Mainak Patel, Visiting Assistant Professor

Contact Info:

Office Location:	Mathematics 114
Office Phone:	(919) 660-6979
Email Address:

Teaching (Fall 2013):

• MATH 353.03, ORD AND PRTL DIFF EQUATIONS Synopsis

  Physics 259, TuTh 06:15 PM-07:30 PM

Office Hours:

Tuesday 5-6pm
Friday 2-3pm

Education:

PhD	New York University, Courant Institute for Mathematical Sciences	2011
MD	New York University School of Medicine	2011

Specialties:

Applied Math

Research Interests: Mathematical Biology

Current projects: Odor encoding within the insect olfactory system, , Dynamics of stimulus selection in the owl optic tectum, , Phase delayed inhibition as a mechanism for decoding synchronized oscillations, , Reciprocal inhibition and switching behavior: distributions of on and off times and applications to sleep-wake nuclei within the brain

Phase Delayed Inhibition

The widespread presence of synchronized neuronal oscillations within the brain suggests that a mechanism must exist that is capable of decoding such activity. Two realistic designs for such a decoder include: 1) a read- out cell with a high spike threshold, or 2) a phase-delayed inhibition motif. Despite requiring a more elaborate network architecture, phase-delayed inhibition has been observed in multiple systems, suggesting that it may provide inherent advantages over simply imposing a high spike threshold. Computational and mathematical approaches are used to investigate the efficacy of phase-delayed inhibition in detecting synchronized oscillations.


Switching with Reciprocal Inhibition

The stability of sleep and wake states may be maintained by sleep and wake nuclei in the brain that reciprocally inhibit each other, so that the identity of the predominantly active nucleus determines the state of the animal.  In infant rats, the length of sleep and wake bouts have an exponential distribution, while in older animals the length of wake bouts assumes a power law distribution (sleep bouts remain exponentially distributed).  We are using mathematical and computational approaches to study this switching behavior.  We are starting with a pair of mutually inhibitory neurons and examining bout lengths and switching within this simple system, then moving on to more complex network models and investigating the emergence of power law bout distributions.

Areas of Interest:

computational/mathematical biology
synchronized oscillations in the brain
switching behavior in small inhibitory networks
insect olfactory networks
stimulus selection in the owl optic tectum
spike timing precision in the auditory system

Recent Publications   (search)

1. M. Patel, A.V. Rangan, D. Cai, A large-scale model of the locust antennal lobe, Journal of Computational Neuroscience, vol. 27 no. 3 (2009), pp. 553-567 [19548077]  [abs]