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Math @ Duke



Mainak Patel, Visiting Assistant Professor

Contact Info:
Office Location:  Mathematics 114
Office Phone:  (919) 660-6979
Email Address: send me a message

Office Hours:

Tuesday 5-6pm
Friday 3-4pm

PhDNew York University, Courant Institute for Mathematical Sciences2011
MDNew York University School of Medicine2011

Mathematical Biology
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   (More Publications)   (search)

  1. M. Patel, B. Joshi, Decoding synchronized oscillations within the brain: Phase-delayed inhibition provides a robust mechanism for creating a sharp synchrony filter, Journal of Theoretical Biology, vol. 334C (2013), pp. 13-25 [23747525]  [abs]
  2. M. Patel, B. Joshi, Switching mechanisms and bout times in a pair of reciprocally inhibitory neurons, Journal of Computational Neuroscience [ePub ahead of print] (2013) [23820857]  [abs]
  3. M. Patel, Stimulus encoding within the barn owl optic tectum using gamma oscillations vs. spike rate: A modeling approach., Network, vol. 24 no. 2 (2013), pp. 52-74 [23406211]  [abs]
  4. B. Joshi, M. Patel, Encoding with synchrony: Phase-delayed inhibition allows for reliable and specific stimulus detection., Journal of Theoretical Biology, vol. 328 (2013), pp. 26-32 [23524360]  [abs]
  5. M. Patel, AV Rangan, D Cai, Coding of odors by temporal binding within a model network of the locust antennal lobe., Frontiers in Computational Neuroscience, vol. 7 (2013), pp. 50-67 [23630495]  [abs]
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320