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Abstract: We present new, original and alternative method for searching signals coded in noisy data. The method is based on the properties of random matrix eigenvalue spectra. First, we describe gener...
Generic matrix superpotentials     Generic matrix superpotentials  Mathematical Physics  Quantum Physics       font style='font-size:12px;'> 2011/9/5
Abstract: A simple and algorithmic description of matrix shape invariant potentials is presented. The complete lists of generic matrix superpotentials of dimension $2\times2$ and of special superpoten...
Abstract: The concept of an $I$-matrix in the full $2\times 2$ matrix ring $M_2(R/I)$, where $R$ is an arbitrary UFD and $I$ is a nonzero ideal in $R$, is introduced. We obtain a concrete description ...
Matrix divisibility sequences     Matrix divisibility sequences  Number Theory       font style='font-size:12px;'> 2011/9/2
Abstract: We show that many existing divisibility sequences can be seen as sequences of determinants of matrix divisibility sequences, which arise naturally as Jacobian matrices associated to groups o...
Abstract: In this paper we form relations for the determination of the elements of the E\"otv\"os matrix of the Earth's normal gravity field. In addition a relation between the Gauss curvature of the ...
Abstract: An interpretation of the Moore-Penrose generalized inverse of a singular Fisher information matrix (FIM) is presented in this paper, from the perspective of Cramer-Rao bound (CRB). CRB is a ...
Abstract: The corner transfer matrix renormalization group method is an efficient method for evaluating physical quantities in statistical mechanical models. It originates from Baxter's corner transfe...
Decoding of Matrix-Product Codes     Linear Codes  Matrix-Product Codes  Decoding Algorithm  Minimum Distance       font style='font-size:12px;'> 2011/8/30
Abstract: We propose a decoding algorithm for the $(u\mid u+v)$-construction that decodes up to half of the minimum distance of the linear code. We extend this algorithm for a class of matrix-product ...
Abstract: We show that any symmetric norm on $\bR^n$ induces a metric on U(n), the group of all $n\times n$ unitary matrices. Using the same technique, we prove an inequality concerning the eigenvalue...
Abstract: We prove the existence of a 1/N expansion to all orders in beta matrix models with a confining, off-critical potential corresponding to an equilibrium measure with a connected support. Thus,...
Abstract: The sparsity constrained rank-one matrix approximation problem is a difficult mathematical optimization problem which arises in a wide array of useful applications in engineering, machine le...
Abstract: Matrix computations, especially iterative PDE solving (and the sparse matrix vector multiplication subproblem within) using conjugate gradient algorithm, and LU/Cholesky decomposition for so...
Divide-and-Conquer Matrix Factorization     Divide-and-Conquer Matrix Factorization  Numerical Analysis       font style='font-size:12px;'> 2011/9/29
Abstract: This work introduces SubMF, a parallel divide-and-conquer framework for noisy matrix factorization. SubMF divides a large-scale matrix factorization task into smaller subproblems, solves eac...
Abstract: Let $(\Omega,\mathscr{F},\mathbb{P})$ be a probability space and $\bS=\{\mathrm{S}_1,...,\mathrm{S}_K\}$ a discrete-topological space that consists of $K$ real $d$-by-$d$ matrices, where $K$...
Abstract: Let $\bS=\{S_1,...,S_K\}$ be a finite set of complex $d\times d$ matrices and $\varSigma_{K}^+$ the compact space of all one-sided infinite sequences $i_{\bcdot}\colon\mathbb{N}\rightarrow\{...

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