Graduate Student Seminar

Speaker 1: Serap Tay

Title

Stability analysis for multidimensional opinion dynamics in continuous time

Abstract

We analyze a bounded confidence multidimensional opinion dynamics model in continuous time. In the bounded confidence opinion dynamics model, the opinion of each agent is only affected by other agents whose opinions lie within a confidence bound. We show that all trajectories approach an equilibrium as t→∞. We investigate two forms of stability of equilibria. We prove the Lyapunov stability of all equilibria in the relative interior of the set of equilibria. We provide a necessary condition and a sufficient condition for a form of structural stability of the equilibria. This structural stability is a notion of stability introduced by Blondel et al.  where a new agent with an arbitrarily small weight is introduced to a system in equilibrium.

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.  Programming implementations were used to examine the predictive ability of the THPAM processing unit on the sample datasets available through the UCI Machine Learning Repository. Performance of the processing unit is measured using repeated 10-fold cross-validation. These computational results demonstrate the ability of the processing unit to serve as a pattern recognizer.