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…

This article provides a Wilsonian description of the perturbatively renormalizable Tensorial Group Field Theory introduced in arXiv:1303.6772 [hep-th…

Biased stochastic estimators, such as finite-differences for noisy gradient estimation, often contain parameters that need to be properly chosen to b…

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 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…

The rules to write out any one of the linearly independent functions belonging to the infinite set of those in polynomial form that satisfy the sourc…

Jet quenching has become an essential signal for the characterization of the medium formed in experiments of heavy-ion collisions. After a brief intr…

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…

We study an inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map as the data. We consider piecewise constant …

In this paper, we study the stabilization problem for the Ito systems with both multiplicative noise and multiple delays which exist widely in applic…

This thesis considers channel estimation and multiuser (MU) data transmission for massive MIMO systems with fully digital/hybrid structures in mmWave…

We study a class of discrete focusing nonlinear Schr{\"o}dinger equations (DNLS) with general nonlocal interactions. We prove the existence of onsite…

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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