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My Research Interests
Andrew Leach
University of Arizona
31 May 2013
A. Leach (University of Arizona) My Research Interests May 2013 1 / 9
About Me
A. Leach (University of Arizona) My Research Interests May 2013 2 / 9
About Me
How I got into Mathematics
Curiosity
I’ve always asked a lot of questions
Sometimes the answers are unknown
What I aim to do as a Mathematician
Computational techniques to give insight into mathematical problems
Examples include:
Collective rhythm of firefly flashesFormation of magnetism from interactions on the scale of atomsNetworks of neurons, the building blocks of the nervous system
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Networks of Neurons
The nervous system is composed of cells called neurons
They are connected in complex networks
They use electrical impulses to communicate
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Networks of Neurons
Input Signal Neurons
The electrical impulses from other neurons can cause a neuron to fire
Can simulate on a computer how a network responds to an inputsignal
Some networks will respond differently every time, even when thesignal is the same!
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Networks of Neurons
Input SignalSensory Input
The input signal may be sensory input or another group of neurons
Networks of neurons close to the sensory input usually respondconsistently
Networks of neurons further away from the sensory input may respondinconsistently
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Chaos
Chaos: Small changes grow over time
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Chaos
Input Signal Neurons
Varying network response is a result of chaos!
My goal:
Biological: Understand characteristics of chaotic networks of neuronsMathematical: Develop tools and theory in a more general setting
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Thank you!
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