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From the microscopic electroporation to the irregular distribution of cell populations, the inactivation efficacy of pulsed electric fields (PEFs) from in vitro experiments has lacked a unified physical model due to its cross-scale complexity. Inspired by a coarse-grained approach from the percolation theory, the inactivation process is simulated from a simple yet robust lattice model, where the spatiotemporal heterogeneity of the collective structure and the stochastic PEF strike are portrayed as random matrices, while also accounting for the rules of single-cell electroporation and subsequent death. Beyond successfully simulating the inactivation of monolayer adherent cells and suspended cells, which are in good agreement with in vitro results, our model reveals that (1) macroscopically three-staged inactivation pattern originates from the "accelerate–uniform–decelerate" transition of inactivation velocity, and (2) the inactivation patterns obey a universal scaling law under varied field strength, which is not satisfied under varied pulsed widths. The simulation not only sheds light on the PEF inactivation of the macroscopic cell collectives but also provides a simple and generalized numerical method for predicting PEF efficacy in experiments or engineering. [ABSTRACT FROM AUTHOR]

In this paper, we consider the recovery of fusion frame sparse signals from incomplete structured measurements. This signal has energy only in a few subspaces of the fusion frame. The sufficient condition for uniform recovery of fusion frame sparse signal is a fusion restricted isometry property (FRIP) which is the fusion frame version of restricted isometry property (RIP) in the standard compressed sensing (CS) settings. Different classes of random matrices are well known to satisfy FRIP, but such matrices do not possess any structure that emerged from the practical sensing systems. In this paper, we give the theoretical results to bridge this gap by proving that a random sampling matrix associated with a bounded orthonormal system satisfies the FRIP with high probability. In detail, we established the uniform recovery guarantees for fusion frames and structured measurements, which may be the beginning of practical applications relating to the fusion frame sparse signal model. [ABSTRACT FROM AUTHOR]

To address the limitations of reduced accuracy in graph diffusion methods when handling complex edge relationships, this paper proposed a curvature-based graph diffusion neural network. The method introduced Ollivier-Ricci curvature to quantify edge curvature, providing a geometric measure of graph structure. The algorithm adjusted the weights of the random transition matrix using curvature, modifying them based on geometric relationships. It then combined the processed curvature matrix with the graph diffusion matrix to update the weight coefficients for model training. Experimental results show that the improved method maintains the advantages of smoothing graph signals effectively and reducing high-frequency noise. It increased accuracy by 0. 3 to 2.0 percentage points on datasets with varying numbers of edges and nodes. The method optimized message aggregation in graph diffusion, utilizing node information and edge weights within the graph structure more effectively. This enhancement improves model performance in node classification tasks and provides a reliable method and experimental basis for future graph-based research. [ABSTRACT FROM AUTHOR]

Our study emphasizes the efficacy of employing matrices resembling Wishart matrices, derived from magnetization time series data within specific dynamics, to elucidate phase transitions and critical phenomena in the Q-state Potts model. Through the application of appropriate statistical methods, we not only identify second-order transitions but also distinguish weaker first-order transitions by carefully analyzing the density of eigenvalues and their fluctuations. Additionally, we investigate the method's sensitivity to stronger first-order transition points. Notably, we establish a robust correlation between the system's actual thermodynamics and the spectral thermodynamics encapsulated within the eigenvalues. Our findings are further supported by correlation histograms of the time series data, revealing insightful patterns. Building upon our core results, we provide a didactic analysis that draws parallels between the spectral properties of criticality in a spin system and matrices intentionally imbued with correlations (a toy model). Within this framework, we observe a universal behavior characterized by the distribution of eigenvalues into two distinct groups, separated by a gap dependent on the level of correlation, influenced by temperature-induced changes in the spin system. [ABSTRACT FROM AUTHOR]

This article investigates the consequences of using Singular Spectral Analysis (SSA) to construct a time series bootstrap. The bootstrap replications are obtained via a SSA decomposition obtained using rescaled trajectories (RT‐SSA), a procedure that is particularly useful in the analysis of time series that exhibit nonlinear, non‐stationary and intermittent or transient behaviour. The theoretical validity of the RT‐SSA bootstrap when used to approximate the sampling properties of a general class of statistics is established under regularity conditions that encompass a very broad range of data generating processes. A smeared and a boosted version of the RT‐SSA bootstrap are also presented. Practical implementation of the bootstrap is considered and the results are illustrated using stationary, non‐stationary and irregular time series examples. [ABSTRACT FROM AUTHOR]

Let A be drawn uniformly at random from the set of all n\times n symmetric matrices with entries in \{-1,1\}. We show that \[ \mathbb {P}(\det (A) = 0) \leqslant e^{-cn}, \] where c>0 is an absolute constant, thereby resolving a long-standing conjecture. [ABSTRACT FROM AUTHOR]

We study the GMRES algorithm applied to linear systems of equations involving a scaled and shifted N\times N matrix whose entries are independent complex Gaussians. When the right-hand side of this linear system is independent of this random matrix, the N\to \infty behavior of the GMRES residual error can be determined exactly. To handle cases where the right hand side depends on the random matrix, we study the pseudospectra and numerical range of Ginibre matrices and prove a restricted version of Crouzeix's conjecture. [ABSTRACT FROM AUTHOR]

For decades, fossil fuels have accounted for 70% to 80% of global primary energy demand. Far from ending this trend, O&G companies continue to be the main fore-runners in providing secure, versatile and widespread energy to the entire world. The relevance of this sector in the economic-financial landscape and the concern for its stability, makes that the high interest of the scientific community to explore the factors that explain the O&G cross-sectional expected returns remains intact. Through a new approach from the Random Matrix Theory, the aim is to know how many are the factors that explain the market performance of the O&G subsectors (upstream, midstream & downstream), and also if the Brent price can be considered an explanatory factor. We will show that for certain periods, Brent becomes the only factor explaining the movements in the upstream and midstream subsectors, while for most of the time the only factor is the market. Other interesting finding is that no significant factors are found for the downstream subsector, except in certain periods. With a purely statistical approach, we show the factors that explain the cross-sectional expected return of the O&G companies, providing information of special relevance for the decision making of investors, executives and politicians. [ABSTRACT FROM AUTHOR]

This study explores the intricate dynamics of volatility within high-frequency financial markets, focusing on 225 of Chinese listed companies from 2016 to 2023. Utilizing 5-minute high-frequency data, we analyze the realized volatility of individual stocks across six distinct time scales: 5-minute, 10-minute, 30-minute, 1-hour, 2-hour, and 4-hour intervals. Our investigation reveals a consistent power law decay in the auto-correlation function of realized volatility across all time scales. After constructing cross-correlation matrices for each time scale, we analyze the eigenvalues, eigenvectors, and probability distribution of Cij based on Random Matrix Theory. Notably, we find stronger correlations between stocks at higher frequencies, with distinct eigenvector patterns associated with large eigenvalues across different time scales. Employing Planar Maximally Filtered Graphs method, we uncover evolving community structures across the six time scales. Finally, we explore reaction speed across multiple time scales following big events and compare industry-specific reactions. Our findings underscore the faster reaction speed at higher frequency scales, shedding light on the multifaceted dynamics of high-frequency financial markets. [ABSTRACT FROM AUTHOR]

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 obs ervables 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. Our results hold under very general conditions on the variance profile, even allowing many vanishing entries, demonstrating that Eigenstate Thermalization occurs robustly across a diverse class of random matrix ensembles, for which the underlying quantum system has a non-trivial spatial structure. [ABSTRACT FROM AUTHOR]

In power systems, the application of wind power generation equipment and power electronic devices leads to an increased frequency of broadband oscillation events, and the detection of oscillation information becomes extremely difficult, due to the limitations of communication bandwidth and the sampling theorem. To ensure the safety and stability of a power system, this paper presents a new recognition method of broadband oscillation information, which combines compressed sensing (CS) technology and an ensemble empirical mode decomposition (EEMD) algorithm to solve the problem of wideband oscillation recognition. Firstly, the broadband oscillation signal data collected by the phasor measuring unit (PMU) is compressed and sampled by a Gaussian random matrix in the substation, then the low-dimensional data obtained is uploaded to the main station. Secondly, in the main station, the subspace pursuit (SP) algorithm is used to reconstruct the low-dimensional signal; the broadband oscillation signal is recovered without losing the main features of the signal. Finally, we use the EEMD algorithm to decompose the reconstructed signal; the intrinsic mode function (IMF) components containing wideband oscillation information are screened by the energy coefficient, and the wideband oscillation information is identified. [ABSTRACT FROM AUTHOR]

The quantum conductance and its classical wave analogue, the transmittance, are given by the sum of the eigenvalues of the transmission matrix. However, neither measurements nor theoretical analysis of the transmission eigenchannels have been carried out to explain the dips in conductance found in simulations as new channels are introduced. Here, we measure the microwave transmission matrices of random waveguides and find the spectra of all transmission eigenvalues, even at dips in the lowest transmission eigenchannel that are orders of magnitude below the noise in the transmission matrix. Transmission vanishes both at topological transmission zeros, where the energy density at the sample output vanishes, and at crossovers to new channels, where the longitudinal velocity vanishes. Zeros of transmission pull down all the transmission eigenvalues and thereby produce dips in the transmittance. These dips and the ability to probe the characteristics of even the lowest transmission eigenchannel are due to correlation among the eigenvalues. The precise tracking of dips in the conductance by peaks in the density of states points to a further correlation between zeros and poles of the transmission matrix. The conductance approaches Ohm's law as the sample width increases in accord with the correspondence principle. Here the researchers demonstrate and capture all eigenvalue spectra by measuring microwave transmission in random waveguides, uncovering insights into conductance dips as the number of channels increased and thereby advance our understanding of mesoscopic transport. [ABSTRACT FROM AUTHOR]

In this paper, we consider a coupled system of fractional stochastic differential equations involving the Hilfer derivative of order 1 2 < α < 1 \frac{1}{2}<\alpha<1 . Under some assumptions, we prove the existence of mild solutions for our system based on Perov’s and Schaefer’s fixed point theorems. An example illustrating our results is also provided. [ABSTRACT FROM AUTHOR]

We show that, under mild assumptions, the spectrum of a sum of independent random matrices is close to that of the Gaussian random matrix whose entries have the same mean and covariance. This nonasymptotic universality principle yields sharp matrix concentration inequalities for general sums of independent random matrices when combined with the Gaussian theory of Bandeira, Boedihardjo, and Van Handel. A key feature of the resulting theory is that it is applicable to a broad class of random matrix models that may have highly nonhomogeneous and dependent entries, which can be far outside the mean-field situation considered in classical random matrix theory. We illustrate the theory in applications to random graphs, matrix concentration inequalities for smallest singular values, sample covariance matrices, strong asymptotic freeness, and phase transitions in spiked models. [ABSTRACT FROM AUTHOR]

We define quantization scheme for discrete-time random walks on the half-line consistent with Szegedy's quantization of finite Markov chains. Motivated by the Karlin and McGregor description of discrete-time random walks in terms of polynomials orthogonal with respect to a measure with support in the segment [ - 1 , 1 ] , we represent the unitary evolution operator of the quantum walk in terms of orthogonal polynomials on the unit circle. We find the relation between transition probabilities of the random walk with the Verblunsky coefficients of the corresponding polynomials of the quantum walk. We show that the both polynomials systems and their measures are connected by the classical Szegő map. Our scheme can be applied to arbitrary Karlin and McGregor random walks and generalizes the so-called Cantero–Grünbaum–Moral–Velázquez method. We illustrate our approach on example of random walks related to the Jacobi polynomials. Then we study quantization of random walks with constant transition probabilities where the corresponding polynomials on the unit circle have two-periodic real Verblunsky coefficients. We present geometric construction of the spectrum of such polynomials (in the general complex case) which generalizes the known construction for the Geronimus polynomials. In the Appendix, we present the explicit form, in terms of Chebyshev polynomials of the second kind, of polynomials orthogonal on the unit circle and polynomials orthogonal on the real line with coefficients of arbitrary period. [ABSTRACT FROM AUTHOR]

Mental disorders present challenges in diagnosis and treatment due to their complex and heterogeneous nature. Electroencephalogram (EEG) has shown promise as a source of potential biomarkers for these disorders. However, existing methods for analyzing EEG signals have limitations in addressing heterogeneity and capturing complex brain activity patterns between regions. This paper proposes a novel random effects state-space model (RESSM) for analyzing large-scale multi-channel resting-state EEG signals, accounting for the heterogeneity of brain connectivities between groups and individual subjects. We incorporate multi-level random effects for temporal dynamical and spatial mapping matrices and address non-stationarity so that the brain connectivity patterns can vary over time. The model is fitted under a Bayesian hierarchical model framework coupled with a Gibbs sampler. Compared to previous mixed-effects state-space models, we directly model high-dimensional random effects matrices of interest without structural constraints and tackle the challenge of identifiability. Through extensive simulation studies, we demonstrate that our approach yields valid estimation and inference. We apply RESSM to a multi-site clinical trial of major depressive disorder (MDD). Our analysis uncovers significant differences in resting-state brain temporal dynamics among MDD patients compared to healthy individuals. In addition, we show the subject-level EEG features derived from RESSM exhibit a superior predictive value for the heterogeneous treatment effect compared to the EEG frequency band power, suggesting the potential of EEG as a valuable biomarker for MDD. [ABSTRACT FROM AUTHOR]

We give Hoeffding- and Bernstein-type concentration inequalities for the largest eigenvalue of sums of random matrices arising from a Markov chain. We consider time-dependent matrix-valued functions on a general state space, generalizing previous results that had only considered Hoeffding-type inequalities, and only for time-independent functions on a finite state space. In particular, we study a kind of non-commutative moment generating function, provide tight bounds on this object and use a method of Garg et al. (A matrix expander Chernoff bound. In Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2018, page 1102–1114, New York, NY, USA, 2018. Association for Computing Machinery) to turn this into tail bounds. Our proof proceeds spectrally, bounding the norm of a certain perturbed operator. In the process we make an interesting connection to dynamical systems and Banach space theory to prove a crucial result on the limiting behaviour of our moment generating function that may be of independent interest. [ABSTRACT FROM AUTHOR]

We consider a class of statistical estimation problems in which we are given a random data matrix |${\boldsymbol{X}}\in{\mathbb{R}}^{n\times d}$| (and possibly some labels |${\boldsymbol{y}}\in{\mathbb{R}}^{n}$|⁠) and would like to estimate a coefficient vector |${\boldsymbol{\theta }}\in{\mathbb{R}}^{d}$| (or possibly a constant number of such vectors). Special cases include low-rank matrix estimation and regularized estimation in generalized linear models (e.g. sparse regression). Firstorder methods proceed by iteratively multiplying current estimates by |${\boldsymbol{X}}$| or its transpose. Examples include gradient descent or its accelerated variants. Under the assumption that the data matrix |${\boldsymbol{X}}$| is standard Gaussian, Celentano, Montanari, Wu (2020, Conference on Learning Theory, pp. 1078–1141. PMLR) proved that for any constant number of iterations (matrix vector multiplications), the optimal firstorder algorithm is a specific approximate message passing algorithm (known as 'Bayes AMP'). The error of this estimator can be characterized in the high-dimensional asymptotics |$n,d\to \infty $|⁠ , |$n/d\to \delta $|⁠ , and provides a lower bound to the estimation error of any firstorder algorithm. Here we present a simpler proof of the same result, and generalize it to broader classes of data distributions and of firstorder algorithms, including algorithms with non-separable nonlinearities. Most importantly, the new proof is simpler, does not require to construct an equivalent tree-structured estimation problem, and is therefore susceptible of a broader range of applications. [ABSTRACT FROM AUTHOR]

Rudnick recently proved that the spectral number variance for the Laplacian of a large compact hyperbolic surface converges, in a certain scaling limit and when averaged with respect to the Weil–Petersson measure on moduli space, to the number variance of the Gaussian Orthogonal Ensemble of random matrix theory. In this article we extend Rudnick's approach to show convergence to the Gaussian Unitary Ensemble for twisted Laplacians that break time-reversal symmetry, and to the Gaussian Symplectic Ensemble for Dirac operators. This addresses a question of Naud, who obtained analogous results for twisted Laplacians on high degree random covers of a fixed compact surface. [ABSTRACT FROM AUTHOR]

Symmetric spaces arise in wide variety of problems in Mathematics and Physics. They are mostly studied in Representation theory, Harmonic analysis and Differential geometry. As many physical systems have symmetric spaces as their configuration spaces, the study of controllability on symmetric space is quite interesting. In this paper, a driftless control system of type x ˙ = ∑ i = 1 m u i f i (x) is considered on a symmetric space. For this we have established global controllability condition which is illustrated by few examples of exponential submanifolds of SE(3) and random matrix ensembles. [ABSTRACT FROM AUTHOR]

Moments of moments of the Riemann zeta function, defined by $$ \text{MoM}_T(k,\beta) := \frac{1}{T}\int_T^{2T} \Bigg(\,\int\limits_{ |h|\leq (\log T)^\theta}|\zeta(\frac{1}{2} + i t + ih)|^{2\beta}\ dh\Bigg)^k\ dt, $$ where |$k,\beta \geq 0$| and |$\theta \gt -1$| were introduced by Fyodorov and Keating, Freezing transitions and extreme values: random matrix theory, and disordered landscapes, Philos. Trans. Roy. Soc. A: 372 no. 2007 (2014), 20120503 A doi:10.1098/rsta.2012.0503 when comparing extreme values of zeta in short intervals to those of characteristic polynomials of random unitary matrices. We study the k  = 2 case as |$T \rightarrow \infty$| and obtain sharp upper bounds for |$\text{MoM}_T(2,\beta)$| for all real |$0\leq \beta \leq 1$| as well as lower bounds of the conjectured order for all |$\beta \geq 0$|⁠. In particular, we show that the second moment of moments undergoes a freezing phase transition with critical exponent |$\beta = \frac{1}{\sqrt{2}}$|⁠. The main technical ingredient is a new estimate for the correlation of two shifted |$2\beta^{\text{th}}$| powers of zeta with |$0\leq \beta \leq 1$|⁠. [ABSTRACT FROM AUTHOR]

Conventional spectral probes of quantum chaos require eigenvalues, and sometimes, eigenvectors of the quantum Hamiltonian. This involves computationally expensive diagonalization procedures. We test whether an unsupervised neural network can detect quantum chaos directly from the Hamiltonian matrix. We use a single-body Hamiltonian with an underlying random graph structure and random coupling constants, with a parameter that determines the randomness of the graph. The spectral analysis shows that increasing the amount of randomness in the underlying graph results in a transition from integrable spectral statistics to chaotic ones. We show that the same transition can be detected via unsupervised neural networks, or more specifically, self-organizing maps by feeding the Hamiltonian matrix directly into the neural network, without any diagonalization procedure. [ABSTRACT FROM AUTHOR]

For sustainable conservation and management of wetlands, it is essential to quantify the evolution progress and driving mechanisms of wetlands. This study examined Baiyangdian Wetland as a research area, and remote images and statistical yearbooks were used as data sources. Dominant zones of wetland were defined based on spatial characteristics of land cover frequency. A transfer matrix and random forest were used to analyze the evolution process and driving mechanism of typical wetlands in the North China Plain. Based on the results, following conclusions were arrived: (1) There was significant spatial differentiation of land cover frequency characteristics in the Baiyangdian wetland, with the cultivated land-dominated zone, the aquatic vegetation-dominated zone, and the water body-dominated zone being the three core zones of wetland ecosystem evolution. (2) There was a frequent and significant change of the Baiyangdian wetland due to extreme climatic conditions. Between 1987 and 2017, the built-up land area and the water body area increased by 4.62 and 16.17 km2, respectively, while the aquatic vegetation area decreased by 20.70 km2. A combination of natural and human factors caused changes in the wetland's structure. (3) The driving mechanisms of ecosystem evolution in the Baiyangdian wetland were influenced significantly by space, time, and land cover types. Specifically, on a spatial scale, social factors were the predominant factors contributing to changes in water body and cultivated land in the cultivated land-dominant zone and the aquatic vegetation-dominant zone. In contrast, natural factors were the dominant factors leading to changes in aquatic vegetation. There was a greater contribution from social factors to the driving mechanism of changes in the water body, aquatic vegetation, and cultivated land in the water body-dominant zone than from natural factors. On a temporal scale, it was primarily influenced by natural factors in the early stages and socio-economic factors in the late stages, with the year 2002 serving as a turning point. The scale of land cover types can be seen primarily in the differences among the agricultural lands, aquatic vegetation, and water body. In particular, the Secondary Industry Out Value (SIOV) was highly sensitive to changes in the cultivated area. In addition, cumulative evaporation (EC) has been identified as the main factor responsible for the evolution of aquatic vegetation, which is closely related to the changes in water body. [ABSTRACT FROM AUTHOR]

We consider the problem of testing linear hypotheses under a multivariate regression model with a high-dimensional response and spiked noise covariance. The proposed family of tests consists of test statistics based on a weighted sum of projections of the data onto the estimated latent factor directions, with the weights acting as the regularization parameters. We establish asymptotic normality of the test statistics under the null hypothesis. We also establish the power characteristics of the tests and propose a data-driven choice of the regularization parameters under a family of local alternatives. The performance of the proposed tests is evaluated through a simulation study. Finally, the proposed tests are applied to the Human Connectome Project data to test for the presence of associations between volumetric measurements of human brain and behavioral variables. Supplementary materials for this article are available online including a standardized description of the materials available for reproducing the work. [ABSTRACT FROM AUTHOR]

Community detection is a crucial task in network analysis that can be significantly improved by incorporating subject-level information, ie, covariates. Existing methods have shown the effectiveness of using covariates on the low-degree nodes, but rarely discuss the case where communities have significantly different density levels, ie, multiscale networks. In this paper, we introduce a novel method that addresses this challenge by constructing network-adjusted covariates, which leverage the network connections and covariates with a node-specific weight for each node. This weight can be calculated without tuning parameters. We present novel theoretical results on the strong consistency of our method under degree-corrected stochastic blockmodels with covariates, even in the presence of misspecification and multiple sparse communities. Additionally, we establish a general lower bound for the community detection problem when both the network and covariates are present, and it shows that our method is optimal for connection intensity up to a constant factor. Our method outperforms existing approaches in simulations and a LastFM app user network. We then compare our method with others on a statistics publication citation network where 30 % of nodes are isolated, and our method produces reasonable and balanced results. Our method is implemented in the R package NAC. [ABSTRACT FROM AUTHOR]

The canonical equation K 107 is founded for random zebra-structured matrices. [ABSTRACT FROM AUTHOR]

The limit theorem for the estimator G 59 for the regularized solution of the Kolmogorov–Wiener filter is proved. [ABSTRACT FROM AUTHOR]

This work considers the low‐rank approximation of a matrix A(t)$$ A(t) $$ depending on a parameter t$$ t $$ in a compact set D⊂ℝd$$ D\subset {\mathbb{R}}^d $$. Application areas that give rise to such problems include computational statistics and dynamical systems. Randomized algorithms are an increasingly popular approach for performing low‐rank approximation and they usually proceed by multiplying the matrix with random dimension reduction matrices (DRMs). Applying such algorithms directly to A(t)$$ A(t) $$ would involve different, independent DRMs for every t$$ t $$, which is not only expensive but also leads to inherently non‐smooth approximations. In this work, we propose to use constant DRMs, that is, A(t)$$ A(t) $$ is multiplied with the same DRM for every t$$ t $$. The resulting parameter‐dependent extensions of two popular randomized algorithms, the randomized singular value decomposition and the generalized Nyström method, are computationally attractive, especially when A(t)$$ A(t) $$ admits an affine linear decomposition with respect to t$$ t $$. We perform a probabilistic analysis for both algorithms, deriving bounds on the expected value as well as failure probabilities for the approximation error when using Gaussian random DRMs. Both, the theoretical results and numerical experiments, show that the use of constant DRMs does not impair their effectiveness; our methods reliably return quasi‐best low‐rank approximations. [ABSTRACT FROM AUTHOR]

This paper studies the asymptotic behavior of several central objects in Dunkl theory as the dimension of the underlying space grows large. Our starting point is the observation that a recent result from the random matrix theory literature implies a large deviations principle for the hydrodynamic limit of radial Dunkl processes. Using this fact, we prove a variational formula for the large-N asymptotics of generalized Bessel functions, as well as a large deviations principle for the more general family of radial Heckman–Opdam processes. As an application, we prove a theorem on the asymptotic behavior of weight multiplicities of irreducible representations of compact or complex simple Lie algebras in the limit of large rank. The theorems in this paper generalize several known results describing analogous asymptotics for Dyson Brownian motion, spherical matrix integrals, and Kostka numbers. [ABSTRACT FROM AUTHOR]

Associated to two given sequences of eigenvalues λ 1 ≥ ⋯ ≥ λ n and μ 1 ≥ ⋯ ≥ μ n is a natural polytope, the polytope of augmented hives with the specified boundary data, which is associated to sums of random Hermitian matrices with these eigenvalues. As a first step towards the asymptotic analysis of random hives, we show that if the eigenvalues are drawn from the GUE ensemble, then the associated augmented hives exhibit concentration as n → ∞ . Our main ingredients include a representation due to Speyer of augmented hives involving a supremum of linear functions applied to a product of Gelfand–Tsetlin polytopes; known results by Klartag on the KLS conjecture in order to handle the aforementioned supremum; covariance bounds of Cipolloni–Erdős–Schröder of eigenvalue gaps of GUE; and the use of the theory of determinantal processes to analyze the GUE minor process. [ABSTRACT FROM AUTHOR]

In multiple extended object tracking, the Poisson multi-Bernoulli mixture (PMBM) tracker is considered state-of-the-art. Originally, it was presented with the gamma Gaussian inverse Wishart (GGIW) target model, which is a random matrix model. When tracking larger objects using a light detection and ranging (LiDAR) sensor, measurements are generated by the contour rather than the whole target surface, and it is beneficial to model this with the target model. A target model that has this capability is the Gaussian process (GP) extent model. This paper presents a PMBM tracker using this target model. We also discuss considerations related to the use of the GP model in the PMBM framework. Secondly, we present improvements in the target model that increase the robustness of the model by dealing with the inherent non-linearities using the Gauss--Newton method. Furthermore, we incorporate an improvement to the tracker that utilizes the concept of negative information to generate virtual measurements that are then used in the Gauss-- Newton optimization. In relation to this, we also present an occlusion model that utilizes the same negative information model to ensure that the state estimate is consistent in the presence of occluding targets. [ABSTRACT FROM AUTHOR]

We explore the limiting spectral distribution of large-dimensional random permutation matrices, assuming the underlying population distribution possesses a general dependence structure. Let $\textbf X = (\textbf x_1,\ldots,\textbf x_n)$ $\in \mathbb{C} ^{m \times n}$ be an $m \times n$ data matrix after self-normalization (n samples and m features), where $\textbf x_j = (x_{1j}^{*},\ldots, x_{mj}^{*})^{*}$. Specifically, we generate a permutation matrix $\textbf X_\pi$ by permuting the entries of $\textbf x_j$ $(j=1,\ldots,n)$ and demonstrate that the empirical spectral distribution of $\textbf {B}_n = ({m}/{n})\textbf{U} _{n} \textbf{X} _\pi \textbf{X} _\pi^{*} \textbf{U} _{n}^{*}$ weakly converges to the generalized Marčenko–Pastur distribution with probability 1, where $\textbf{U} _n$ is a sequence of $p \times m$ non-random complex matrices. The conditions we require are $p/n \to c >0$ and $m/n \to \gamma > 0$. [ABSTRACT FROM AUTHOR]

We study the rank of the adjacency matrix A$$ A $$ of a random Erdős‐Rényi graph G∼픾(n,p). It is well known that when p=(log(n)−ω(1))/n$$ p=\left(\log (n)-\omega (1)\right)/n $$, with high probability, A$$ A $$ is singular. We prove that when p=ω(1/n)$$ p=\omega \left(1/n\right) $$, with high probability, the corank of A$$ A $$ is equal to the number of isolated vertices remaining in G$$ G $$ after the Karp‐Sipser leaf‐removal process, which removes vertices of degree one and their unique neighbor. We prove a similar result for the random matrix B$$ B $$, where all entries are independent Bernoulli random variables with parameter p$$ p $$. Namely, we show that if H$$ H $$ is the bipartite graph with bi‐adjacency matrix B$$ B $$, then the corank of B$$ B $$ is with high probability equal to the max of the number of left isolated vertices and the number of right isolated vertices remaining after the Karp‐Sipser leaf‐removal process on H$$ H $$. Additionally, we show that with high probability, the k$$ k $$‐core of 픾(n,p) is full rank for any k≥3$$ k\ge 3 $$ and p=ω(1/n)$$ p=\omega \left(1/n\right) $$. This partially resolves a conjecture of Van Vu for p=ω(1/n)$$ p=\omega \left(1/n\right) $$. Finally, we give an application of the techniques in this paper to gradient coding, a problem in distributed computing. [ABSTRACT FROM AUTHOR]

Compressed sensing (CS) is an innovative signal acquisition and reconstruction technology that has broken through the limit of the Nyquist sampling theory. It is widely employed to optimize the measurement processes in various applications. One of the core challenges of CS is the construction of a measurement matrix. However, traditional random measurement matrices are often impractical. Additionally, many existing deterministic binary measurement matrices fail to provide the required flexibility for practical applications. In this study, inspired by the observation that pseudo-random sequences share similar properties with random sequences, we constructed a deterministic sparse measurement matrix with a flexible measurement number based on an pseudo-random sequence—the Legendre sequence. Empirical analysis of the phase transition and an assessment of the practical features of the proposed measurement matrix were conducted. We validated the effectiveness of the proposed measurement matrix on randomly synthesized signals and images. The results of our simulations reveal that our proposed measurement matrix performs better than several other measurement matrices, particularly in terms of accuracy and efficiency. [ABSTRACT FROM AUTHOR]

In [H. H. Nguyen and R. Van Peski, Universality for cokernels of random matrix products, Adv. Math. 438 2024, Paper No. 109451], Nguyen and Van Peski raised the question of whether the surjective flag of ℤ p {{\mathbb{Z}}_{p}} -modules modeled by cok ⁢ ( M 1 ⁢ … ⁢ M k ) ↠ ⋯ ↠ cok ⁢ ( M 1 ) \mathrm{cok}(M_{1}\dots M_{k})\twoheadrightarrow\cdots\twoheadrightarrow% \mathrm{cok}(M_{1}) for independent random matrices M 1 , … , M k ∈ Mat n ⁡ ( ℤ p ) M_{1},\dots,M_{k}\in\operatorname{Mat}_{n}({\mathbb{Z}}_{p}) satisfies the Cohen–Lenstra heuristic. We answer the question affirmatively when M 1 , … , M k {M_{1},\dots,M_{k}} follow the Haar measure, and our proof demonstrates how classical ideas in Cohen–Lenstra heuristic adapt naturally to the flag setting. We also prove an analogue for non-square matrices. [ABSTRACT FROM AUTHOR]

Hierarchical count histograms involve the publication of count statistics at various granularities based on a predefined hierarchy within a dimension table in a data warehouse. This task finds extensive applications in on-line analytical processing (OLAP) scenarios. This paper focuses on the rigorous privacy-preserving constraint when dealing with an untrusted server. We conduct a systematic investigation of this task and uncover the limitations of the straightforward baseline approach using local differential privacy, as it fails to strike an optimal balance between privacy and utility. We are thus motivated to propose DP-HORUS, a novel crypto-assisted Differentially Private framework for Hierarchical cOunt histogRams under Untrusted Server. DP-HORUS consists of a series of novel designs, including (1) Encrypted hierarchical tree (EHT) structure, which maintains the concept hierarchy in the input data; (2) Random matrix (RM), which reduces communication and computational cost; (3) To further boosted the utility, we propose DP-HORUS+ encompassing two additional modules of histograms structure (HS) and hierarchical consistency (HC), which are respectively introduced to reduce the noise caused by data sparsity and to ensure the hierarchy consistency; (4) To further boost the robust performance, we propose a series of schemes for workload queries based on DP-HORUS. We provide both theoretical analysis and extensive empirical study on both real-world and synthetic datasets, which demonstrates the superior utility of the proposed methods over the state-of-the-art solutions while ensuring strict privacy guarantee. [ABSTRACT FROM AUTHOR]

The current high‐dimensional linear factor models fail to account for the different types of variables, while high‐dimensional nonlinear factor models often overlook the overdispersion present in mixed‐type data. However, overdispersion is prevalent in practical applications, particularly in fields like biomedical and genomics studies. To address this practical demand, we propose an overdispersed generalized factor model (OverGFM) for performing high‐dimensional nonlinear factor analysis on overdispersed mixed‐type data. Our approach incorporates an additional error term to capture the overdispersion that cannot be accounted for by factors alone. However, this introduces significant computational challenges due to the involvement of two high‐dimensional latent random matrices in the nonlinear model. To overcome these challenges, we propose a novel variational EM algorithm that integrates Laplace and Taylor approximations. This algorithm provides iterative explicit solutions for the complex variational parameters and is proven to possess excellent convergence properties. We also develop a criterion based on the singular value ratio to determine the optimal number of factors. Numerical results demonstrate the effectiveness of this criterion. Through comprehensive simulation studies, we show that OverGFM outperforms state‐of‐the‐art methods in terms of estimation accuracy and computational efficiency. Furthermore, we demonstrate the practical merit of our method through its application to two datasets from genomics. To facilitate its usage, we have integrated the implementation of OverGFM into the R package GFM. [ABSTRACT FROM AUTHOR]

Few-shot learning (FSL) uses prior knowledge and supervised experience to effectively classify hyperspectral images (HSIs), thereby reducing the cost of large numbers of labeled samples. However, existing few-shot methods ignore the correlation between cross-domain feature channels, and the feature representation ability is insufficient. To address above issue, this paper proposes a novel Residual Channel Attention Based Sample Adaptation Few-Shot Learning for Hyperspectral Image Classification(RCASA-FSL) for hyperspectral image classification (HSIC), which can capture and enhance cross-domain dependencies through multi-layer residual connection and random-based feature recalibration. Specifically, a Deep Residual Feature Channel Attention Mechanism (DRFCAM) is designed to obtain cross-domain dependencies by residual concatenation, and further the residual structure is stacked for mining depth discrimination information. Furthermore, a new Random-based Feature Recalibration Module (RFRM) is proposed to reassign the feature weights via random matrix, which fully explore feature weight relationships to guide the sample adaptation process. Besides, we design a joint loss function with combining the FSL loss and domain adaptive loss for further optimization model. Experiments conducted on several standard hyperspectral datasets demonstrate that the proposed RCASA-FSL is superior to other FSL techniques in both quantitative and qualitative aspects. [ABSTRACT FROM AUTHOR]

In this paper, we propose two random matrix based extended target tracking models, which apply to the trajectory‐aligned and drifting target motions. The trajectory‐aligned model is specifically designed to handle targets moving along the direction of their extent orientations, while the drift model is tailored to targets whose trajectories deviate from their orientations in time. We utilise the well‐known variational Bayes method to perform inference and obtain posterior densities via computationally efficient, analytical, iterative steps. Through comprehensive experiments conducted on simulated and real data, our methods have demonstrated superior performance compared to previous approaches in scenarios involving both drifting and trajectory‐aligned targets. These results highlight the efficacy of our proposed models in accurately tracking targets and estimating their extent. [ABSTRACT FROM AUTHOR]

This paper introduces a novel approach that combines symbolic data analysis with matrix theory through the concept of interval-valued random matrices. This framework is designed to address the complexities of real-world data, offering enhanced statistical modeling techniques particularly suited for large and complex datasets where traditional methods may be inadequate. We develop both frequentist and Bayesian methods for the statistical inference of interval-valued random matrices, providing a comprehensive analytical framework. We conduct extensive simulations to compare the performance of these methods, demonstrating that Bayesian estimators outperform maximum likelihood estimators under the Frobenius norm loss function. The practical utility of our approach is further illustrated through an application to climatology and temperature data, highlighting the advantages of interval-valued random matrices in real-world scenarios. [ABSTRACT FROM AUTHOR]

We consider the asymptotics of the partition function of the extended Gross–Witten–Wadia unitary matrix model by introducing an extra logarithmic term in the potential. The partition function can be written as a Toeplitz determinant with entries expressed in terms of the modified Bessel functions of the first kind and furnishes a τ$\tau$‐function sequence of the Painlevé III′$\text{III}^{\prime }$ equation. We derive the asymptotic expansions of the Toeplitz determinant up to and including the constant terms as the size of the determinant tends to infinity. The constant terms therein are expressed in terms of the Riemann zeta‐function and the Barnes G$G$‐function. A third‐order phase transition in the leading terms of the asymptotic expansions is also observed. [ABSTRACT FROM AUTHOR]

AbstractIn this article, we propose a new test for testing the equality of two population covariance matrices in the ultra-high dimensional setting that the dimension is much larger than the sizes of both of the two samples. Our proposed methodology relies on a data splitting procedure and a comparison of a set of well selected eigenvalues of the sample covariance matrices on the split datasets. Compared to the existing methods, our methodology is adaptive in the sense that (i). it does not require specific assumption (e.g., comparable or balancing, etc.) on the sizes of two samples; (ii). it does not need quantitative or structural assumptions of the population covariance matrices; (iii). it does not need the parametric distributions or the detailed knowledge of the moments of the two populations. Theoretically, we establish the asymptotic distributions of the statistics used in our method and conduct the power analysis. We justify that our method is powerful under weak alternatives. We conduct extensive numerical simulations and show that our method significantly outperforms the existing ones both in terms of size and power. Analysis of two real datasets is also carried out to demonstrate the usefulness and superior performance of our proposed methodology. An R package UHDtst is developed for easy implementation of our proposed methodology. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work. [ABSTRACT FROM AUTHOR]

In this article we investigate no-resonance conditions for quantum many body chaotic systems and random matrix models. No-resonance conditions are properties of the spectrum of a model, usually employed as a theoretical tool in the analysis of late time dynamics. The first order no-resonance condition holds when a spectrum is non-degenerate, while higher order no-resonance conditions imply sums of an equal number of energies are non-degenerate outside of permutations of the indices. This resonance condition is usually assumed to hold for quantum chaotic models. In this work we use several tests from random matrix theory to demonstrate that the statistics of sums of eigenvalues, that are of interest to due to the no-resonance conditions, have Poisson statistics, and lack level repulsion. This result is produced for both a quantum chaotic Hamiltonian as well as the Gaussian Unitary Ensemble and Gaussian Orthogonal Ensemble. This implies some models may have violations of the no-resonance condition or "near" violations. We finish the paper by generalizing important bounds in quantum equilibration theory to cases where the no-resonance conditions are violated, and to the case of random matrix models. [ABSTRACT FROM AUTHOR]

This article, using generalized inverses of matrices, studies the spaces whose elements are matrices. Based on the results obtained, for linear models for random matrices, the article explores the role of ordinary least square estimators in identifying linear estimable functions, and the role of minimum norm ordinary least square estimators in creating linear unbiased estimators. With added conditions on the covariance matrix for vectorized response, it is shown that a linear unbiased estimator constructed from the minimum norm ordinary least square estimator is a best linear unbiased estimator with respect to the risk induced from squared distance loss. [ABSTRACT FROM AUTHOR]

We establish novel two-sided bounds for the tracial seminorm of multilinear Schur multipliers that tighten previously known bounds. The result is obtained by a newly developed method based on polynomial chaoses. [ABSTRACT FROM AUTHOR]

With the continuous development of composite materials for various application fields, the demand for their performance has increased substantially. Particle-reinforced composites are very promising owing to the unique comprehensive properties. However, the effects of NbC particles on the mechanical characteristics of steel matrix composites are still not fully clear. In this paper, a finite element model was established based on the real microstructure of NbC-Fe composites. The particle shape and shape combination design were studied by taking into consideration the plastic deformation and ductile cracking of the matrix, as well as the debonding of the matrix–particle interface. The influences of parameters on the damage mechanism of particle-reinforced metal matrix composites were also examined. The results revealed that the microstructure-based model effectively described the main material deformation and failure mechanisms. Stress concentrations mainly occurred on the aggregated particles, especially at particle sharp corners, particle–matrix interfaces, and edges along the loading direction. The stress in the matrix was much lower than that in the particles and spread at 45° along the loading direction concentration. The matrix–particle debonding was insignificant, and fracture took place near the particle sharp corners. Also, the matrix failure was initiated and propagated around the particle crack tip to connect microcracks caused by particle fracture, or through high-stress/strain-concentration areas, resulting in failure of the entire workpiece. The predicted numerical data provided a better understanding of the mechanical phenomena of NbC-Fe composites at the nanoscale, which is relevant for future research on the micromechanical mechanism of NbC-Fe composites. [ABSTRACT FROM AUTHOR]

In this work, we study a univariate as well as a multivariate Jacobi polynomial-based estimator for solving the fundamental problem of non parametric (NP) regression. The proposed NP regression estimator aims to approximate a possibly very low regular regression function from the knowledge of its noised values given at some n random sampling points. We first study the univariate version of the proposed estimator, then extend this study to the general multivariate case with random sampling vectors drawn according to an unknown distribution. Our proposed estimator has the advantage of being stable with reasonable time complexity. Moreover, it has an optimal convergence rate under the weak condition that the regression function has a certain low Sobolev smoothness property. Although the proposed estimators are studied under the hypothesis that the random sampling vectors are supported on the d dimensional unit hypercube, by applying trivial transformations, the results of this work are still valid in the more general setting of any d dimensional hyperrectangle. Finally, the theoretical results of this work are illustrated by some numerical simulations on synthetic as well as real datasets. [ABSTRACT FROM AUTHOR]

Purpose: To improve liver proton density fat fraction (PDFF) and R2*$$ {R}_2^{\ast } $$ quantification at 0.55 T by systematically validating the acquisition parameter choices and investigating the performance of locally low‐rank denoising methods. Methods: A Monte Carlo simulation was conducted to design a protocol for PDFF and R2*$$ {R}_2^{\ast } $$ mapping at 0.55 T. Using this proposed protocol, we investigated the performance of robust locally low‐rank (RLLR) and random matrix theory (RMT) denoising. In a reference phantom, we assessed quantification accuracy (concordance correlation coefficient [ρc$$ {\rho}_c $$] vs. reference values) and precision (using SD) across scan repetitions. We performed in vivo liver scans (11 subjects) and used regions of interest to compare means and SDs of PDFF and R2*$$ {R}_2^{\ast } $$ measurements. Kruskal–Wallis and Wilcoxon signed‐rank tests were performed (p < 0.05 considered significant). Results: In the phantom, RLLR and RMT denoising improved accuracy in PDFF and R2*$$ {R}_2^{\ast } $$ with ρc$$ {\rho}_c $$ >0.992 and improved precision with >67% decrease in SD across 50 scan repetitions versus conventional reconstruction (i.e., no denoising). For in vivo liver scans, the mean PDFF and mean R2*$$ {R}_2^{\ast } $$ were not significantly different between the three methods (conventional reconstruction; RLLR and RMT denoising). Without denoising, the SDs of PDFF and R2*$$ {R}_2^{\ast } $$ were 8.80% and 14.17 s−1. RLLR denoising significantly reduced the values to 1.79% and 5.31 s−1 (p < 0.001); RMT denoising significantly reduced the values to 2.00% and 4.81 s−1 (p < 0.001). Conclusion: We validated an acquisition protocol for improved PDFF and R2*$$ {R}_2^{\ast } $$ quantification at 0.55 T. Both RLLR and RMT denoising improved the accuracy and precision of PDFF and R2*$$ {R}_2^{\ast } $$ measurements. [ABSTRACT FROM AUTHOR]

The simulation of random correlation matrices is an essential procedure in different research areas. This study presents a method called Custom Matrix generator, which generates valid correlation matrices. Furthermore, we offer the possibility of generating matrices whose correlations are always contained in a pre-fixed interval. The method can also provide sub-optimal solutions to the problem of generating correlation matrices with more advanced levels of customization. Custom correlation matrices are very useful for different applications in different studies. Moreover, the method is efficient regarding computational time and minimizes errors in generating customized correlation matrices. [ABSTRACT FROM AUTHOR]

Motivated by recent results in the statistical physics of spin glasses, we study the recovery of a sparse vector x 0 ∈ S n − 1 , where S n − 1 denotes the n -dimensional unit sphere, ‖ x 0 ‖ ℓ 0 = k < n , from m quadratic measurements of the form (1 − λ) 〈 A i , x 0 x 0 ⊺ 〉 + λ 〈 c i , x 0 〉 where A i , c i have i.i.d. Gaussian entries. This can be related to a constrained version of the 2-spin Hamiltonian with external field for which it was shown (in the absence of any structural constraint and in the asymptotic regime) in [1] that the geometry of the energy landscape becomes trivial above a certain threshold λ > λ c ∈ (0 , 1). Building on this idea, we characterize the recovery of x 0 as a function of λ ∈ [ 0 , 1 ]. We show that recovery of the vector x 0 can be guaranteed as soon as m ≳ k 2 (1 − λ) 2 / λ 2 ∨ k , λ > 1 / 2 provided that this vector satisfies a sufficiently strong incoherence condition, thus retrieving the linear regime for an external field (1 − λ) / λ ≲ k − 1 / 2. A similar result (with a slightly deteriorating sample complexity) can be shown for weaker fields. Our proof relies on an interpolation between the linear and quadratic settings, as well as on standard convex geometry arguments. [ABSTRACT FROM AUTHOR]