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.

When conditioned responses "fire back": bidirectional cross-activation creates learning opportunities in synesthesia

In grapheme-color synesthesia, the letter "c" printed in black may be experienced as red, but typically the color red does not trigger the experience of the letter "c." Therefore, at the level of subjective experience, cross-activation is usually unidirectional. However, recent evidence from digit-color synesthesia suggests that at an implicit level bidirectional cross-activation can occur. Here we demonstrate that this finding is not restricted to this specific type of synesthesia. We introduce a new method that enables the investigation of bidirectionality in other types of synesthesia. We found that a group of grapheme-color synesthetes, but not a control group, showed a startle in response to a color-inducing grapheme after a startle response was conditioned to the specific corresponding color. These results implicate that when the startle response was associated with the real color an association between shock and the grapheme was also established. By this mechanism (i.e. implicit cross-activation) the conditioned response to the real color generalized to the synesthetic color. We suggest that parietal brain areas are responsible for this neural backfiring.