This project develops a mathematical theory that relates the coding properties of neuronal populations to the structure of the local networks to which they belong. An important ingredient is the analysis of topological invariants, such as homology groups, of the stimulus spaces represented by networks of neurons, and how they constrain the connectivity of the underlying networks. This necessitates an approach that blends algebraic-topological methods with more traditional dynamical systems models. The research will produce testable predictions about the structure of networks that support stimulus representation, and will deepen our understanding of the relationship between network structure and function. The theory will be both tested and guided by the analysis of multi-unit electrophysiological recordings in behaving animals.
The brain is a vast collection of interconnected neural circuits. In many brain areas, important neural computations are accomplished by local networks of neurons. However, the structure of local recurrent circuits in the brain is still poorly understood, even in the most studied brain areas such as the hippocampus. In contrast, neuroscience experiments have been much more successful in uncovering coding properties of individual neurons and, more recently, in characterizing patterns of population activity in local neuronal circuits. This research develops a mathematical theory that exploits our knowledge of the representational properties of neuronal populations in order to better understand the structure of the underlying networks. The findings yield new insight into the role of neural circuits in learning and memory, and of how the brain organizes knowledge. Progress in the basic understanding of neural circuits is essential for improving our understanding of learning disabilities and diseases (such as epilepsy and schizophrenia) that are believed to be related to the malfunction of neural circuits.