In classical kinetic or kinetic-like models a particle free path distribution is exponensial, but this is more likely to be an exception than a rule. In this paper we derive a linear Boltzmann-like equation for a general free path distribution in the framework of Alt’s model J. Math. Biol. 9, 147 (1980). In the special case that the free path distribution has at least first and second finite mo...

Statistical mechanics deals with systems having a large number of particles. In statistical mechanics, large scale properties (such as temperature, pressure etc) are studied by applying probability theory to a large number of small particles. Hence this is a probabilistic theory and the behaviour of all of the system is studied using the average individual behaviour of particles. With small num...

In this paper, we apply Restricted Boltzmann Machine and Subspace Restricted Boltzmann Machine to domain adaptation. Moreover, we train these models using the Perturb-and-MAP approach to draw approximate sample from the Gibbs distribution. We evaluate our approach on domain adaptation task between two image corpora: MNIST and Handwritten Character Recognition dataset.

In this research we propose learning a controller for a mobile robot with a topographic Restricted Boltzmann machine (tRBM). The topographic RBM generalizes the previously proposed Map-Initialized Perceptron (MIP) to a probabilistic model which learns a joint distribution of sensory states and continuous actions. Keywords— Topographical Structure, Restricted Boltzmann Machine, Mobile Robot, Imi...

We introduce a new fast numerical method for computing discontinuous solutions to the Boltzmann equation and illustrate it by numerical examples. A combination of adaptive grids for approximation of the distribution function and an approximate fast Fourier transform on non-uniform grids for computing smooth terms in the Boltzmann collision integral is used. 2008 Elsevier Inc. All rights reserved.

The Fourier transform of the Boltzmann collision integral for a gas of Maxwell molecules is calculated explicitly for the bimodal distribution proposed by Mott-Smith for the shock wave structure. The results of Bobylev's approach of Fourier transforming of the Boltzmann equation were used as the starting point.

In this paper we consider a particle moving in a random distribution of obstacles. Each obstacle generates an inverse power law potential " s jxj s , where " is a small parameter and s > 2. Such a rescaled potential is truncated at distance " ?1 , where 2]0;11 is suitably large. We assume also that the scatterer density is diverging as " ?d+1 , where d is the dimension of the physical space. We...

Boltzmann machines are physics informed generative models with broad applications in machine learning. They model the probability distribution of an input data set with latent variables and generate new samples accordingly. Applying the Boltzmann machines back to physics, they are ideal recommender systems to accelerate the Monte Carlo simulation of physical systems due to their flexibility and...