G80.2221, Fall Semester, 2002

Mathematical Tools for Neural Science

Instructor: Eero Simoncelli
TA: Brian Lau
Lectures: Monday/Wednesday 9-11am, Meyer 813

Brief Description:

A graduate course covering basic mathematical techniques for analysis and modeling of neural data and neural systems. Topics to include: Linear algebra, least-squares and total-least-squares regression, eigen-analysis and PCA, linear shift-invariant systems, Fourier transforms, sampling, ordinary differential equations, coupled differential equations, basics of estimation and decision theory, hypothesis testing, bootstrapping, models of neural spike generation, white noise (reverse-correlation) analysis.

Schedule / Handouts

Date Topic Handouts Homework
Sep 4 Linear Algebra I:
vectors, inner products		 Course Description (pdf)
Background Poll (pdf)
  
Sep 6 Special lab session I: intro to matlab
in room 1023 Meyer at 2:30PM		    
Sep 9 Linear Algebra II:
linear transforms, matrices		 Linear Algebra (pdf) HW 1 (pdf), due Sep 18
plotVec (m), mtxExamples (mat, or m)
Sep 11 diagonal / orthogonal matrices
singular value decomposition		    
Sep 6 Special lab session II: more matlab
in room 1023 Meyer at 3PM		 Matlab primer (pdf)
online documentation (html)
U. Utah (pdf)
UNH (html) 		 
Sep 16 No class (Yom Kippur)    
Sep 18 Hodgkin-Huxley Model
[Shapley] 		   
Sep 23 Cable Equations
[Tranchina] 		   
Sep 25 Examples: color matching
& Trichromacy 		  HW 2 (pdf), due Oct 2
colmatch (mat),
Sep 30 Regression I:
least squares 		Least Squares (pdf)  
Oct 2 Regression II:
total least squares, PCA 		  HW 3 (pdf), due Oct 9
regress1 (mat), regress2 (mat), outlierData (mat)
Oct 7 Regression III:
Linear & quadratic constraints 		   
Oct 9 Classification, Fischer linear discrim.    
Oct 14 Linear shift-invariant systems Linear Systems (pdf) HW 4 (pdf), due Oct 21
PCA (mat), constrainedLS (mat),
fisherData (mat)
Oct 16 Sinusoids & LSI systems    
Oct 21 Fourier Transform    
Oct 23 Convolution Theorem    
Oct 28 Convolution: examples and properties   HW 5 (pdf), due Nov 4
bandLimitedSigs (mat), cconv2 (m), mkSine (m)
Oct 30 Sampling, Nyquist Theorem    
Nov 2,4 No Class (Annual Neuroscience meeting)    
Nov 11 Probability I: Random variables,
random vectors, expectations 		   
Nov 13 Probability II: moments, Gaussians    
Nov 18 Estimation I:
models, experiments, statististics 		   
Nov 20 Poisson processes
Reverse correlation 		Chichilnisky paper on
white noise analysis (pdf) 		 
Nov 25 Estimation II: ML,MAP,Bayes   HW 6 (pdf), due Dec 4
makeWhiteNoise (m), simulateSNL (m)
Nov 27 Estimation III: bias/variance, bootstrapping Efron intro chapter
on bootstrapping (hc)		  
Dec 2 Decision theory:
Likelihood ratios, prior/loss, threshold rules 		   
Dec 4 Signal detection theory:
hit/miss/FA/CR, d', ROC, 2AFC 		Signal detection theory (hc) HW 7 (pdf), due Dec 13
measure (m), neurometricData (mat)
Dec 9 Neural decisions [Lau]    


Additional Resources

Electronic:

Dead Trees:

Revised: 23 September 2003. Feedback/comments to:
eero AT cns.nyu.edu		 Top of page