G63.2852.001/G80.3042.001 -- Spring, 2010

Advanced Topics in Mathematical Biology:
Computational Modeling of Neuronal Systems

Instructors: John Rinzel & Eero Simoncelli
Time: Tues 9:30-11:20 am
Location: Warren Weaver Hall, Rm 1314
Prerequisites: familiarity with linear algebra, basic probability/statistics, differential equations. Some programming experience, e.g. matlab.

Brief Description:

We will survey various approaches to computational modeling of neuronal systems, from cellular to system level, from models of physiological mechanisms to more abstract models of information encoding and decoding. We will address the characterization of neuronal responses or identification of neuronal computations; how they evolve dynamically; how they are implemented in neural ware; and how they are manifested in human/animal behaviors. Modeling will involve deterministic and stochastic differential equations, information theory, and Bayesian estimation and decision theory.

Schedule:

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Date Lecturer Topic Materials Homework
19 Jan J.Rinzel Intro to computational neuroscience: mechanistic vs. descriptive.
Nonlinear neuronal dynamics I: cellular excitability and oscillations 		Course schedule
Reference chapter
Lecture slides 		HW 1
26 Jan J. Rinzel Nonlinear neuronal dynamics II: networks;
Case study #1: Spont rhythms in spinal cord. 		Lec Slides:MSO Type 3
Lec Slides: Rate models #1
XPP Demo
XPP Demo odes
2 Feb E. Simoncelli Descriptive models of sensory encoding: model fitting; linear/nonlinear cascade; integ & fire Lecture slides  
9 Feb R. Shapley V1 network models and gamma "oscillations" Lecture Slides
16 Feb A. Rangan Model for olfactory representation
23 Feb J. de la Rocha Modeling the stochastic activity of recurrent balanced cortical circuits Lecture Slides
Reference paper
2 Mar D. Tranchina Population Density Methods and Applications to Gain Control in Neural Networks. Reference papers
9 Mar A. Reyes Cascade networks, auditory RF properties. Lec Slides: Part I
Lec Slides: Part II
Fokker-Planck sims
16 Mar No Class
[Spring Break]
23 Mar B. Pesaran Correlation between different brain areas; LFPs. Lecture slides (pdf)
30 Mar E. Simoncelli Sensory Decoding: estimation/decision from neural populations. Lecture slides (pdf)
Seung & Sompolinsky 1993;    Ma et. al. 2006;    Simoncelli 2009
6 Apr T. Movshon Cortical processing of visual motion signals. Lecture slides (pdf)
Rust et. al. 2006
13 Apr N. Rubin Dynamics of perceptual bistability.
20 Apr P. Glimcher Neuroeconomics; Decision making Lecture slides (pdf)
Kable & Glimcher 2009
27 Apr N. Daw Decision making; reinforcement learning Lecture slides (pdf)
Maia review_2009
Dayan&Daw review 2008

Relevant books.

  • ..... computational approaches:
  • Theoretical Neuroscience , by Dayan & Abbott. MIT Press, 2001.
  • Spikes: Exploring the Neural Code, by Rieke, Warland, de Ruyter, & Bialek. MIT Press, 1997.
  • Biophysics of Computation, by Koch. Oxford University Press, 1999.
  • ..... basic neuroscience:
  • From Neuron to Brain , by Nicholls, Martin, Wallace & Fuchs. Sinauer, 4th edn, 2001.
  • The Brain: A Neuroscience Primer , by Thompson. Worth, 3rd edn, 2000.

    XPP codes for models:

    Hodgkin-Huxley XPP
    Morris-Lecar XPP
    Wilson-Cowan XPP

    Matlab codes for models:

    Hodgkin-Huxley Matlab
    FitzHugh-Nagumo Matlab