Thomas Goodwin
University of Technology Sydney
Biography
Tom is a third-year student studying a Bachelor of Science in Mathematics. He intends to do honours in mathematics with a particular interest in Mathematical modelling in Biology. When away from studying he as a avid drum player and music fan.
The Mathematics of Neuron Flows in the Brain
The project will introduce new techniques for modelling neuron flows in the brain, using non-homogeneous Markov measures. This will allow the modelling of connected neurons with different parameters: by placing different weights on the individual neurons in the network of a Bratteli-Vershik diagram, we will provide a more realistic model of brain activity. A Bratteli-Vershik system (BV system) is an ordered graph whose vertices are organised in countably many layers, and with edges joining the layers. It is equipped with the Vershik operator, which is a generalisation of the odometer of classical ergodic theory, and a probability measure defined by weights on the edges, which can be understood as a non-homogeneous Markov measure. Dooley and Hamachi [DH] actually showed that every non-singular dynamical system is orbit equivalent to a Bratteli-Vershik system.