Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, April 08, 2008, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Joel Spencer (Courant Institute, New York Univ.)

Neuron Firing

We examine a model developed by Prof. Charles Peskin with $N$ neurons ($N$ very large), each having a small number $K$ (e.g., $K=10$) states $0,1,\ldots,K-1$. Neurons are randomly excited and move up one state. But, critically, when a neuron reaches state $K$ it fires. Other neurons are then excited with independent probability $p$. This may (or may not!) set off a chain reaction with a large number of neurons firing. After the chain reaction, those neurons that have fired are reset to state $0$. The nature of the process depends on the relationship of $p$ to $N$ and $K$. There are strong connections to the Erdős-Rényi percolation discussed in the Monday Lecture. This is a ``work in progress" with many open questions.

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