Homologous Burst-Synchronizing Networks

My project aims to use the mathematical structure that can be found in biological networks composed of neurons. Using tools from the field of math called algebraic topology we are trying to find which synapses are essential to the behavior of the network and which can be removed with negligible effect on the system. If…
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Full Synapse Ablation Simulation

I finally got a full run on a small network ablating synapses one at a time. My project focuses on how the mathematical structure of a neural network affects its ability to stay synchronized. My goal is to show that if a synapse is removed that does not change the homology of the network then…
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Quantifying Dynamics of Synchronization

My research looks at the dynamical behavior of biological neural networks and the model I’m using partially simulated the Pre-Botzinger complex of the brainstem found in mammals that regulates breathing. The neurons in the network rhythmically activate and deactivate together to form a synchronized pattern. The model I created in python plots the 3 different…
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Simplicial Homology & Neural Networks: Abstract

This project merges the mathematical field of algebraic topology with the analytic study of biological neural networks. My approach to this will consist of investigating the algebraic structure of neural networks found in biology and comparing them to different possible networks that do not occur in nature in an effort to discover why biology has…
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