2015 Summer Undergraduate REU Program

University of Pittsburgh

UP - Department of Mathematics

Topic 1:

Understanding how patterned activity arises in biological systems - Bard Ermentrout

Project Description:

Dr. Ermentrout’s research program examines how patterned activity such as waves, oscillations, and complex spatio-temporal dynamics arise in biological systems. For example, what circuitry in the brain allows and/or prevents the propagation of neural activity from one region to another? How does the topology of networks of biological oscillators interact with their internal dynamics to determine if they will synchronize or not? What mechanisms and disruptions of normal activity in the brain lead to pathologies like schizophrenia, seizures, and hallucinations?  Students mentored by Dr. Ermentrout will apply mathematics (typically differential equations) to these problems, and will develop skills in modeling and simulation of biological systems and in analyzing the resulting equations.

Topic 2:

Modeling the actions of the piriform cortex in odor detection - Brent Doiron

Project Description:

Neurons in the olfactory system encode for the odor identity (banana vs. cherry) and intensity (strong banana vs. weak banana) of olfactory scenes.  How exactly populations of neurons in the piriform cortex (odor cortex) disentangle these two aspects of an odor input and transmit a unique code is a topic of current research.  This is made more difficult given the seemingly random and unstructured projections made to the piriform cortex from lower order areas, as well as from within the piriform cortex itself.  We will use theories of networks with balanced excitation and inhibition to explore how the piriform cortex gives optimal odor identity/intensity codes despite the lack of a clear stimulus-related structure in the cortical wiring.  Students working on this project will program and apply large-scale simulations of interacting neurons, as well as mean field theory techniques borrowed from statistical mechanics.