Tootfinder

People wonder why machines would build a Matrix for humans but then we humans build a Matrix for cows to “stop” animal suffering.
If I recall the franchise correctly the original Matrix :the_matrix: was supposed to be a utopia for humans, but they rejected it for being too unrealistic. I wonder when the enshittification of the cow Matrix occurs.

The Matrix Is Real (For Cows)
Do moos believe in fate?

This https://arxiv.org/abs/2404.00444 has been replaced.
link: https://scholar.google.com/scholar?q=a

A new method for the solution of the two-body Dirac equation: Estimation of the weights of $C$, $P$ and $CP$ symmetry violating terms in positronium
A new theoretical method is developed for the solution of the two-body bound-state Dirac equation for positronium. Only Coulomb potential was included in the Dirac Hamiltonian. It is shown that the two-body Dirac Hamiltonian can be written in the Hermitian matrix form of the $4\times 4$ size and contains terms, responsible for the violation of the $P$, $C$, and $CP$ symmetries. Numerical results for the energy spectrum of the para- and ortho-positronium ground states performed within the variat…

This https://arxiv.org/abs/2402.06641 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A Survey of a Random Matrix Model for a Family of Cusp Forms
The Katz-Sarnak philosophy states that statistics of zeros of $L$-function families near the central point as the conductors tend to infinity agree with those of eigenvalues of random matrix ensembles as the matrix size tends to infinity. While numerous results support this conjecture, S. J. Miller observed that for finite conductors, very different behavior can occur for zeros near the central point in elliptic curve families. This led to the excised model of Dueñez, Huynh, Keating, Miller, a…

Things are looking pretty good. Got the `setPixel` and `loadImage` functions up and running, and both use a buffer to help out with writing to the LED matrix IC. Now I need to start work on loading stuff from the SD card and see if I can animate some stuff... #electronics #arduino

Deformation of superintegrability in the Miwa-deformed Gaussian matrix model
A. Mironov, A. Morozov, A. Popolitov, Sh. Shakirov
https://arxiv.org/abs/2403.09670

Deformation of superintegrability in the Miwa-deformed Gaussian matrix model
We consider an arbitrary deformation of the Gaussian matrix model parameterized by Miwa variables $z_a$. One can look at it as a mixture of the Gaussian and logarithmic (Selberg) potentials, which are both superintegrable. The mixture is not, still one can find an explicit expression for an arbitrary Schur average as a linear transform of a {\it finite degree} polynomial made from the values of skew Schur functions at the Gaussian locus $p_k=δ_{k,2}$. This linear operation includes multiplicat…

The EDGE Language: Extended General Einsums for Graph Algorithms
Toluwanimi O. Odemuyiwa, Joel S. Emer, John D. Owens
https://arxiv.org/abs/2404.11591 http…

The EDGE Language: Extended General Einsums for Graph Algorithms
In this work, we propose a unified abstraction for graph algorithms: the Extended General Einsums language, or EDGE. The EDGE language expresses graph algorithms in the language of tensor algebra, providing a rigorous, succinct, and expressive mathematical framework. EDGE leverages two ideas: (1) the well-known foundations provided by the graph-matrix duality, where a graph is simply a 2D tensor, and (2) the power and expressivity of Einsum notation in the tensor algebra world. In this work, we…

Finiteness of the number of irreducible $\lambda$-quiddities over a finite commutative and unitary ring
Flavien Mabilat
https://arxiv.org/abs/2404.10521 ht…

Finiteness of the number of irreducible $λ$-quiddities over a finite commutative and unitary ring
$λ$-quiddities of size $n$ are $n$-tuples of elements of a fixed set, solutions of a matrix equation appearing in the study of Coxeter's friezes. The study of these solutions involves in particular the use of a notion of irreducibility. The main objective of this text is to show that there is a finite number of irreducible $λ$-quiddities over a finite unitary commutative ring and to obtain in this case an upper bound of the maximal size of them.

This https://arxiv.org/abs/2210.14598 has been replaced.
link: https://scholar.google.com/scholar?q=a

Manifold Gaussian Variational Bayes on the Precision Matrix
We propose an optimization algorithm for Variational Inference (VI) in complex models. Our approach relies on natural gradient updates where the variational space is a Riemann manifold. We develop an efficient algorithm for Gaussian Variational Inference whose updates satisfy the positive definite constraint on the variational covariance matrix. Our Manifold Gaussian Variational Bayes on the Precision matrix (MGVBP) solution provides simple update rules, is straightforward to implement, and the…

On the Use of Cramer-Rao Lower Bound for Least-Variance Circuit Parameters Identification of Li-ion Cells
Vladimir Sovljanski, Mario Paolone
https://arxiv.org/abs/2403.10435

On the Use of Cramer-Rao Lower Bound for Least-Variance Circuit Parameters Identification of Li-ion Cells
Electrochemical Impedance Spectroscopy (EIS) and Equivalent Circuit Models (ECMs) are widely used to characterize the impedance and estimate parameters of electrochemical systems such as batteries. We use a generic ECM with ten parameters grouped to model different frequency regions of the Li-ion cell's impedance spectrum. We derive a noise covariance matrix from the measurement model and use it to assign weights for the fitting technique. The paper presents two formulations of the parameters i…

Matrix Completion via Nonsmooth Regularization of Fully Connected Neural Networks
Sajad Faramarzi, Farzan Haddadi, Sajjad Amini, Masoud Ahookhosh
https://arxiv.org/abs/2403.10232 …

Matrix Completion via Nonsmooth Regularization of Fully Connected Neural Networks
Conventional matrix completion methods approximate the missing values by assuming the matrix to be low-rank, which leads to a linear approximation of missing values. It has been shown that enhanced performance could be attained by using nonlinear estimators such as deep neural networks. Deep fully connected neural networks (FCNNs), one of the most suitable architectures for matrix completion, suffer from over-fitting due to their high capacity, which leads to low generalizability. In this paper…

This https://arxiv.org/abs/2311.06605 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Sparsity and integrality gap transference bounds for integer programs
We obtain new transference bounds that connect two active areas of research: proximity and sparsity of solutions to integer programs. Specifically, we study the additive integrality gap of the integer linear programs min{cx: x in P, x integer}, where P={x: Ax=b, x nonnegative} is a polyhedron in the standard form determined by an integer mxn matrix A and an integer vector b. The main result of the paper shows that the integrality gap drops exponentially in the size of support of the optimal sol…

Walmart charging for self-checkout and LinkedIn pivoting to gaming…
…I think the Matrix has sprung a memory leak.

Supplement Matrix and a Practical Method for Computing Eigenvalues of a Dual Hermitian Matrix
Liqun Qi, Chunfeng Cui
https://arxiv.org/abs/2403.10308 https…

Supplement Matrix and a Practical Method for Computing Eigenvalues of a Dual Hermitian Matrix
We study dual number symmetric matrices, dual complex Hermitian matrices and dual quaternion Hermitian matrices in a unified frame of dual Hermitian matrices. Suppose we have a ring, which can be the real field, the complex field, or the quaternion ring. Then an $n \times n$ dual Hermitian matrix has $n$ dual number eigenvalues. We define supplement matrices for a dual Hermitian matrix. Supplement matrices are Hermitian matrices in the original ring. The standard parts of the eigenvalues of t…

Representations from matrix varieties, and filtered RSK
Abigail Price, Ada Stelzer, Alexander Yong
https://arxiv.org/abs/2403.09938 https://

Representations from matrix varieties, and filtered RSK
Matrix Schubert varieties (Fulton '92) carry natural actions of Levi groups. Their coordinate rings are thereby Levi-representations; what is a combinatorial counting rule for the multiplicities of their irreducibles? When the Levi group is a torus, (Knutson-Miller '04) answers the question. We present a general solution, a common refinement of the multigraded Hilbert series, the Cauchy identity, and the Littlewood-Richardson rule. Our result applies to any ``bicrystalline'' algebraic variety; …

Coordination in Noncooperative Multiplayer Matrix Games via Reduced Rank Correlated Equilibria
Jaehan Im, Yue Yu, David Fridovich-Keil, Ufuk Topcu
https://arxiv.org/abs/2403.10384

Coordination in Noncooperative Multiplayer Matrix Games via Reduced Rank Correlated Equilibria
Coordination in multiplayer games enables players to avoid the lose-lose outcome that often arises at Nash equilibria. However, designing a coordination mechanism typically requires the consideration of the joint actions of all players, which becomes intractable in large-scale games. We develop a novel coordination mechanism, termed reduced rank correlated equilibria, which reduces the number of joint actions to be considered and thereby mitigates computational complexity. The idea is to approx…

Efficient Batch and Recursive Least Squares for Matrix Parameter Estimation with Application to Adaptive MPC
Brian Lai, Dennis S. Bernstein
https://arxiv.org/abs/2404.10911

Efficient Batch and Recursive Least Squares for Matrix Parameter Estimation with Application to Adaptive MPC
Traditionally, batch least squares (BLS) and recursive least squares (RLS) are used for identification of a vector of parameters that form a linear model. In some situations, however, it is of interest to identify parameters in a matrix structure. In this case, a common approach is to transform the problem into standard vector form using the vectorization (vec) operator and the Kronecker product, known as vec-permutation. However, the use of the Kronecker product introduces extraneous zero term…

This https://arxiv.org/abs/2309.09656 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Compressed commuting graphs of matrix rings
In this paper we introduce compressed commuting graph of rings. It can be seen as a compression of the standard commuting graph (with the central elements added) where we identify the vertices that generate the same subring. The compression is chosen in such a way that it induces a functor from the category of rings to the category of graphs, which means that our graph takes into account not only the commutativity relation in the ring, but also the commutativity relation in all of its homomorph…

This https://arxiv.org/abs/2106.10200 has been replaced.
link: https://scholar.google.com/scholar?q=a

Quenched universality for deformed Wigner matrices
Following E. Wigner's original vision, we prove that sampling the eigenvalue gaps within the bulk spectrum of a fixed (deformed) Wigner matrix $H$ yields the celebrated Wigner-Dyson-Mehta universal statistics with high probability. Similarly, we prove universality for a monoparametric family of deformed Wigner matrices $H+xA$ with a deterministic Hermitian matrix $A$ and a fixed Wigner matrix $H$, just using the randomness of a single scalar real random variable $x$. Both results constitute que…

Around fifteen months ago, we switched from IRC to self-hosted Matrix. It has been far from perfect, but better than IRC for our team.
Now that we know what we’re doing, and now that Element’s unread indicators aren’t in constant gaslighting mode, it’s actually pretty good (despite some recent rumblings about the encryption implementation, and the usual Other People’s Software concerns).
Avoiding Slack was a primary goal (for privacy reasons). I actually kind of hate being this …

Given the plethora of at-least-as-good #libre messaging platforms (see Matrix, Rocket.Chat, Zulip, Mattermost, NextCloud Talk, etc.) that aren't
* exploiting your data,
* pestering you to pay more,
* reducing 'free tier' features (to get you to pay $),
* blocking integrations you want,
* failing to live up to their security promises, or
* simply being…

This https://arxiv.org/abs/2404.02713 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Quantum conjugate gradient method using the positive-side quantum eigenvalue transformation
Quantum algorithms are still challenging to solve linear systems of equations on real devices. This challenge arises from the need for deep circuits and numerous ancilla qubits. We introduce the quantum conjugate gradient (QCG) method using the quantum eigenvalue transformation (QET). The circuit depth of this algorithm depends on the square root of the coefficient matrix's condition number $κ$, representing a square root improvement compared to the previous quantum algorithms. The number of a…

It’s been more than 3 mos since my finger was broken/injured. The bone has healed but it’s not right, & the nail is a huge mess. I showed it to my GP yesterday, & she said the matrix was damaged & it will prolly never grow out/return to normal.

WTH do I do with it?

Sample complexity of matrix product states at finite temperature
Atsushi Iwaki, Chisa Hotta
https://arxiv.org/abs/2403.10018 https://…

Sample complexity of matrix product states at finite temperature
For quantum many-body systems in one dimension, computational complexity theory reveals that the evaluation of ground-state energy remains elusive on quantum computers, contrasting the existence of a classical algorithm for temperatures higher than the inverse logarithm of the system size. This highlights a qualitative difference between low- and high-temperature states in terms of computational complexity. Here, we describe finite-temperature states using the matrix product state formalism. Wi…

Existence and uniqueness for the solutions of non-autonomous stochastic differential algebraic equations with locally Lipschitz coefficients
Oana Silvia Serea, Antoine Tambue, Guy Tsafack
https://arxiv.org/abs/2403.09778

Existence and uniqueness for the solutions of non-autonomous stochastic differential algebraic equations with locally Lipschitz coefficients
In this paper, we study the well-posedness and regularity of non-autonomous stochastic differential algebraic equations (SDAEs) with nonlinear, locally Lipschitz and monotone (2) coefficients of the form (1). The main difficulty is the fact that the operator A(.) is non-autonomous, i.~e. depends on t and the matrix $A(t)$ is singular for all $t\in \left[0,T\right]$. Our interest is in SDAE of index-1. This means that in order to solve the problem, we can transform the initial SDAEs into an ordi…

Tensor product random matrix theory
Alexander Altland, Tobias Micklitz, Joaquim Telles de Miranda
https://arxiv.org/abs/2404.10919 https://

Tensor product random matrix theory
The evolution of complex correlated quantum systems such as random circuit networks is governed by the dynamical buildup of both entanglement and entropy. We here introduce a real-time field theory approach -- essentially a fusion of the $G Σ$-functional of the SYK-model and the field theory of disordered systems -- enigneered to microscopically describe the full range of such crossover dynamics: from initial product states to a maximum entropy ergodic state. To showcase this approach in the s…

Deformation of superintegrability in the Miwa-deformed Gaussian matrix model
A. Mironov, A. Morozov, A. Popolitov, Sh. Shakirov
https://arxiv.org/abs/2403.09670

Deformation of superintegrability in the Miwa-deformed Gaussian matrix model
We consider an arbitrary deformation of the Gaussian matrix model parameterized by Miwa variables $z_a$. One can look at it as a mixture of the Gaussian and logarithmic (Selberg) potentials, which are both superintegrable. The mixture is not, still one can find an explicit expression for an arbitrary Schur average as a linear transform of a {\it finite degree} polynomial made from the values of skew Schur functions at the Gaussian locus $p_k=δ_{k,2}$. This linear operation includes multiplicat…

AI chip developer Rivos, which recently settled with Apple over trade secret theft, raised $250M led by Matrix to compete with Nvidia using its RISC-V chips (Jane Lanhee Lee/Bloomberg)
https://www.bloomberg.com/news/articles/20

Chip Startup Rivos Raises More Than $250 Million to Tap AI Boom
Silicon Valley chip developer Rivos Inc. raised more than $250 million as it works toward bringing out its first product, underscoring the push for new hardware to meet the needs of artificial intelligence.

This https://arxiv.org/abs/2404.00483 has been replaced.
link: https://scholar.google.com/scholar?q=a

Chromomagnetic dipole moments of light quarks in the Bestest Little Higgs Model
In this paper, we research into the anomalous Chromomagnetic Dipole Moment (CMDM), denoted as $\hatμ_{q}^{BLHM}$, of the light quarks $q=(u, c, d, s, b)$ within the framework of the Bestest Little Higgs Model (BLHM) as an extension of the Standard Model (SM). Our investigation encompasses novel interactions among the light quarks, the heavy quark $B$, and the heavy bosons $(W^{\prime\pm}, H^{\pm}, ϕ^{\pm}, η^{\pm})$, incorporating the extended Cabibbo-Kobayashi-Maskawa (CKM) matrix character…

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

Kernelization Algorithms for the Eigenvalue Deletion Problems
Ajinkya Gaikwad, Hitendra Kumar, Soumen Maity
https://arxiv.org/abs/2404.10023 https://

Kernelization Algorithms for the Eigenvalue Deletion Problems
Given a graph $G=(V,E)$ and an integer $k\in \mathbb{N}$, we study {\sc 2-Eigenvalue Vertex Deletion} (2-EVD), where the goal is to remove at most $k$ vertices such that the adjacency matrix of the resulting graph has at most 2 eigenvalues. It is known that the adjacency matrix of a graph has at most 2 eigenvalues if and only if the graph is a collection of equal sized cliques. So {\sc 2-Eigenvalue Vertex Deletion} amounts to removing a set of at most $k$ vertices such that the resulting graph …

An extended version of the $_{r 1}R_{s,k}(B,C,z)$ matrix function
Ayman Shehata
https://arxiv.org/abs/2403.09664 https://arxiv.org/pd…

An extended version of the $_{r+1}R_{s,k}(B,C,z)$ matrix function
Recently, Shehata et al. [37] introduced the $_{r+1}R_{s,k}(B,C,z)$ matrix function and established some properties. The aim of this study established to devote and derive certain basic properties including analytic properties, recurrence matrix relations, differential properties, new integral representations, $k$-Beta transform, Laplace transform, fractional k-Fourier transform, fractional integral properties, the $k$-Riemann-Liouville and $k$-Weyl fractional integral and derivative operators …

Finiteness of the number of irreducible $\lambda$-quiddities over a finite commutative and unitary ring
Flavien Mabilat
https://arxiv.org/abs/2404.10521 ht…

Finiteness of the number of irreducible $λ$-quiddities over a finite commutative and unitary ring
$λ$-quiddities of size $n$ are $n$-tuples of elements of a fixed set, solutions of a matrix equation appearing in the study of Coxeter's friezes. The study of these solutions involves in particular the use of a notion of irreducibility. The main objective of this text is to show that there is a finite number of irreducible $λ$-quiddities over a finite unitary commutative ring and to obtain in this case an upper bound of the maximal size of them.

Quantum phase transition and critical behavior between the gapless topological phases
Hao-Long Zhang, Han-Ze Li, Sheng Yang, Xue-Jia Yu
https://arxiv.org/abs/2404.10576

Quantum phase transition and critical behavior between the gapless topological phases
The phase transition between gapped topological phases represents a class of unconventional criticality beyond the Landau paradigm. However, recent research has shifted attention to topological phases without a bulk gap, where the phase transitions between them are still elusive. In this work, based on large-scale density matrix renormalization group techniques, we investigate the critical behaviors of the extended quantum XXZ model obtained by the Kennedy-Tasaki transformation. Using fidelity …

Cokernels of random matrix products and flag Cohen--Lenstra heuristic
Yifeng Huang
https://arxiv.org/abs/2403.09909 https://arxiv.org…

Cokernels of random matrix products and flag Cohen--Lenstra heuristic
In [NVP22], Nguyen and Van Peski raised the question of whether the surjective flag of $\mathbb Z_p$-modules modeled by $\mathrm{cok}(M_1\cdots M_k)\twoheadrightarrow \dots\twoheadrightarrow \mathrm{cok}(M_1)$ for independent random matrices $M_1,\dots,M_k\in \mathrm{Mat}_n(\mathbb Z_p)$ satisfies the Cohen--Lenstra heuristic. We answer the question affirmatively when $M_1,\dots,M_k$ follow the Haar measure, and our proof demonstrates how classical ideas in Cohen--Lenstra heuristic adapt natura…

Alright, the second revision of the LED matrix comes in today so I've got a ton of LEDs to solder again. Hopefully the PCB fixes solve the issues I saw with the first version. #electronics

This https://arxiv.org/abs/2306.03116 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csHC_…

Transferring Annotator- and Instance-dependent Transition Matrix for Learning from Crowds
Learning from crowds describes that the annotations of training data are obtained with crowd-sourcing services. Multiple annotators each complete their own small part of the annotations, where labeling mistakes that depend on annotators occur frequently. Modeling the label-noise generation process by the noise transition matrix is a power tool to tackle the label noise. In real-world crowd-sourcing scenarios, noise transition matrices are both annotator- and instance-dependent. However, due to …

Warner: Fünfter Teil von "The Matrix" in Arbeit
Warner will die "The Matrix"-Reihe mit einem fünften Teil fortsetzen. Ob Keanu Reeves und Carrie-Anne Moss erneut dabei sind, ist offen.
https://w…

Measuring the Predictability of Recommender Systems using Structural Complexity Metrics
Alfonso Valderrama, Andr\'es Abeliuk
https://arxiv.org/abs/2404.08829

Measuring the Predictability of Recommender Systems using Structural Complexity Metrics
Recommender systems (RS) are central to the filtering and curation of online content. These algorithms predict user ratings for unseen items based on past preferences. Despite their importance, the innate predictability of RS has received limited attention. This study introduces data-driven metrics to measure the predictability of RS based on the structural complexity of the user-item rating matrix. A low predictability score indicates complex and unpredictable user-item interactions, while a h…

Wigner kernel and Gabor matrix of operators
Elena Cordero, Gianluca Giacchi, Luigi Rodino
https://arxiv.org/abs/2404.08332 https://ar…

Wigner kernel and Gabor matrix of operators
We exhibit the connection between the Wigner kernel and the Gabor matrix of a linear bounded operator T : $\mathcal{S}(\mathbb{R}^d) \to \mathcal{S}' (\mathbb{R}^d)$. The smoothing effect of the Gabor matrix is highlighted by basic examples. This connection allows a comparison between the classes of Fourier integral operators defined by means of the Gabor matrix and the Wigner kernel, showing the nice off-diagonal decay of the Gabor class with respect to the Wigner kernel one and suggesting fur…

Tonight, I drove a Canadian-spec car with actually *functional* matrix LED headlights and it was AMAZING. Bright lights where they mattered, dark holes where other drivers were. Best of both worlds.
Shame on the US for screwing up our legislation/rules and preventing this convenient and safety-enhancing feature from appearing on US-spec cars. The rest of the world has had this tech for decades, and we can’t even turn them on in this country, smh.

Since Discord's latest ToS is just proving my worries more, I'm exploring Matrix. I doubt it will ever outright replace it, but it's good to reduce my dependence on Discord. My handle is @the-pink-hacker:gnulinux.club.
#Discord #Matrix

This https://arxiv.org/abs/2305.08735 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The Non-Strict Projection Lemma
The projection lemma (often also referred to as the elimination lemma) is one of the most powerful and useful tools in the context of linear matrix inequalities for system analysis and control. In its traditional formulation, the projection lemma only applies to strict inequalities, however, in many applications we naturally encounter non-strict inequalities. As such, we present, in this note, a non-strict projection lemma that generalizes both its original strict formulation as well as an earl…

This https://arxiv.org/abs/2404.07515 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIT_…

Stability in Phase Retrieval: Characterizing Condition Numbers and the Optimal Vector Set
In this paper, we primarily focus on analyzing the stability property of phase retrieval by examining the bi-Lipschitz property of the map $Φ_{\boldsymbol{A}}(\boldsymbol{x})=|\boldsymbol{A}\boldsymbol{x}|\in \mathbb{R}_+^m$, where $\boldsymbol{x}\in \mathbb{H}^d$ and $\boldsymbol{A}\in \mathbb{H}^{m\times d}$ is the measurement matrix for $\mathbb{H}\in\{\mathbb{R},\mathbb{C}\}$. We define the condition number $β_{\boldsymbol{A}}:=\frac{U_{\boldsymbol{A}}}{L_{\boldsymbol{A}}}$, whe…

On $\tau$-preconditioners for a quasi-compact difference scheme to Riesz fractional diffusion equations with variable coefficients
Zi-Hang She, Xue Zhang, Xian-Ming Gu, Stefano Serra-Capizzano
https://arxiv.org/abs/2404.10221

On $τ$-preconditioners for a quasi-compact difference scheme to Riesz fractional diffusion equations with variable coefficients
In the present study, we consider the numerical method for Toeplitz-like linear systems arising from the $d$-dimensional Riesz space fractional diffusion equations (RSFDEs). We apply the Crank-Nicolson (CN) technique to discretize the temporal derivative and apply a quasi-compact finite difference method to discretize the Riesz space fractional derivatives. For the $d$-dimensional problem, the corresponding coefficient matrix is the sum of a product of a (block) tridiagonal matrix multiplying a…

“Though the last Matrix movie was basically a warning about corporations sucking the life out of iconic pieces of subversive IP, Warner Bros. Discovery is already going back to the well.”
The Matrix is coming back for a fifth movie https://www.theverge.com/24120122/the-matr

The Matrix is coming back for a fifth movie
Following the release of The Matrix Resurrections in 2021, Warner Bros. Discovery is making a new film in the franchise with writer / director Drew Goddard.

This https://arxiv.org/abs/2404.07459 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Safe subspace screening for the adaptive nuclear norm regularized trace regression
Matrix form data sets arise in many areas, so there are lots of works about the matrix regression models. One special model of these models is the adaptive nuclear norm regularized trace regression, which has been proven have good statistical performances. In order to accelerate the computation of this model, we consider the technique called screening rule. According to matrix decomposition and optimal condition of the model, we develop a safe subspace screening rule that can be used to identif…

Multiple Mobile Target Detection and Tracking in Active Sonar Array Using a Track-Before-Detect Approach
Avi Abu, Nikola Miskovic, Oleg Chebotar, Neven Cukrov, Roee Diamant
https://arxiv.org/abs/2404.10316

Multiple Mobile Target Detection and Tracking in Active Sonar Array Using a Track-Before-Detect Approach
We present an algorithm for detecting and tracking underwater mobile objects using active acoustic transmission of broadband chirp signals whose reflections are received by a hydrophone array. The method overcomes the problem of high false alarm rate by applying a track-before-detect ap- proach to the sequence of received reflections. A 2D time- space matrix is created for the reverberations received from each transmitted probe signal by performing delay and sum beamforming and pulse compressio…

Invariant Kalman Filtering with Noise-Free Pseudo-Measurements
Sven Goffin, Silv\`ere Bonnabel, Olivier Br\"uls, Pierre Sacr\'e
https://arxiv.org/abs/2404.10687

Invariant Kalman Filtering with Noise-Free Pseudo-Measurements
In this paper, we focus on developing an Invariant Extended Kalman Filter (IEKF) for extended pose estimation for a noisy system with state equality constraints. We treat those constraints as noise-free pseudo-measurements. To this aim, we provide a formula for the Kalman gain in the limit of noise-free measurements and rank-deficient covariance matrix. We relate the constraints to group-theoretic properties and study the behavior of the IEKF in the presence of such noise-free measurements. We …

This https://arxiv.org/abs/2211.11368 has been replaced.
link: https://scholar.google.com/scholar?q=a

Precise Asymptotics for Spectral Methods in Mixed Generalized Linear Models
In a mixed generalized linear model, the objective is to learn multiple signals from unlabeled observations: each sample comes from exactly one signal, but it is not known which one. We consider the prototypical problem of estimating two statistically independent signals in a mixed generalized linear model with Gaussian covariates. Spectral methods are a popular class of estimators which output the top two eigenvectors of a suitable data-dependent matrix. However, despite the wide applicability…

This https://arxiv.org/abs/2401.08055 has been replaced.
initial toot: https://mastoxiv.page/@ar…

A Programmable and Reconfigurable Photonic Simulator for Classical XY Models
In this work, we proposed and experimentally demonstrated a photonic simulator for XY models, which is a typical kind of classical spin models. By encoding the XY spins on the phase term of the input light field, the corresponding XY Hamiltonian could be performed on the output light intensities. The simulator is mainly based on a programmable and reconfigurable optical vector-matrix multiplication system, which can map arbitrary XY models within the dimensionality limit. Here, we demonstrated …

Local control on quaternionic Heisenberg group of dimension $7$
Jan Eisner, Lenka Zalabov\'a
https://arxiv.org/abs/2404.08953 https://

Local control on quaternionic Heisenberg group of dimension $7$
We describe the quaternionic Heisenberg group in the dimension $7$ as a matrix group. We study the local control of a compatible left-invariant control system. We describe the impact of symmetries of the corresponding sub-Riemannian structure on the optimality of geodesics.

Sample complexity of matrix product states at finite temperature
Atsushi Iwaki, Chisa Hotta
https://arxiv.org/abs/2403.10018 https://…

Sample complexity of matrix product states at finite temperature
For quantum many-body systems in one dimension, computational complexity theory reveals that the evaluation of ground-state energy remains elusive on quantum computers, contrasting the existence of a classical algorithm for temperatures higher than the inverse logarithm of the system size. This highlights a qualitative difference between low- and high-temperature states in terms of computational complexity. Here, we describe finite-temperature states using the matrix product state formalism. Wi…

Classifying Sums of Exponentially Damped Sinusoids Using an Associated Numerical Range
Raymundo Albert, Cecilia G. Galarza
https://arxiv.org/abs/2404.11413

Classifying Sums of Exponentially Damped Sinusoids Using an Associated Numerical Range
The matrix pencil method (MPM) is a well-known technique for estimating the parameters of exponentially damped sinusoids in noise by solving a generalized eigenvalue problem. However, in several cases, this is an ill-conditioned problem whose solution is highly biased under small perturbations. When the estimation is performed to classify the observed signal into two categories, the estimation errors induce several misclassifications. In this work we propose a novel signal classification criter…

Tensor product random matrix theory
Alexander Altland, Tobias Micklitz, Joaquim Telles de Miranda
https://arxiv.org/abs/2404.10919 https://

Tensor product random matrix theory
The evolution of complex correlated quantum systems such as random circuit networks is governed by the dynamical buildup of both entanglement and entropy. We here introduce a real-time field theory approach -- essentially a fusion of the $G Σ$-functional of the SYK-model and the field theory of disordered systems -- enigneered to microscopically describe the full range of such crossover dynamics: from initial product states to a maximum entropy ergodic state. To showcase this approach in the s…

This https://arxiv.org/abs/2402.02530 has been replaced.
link: https://scholar.google.com/scholar?q=a

Polyhedral bounds on the joint spectrum and temperedness of locally symmetric spaces
Given a real semisimple connected Lie group $G$ and a discrete torsion-free subgroup $Γ< G$ we prove a precise connection between growth rates of the group $Γ$, polyhedral bounds on the joint spectrum of the ring of invariant differential operators, and the decay of matrix coefficients. In particular, this allows us to completely characterize temperedness of $L^2(Γ\backslash G)$ in this general setting.

This https://arxiv.org/abs/2402.18254 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hepp…

Photon quantum kinetic equations and collective modes in an axion background
We develop a quantum kinetic theory for photons in the presence of an axion background and in the collisioness limit. In deriving the classical regime of our quantum kinetic equations, we observe that they capture well known features of axion electrodynamics. By projecting the Wigner function onto a polarization basis, relating the Wigner matrix function with the Stokes parameters, we establish the dispersion relations and transport equations for each polarization space component. Additionally,…

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 approximability of the Permanent of PSD matrices
Farzam Ebrahimnejad, Ansh Nagda, Shayan Oveis Gharan
https://arxiv.org/abs/2404.10959 https://

On approximability of the Permanent of PSD matrices
We study the complexity of approximating the permanent of a positive semidefinite matrix $A\in \mathbb{C}^{n\times n}$. 1. We design a new approximation algorithm for $\mathrm{per}(A)$ with approximation ratio $e^{(0.9999 + γ)n}$, exponentially improving upon the current best bound of $e^{(1+γ-o(1))n}$ [AGOS17,YP22]. Here, $γ\approx 0.577$ is Euler's constant. 2. We prove that it is NP-hard to approximate $\mathrm{per}(A)$ within a factor $e^{(γ-ε)n}$ for any $ε>0$. This is the first …

This https://arxiv.org/abs/2205.05100 has been replaced.
link: https://scholar.google.com/scholar?q=a

Bounds on Path Energy of Graphs
Given a graph $M,$ path eigenvalues are eigenvalues of its path matrix. The path energy of a simple graph $M$ is equal to the sum of the absolute values of the path eigenvalues of the graph $M$ (Shikare et. al, 2018). We have discovered new upper constraints on path energy in this study, expressed in terms of a graph's maximum degree. Additionally, a relationship between a graph's energy and path energy is given.

This https://arxiv.org/abs/2402.06372 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Spectral properties of the Dirichlet-to-Neumann operator for spheroids
We study the spectral properties of the Dirichlet-to-Neumann operator and the related Steklov problem in spheroidal domains ranging from a needle to a disk. An explicit matrix representation of this operator for both interior and exterior problems is derived. We show how the anisotropy of spheroids affects the eigenvalues and eigenfunctions of the operator. As examples of physical applications, we discuss diffusion-controlled reactions on spheroidal partially reactive targets and the statistics…

On $\tau$-preconditioners for a quasi-compact difference scheme to Riesz fractional diffusion equations with variable coefficients
Zi-Hang She, Xue Zhang, Xian-Ming Gu, Stefano Serra-Capizzano
https://arxiv.org/abs/2404.10221

On $τ$-preconditioners for a quasi-compact difference scheme to Riesz fractional diffusion equations with variable coefficients
In the present study, we consider the numerical method for Toeplitz-like linear systems arising from the $d$-dimensional Riesz space fractional diffusion equations (RSFDEs). We apply the Crank-Nicolson (CN) technique to discretize the temporal derivative and apply a quasi-compact finite difference method to discretize the Riesz space fractional derivatives. For the $d$-dimensional problem, the corresponding coefficient matrix is the sum of a product of a (block) tridiagonal matrix multiplying a…

Quantum phase transition and critical behavior between the gapless topological phases
Hao-Long Zhang, Han-Ze Li, Sheng Yang, Xue-Jia Yu
https://arxiv.org/abs/2404.10576

Quantum phase transition and critical behavior between the gapless topological phases
The phase transition between gapped topological phases represents a class of unconventional criticality beyond the Landau paradigm. However, recent research has shifted attention to topological phases without a bulk gap, where the phase transitions between them are still elusive. In this work, based on large-scale density matrix renormalization group techniques, we investigate the critical behaviors of the extended quantum XXZ model obtained by the Kennedy-Tasaki transformation. Using fidelity …

A preconditioner for solving linear programming problems with dense columns
Catalina J. Villalba, Aurelio R. L. Oliveira
https://arxiv.org/abs/2404.10930 h…

A preconditioner for solving linear programming problems with dense columns
The Interior-Point Methods are a class for solving linear programming problems that rely upon the solution of linear systems. At each iteration, it becomes important to determine how to solve these linear systems when the constraint matrix of the linear programming problem includes dense columns. In this paper, we propose a preconditioner to handle linear programming problems with dense columns, and we prove theoretically that the final linear system to solve is uniformly bounded when the Inter…

This https://arxiv.org/abs/2309.11651 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

Drift Control of High-Dimensional RBM: A Computational Method Based on Neural Networks
Motivated by applications in queueing theory, we consider a stochastic control problem whose state space is the $d$-dimensional positive orthant. The controlled process $Z$ evolves as a reflected Brownian motion whose covariance matrix is exogenously specified, as are its directions of reflection from the orthant's boundary surfaces. A system manager chooses a drift vector $θ(t)$ at each time $t$ based on the history of $Z$, and the cost rate at time $t$ depends on both $Z(t)$ and $θ(t)$. In …

Warner Bros. hat offiziell einen fünften Teil der Sci-Fi-Reihe "The Matrix" angekündigt.
Ob Stars wie Keanu Reeves und Carrie-Anne Moss im fünften "Matrix"-Film mitspielen werden, ist bisher noch unklar.
Zum Artikel: https://

Computing the Determinant of a Dense Matrix over Z
John Abbott, Claus Fieker
https://arxiv.org/abs/2404.08358 https://arxiv.org/pdf/2…

Computing the Determinant of a Dense Matrix over Z
We present a new, practical algorithm for computing the determinant of a non-singular dense, uniform matrix over Z; the aim is to achieve better practical efficiency, which is always at least as good as currently known methods. The algorithm uses randomness internally, but the result is guaranteed correct. The main new idea is to use a modular HNF in cases where the Pauderis--Storjohann HCOL method performs poorly. The algorithm is implemented in OSCAR~1.0.

So, I now have two working "prototypes": a rev 0.1 and a rev 0.2...and I have 351 bright amber LEDs. The schematic for this part of the badge is good, now it's time to write a library to turn pixels off and on. Adafruit has a library for the LED matrix IC, but it only supports RGB for some odd reason. However, first win of the project. #electronics

Eigenstate Thermalization Hypothesis for Wigner-type Matrices
Volodymyr Riabov, L\'aszl\'o Erd\H{o}s
https://arxiv.org/abs/2403.10359 https://

Eigenstate Thermalization Hypothesis for Wigner-type Matrices
We prove the Eigenstate Thermalization Hypothesis for general Wigner-type matrices in the bulk of the self-consistent spectrum, with optimal control on the fluctuations for observables of arbitrary rank. As the main technical ingredient, we prove rank-uniform optimal local laws for one and two resolvents of a Wigner-type matrix with regular observables.

An efficient asymptotic DC method for sparse and low-rank matrix recovery
Mingcai Ding, Xiaoliang Song, Bo Yu
https://arxiv.org/abs/2403.10180 https://

An efficient asymptotic DC method for sparse and low-rank matrix recovery
The optimization problem of sparse and low-rank matrix recovery is considered, which involves a least squares problem with a rank constraint and a cardinality constraint. To overcome the challenges posed by these constraints, an asymptotic difference-of-convex (ADC) method that employs a Moreau smoothing approach and an exact penalty approach is proposed to transform this problem into a DC programming format gradually. To solve the gained DC programming, by making full use of its DC structure, …

SIFt-RLS: Subspace of Information Forgetting Recursive Least Squares
Brian Lai, Dennis S. Bernstein
https://arxiv.org/abs/2404.10844 https://

SIFt-RLS: Subspace of Information Forgetting Recursive Least Squares
This paper presents subspace of information forgetting recursive least squares (SIFt-RLS), a directional forgetting algorithm which, at each step, forgets only in row space of the regressor matrix, or the \textit{information subspace}. As a result, SIFt-RLS tracks parameters that are in excited directions while not changing parameter estimation in unexcited directions. It is shown that SIFt-RLS guarantees an upper and lower bound of the covariance matrix, without assumptions of persistent excit…

This https://arxiv.org/abs/2310.18510 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hepp…

Entanglement entropy of proton and its relation to thermodynamics entropy
I discuss the thermodynamics-based derivation of the formula for the entanglement entropy of a system of gluons. The derivation is based on an approach where saturation and the Unruh effect were used to obtain and discuss the entropy of gluons. The formula agrees, in the high-energy limit, up to a numerical factor, with more recent results, where arguments based on the density matrix and bipartition of the proton were used to obtain the formula. I also discuss the relation of entropy as obtaine…

This https://arxiv.org/abs/2310.15279 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The linear system for Sudoku and a fractional completion threshold
We study a system of linear equations associated with Sudoku latin squares. The coefficient matrix $M$ of the normal system has various symmetries arising from Sudoku. From this, we find the eigenvalues and eigenvectors of $M$, and compute a generalized inverse. Then, using linear perturbation methods, we obtain a fractional completion guarantee for sufficiently large and sparse rectangular-box Sudoku puzzles.

This https://arxiv.org/abs/2312.14615 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

A fixed-point algorithm for matrix projections with applications in quantum information
We develop a simple fixed-point iterative algorithm that computes the matrix projection with respect to the Bures distance on the set of positive definite matrices that are invariant under some symmetry. We prove that the fixed-point iteration algorithm converges exponentially fast to the optimal solution in the number of iterations. Moreover, it numerically shows fast convergence compared to the off-the-shelf semidefinite program solvers. Our algorithm, for the specific case of matrix barycent…

R\'enyi entropy of the permutationally invariant part of the ground state across a quantum phase transition
Yuki Miyazaki, Giacomo Marmorini, Nobuo Furukawa, Daisuke Yamamoto
https://arxiv.org/abs/2404.08389

Rényi entropy of the permutationally invariant part of the ground state across a quantum phase transition
We investigate the role of the permutationally invariant part of the density matrix (PIDM) in capturing the properties of the ground state of the system during a quantum phase transition. In the context of quantum state tomography, PIDM is known to be obtainable with only a low number of measurement settings, namely $\mathcal{O}(L^2)$, where $L$ is the system size. Considering the transverse-field Ising chain as an example, we compute the second-order Rényi entropy of PIDM for the ground state…

Generalized Hydrodynamics for the Volterra lattice: Ballistic and nonballistic behavior of correlation functions
Guido Mazzuca
https://arxiv.org/abs/2404.08499

Generalized Hydrodynamics for the Volterra lattice: Ballistic and nonballistic behavior of correlation functions
In recent years, a lot of effort has been put in describing the hydrodynamic behavior of integrable systems. In this paper, we describe such picture for the Volterra lattice. Specifically, we are able to explicitly compute the susceptibility matrix and the current-field correlation matrix in terms of the density of states of the Volterra lattice endowed with a Generalized Gibbs ensemble. Furthermore, we apply the theory of linear Generalized Hydrodynamics to describe the Euler scale behavior of…

Computing the Determinant of a Dense Matrix over Z
John Abbott, Claus Fieker
https://arxiv.org/abs/2404.08358 https://arxiv.org/pdf/2…

Computing the Determinant of a Dense Matrix over Z
We present a new, practical algorithm for computing the determinant of a non-singular dense, uniform matrix over Z; the aim is to achieve better practical efficiency, which is always at least as good as currently known methods. The algorithm uses randomness internally, but the result is guaranteed correct. The main new idea is to use a modular HNF in cases where the Pauderis--Storjohann HCOL method performs poorly. The algorithm is implemented in OSCAR~1.0.

Phase diagram of the quantum spin-1/2 Heisenberg-$\Gamma$ model on a frustrated zigzag chain
Hidehiro Saito, Chisa Hotta
https://arxiv.org/abs/2404.10615 h…

Phase diagram of the quantum spin-1/2 Heisenberg-$Γ$ model on a frustrated zigzag chain
We investigate the quantum spin-1/2 zigzag chain with frustrated $J_1$-$J_2$ Heisenberg interactions, incorporating additional off-diagonal exchange interactions known as the $Γ$-term, both with and without an applied magnetic field. Based on the density-matrix renormalization group calculation, we map out the ground state phase diagram that shows a variety of magnetic and nonmagnetic phases including multicritical points and several exactly solvable points. Upon introducing a finite $Γ$-term…

This https://arxiv.org/abs/2403.14600 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Wall-Crossing Effects on Quiver BPS Algebras
BPS states in supersymmetric theories can admit additional algebro-geometric structures in their spectra, described as quiver Yangian algebras. Equivariant fixed points on the quiver variety are interpreted as vectors populating a representation module, and matrix elements for the generators are then defined as Duistermaat-Heckman integrals in the vicinity of these points. The well-known wall-crossing phenomena are that the fixed point spectrum establishes a dependence on the stability (Fayet-I…

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

This https://arxiv.org/abs/2211.01314 has been replaced.
link: https://scholar.google.com/scholar?q=a

The $μ$-$τ$ mixed symmetry and neutrino mass matrix
We propose an elegant neutrino mass matrix texture entitled $μ$-$τ$ mixed symmetry highlighting two simple correlations among its elements and a detailed analysis is carried out to see its phenomenological implications. The proposed texture is motivated in the framework of Seesaw mechanism in association with $A_4$ symmetry

A $\tau$-preconditioner for space fractional diffusion equation with non-separable variable coefficients
Xue-Lei Lin, Michael K. Ng
https://arxiv.org/abs/2404.11390

A $τ$-preconditioner for space fractional diffusion equation with non-separable variable coefficients
In this paper, we study a $τ$-matrix approximation based preconditioner for the linear systems arising from discretization of unsteady state Riesz space fractional diffusion equation with non-separable variable coefficients. The structure of coefficient matrices of the linear systems is identity plus summation of diagonal-times-multilevel-Toeplitz matrices. In our preconditioning technique, the diagonal matrices are approximated by scalar identity matrices and the Toeplitz matrices are approxi…

This https://arxiv.org/abs/2302.08781 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Interpolation Conditions for Linear Operators and Applications to Performance Estimation Problems
The Performance Estimation Problem methodology makes it possible to determine the exact worst-case performance of an optimization method. In this work, we generalize this framework to first-order methods involving linear operators. This extension requires an explicit formulation of interpolation conditions for those linear operators. We consider the class of linear operators $\mathcal{M}:x \mapsto Mx$ where matrix $M$ has bounded singular values, and the class of linear operators where $M$ is s…

Divisible design graphs from the symplectic graph
Bart De Bruyn, Sergey Goryainov, Willem Haemers, Leonid Shalaginov
https://arxiv.org/abs/2404.09902 https…

Divisible design graphs from the symplectic graph
A divisible design graph is a graph whose adjacency matrix is an incidence matrix of a (group) divisible design. Divisible design graphs were introduced in 2011 as a generalization of $(v,k,λ)$-graphs. Here we describe four new infinite families that can be obtained from the symplectic strongly regular graph $Sp(2e,q)$ ($q$ odd, $e\geq 2$) by modifying the set of edges. To achieve this we need two kinds of spreads in $PG(2e-1,q)$ with respect to the associated symplectic form: the symplectic s…

Phase diagram of the quantum spin-1/2 Heisenberg-$\Gamma$ model on a frustrated zigzag chain
Hidehiro Saito, Chisa Hotta
https://arxiv.org/abs/2404.10615 h…

Phase diagram of the quantum spin-1/2 Heisenberg-$Γ$ model on a frustrated zigzag chain
We investigate the quantum spin-1/2 zigzag chain with frustrated $J_1$-$J_2$ Heisenberg interactions, incorporating additional off-diagonal exchange interactions known as the $Γ$-term, both with and without an applied magnetic field. Based on the density-matrix renormalization group calculation, we map out the ground state phase diagram that shows a variety of magnetic and nonmagnetic phases including multicritical points and several exactly solvable points. Upon introducing a finite $Γ$-term…

SO(n) AKLT Chains as Symmetry Protected Topological Quantum Ground States
Michael Ragone
https://arxiv.org/abs/2403.09951 https://arx…

SO(n) AKLT Chains as Symmetry Protected Topological Quantum Ground States
This thesis studies a pair of symmetry protected topological (SPT) phases which arise when considering one-dimensional quantum spin systems possessing a natural orthogonal group symmetry. Particular attention is given to a family of exactly solvable models whose ground states admit a matrix product state description and generalize the AKLT chain. We call these models ``$SO(n)$ AKLT chains'' and the phase they occupy the ``$SO(n)$ Haldane phase''. We present new results describing their ground s…

Numerical Discretization Methods for the Extended Linear Quadratic Control Problem
Zhanhao Zhang, Jan Lorenz Svensen, Morten Wahlgreen Kaysfeld, Anders Hilmar Damm Christensen, Steen H{\o}rsholt, John Bagterp J{\o}rgensen
https://arxiv.org/abs/2404.09316

Numerical Discretization Methods for the Extended Linear Quadratic Control Problem
In this study, we introduce numerical methods for discretizing continuous-time linear-quadratic optimal control problems (LQ-OCPs). The discretization of continuous-time LQ-OCPs is formulated into differential equation systems, and we can obtain the discrete equivalent by solving these systems. We present the ordinary differential equation (ODE), matrix exponential, and a novel step-doubling method for the discretization of LQ-OCPs. Utilizing Euler-Maruyama discretization with a fine step, we r…

The Norton-balanced condition for $Q$-polynomial distance-regular graphs
Paul Terwilliger
https://arxiv.org/abs/2404.09346 https://ar…

The Norton-balanced condition for $Q$-polynomial distance-regular graphs
Let $Γ$ denote a $Q$-polynomial distance-regular graph, with vertex set $X$ and diameter $D\geq 3$. The standard module $V$ has a basis $\lbrace {\hat x} \vert x \in X\rbrace$, where ${\hat x}$ denotes column $x$ of the identity matrix $I \in {\rm Mat}_X(\mathbb C)$. Let $E$ denote a $Q$-polynomial primitive idempotent of $Γ$. The eigenspace $EV$ is spanned by the vectors $\lbrace E {\hat x} \vert x \in X\rbrace$. It was previously known that these vectors satisfy a condition called the…

Large-Parameter Asymptotics of Generalized Hasting-McLeod Functions
Kurt Schmidt, Robert Buckingham
https://arxiv.org/abs/2404.08142 https://

Large-Parameter Asymptotics of Generalized Hasting-McLeod Functions
The generalized Hastings-McLeod solutions to the inhomogeneous Painlevé-II equation arise in multi-critical unitary random matrix ensembles, the chiral two-matrix model for rectangular matrices, non-intersecting squared Bessel paths, and non-intersecting Brownian motions on the circle. We establish the leading-order asymptotic behavior of the generalized Hastings-McLeod functions as the inhomogeneous parameter approaches infinity using the Deift-Zhou nonlinear steepest-descent method for Riema…

This https://arxiv.org/abs/2211.15643 has been replaced.
link: https://scholar.google.com/scholar?q=a

A posteriori error bounds for the block-Lanczos method for matrix function approximation
We extend the error bounds from [SIMAX, Vol. 43, Iss. 2, pp. 787-811 (2022)] for the Lanczos method for matrix function approximation to the block algorithm. Numerical experiments suggest that our bounds are fairly robust to changing block size and have the potential for use as a practical stopping criteria. Further experiments work towards a better understanding of how certain hyperparameters should be chosen in order to maximize the quality of the error bounds, even in the previously studied …

A Gray-Box Stability Analysis Mechanism for Power Electronic Converters
Rui Kong, Subham Sahoo, Yubo Song, Frede Blaabjerg
https://arxiv.org/abs/2404.09801

A Gray-Box Stability Analysis Mechanism for Power Electronic Converters
This paper proposes a gray-box stability analysis mechanism based on data-driven dynamic mode decomposition (DMD) for commercial grid-tied power electronics converters with limited information on its control parameters and topology. By fusing the underlying physical constraints of the state equations into data snapshots, the system dynamic state matrix and input matrix are simultaneously approximated to identify the dominant system dynamic modes and eigenvalues using the DMD with control (DMDc)…

This https://arxiv.org/abs/2307.00898 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Periodicity of general multidimensional continued fractions using repetend matrix form
We consider expansions of vectors by a general class of multidimensional continued fraction algorithms. If the expansion is eventually periodic, then we describe the possible structure of a matrix corresponding to the repetend, and use it to prove that a number of vectors has an eventually periodic expansion in the Algebraic Jacobi--Perron Algorithm. Further, we give criteria for vectors to have purely periodic expansions; in particular, the vector cannot be totally positive.

On the induced subgraphs of the zero-divisor graph of a matrix ring over number rings
WonTae Hwang, Ei Thu Thu Kyaw
https://arxiv.org/abs/2403.08349 https:…

On the induced subgraphs of the zero-divisor graph of a matrix ring over number rings
We provide a construction of the induced subgraphs of the zero-divisor graph of $M_2(R)$ for the ring $R$ of algebraic integers of some number fields that are neither complete nor connected, and study the structure of the induced subgraphs explicitly. As an application, we prove that the automorphism group of the zero-divisor graph of $M_2(R)$ is not a Jordan group.

This https://arxiv.org/abs/2010.07282 has been replaced.
link: https://scholar.google.com/scholar?q=a

Monotonicity of $Q^3$ spectral element method for discrete Laplacian
The monotonicity of discrete Laplacian, i.e., inverse positivity of stiffness matrix, implies discrete maximum principle, which is in general not true for high order accurate schemes on unstructured meshes. On the other hand, it is possible to construct high order accurate monotone schemes on structured meshes. All previously known high order accurate inverse positive schemes are fourth order accurate schemes, which is either an M-matrix or a product of two M-matrices. For the $Q^3$ spectral el…

This https://arxiv.org/abs/2307.03590 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Accelerated Optimization Landscape of Linear-Quadratic Regulator
Linear-quadratic regulator (LQR) is a landmark problem in the field of optimal control, which is the concern of this paper. Generally, LQR is classified into state-feedback LQR (SLQR) and output-feedback LQR (OLQR) based on whether the full state is obtained. It has been suggested in existing literature that both SLQR and OLQR could be viewed as \textit{constrained nonconvex matrix optimization} problems in which the only variable to be optimized is the feedback gain matrix. In this paper, we i…

Numerical Discretization Methods for Linear Quadratic Control Problems with Time Delays
Zhanhao Zhang, Steen H{\o}rsholt, John Bagterp J{\o}rgensen
https://arxiv.org/abs/2404.08440

Numerical Discretization Methods for Linear Quadratic Control Problems with Time Delays
This paper presents the numerical discretization methods of the continuous-time linear-quadratic optimal control problems (LQ-OCPs) with time delays. We describe the weight matrices of the LQ-OCPs as differential equations systems, allowing us to derive the discrete equivalent of the continuous-time LQ-OCPs. Three numerical methods are introduced for solving proposed differential equations systems: 1) the ordinary differential equation (ODE) method, 2) the matrix exponential method, and 3) the …

This https://arxiv.org/abs/2307.03590 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Accelerated Optimization Landscape of Linear-Quadratic Regulator
Linear-quadratic regulator (LQR) is a landmark problem in the field of optimal control, which is the concern of this paper. Generally, LQR is classified into state-feedback LQR (SLQR) and output-feedback LQR (OLQR) based on whether the full state is obtained. It has been suggested in existing literature that both SLQR and OLQR could be viewed as \textit{constrained nonconvex matrix optimization} problems in which the only variable to be optimized is the feedback gain matrix. In this paper, we i…

Tensor Deli: Tensor Completion for Low CP-Rank Tensors via Random Sampling
Cullen Haselby, Mark Iwen, Santhosh Karnik, Rongrong Wang
https://arxiv.org/abs/2403.09932

Tensor Deli: Tensor Completion for Low CP-Rank Tensors via Random Sampling
We propose two provably accurate methods for low CP-rank tensor completion - one using adaptive sampling and one using nonadaptive sampling. Both of our algorithms combine matrix completion techniques for a small number of slices along with Jennrich's algorithm to learn the factors corresponding to the first two modes, and then solve systems of linear equations to learn the factors corresponding to the remaining modes. For order-$3$ tensors, our algorithms follow a "sandwich" sampling strategy …

Link patterns and elliptic Hecke algebra
Andrzej Weber
https://arxiv.org/abs/2404.08911 https://arxiv.org/pdf/2404.08911

Link patterns and elliptic Hecke algebra
We compare the following three families of geometric objects: Schubert varieties in flag manifolds, matrix Schubert varieties, and Borel orbits of 2-nilpotent matrices. The first family is governed by permutations, the second by partial permutations, and the last one by "link patterns". These geometric objects admit characteristic classes in equivariant elliptic cohomology obtained within the framework created by Borisov and Libgober. We construct a Hecke-type algebra for computing elliptic cla…

Combinatorics of Complex Maximal Determinant Matrices
Guillermo Nu\~nez Ponasso
https://arxiv.org/abs/2404.09040 https://arxiv.org/pd…

Combinatorics of Complex Maximal Determinant Matrices
This doctoral thesis covers several topics related to the construction and study of maximal determinant matrices with complex entries. The first three chapters are devoted to number-theoretic tools to prove the non-solvability of Gram matrix equations over certain fields, with a focus on combinatorial applications. Chapter 4 gives a survey on Butson-type Hadamard matrices, and shows an improved lower bound on primes $p$ for the existence of $BH(12p, p)$ matrices. Chapter 5 contains the main con…

This https://arxiv.org/abs/2208.05013 has been replaced.
link: https://scholar.google.com/scholar?q=a

Computing Brascamp-Lieb Constants through the lens of Thompson Geometry
This paper studies algorithms for efficiently computing Brascamp-Lieb constants, a task that has recently received much interest. In particular, we reduce the computation to a nonlinear matrix-valued iteration, whose convergence we analyze through the lens of fixed-point methods under the well-known Thompson metric. This approach permits us to obtain (weakly) polynomial time guarantees, and it offers an efficient and transparent alternative to previous state-of-the-art approaches based on Riema…