Heterogeneity is often natural in many contemporary applications involving massive data. While posing new challenges to effective learning, it can pl…

The present issue of the series <<Modern Problems in Mathematical Physics>> represents the Proceedings of the Students Training Contest Olympiad in M…

For the large-scale linear discrete ill-posed problem $\min\|Ax-b\|$ or $Ax=b$ with $b$ contaminated by a white noise, Lanczos bidiagonalization base…

We present an analysis of wave propagation in a two step-index, parallel waveguide system. The goal is to quantify the effect of scattering at random…

We present a mathematical theory of time-harmonic wave propagation and reflection in a two-dimensional random acoustic waveguide with sound soft boun…

We analyze long range wave propagation in three-dimensional random waveguides. The waves are trapped by top and bottom boundaries, but the medium is …

We investigate a quasicontinuum method by means of analytical tools. More precisely, we compare a discrete-to-continuum analysis of an atomistic one-…

We introduce {\em vector diffusion maps} (VDM), a new mathematical framework for organizing and analyzing massive high dimensional data sets, images …

We study efficient and reliable methods of capturing and sparsely representing anisotropic structures in 3D data. As a model class for multidimension…

We study long range propagation of electromagnetic waves in random waveguides with rectangular cross-section and perfectly conducting boundaries. The…

We summarize the results of the paper.

The positive and not completely positive maps of density matrices, which are contractive maps, are discussed as elements of a semigroup. A new kind o…

Inspired by the success of AlphaGo Zero (AGZ) which utilizes Monte Carlo Tree Search (MCTS) with Supervised Learning via Neural Network to learn the …

Alternating projection (AP) of various forms, including the Parallel AP (PAP), Real-constrained AP (RAP) and the Serial AP (SAP), are proposed to sol…

In this work we present an analytical model, based on the path-integral formalism of Statistical Mechanics, for pricing options using first-passage t…

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