We study a topological field theory describing confining phases of gauge theories in four dimensions. It can be formulated on a lattice using a discrete 2-form field talking values in a finite abelian group (the magnetic gauge group). We show that possible theta-angles in such a theory are quantized and labeled by quadratic functions on the magnetic gauge group. When the theta-angles vanish, th...

This paper deals with the numerical solution of a class of reaction diffusion equations arises from ecological phenomena. When two species are introduced into unoccupied habitat, they can spread across the environment as two travelling waves with the wave of the faster reproducer moving ahead of the slower.The mathematical modelling of invasions of species in more complex settings that include ...

Positive results are proved here about the ability of numerical simulations to reproduce the exponentialmean-square stability of stochastic differential equations (SDEs). The first set of results applies under finite-time convergence conditions on the numerical method. Under these conditions, the exponential mean-square stability of the SDE and that of the method (for sufficiently small step si...

A differential-difference operator is used to model the heat equation on a finite graph analogue of Poincaré’s upper half-plane. Finite analogues classical theta functions are shown be solutions in this setting.

This paper examines stability analysis of two classes of improved backward Euler methods, namely split-step $(theta, lambda)$-backward Euler (SSBE) and semi-implicit $(theta,lambda)$-Euler (SIE) methods, for nonlinear neutral stochastic delay differential equations (NSDDEs). It is proved that the SSBE method with $theta, lambdain(0,1]$ can recover the exponential mean-square stability with some...

In this article, we introduce a new approach towards the statistical learning problem $\operatorname{argmin}_{\rho(\theta) \in \mathcal P_{\theta}} W_{Q}^2 (\rho_{\star},\rho(\theta))$ to approximate target quantum state $\rho_{\star}$ by set of parametrized states $\rho(\theta)$ in $L^2$-Wasserstein metric. We solve estimation considering Wasserstein natural gradient flows for density operator...

Objective: Tonic and phasic (event-related) theta band power changes were analyzed in a sample of 8 dyslexic and 8 control children. Previous research with healthy subjects suggests that electroencephalograph (EEG) theta activity re ̄ects the encoding of new information into working memory. The aim of the present study was to investigate whether the processing de®cits of dyslexics are related to...