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Professor Chad Giusti has been awarded AFOSR funding for a half-million-dollar, three-year project to develop new mathematical and computational tools for the study of neural computation and coding in the brain. The funding will provide salary and research support for a team to work on the project including a postdoctoral researcher and graduate students.
A fundamental goal in theoretical neuroscience is the creation of quantitative frameworks for describing and reasoning about how neural systems encode and process information. This project will contribute to the development of such a framework by leveraging the “stimulus space" model for neural population coding. Stimulus spaces provide geometric representations of the structure of information in neural populations. Neuroscientists have informally used such models to work with population-wide activity patterns for decades. However, the underlying mathematical formalism is still underdeveloped, and thus much of the power of this model remains inaccessible.
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In particular, this project will study how a ubiquitous population activity profile called “cyclicity" is represented within and across neural populations. Cyclic activity profiles – well represented by circular stimulus space models – encode a broad range of phenomena, including rotational information like head direction, repetitive or periodic stimuli and obstacles in complex environments. Building on Professor Giusti's previous development of methods in applied algebraic topology to characterize population dynamics, the team will develop a general tool kit for the rigorous and systematic study of neural coding of cyclic features.
The goals of the project include development of theoretical and software tools to rigorously identify and verify correspondences between cyclic features coded by related neural populations or expressed in response to cyclic features of external stimuli; investigating how the structure of feed-forward networks permits and inhibits the propagation of coded cyclic features between connected neural systems, via both theoretical analysis and computational experiments; and developing methodologies for designing closed-loop activity regulation control systems inside recurrent neural networks.