2014 Summer Undergraduate REU Program

University of Pittsburgh

UP - Department of Mathematics

Topic 1:

The impact of synaptic variability on irregularity in balanced networks of spiking neuron models - Brent Doiron

Project Description:

The nervous system has a large degree of irregularity in its response, often thought of as a "noisy" brain dynamics. However, stochastic neural response may be the result of several mechanisms that operate at different spatial and temporal scales in networks of neurons. At the cellular level, individual synapses have a probabilistic response, and the amount of transmitter has a significant random component. At the network level, excitation and inhibition can balance one another to promote very irregular dynamics that are akin to high dimensional chaos, and as such can be modeled with a deterministic network. How truly stochastic synaptic variability interacts with network level chaos is unknown. The student will use techniques from stochastic processes, nonlinear dynamics, and high performance computing to investigate how synaptic variability impacts network level irregularity in balanced networks of spiking neuron models.

Topic 2:

Determining how neuronal population rhythms are shifted by inputs - Bard Ermentrout

Project Description:

Populations of neurons can undergo rhythms and such rhythms, just like individual oscillators, are able to be entrained and can interact with other populations. Associated with any stable rhythm is the phase-resetting curve. We will use a combination of analytic and numerical methods to compute how population rhythms are shifted by inputs. Methods such as averaging, mean field analysis, and population density equations will be used to study populations of excitatory neurons with adaptation and also populations of excitatory and inhibitory neurons.