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.

Revision of a Liquid Fuel Airblast Atomizer and Installation of a Laser Extinction System for Measurement of Soot Produced During Liquid Fuel Combustion

Studying liquid fuel combustion is necessary to better design combustion systems. Through more efficient combustors and alternative fuels, it is possible to reduce greenhouse gases and harmful emissions. In particular, coal-derived and Fischer-Tropsch liquid fuels are of interest because, in addition to producing fewer emissions, they have the potential to drastically reduce the United States' dependence on foreign oil. Major academic research institutions like the Pennsylvania State University perform cutting-edge research in many areas of combustion. The Combustion Research Laboratory (CRL) at Bucknell University is striving to develop the necessary equipment to be capable of both independent and collaborative research efforts with Penn State and in the process, advance the CRL to the forefront of combustion studies. The focus of this thesis is to advance the capabilities of the Combustion Research Lab at Bucknell. Specifically, this was accomplished through a revision to a previously designed liquid fuel injector, and through the design and installation of a laser extinction system for the measurement of soot produced during combustion. The previous liquid fuel injector with a 0.005" hole did not behave as expected. Through spray testing the 0.005" injector with water, it was determined that experimental errors were made in the original pressure testing of the injector. Using data from the spray testing experiment, new theoretical hole sizes of the injector were calculated. New injectors with 0.007" and 0.0085" orifices were fabricated and subsequently tested to qualitatively validate their behavior. The injectors were installed in the combustion rig in the CRL and hot-fire tested with liquid heptane. The 0.0085" injector yielded a manageable fuel pressure and produced a broad flame. A laser extinction system was designed and installed in the CRL. This involved the fabrication of a number of custom-designed parts and the specification of laser extinction equipment for purchase. A standard operating procedure for the laser extinction system was developed to provide a consistent, safe method for measuring soot formation during combustion.