Event chains and inverse problems with applications to neuroscience

Abstract

Over the last half century, mathematical modeling of the biological interaction of neurons has mainly comprised the field of Computational Neuroscience. Our goal is to define a set of brain models that simulate biologically consistent neuronal interaction and use event-chain data to study behavioral characteristics. Randomly stimulating the brain model leads to data of successive neuronal firings. In this thesis, we study how well such data characterizes brain models. In particular, we examine the effect of the size of the brain model, inhibitory and excitatory weight distributions, and damage effects. We find that modifying physical structure produces a measurable change in behavior, using event-chain data and the Hellinger distance as a metric.

Of particular interest is whether brains subjected to learning can be distinguished from brains generated by statistical procedures. The learning algorithms implemented include Hebbian, Anti-Hebbian, Oja, and Sanger's rule. All of these rules adaptively modify the connection strengths, and allow for the creation of new connections. The event-chain data shows conclusively that brains that have undergone learning are significantly different. This unique structure and behavior of learned brains allows for identification based on purely behavioral characteristics; specifically, the event-chain data is sufficient to distinguish between learned and unlearned brains models.