Date of Submission

Fall 2017

Academic Programs and Concentrations

Mathematics

Project Advisor 1

Jim Belk

Project Advisor 2

Arseny Khakhalin

Abstract/Artist's Statement

The brain is constantly changing during development as a result of various stimuli: memories, language, visual patterns and other sensory information. As a result, networks need to have specific learning rules to function being both plastic and stable. In this project, I’ve constructed a mathematical model based on a biological neural network during development. I’ve written differential equations to describe these specific learning rules as well as methods of visual input to the network. I’ve changed my model, using Euler’s method, to create a discrete-time version of this biological phenomenon to implement on the computer. I’ve successfully coded this, using difference equations in MATLAB to simulate developmental neurons in the retina responding to visual stimuli. This project is at the cutting edge of the computational neuroscience field, particularly, because it remains unknown exactly how the topology of neural networks changes in development and how neurons self-organize from a previously random network of connections. Ultimately, I’ve found specific ways that synaptic connections evolve over time, and my graphs illustrate the maturation of a previously unrefined network. This gives us insights into how learning takes place during an organism’s critical period of development.

Open Access Agreement

Open Access

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

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