Discovering the structure inherent in a set of patterns is a fundamental aim of statistical inference or learning. One fruitful approach is to build a parameterized stochastic generative model, independent draws from which are likely to produce the patterns. For all but the simplest generative models, each pattern can be generated in exponentially many ways. It is thus intractable to adjust the...

Unsupervised training of deep generative models containing latent variables and performing inference remains a challenging problem for complex, high dimensional distributions. One basic approach to this problem is the so called Helmholtz machine and it involves training an auxiliary model that helps to perform approximate inference jointly with the generative model which is to be fitted to the ...

Using tools of nonequilibirum mechanics, we study a model of self-propelled hard rods on a substrate in two dimensions to quantify the interplay of self-propulsion and excluded-volume effects. We derive of a Smoluchowski equation for the configurational probability density of self-propelled rods that contains several modifications as compared to the familiar Smoluchowski equation for thermal ro...

In 1917, Marian von Smoluchowski presented a simple mathematical description of diffusioncontrolled reactions on the scale of individual molecules. His model postulated that a reaction would occur when two reactants were sufficiently close and, more specifically, presented a succinct relationship between the relative proximity of two reactants at the moment of reaction and the macroscopic react...

Theory and practice of reaction dynamics on two-dimensional potential energy surfaces is investigated. Nonequilibrium multidimensional barrier crossing, occurring when the initial density is located near the ridgeline separating reactants and products, is treated by solving the time-dependent Smoluchowski equation as a function of diffusion anisotropy. For a locally separable potential, and slo...

An efficient finite volume approach has been used to develop a three dimensional Helmholtz acoustic solver for complex geometries. This acoustic solver was utilized to obtain characteristic mode shapes and frequencies of a baffled combustion chamber. An experimental setup, including stationary and moving sensors, has also been used to measure these quantities for the same model combustion chamb...

The convergence of stochastic particle systems representing physical advection, inflow, outflow and coagulation is considered. The problem is studied on a bounded spatial domain such that there is a general upper bound on the residence time of a particle. The laws on the appropriate Skorohod path space of the empirical measures of the particle systems are shown to be relatively compact. The pat...

Efficient unsupervised training and inference in deep generative models remains a challenging problem. One basic approach, called Helmholtz machine or Variational Autoencoder, involves training a top-down directed generative model together with a bottom-up auxiliary model used for approximate inference. Recent results indicate that better generative models can be obtained with better approximat...

This paper presents an approach to the topic extraction from text documents using probabilistic graphical models. Multiple-cause networks with latent variables are used and the Helmholtz machines are utilized to ease the learning and inference. The learning in this model is conducted in a purely data-driven way and does not require prespecified categories of the given documents. Topic words ext...

We propose a kinetic model for the self-aggregation by amyloid proteins. By extending several well-known models for protein aggregation, the time evolution of aggregate concentrations containing r proteins, denoted c(r)(t), can be written in terms of generalized Smoluchowski kinetics. With this approach, we take into account all possible aggregation and fragmentation reactions involving cluster...