- Series
- Mathematical Biology Seminar
- Time
- Wednesday, November 9, 2011 - 11:00am for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Andrei Olifer – Georgia Gwinnett College
- Organizer
- Leonid Bunimovich
Information processing in neurons and their networks is understood
incompletely, especially when neuronal inputs have indirect
correlates with external stimuli as for example in the hippocampus.
We study a case when all neurons in one network receive inputs from
another network within a short time window. We consider it as a
mapping of binary vectors of spiking activity ("spike" or "no
spike") in an input network to binary vectors of spiking activity in
the output network. Intuitively, if an input pattern makes a neuron
spike then the neuron should also spike in response to similar
patterns - otherwise, neurons would be too sensitive to noise. On
the other hand, neurons should discriminate between sufficiently
different input patterns and spike selectively. Our main goal was
to quantify how well neurons discriminate input patterns depending
on connectivity between networks, spiking threshold of neurons and
other parameters. We modeled neurons with perceptrons that have
binary weights. Most recent results on perceptron neuronal models
are asymptotic with respect to some parameters. Here, using
combinatorial analysis, we complement them by exact formulas. Those
formulas in particular predict that the number of the inputs per
neuron maximizes the difference between the neuronal and network
responses to similar and distinct inputs.
A joint work with Jean Vaillant (UAG).