Math 577 -- Dynamical Models of Neuronal Computation

Spring 2009

Note. This syllabus is a very rough guide to the topics I'd like to cover. As the semester progresses, some topics may get dropped, while others may get expanded or added. I'll try to keep this page up-to-date. This page was last updated on April 28, 2009.

Relevant references for each topic are given in [...].

[DA] = Dayan and Abbott
[GK] = Gerstner and Kistler

Part I: Single neuron models

1/15: "Big picture" intro.  Basic facts: membranes,
voltages, ion channels [GK 2.1; DA 5.2].

1/20 - 1/22: Equilibrium potential; Hodgkin-Huxley
equations [GK 2.2; DA 5.3].  Markovian models of ion
channels [GK 2.3; DA 5.7].

1/27 - 1/29: More on ion channels; synapses [GK 2.4;
DA 5.5, 5.8].  Derivation of the cable equation [GK 2.5,
2.6; DA 6.3, 6.4].

2/3 - 2/5: Linear cable equation; compartmental
models [GK 2.5, 2.6; DA 6.3, 6.4].  Intro to reduced point
neuron models [GK 3.1].

2/10 - 2/12: Dimension reduction for HH-like models
[GK 3.1].  Basic phase plane analysis [GK 3.2, see also
Strogatz].

2/17 - 2/19: Phase plane continued.  Limit cycles and
oscillations [GK 3.2, Strogatz, Izhikevich book].

2/24 - 2/26: Bifurcations.  Threshold and
excitability in Type I and Type II neurons [GK 3.3;
Rinzel-Ermentrout].

3/3 - 3/5: Threshold and excitability continued
[Rinzel-Ermentrout].  Integrate-and-fire, Theta neuron, and
other 1-D models [GK 4.1; DA 5.4, 5.9].

Part II: Network models

3/10 - 3/12: Rate-based network models [DA 7.1, 7.2].

3/17 - 3/19: SPRING BREAK

3/24 - 3/26: Linear rate-based network models.
Examples: integration and selective amplification [DA 7.4].

3/31 - 4/2: LTI systems and their frequency response
[DA App. 1].  Nonlinear networks, excitatory-inhibitory
networks, and oscillations [DA 7.5].  Linear response from
a population density model [GK 6.2; Knight].

Part III: Spike train statistics and neural coding

Reference: [DA] Ch 1-4

4/7 - 4/9: Brief review of probability [Gershenfeld;
???].  The Poisson model of spike train statistics [from DA
Ch 1 & 2].  Spike-triggered averages; Volterra expansions
[from DA Ch 2].

4/14 - 4/16: More on Wiener-Volterra expansions and
reverse correlations.  Volterra kernel as correlation
function response to white noise.  Example: spacetime
receptive fields of simple cells in V1.  Discrimination
[from DA Ch 3]; information theory and neural decoding [from
DA Ch 4].

Part IV: Selected topics

4/21 - 4/23; 4/28 Models of plasticity and learning.

4/30 - 5/5: student presentations

This page was last updated on April 28, 2009.