- Main
Normative Approaches to the Analysis of Neural Dynamics and Connectivity
- Kumar, Ankit
- Advisor(s): Bouchard, Kristofer E;
- DeWeese, Michael
Abstract
Brain functions, ranging from perception to cognition to action are produced by the col- lective dynamics of populations of neurons. Our ability to simultaneously record from and map the connectivity between large numbers of neurons across brain areas has increased substantially over the past decade. In contrast, our understanding of the resulting com- plex and dynamic data in terms of principles of brain computations is lacking. This thesis presents theory and statistical methods that address this gap. I first describe a novel, nor- mative theory of neural population dynamics based on control theory. I introduce novel dimensionality reduction methods that identify subspaces of neural activity that are most amenable to feed-forward (i.e. open-loop) control vs. feedback control (i.e. closed-loop) control. Through new theorems/simulations, I demonstrate that for systems exhibiting non- normal dynamics, generically present in cortex due to Dale’s Law, directions most important for feedforward vs. feedback control are geometrically distinct. I then analyze neural recordings from macaque primary motor and somatosensory cortices and show that the dynamics that are most feedback controllable are aligned with those that generate reaching behavior. These feedback controllable dynamics are shown to be mediated by the functional interac- tions between a population of neurons whose characteristics map to known features of Layer 5 intratellenchephalic neurons. Lastly, I show that feedback controllability provides a nor- mative account for the presence of rotational dynamics in motor cortex. Next, I present an approach an analysis of the Drosophila hemibrain connectome using novel maximum entropy models of random graphs inspired from statistical physics. I provide preliminary results in- dicating that the controllability of Drosophila brain networks relies on emergent principles of connectivity between neurons. Finally, I report on work that characterizes the performance of statistical estimation of sparse linear models in the case when model features exhibited correlated variability, a common issue in neural data analysis. The results provide practical guidelines relevant for the estimation of functional connectivity.
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