New recording methods allow researchers to probe the structure of neural activity with unprecedented scope and detail. As a result there is an explosion of interest in understanding the patterns of activity that emerge in entire neuronal populations and relating these patterns to the function of the nervous system. However, the overwhelming range of different sensory inputs that these populations receive -- and the vast range of different responses that these inputs evoke -- make it impossible to achieve this goal based on empirical observations alone. This challenge is compounded due to the nonlinearity of neuronal network dynamics, which makes it difficult to predict patterns of activity by extrapolation from observations of simpler systems. Predictive mathematical modeling and a deeper understanding of the dynamics of neuronal circuits is therefore required. With previous NSF support, the investigators developed numerical and analytic tools at the interface of statistics, stochastic analysis and nonlinear dynamics, to understand the genesis and impact of correlations in simple, but fundamental microcircuits. They build on these results by extending the underlying mathematical theory to more complex and realistic networks. Using this approach, the team of researchers examines how collective activity is controlled by network architecture, cell dynamics, and stimulus drive in a set of neural networks that typify structures across the nervous system.

Answering these questions will open the door to contemporary biological applications and will meet key theoretical challenges posed by recent technological developments in experimental neuroscience. The key innovation lies in the understanding the collective dynamics of large neural networks that cannot be decomposed into their isolated parts. Through continued interactions with a broad set of experimental collaborators, these ideas are introduced and tested by a broad community of neuroscientists. In the longer term, results on coding in the presence of collective network dynamics will impact the design of neural prosthetics, which code sensory signals via cortical, retinal, and thalamic implants.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Mary Ann Horn
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University of Houston
United States
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