I am an Associate Professor in the Department of Mathematics at William and Mary. My interests lie in applied mathematics, and especially in the applications of mathematical and computational techniques to the study of biological phenomena. In particular, I am interested in the exciting field of computational and mathematical neuroscience.
The brain is an astounding organ, capable of monumental feats of computation that govern every aspect of our mental lives and behavior. Our current knowledge of the brain merely scratches the surface of true understanding, providing tantalizing clues to the mysteries that lie beneath. My work attempts to understand the computations performed by neuronal networks within the brain through mathematical investigations.
My current research focuses on several projects. One involves elucidating the function of the neural circuitry underlying sleep-wake switching behavior in infant mammals; understanding the computations performed by this circuitry, and the changes in this circuitry that occur through early development, can help elucidate the neural basis for the development of sleep-wake behavior and the emergence of sleep pathologies.
I am also interested in the phase-delayed inhibition network architecture, a network motif that recurs often in the brain and is employed as a means to decipher information encoded through population synchrony. The phase-delayed inhibiton network structure can be found in numerous neural systems, including the rodent barrel cortex (which deals with sensory information arising from the whiskers), and is the focus my current project. My current work focuses on studying how features of whisker deflections, such as deflection velocity and angular direction, are dynamically encoded by the barrel cortex network.
My third and primary investigatory focus is the insect olfactory system – the antennal lobe (analogous to the mammalian olfactory bulb) is the initial brain structure tasked with analyzing high dimensional odor information relayed from olfactory sensory neurons. The antennal lobe exhibits rich dynamics through complex network interactions but has well-understood neural components; recent preliminary experimental work from the lab of Hong Lei (ASU) indicates that the antennal lobe is bimodal, and integrates both mechanosensory (wind speed) and chemosensory (odor) information to resolve the spatiotemporal dynamics of environmental odor plumes. The goal of this project is to develop, in collaboration with Hong Lei’s lab, a realistic model of the antennal lobe that uncovers the possible dynamical mechanisms that underlie its observed physiology and guide mid-flight odor tracking.
My research inolves computational investigations of networks of neurons modeled via systems of nonlinear ODEs, as well as analytic techniques from ODE theory, nonlinear dynamics/phase plane analysis, and probability and stochastics. If you are an undergraduate interested in neuroscience and the applications of mathematics in elucidating neurobiological function, please feel free to contact me.
Mainak Patel, MD/PhD
Associate Professor of Mathematics
William & Mary
Office: Jones Hall 121
Email: mjpatel@wm.edu