University of Pittsburgh
June 11 - August 3, 2012 (8 weeks)
UP - Department of Mathematics
(multiple projects available depending on student interests - interacts with existing summer research fellowship program)
Topics Areas (listed by supervising mentor)
Brent Doiron:
- Mechanisms of Cortical Variability. We explore how network architecture and dynamics in cortex contribute to the large variability observed in neural responses. This has consequences for how neural populations code for stimuli. The project involves constructing and analyzing large networks of model spiking neurons driven by fluctuating inputs.
- Models of neural memory/decision making. An analysis of neural models where mechanisms for memory and decision making interact, and how neural variability impacts the performance of these models.
- Mechanisms of neural modulation/adaptation. Recent work has shown how feedback inputs from higher brain centers to lower brain centers can modulate the responses of neurons to stimuli. We have developed mechanisms in auditory brainstem where synaptic plasticity supports neural modulation. We next want to measure the impact of these mechanisms on realistic neural coding schemes for simple auditory inputs.
Bard Ermentrout:
- Neural pathologies. How does the reduction of inhibition or increase in synaptic excitation alter the normal dynamics of cortical processes such as working memory. Diseases such as schizophrenia and epilepsy have been shown to be connected to alterations in the expression of various synaptic receptors such as GABA (inhibition) and NMDA (slow excitation). Computational models of different cortical circuits when various parameters are altered can provide insights into the underlying dynamical mechanisms of these pathologies.
- What determines when neural oscillators will synchronize? Individual properties of neurons determine how these neurons respond to stimuli; in particular, how the timing of output spikes depends on the timing of input spikes. In this project, we explore how the individual neuronal properties, the topology of connectivity, and the types of connections determine whether networks of neurons synchronize. We use perturbation methods to reduce systems of coupled neural oscillators to simplified phase models.
- What determines the properties of spatiotemporal dynamics in cortical networks. It is known that much of the activity, both evoked and spontaneous, in cortex is organized into wavelike patterns. In this project, we use neural field models to study the properties of these waves in single and multilayer networks. We use a combination of computational and perturbation methods.
Jonathan Rubin:
- Interaction of rhythm generators and feedback in locomotion. Models for various types of locomotor systems will be developed (e.g., passive walking devices, neural locomotor rhythm generators). These models will be compared to explore what advantages (e.g., stability against perturbations) are gained by including feedback from muscles and other sources.
- Exploration of parameter space for existing central pattern generator models. Past work by various groups has led to the development of models that generate physiological rhythms (e.g. digestive, locomotor, or respiratory rhythms) for many different parameter sets. Computational work is needed to try to find some structure in the successful parameter sets, so that the possible rhythmogenic mechanisms can be identified.
- Development of a computational swimming turtle model. Existing software (e.g. AnimatLab) may be used in an attempt to develop a computational model of an actual swimming turtle.
Prerequisites:
Depending on the project, students should meet one or (ideally) more than one of the following prerequisites: (1) basic experience developing or thinking about ordinary differential equation (ODE) models for biological or physical systems; (2) solid knowledge of standard methods to solve first order and linear ODEs and basic linear algebra; (3) computational experience (e.g., writing basic programs in Matlab or using XPPAUT); also, students should be enthusiastic about doing/learning to do all of the above and should be willing to learn LaTeX.
