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.

COMPARATIVE STUDY OF INFORMAL HEALTH CARE NETWORKS AND ELDERLY HEALTH STATUS IN ARGENTINA AND CUBA

This study will explore familial and friend support networks and living arrangements among elderly individuals in Latin America and the impact that this type of support has on the health of the elderly individuals in the countries of interest. Using data from the Survey on Health and Well-Being of Elders (SABE) from 1999-2000, I will explore which type of support has a larger impact on overall health. I will also measure differences in unmet needs for certain health services. This topic is particularly interesting because it will help to uncover what policies are best for aiding in the healthcare of the elderly in aging population. Lastly, the investigation of this topic will allow me to draw conclusions about the most effective means of social and public policy for the elderly community and provide me with information about the role of both informal provisions of support from family and friends, and formal provisions of support from the government. My primary focus will be on Argentina, using Buenos Aires as the sample city, and Cuba, using Havana as the sample city. These two countries have increasingly aging populations, poorer resources and vast inequalities, but, extremely different political, economic and cultural situations. Comparing the two countries will further allow me to determine correlations between health and the existence of support networks, as well as provide me with information to make more general claims that may be of use in the United States. Argentina is particularly interesting to me because of my abroad experience and homestay experience with an older Argentine woman who lived alone but depended upon her family for many healthcare needs, doctors’ visits and general well-being. In Argentina, I experienced a different form of living than I am used to in the United States, where many older individuals or couples live in nursing homes or assisted living facilities rather than alone or with family. The changing economic climate of the two countries coupled with labor patterns of women returning to work at rapid rates indicates that policies cannot just rely on either the formal or informal sector but require a combination of the two sectors working together.This paper will first give background on the difference in the economies and the health care systems in Argentina and Cuba and will show why it interesting to study and compare these two countries. I will then discuss the health status of the elderly in each population as well as discuss the informal care networks and the role of family in each country. This section will then be followed by a description of the data and methods used. I will end by drawing conclusions about the study and the outcomes, and then I will attempt to make suggestions about effective health care policies for the elderly.

Verifying Harder's Conjecture for Classical and Siegel Modular Forms

A conjecture by Harder shows a surprising congruence between the coefficients of “classical” modular forms and the Hecke eigenvalues of corresponding Siegel modular forms, contigent upon “large primes” dividing the critical values of the given classical modular form. Harder’s Conjecture has already been verified for one-dimensional spaces of classical and Siegel modular forms (along with some two-dimensional cases), and for primes p 37. We verify the conjecture for higher-dimensional spaces, and up to a comparable prime p.