Dynamics of Neurons and Networks
AMATH 534
| Instructor |
|---|
| Eric Shea-Brown |
| 325 Lewis Hall |
| Office hours: Thurs 1:00-2:00 |
Text: Neuronal Dynamics by Gerstner, Kistler, Naud, and Paninski. Book and resources freely available online here, or softcovers should be in the bookstore, or can be ordered from Amazon, etc.
We will also read and base lectures on a number of research articles.
Copies of Eric's (rough) handwritten notes from lectures.
Copies of slides from Eric's lectures
Syllabus and readings
(1) Nonlinear dynamics of single neurons- What we expect to find: a bifurcation perspective
- Type I and Type II cells
- Firing rate curves
- Resonators and Integrators
- Phase response curves
- Why (dimension) reduced models work: timescale separation and geometry
- Generalized integrate and fire models
- Fitting reduced neuronal models to data
- "Direct" fits of generalized integrate and fire models
- Filter-and-Fire / Generalized Linear Models
- Likelihood-based methods and convexity
- Guest lecture by Stefan Mihalas: GLIF models and the cell types
READINGS:(2) Coordinated spiking and spike patterns
- Gerstner: Ch. 1, 4, 5, 6, 10
- On Bifurcations to periodic firing, and phase repsonse curves: Sections 1,2,3 only of Brown et al '04
- Stefan Mihalas' lecture slides: GLIF and cortical modeling
- Teeter, Mihalas et al paper: Generalized Leaky Integrate-And-Fire Models Classify Multiple Neuron Types
- Paninksi, Pillow, Lewi Chapter on point process models and decoding
- Pillow et al, Retinal coding and encoding, Nature 2008
- Spike time correlations
- Reliable exponents, lyapunov exponents, and the idea of stimulus-driven "random" attractors: Experiment and theory
- Mutual information in spike trains and neural coding
READINGS:
- Slides
- Gerstner: Ch. 7
- Strong et al, PRL 1998
- Optional: Lin et al, 2009
- The population density formulation
- Diffusion approximations and stochastic-differential equations
- Firing rate responses and their modulation
- Mean- and fluctuation-driven firing regimes
- Balanced networks and rapid computation
- Transformations over time: persistent activity and neural integrators
- Gerstner: Ch. 8, 12, 13
- Nykamp and Tranchina, JCNS, 2000
- Rough notes from class
- Optional: Richardson, PRE, 2007
- Nonlinear firing rate models for neural networks
- Recurrent network models
- Spike time dependent plasticity and self-consitent rules for spiking networks
- Guest lecture by Michael Buice: deep neural networks
- Guest lecture by Rajesh Rao on predictive coding
- Gerstner: Ch. 16
- Rough handwritten notes on STDP in spiking systems
- Ocker, Litwin-Kumar, and Doiron, PLOS CB 2015
Course structure and evaluation
We'll run the class in larger part like a graduate seminar -- much more participatory and informal than a usual class. Over the course of the term, teams of students will give two presentations on a published research article of interest to them, that builds from the lectures that I and guests will be giving on the topics above. The first presentation will describe the main findings in the article and a plan to extend them in a new research direction, and the second, at the end of the quarter, will present the group's progress to date in doing so.
Each team of students will develop the second of these presentations into a ~10 page project paper where they take the analysis or simulations in this article in one interesting new direction (together, the presentations will be 20% of the grade and paper will be 40% of the course grade). The first presentation will be in class on Feb 20, the final presentation in class on March 12, and papers are due via online submission (canvas) on March 17 (end of quarter) at noon.
GUIDELINES FOR PRESENTATIONS AND PROJECT PAPER (link).
We'll also have several problem sets, handed out on select days in class and due in class 2-3 weeks later, to reinforce learning. These will make up the rest of the grade.
Religious Accommodation Policy: Washington state law requires that UW develop a policy for accommodation of student absences or significant hardship due to reasons of faith or conscience, or for organized religious activities. The UW’s policy, including more information about how to request an accommodation, is available at Faculty Syllabus Guidelines and Resources. Accommodations must be requested within the first two weeks of this course using the Religious Accommodations Request form available at https://registrar.washington.edu/students/religious-accommodations-request/ (Links to an external site.).