We consider the multidimensional generalised stochastic Burgers equation in the space-periodic setting: $ \partial \mathbf{u}/\partial t+$ $(\nabla…

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

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 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 prove well-posedness of time-dependent Ginzburg--Landau system in a nonconvex polygonal domain, and decompose the solution as a regular part plus …

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…

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

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

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

The translation of a bubble under the action of an acoustic forcing finds applications in fields ranging from drug delivery to sonoluminesce. This ph…

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