Quantitative Methods in Neuroscience

The University of Texas at Austin
NEU 366M, Fall 2014
 
location: PAR 208
time: Tues/Thurs 12:30-2:00 pm
 
instructor: Professor Ila Fiete (fiete [at] mail.clm.utexas.edu)
teaching assistants:
Kijung Yoon (kijung.yoon [at] utexas.edu)
Berk Gercek (UGTA) (gercek.berk [at] gmail.com)
office hours:
Dr. Fiete: Thurs 11-noon (NHB 3.354) and by appt.
Kijung: Mon 4- 5.30 (NHB 3.350), Fri 10.30 - noon (SEA 2.122) and by appt.
Berk: Fri 3-4.30 (NHB 3.350)
 
syllabus: PDF
textbook: Mathematics for Neuroscientists Gabbiani and Cox 2010, @UT Library
MATLAB tutorials:
Mathworks tutorial page
Matlab plotting basics
Matlab primer (pdf)
course schedule
DateTopic Reading/Supp Material Homework
Thur 8.28 Preliminaries: Introduction to course aims. Linear algebra, vectors: Cricket cercal system. Textbook Secs 1.3, 1.4, slides (pptx). Supplemental reading (optional): Review article on the cercal system (pdf)
Fri 8.29, 11-12pm and 4-5pm
@SEA 2.122
MATLAB tutorial part I Tutorial I slides, test.m file with examples
Tues 9.02 Linear algebra: Vector spaces.
Tues 9.02, 6-7pm and 7-8pm
@SEA 2.122
MATLAB tutorial part II Tutorial II slides Homework 1 assigned
Thur 9.04 Linear algebra: matrices, matrix products, intro to trichromacy. Linear algebra primer and slides. (Optional: more detailed Linear algebra primer II, pp. 1-15.)
Fri 9.5, 4-5pm and 7-8pm
@SEA 2.122
MATLAB tutorial part III Tutorial III slides
Tues 9.09 Decoding the Cercal system response (population vector). Systems of linear equations, exact solution. Supplemental reading (optional): Article on decoding the cercal system (pdf) Homework 2 assigned Datafiles Sample matlab file for decoding
Thur 9.11 Under- and over-determined systems: Pseudoinverse solution.
Tues 9.16 Coding session, interim review. Homework 3 assigned Datafile
Thur 9.18 Pseudoinverse as linear least-squares regression (overdetermined) or picking smallest L2-norm solution (underdetermined). Intro to non-linear least-squares regression.
Tues 9.23 Overfitting and cross-validation in non-linear regression. Back to linear systems: correlation and covariance. Slides similar to material we covered in class Homework 4 assigned Datafiles and matlab code
Thurs 9.25 Linear dependence: Variance, covariance, and the Pearson correlation coefficient. Linear regression on a single pair of variables in terms of covariance.
Tues 9.30 Covariance matrices. Cross-correlation and autocorrelation functions. Analyzing temporal structure in spike trains. Notes on cross-correlation and covariance (from Seung) Homework 5 assigned Datafile
Thurs 10.02 Convolution and applications: smoothing, generating rates from spike trains. Notes on cross-correlation and covariance (from Seung)
Tues 10.07 Convolution and applications: Mach bands, edge-detection in the retina. Supplemental readings (optional): Hartline Nobel address on Limulus retina, Mach bands; Marr article on edge detection. Homework 6 assigned Matlab code to generate data
Thur 10.09 Convolution review, more examples. Q&A for midterm.
Tues 10.14 In-class midterm No new homework
Thur 10.16 Wiener-Hopf equations (reverse correlation) and the spike-triggered average.
Tues 10.21 Eigenvalues, eigenvectors and the spectral theorem. Homework 7 assigned Matlab code to generate data
Thur 10.23 Change of basis. PCA and applications. Supplemental reading on PCA (optional): Shlens Tutorial. Sound separation demo (ICA): Readme file, Demo files.
Tues 10.28 Dimensionality reduction, denoising with PCA. Intro to probability. Homework 8 assigned Datafiles and matlab code
Thur 10.30 Discrete probability distributions. Bayes Rule.
Tues 11.04 Common probability distrubtions and densities in Neuroscience.
Thur 11.06 Maximum likelihood estimation. Homework 9 assigned Datafiles and matlab code
Tues 11.11 Nernst potential and subthreshold neural dynamics. Textbook chapter 2 (excluding 2.5), Section 3.4
Thur 11.13 Analytical and numerical integration of the membrane voltage equation. Textbook Sections 2.5, 3.1, 3.4-3.5 Homework 10 assigned Matlab code
Tues 11.18 The leaky integrate-and-fire model; spike-frequency adaptation. Textbook Section 10.1
Thur 11.20 Similarities between dynamical and statistical modeling and how they differ. Simple networks: 1-neuron circuit (autapse).
Tues 11.25
Thur 11.27
Tues 12.02
Thur 12.04
Fri 12.xx
Fri 12.xx
 
further reading:
  If you leave this class with a bigger appetite for computational neuroscience (and I hope you do!), there are a number of next steps. Besides our text, I recommend reading Theoretical Neuroscience (by Dayan and Abbott; brief surveys of a large number of topics), Spikes (Rieke et al.; a monograph on information in neural activity and codes), Biophysics of Computation (Koch; a monograph focused on single-neuron biophysics), and Analysis of Neural Data (by Brown; the title says it all -- statistical analysis of neural data). These are generally upper-division undergraduate/graduate texts, but are relatively accessible nevertheless.
 
 

page maintained by Ila Fiete and Kijung Yoon