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Sparse signal recovery based on nonconvex and nonsmooth optimization problems has significant applications and demonstrates superior performance in signal processing and machine learning. This work deals with a scale-invariant…
The increased sensitivity of future radio telescopes will result in requirements for higher dynamic range within the image as well as better resolution and immunity to interference. In this paper we propose a new matrix formulation of the…
We apply the density matrix renormalization group (DMRG) method to a non-equilibrium problem: the asymmetric exclusion process in one dimension. We study the stationary state of the process to calculate the particle density profile…
The goal of this paper is to develop a novel numerical method for efficient multiplicative noise removal. The nonlocal self-similarity of natural images implies that the matrices formed by their nonlocal similar patches are low-rank. By…
Many practical problems involve the recovery of a binary matrix from partial information, which makes the binary matrix completion (BMC) technique received increasing attention in machine learning. In particular, we consider a special case…
The spectral numerical mode-matching (SNMM) method is developed to simulate the 3D layered multi-region structures. The SNMM method is a semi-analytical solver having the properties of dimensionality reduction to reduce computational costs;…
A new density matrix renormalisation group (DMRG) approach is presented for quantum systems of two spatial dimensions. In particular, it is shown that it is possible to create a multi-chain-type 2D DMRG approach which utilises previously…
We present a new numerical method for the isometric embedding of 2-geometries specified by their 2-metrics in three dimensional Euclidean space. Our approach is to directly solve the fundamental embedding equation supplemented by six…
Recently, it has been shown, that the pair density of the homogeneous electron gas can be parametrized in terms of 2-body wave functions (geminals), which are scattering solutions of an effective 2-body Schr\"odinger equation. For the…
The density matrix renormalization group (DMRG) method generates the low-energy states of linear systems of $N$ sites with a few degrees of freedom at each site by starting with a small system and adding sites step by step while keeping…
Many electronic structure methods rely on the minimization of the energy of the system with respect to the one-body reduced density matrix (1-RDM). To formulate a minimization algorithm, the 1-RDM is often expressed in terms of its…
We generalize the spectral sum rule preserving density matrix numerical renormalization group (DM-NRG) method in such a way that it can make use of an arbitrary number of not necessarily Abelian, local symmetries present in the quantum…
We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving empirical risk minimization (ERM) problems with a nonsmooth regularization term. Our algorithm is applicable…
Pulay's Residual Metric Minimization (RMM) method is one of the standard techniques for achieving self consistency in ab initio electronic structure calculations. We describe a reformulation of Pulay's RMM which guarantees reduction of the…
Residual minimization is a widely used technique for solving Partial Differential Equations in variational form. It minimizes the dual norm of the residual, which naturally yields a saddle-point (min-max) problem over the so-called trial…
A computational method for the scattering of light by multiple nonclassical plasmonic nanospheres, each of which has multiple (non-)concentric dielectric or metallic layers, is presented. The electromagnetic (EM) response of the free…
The success of any machine learning system depends critically on effective representations of data. In many cases, it is desirable that a representation scheme uncovers the parts-based, additive nature of the data. Of current representation…
The methods of quantum chemistry and solid state theory to solve the many-body problem are reviewed. We start with the definitions of reduced density matrices, their properties (contraction sum rules, spectral resolutions, cumulant…
In many statistical and econometric applications, we gather individual samples from various interconnected populations that undeniably exhibit common latent structures. Utilizing a model that incorporates these latent structures for such…
As we all known, the nonnegative matrix factorization (NMF) is a dimension reduction method that has been widely used in image processing, text compressing and signal processing etc. In this paper, an algorithm for nonnegative matrix…