Graduate Student Seminar

Speaker 1: Preston Donovan

Title

Diffusion in Obstructed Media

Abstract

Understanding the diffusion of solute particles in obstructed media gives insight into drug delivery, tissue engineering, and other areas of biotechnology.  However, probing diffusion in real time can be difficult and unreliable.  We model this process via the random walk of a three-dimensional sphere (the solute) in a domain containing periodic, stationary spheres (an obstructing polymer).  First, a Monte Carlo simulation is used to determine whether Brownian motion can accurately describe the solute’s movement.  The simulations reveal excellent agreement between a Brownian motion and kinetic motion model.

Because the heat equation characterizes the probability density of a Brownian particle, this motivates solving the heat equation on the obstructed domain.  Finding such a solution on geometrically complicated domains is computationally expensive and thus we instead solve the homogenized heat equation for an effective diffusivity coefficient.  The results reveal excellent agreement between the computer simulation and homogenization theory across a wide range of domains and time scales.

Speaker 2: Bryce Carey

Title

Developing a Computational Model of Neural Networks into a Learning Machine

Abstract

Temporal hierarchical probabilistic associative memory (THPAM) is a functional model of biological neural networks comprising models of dendritic trees, neurons, supervised and unsupervised learning mechanisms, and a generalization mechanism. THPAM can be viewed as a recurrent multilayer network of processing units, which are pattern recognizers composed of dendritic trees, spiking and nonspiking neurons, synaptic weights, and a learning mechanism for updating these synaptic weights. The processing unit model is primarily composed of linear algebra operations, which can be easily implemented as a computer program with parallel architecture. This implementation was used to examine the application of the THPAM processing unit on the Car Evaluation and Iris data sets available in the UCI Machine Learning Repository. Performance is measured using repeated 10-fold cross-validation, and all results were produced using the parallel computing cluster of the UMBC High Performance Computing Facility.