THE RESONATE-AND-FIRE NEURON: TIME DEPENDENT AND FREQUENCY SELECTIVE NEURONS IN NEURAL NETWORKS

The means through which the nervous system perceives its environment is one of the most fascinating questions in contemporary science. Our endeavors to comprehend the principles of neural science provide an instance of how biological processes may inspire novel methods in mathematical modeling and engineering. The application ofmathematical models towards understanding neural signals and systems represents a vibrant field of research that has spanned over half a century. During this period, multiple approaches to neuronal modeling have been adopted, and each approach is adept at elucidating a specific aspect of nervous system function. Thus while bio-physical models have strived to comprehend the dynamics of actual physical processes occurring within a nerve cell, the phenomenological approach has conceived models that relate the ionic properties of nerve cells to transitions in neural activity. Further-more, the field of neural networks has endeavored to explore how distributed parallel processing systems may become capable of storing memory. Through this project, we strive to explore how some of the insights gained from biophysical neuronal modeling may be incorporated within the field of neural net-works. We specifically study the capabilities of a simple neural model, the Resonate-and-Fire (RAF) neuron, whose derivation is inspired by biophysical neural modeling. While reflecting further biological plausibility, the RAF neuron is also analytically tractable, and thus may be implemented within neural networks. In the following thesis, we provide a brief overview of the different approaches that have been adopted towards comprehending the properties of nerve cells, along with the framework under which our specific neuron model relates to the field of neuronal modeling. Subsequently, we explore some of the time-dependent neurocomputational capabilities of the RAF neuron, and we utilize the model to classify logic gates, and solve the classic XOR problem. Finally we explore how the resonate-and-fire neuron may be implemented within neural networks, and how such a network could be adapted through the temporal backpropagation algorithm.

Identification, discrimination, and selective adaptation of simultaneous musical intervals

Four experiments investigated perception of major and minor thirds whose component tones were sounded simultaneously. Effects akin to categorical perception of speech sounds were found. In the first experiment, musicians demonstrated relatively sharp category boundaries in identification and peaks near the boundary in discrimination tasks of an interval continuum where the bottom note was always an F and the top note varied from A to A flat in seven equal logarithmic steps. Nonmusicians showed these effects only to a small extent. The musicians showed higher than predicted discrimination performance overall, and reaction time increases at category boundaries. In the second experiment, musicians failed to consistently identify or discriminate thirds which varied in absolute pitch, but retained the proper interval ratio. In the last two experiments, using selective adaptation, consistent shifts were found in both identification and discrimination, similar to those found in speech experiments. Manipulations of adapting and test showed that the mechanism underlying the effect appears to be centrally mediated and confined to a frequency-specific level. A multistage model of interval perception, where the first stages deal only with specific pitches may account for the results.