We extend some properties of random walks on hyperbolic groups to convergence groups. In particular, we prove that if a group $G$ acts compact metrizable space $M$ with the property, then can provide $G\cup M$ topology such converge almost surely points in $M$. Furthermore, is finitely generated and walk has finite entropy logarithmic moment respect word metric, $M$, corresponding hitting measu...

The long-time asymptotics of solutions of the viscous quantum hydrodynamic model in one space dimension is studied. This model consists of continuity equations for the particle density and the current density, coupled to the Poisson equation for the electrostatic potential. The equations are a dispersive and viscous regularization of the Euler equations. It is shown that the solutions converge ...

The Molecular Mechanics Poisson-Boltzmann Surface Area (MMPBSA) approach has been widely applied as an efficient and reliable free energy simulation method to model molecular recognition, such as for protein-ligand binding interactions. In this review, we focus on recent developments and applications of the MMPBSA method. The methodology review covers solvation terms, the entropy term, extensio...

In this paper we analyze the convergence rate of solutions of certain drift-diiusion-Poisson systems to their unique steady state. These bi-polar equations model the transport of two populations of charged particles and have applications for semiconductor devices and plasmas. When prescribing a connnement potential for the particles we prove exponential convergence to the equilibrium. Without c...

Several authors have previously discussed the use of log-linear models, often called maximum entropy models, for analyzing spike train data to detect synchrony. The usual log-linear modeling techniques, however, do not allow time-varying firing rates that typically appear in stimulus-driven (or action-driven) neurons, nor do they incorporate non-Poisson history effects or covariate effects. We ...

Let G be a countable group which acts by isometries on a separable, but not necessarily proper, Gromov hyperbolic space X. We say the action of G is weakly hyperbolic if G contains two independent hyperbolic isometries. We show that a random walk on such G converges to the Gromov boundary almost surely. We apply the convergence result to show linear progress and linear growth of translation len...

We develop a set of heuristic arguments to explain several results on planar Poisson-Voronoi tessellations that were derived earlier at the cost of considerable mathematical effort. The results concern Voronoi cells having a large number n of sides. The arguments start from an entropy balance applied to the arrangement of n neighbors around a central cell. It is followed by a simplified evaluat...

We investigate the well posedness of stationary Vlasov-Boltzmann equations both in the simpler case of linear problem with a space varying force field and a collisional integral satisfying the detailed balanced principle with a non-singular scattering function, and, the non-linear Vlasov-Poisson-Boltzmann system. For the former we obtain existence-uniqueness results for arbitrarily large integr...

We present a general holistic theory for the organization of complex networks, both human-engineered and naturally-evolved. Introducing concepts of ‘value’ of interactions and ‘satisfaction’ as generic network performance measures, we show that the underlying organizing principle is to meet an overall performance target for wide-ranging operating or environmental conditions. This design or surv...