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Some Aspects Of The First Passage Time Problem In Neuroscience

Electronic Theses of Indian Institute of Science

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Title Some Aspects Of The First Passage Time Problem In Neuroscience
 
Creator Bhupatiraju, Sandeep
 
Subject Neurophysiology
Neurons - Time Passage
Voltage Impulses
Random Walks
Neurons - Modeling
Spike Trains (Neurons)
Neuroscience
 
Description 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.
 
Contributor Rangarajan, Govindan
 
Date 2011-08-08T12:13:01Z
2011-08-08T12:13:01Z
2011-08-08
2010-03
 
Type Thesis
 
Identifier http://etd.iisc.ernet.in/handle/2005/1343
http://etd.ncsi.iisc.ernet.in/abstracts/1737/G23707-Abs.pdf
 
Language en_US
 
Relation G23707