Emergence and stability of complex structures from stochastic neuronal networks

A single neuron’s connectivity is the key to understanding the network of neurons in the brain. However, it is already a complicated system and many different approaches to understanding it have been taken over the years. One way is from anatomical study, which is to observe the morphology of each neuron and the organization of the neuronal connections. Another way is from physiological study, which describes the specific electrical outputs of the cells. Computational studies have been developed to fill the gaps between these studies. There are several stochastic computational models, but none of them is easy to analyze quantitatively and typically, the analysis resorts to simulations. Many of the previous studies were focused on physiological structures through Monte Carlo simulations, not on the model itself. This thesis introduces a general purpose stochastic model with mathematically rigorous assumptions, so that analysis of the model itself using a Markov chain is applicable. With specific input stimuli and parameters, the model demonstrates rich properties, such as selectivity of input structures and competition between input neurons. This method provides a well-positioned balance between neuro-biological relevance and theoretical tractability. The model is first studied quantitatively to prove theorems about the existence of a controlled Markov chain over an appropriate time scale. Using the Markov chain makes it possible to show the existence of an invariant measure with some convergence rates. In this context, other theorems are introduced to shed insight beyond the simple phenomenological approaches with simulations that others have developed. Then the system is studied qualitatively by simulating the neuronal physiology of visual neurons, which uses more complicated assumptions. This shows the emergence of direction and orientation selectivity, as the visual neuron’s properties. Hence, this selectivity could be an epiphenomenon of the assumptions chosen for the models. The key insight here is that the model shows a robust phenomenon to the initial condition, but not to the input stimulus, which implies the importance of the initial condition and the noisy inputs. These dynamics may explain learning and reinforcement of the visual neurons and could predict results in future experiments.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Computer Science

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2012

Author dc:creator

• Arizumi, Nana

Contributors dc:contributor

• Coleman, Todd P.
• DeVille, Lee
• Olson, Luke N.
• Heath, Michael T.
• Gropp, William D.
• Nelson, Mark E.

• computational neuroscience
• spike-timing- dependent plasticity (STDP)
• neuronal network

Statement dc:rights

• Copyright 2012 Nana Arizumi

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/30961

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/30961