francesco Rubbo
https://arxiv.org/abs/2509.06370 http…

Neural Posterior Unfolding
Differential cross section measurements are the currency of scientific exchange in particle and nuclear physics. A key challenge for these analyses is the correction for detector distortions, known as deconvolution or unfolding. Binned unfolding of cross section measurements traditionally rely on the regularized inversion of the response matrix that represents the detector response, mapping pre-detector (`particle level') observables to post-detector (`detector level') observables. In this pape…

BC-type open $SL(2,\mathbb{C})$ spin chain
P. Antonenko, S. Derkachov, P. Valinevich
https://arxiv.org/abs/2508.04972 https://arxiv.org/pdf/2508.04972

BC-type open $SL(2,\mathbb{C})$ spin chain
We diagonalize the $B$-element of monodromy matrix for noncompact open $SL(2,\mathbb{C})$ spin chain with boundary interaction. The monodromy matrix is defined in terms of $SL(2,\mathbb{C})$ $L$-operator and boundary $K$-matrix. The eigenfunctions of $B$-operator are constructed iteratively using raising $Λ$-operators. The key role in the calculations plays the Baxter $Q$-operator commuting with the $B$-operator. The main building blocks for $Λ$- and $Q$-operators are $\mathcal{K}$-operator -…

Multiparameter quantum metrology at Heisenberg scaling for an arbitrary two-channel linear interferometer with squeezed light
Atmadev Rai, Danilo Triggiani, Paolo Facchi, Vincenzo Tamma
https://arxiv.org/abs/2509.07574

Multiparameter quantum metrology at Heisenberg scaling for an arbitrary two-channel linear interferometer with squeezed light
We present a framework for simultaneously estimating all four real parameters of a general two-channel unitary U(2) with Heisenberg-scaling precision. We derive analytical expressions for the quantum Fisher information matrix and show that all parameters attain the 1/N scaling in the precision by using experimentally feasible Gaussian probes such as two-mode squeezed states or two single-mode squeezed states. Our results extend multiparameter metrology to its most general two-mode setting and e…

Disentangling Initial-State and Evolution Effects in Heavy-Ion Collisions Using EPOS and PHSD
Mahbobeh Jafarpour, Vadym Voronyuk, Klaus Werner, Elena Bratkovskaya, Damien Vintache
https://arxiv.org/abs/2509.05428

Disentangling Initial-State and Evolution Effects in Heavy-Ion Collisions Using EPOS and PHSD
In this study we examine the impact of the initial stage and dynamical evolution on final-state observables in heavy-ion collisions. For this goal we develop a novel approach, EPOSir+PHSDe, which employs EPOS initial conditions as the starting point for parton and hadron evolution within the PHSD microscopic transport approach. By examining the space-time evolution of matter in this model and comparing to EPOS (which starts with an S-matrix approach for parallel scatterings for the initial cond…