IISc Logo    Title

etd AT Indian Institute of Science >
Division of Physical and Mathematical Sciences  >
Mathematics (math) >

Please use this identifier to cite or link to this item: http://hdl.handle.net/2005/1343

Title: Some Aspects Of The First Passage Time Problem In Neuroscience
Authors: Bhupatiraju, Sandeep
Advisors: Rangarajan, Govindan
Keywords: Neurophysiology
Neurons - Time Passage
Voltage Impulses
Random Walks
Neurons - Modeling
Spike Trains (Neurons)
Submitted Date: Mar-2010
Series/Report no.: G23707
Abstract: In the stochastic modeling of neurons, the first passage time problem arises as a natural object of study when considering the inter spike interval distribution. In this report, we study some aspects of this problem as it arises in the context of neuroscience. In the first chapter we describe the basic neurophysiology required to model the neuron. In the second, we study the Poisson model, Stein’s model, and some diffusion models, calculating or indicating methods to compute the density of the first passage time random variable or its moments. In the third and fourth chapters, we study the Fokker-Planck equation, and use it to compute the first passage time in the discrete and continuous time random walk cases. In the final chapter, we study sequences of neurons and the change in the density of the waiting time distributions, and hence in the inter spike intervals, as the output spike train from one neuron is considered as the input in the subsequent neuron.
Abstract file URL: http://etd.ncsi.iisc.ernet.in/abstracts/1737/G23707-Abs.pdf
URI: http://hdl.handle.net/2005/1343
Appears in Collections:Mathematics (math)

Files in This Item:

File Description SizeFormat
G23707.pdf600.01 kBAdobe PDFView/Open

Items in etd@IISc are protected by copyright, with all rights reserved, unless otherwise indicated.

 

etd@IISc is a joint service of SERC & IISc Library ||
Feedback
|| Powered by DSpace || Compliant to OAI-PMH V 2.0 and ETD-MS V 1.01