Behavior arises from neural circuits that are enormously complex dynamic systems. A major goal in neuroscience is to characterize the essential components of these dynamics and to understand how they are generated by the biophysics of neurons and synapses. Toward this goal, I will describe network models that reveal basic features of neural circuit function. In one example, a model of posterior parietal cortex based on calcium imaging data is used to identify the degree of synaptic modification required to generate sequential neural activity through a novel mechanism involving a mixture of input-driven and internal dynamics. In a second example, a model of evidence accumulation reveals an unexpected nonlinear transformation in the representation of the integrated signal, a result verified by comparison with behavioral data. I will also discuss how the development of these models is informed by contributions I have made to random matrix theory and by the use of statistical physics to analyze network dynamics. To conclude my talk, I will discuss four directions where I believe theoretical advances, particularly in collaboration with experimental discoveries, will generate important new insights: Neural sequences as a novel substrate for memory-based and repetitive actions; Acquisition and implementation of cognitive maps to represent abstract contextual variables; Generating and testing hypotheses for computational strategies used by brain circuits; and Developing unsupervised and rewardbased learning procedures to model biological mechanisms of learning.
Kanaka Rajan is a Biophysics Theory Fellow at Princeton University. She specializes in designing mathematical frameworks and computational models to understand how the brain works. Having studied engineering and physics, the range of neuroscientific questions that interest her is broad, but always faithful to the interface between the physical and the biological sciences. Kanaka did her Ph.D. at Columbia University with Larry Abbott, focusing on the mathematical analysis of neural networks and their synaptic connections. This work used methods from random matrix theory and statistical physics to address how the brain interprets subtle sensory cues within the context of its internal experiential and motivational state to extract unambiguous representations of the external world. After her Ph.D., she developed new statistical inference methods to characterize neural responses to natural stimuli, in collaboration with Bill Bialek at Princeton. In subsequent work with David Tank, also at Princeton, she has modeled the neural circuit mechanisms underlying the generation of complex temporal activity in general, and neural sequences in particular. Most recently, she has been working on the dynamic foundations of behaviors within the context of working memory and decision-making tasks, and during task-related computations. Her plans for future research continue to be interdisciplinary and are aimed at making diverse impacts - from mathematics to experimental neuroscience. Kanaka has been the recipient of a Young Investigator Award from the Brain & Behavior Research Foundation, formerly, NARSAD, followed by an Understanding Human Cognition Scholar Award from the James McDonnell Foundation in 2016, the only postdoc to be awarded.