Mathematical Tools for Neural Science
| Instructor: | Eero Simoncelli |
| TA: | Zang (Jenny) Li |
| Lectures: | Monday/Wednesday 9-11am, Meyer 813 |
 |
| Instructor: | Eero Simoncelli |
| TA: | Zang (Jenny) Li |
| Lectures: | Monday/Wednesday 9-11am, Meyer 813 |
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| Date | Topic | Handouts | Homework |
| Sep 5 |
Linear Algebra I: vector spaces, linear systems |
Course Description (pdf) Background Poll (pdf) Geometric LinAlg Review (pdf) |
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| Sep 10 |
Linear Algebra II: linear transforms, matrices, SVD |
HW 1 (pdf),
due Sep24/Oct1 plotVec (m), colmatch (mat) |
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| Sep 12 |
Matlab Intro, in Meyer 157 Rescheduled for 9/19, 5-7pm |
Matlab primer (pdf) | |
| Sep 17 |
Matrix Inversion Color Matching |
Wandell, ch 4 (hc) | |
| Sep 19 | Hodgkin-Huxley [Rinzel] | HH Lecture Notes (hc) | |
| Sep 24 | Cable Equation [Tranchina] | Tranchina HW (hc) due Oct 8 |
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| Sep 26 |
Color Matching / Trichromacy Optimization intro |
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| Oct 1 |
Optimization I: Least Squares Regression |
Least Squares (pdf) | Rinzel HW (pdf), due Oct 15 ODE descriptions (txt) |
| Oct 3 | Phase Plane Analysis [Rinzel] | ||
| Oct 8 |
Optimization II: Total Least Squares Rayleigh Quotient |
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| Oct 10 |
Optimization III: Linear/Quadratic Constraints Fisher Linear Discriminant |
HW 2 (pdf), due Oct 19 (extended) regress1 (mat), regress2 (mat), wtdDataSet (mat), outlierData (mat) | |
| Oct 15 |
Eigenvectors [Li] Linear shift-invariant systems Convolution |
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| Oct 17 |
Sinusoids/complex exponentials Fourier Transform(s) |
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| Oct 22 |
Fourier Transform Family: details/examples |
HW 3 (pdf), due Oct 31 PCA (mat), constrainedLS (mat), fisherData (mat), plotVec (m), cconv2 (m), bandlimitedSigs (mat) |
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| Oct 24 |
Fourier Transform: Properties, Convolution theorem |
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| Oct 29 | Fourier Transform: Examples, LSI charactization | ||
| Oct 31 |
Fourier Transform: Sampling Theorem |
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| Nov 5 |
Probability Basics: densities, marginals, conditionals Gaussian examples |
Linear Systems (HC) | HW4 (txt) (due Nov 9) mkSine (m), mkRamp (m) |
| Nov 7 |
Statistical estimation: Maximum Likelihood. |
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| Nov 12/14 | BREAK: Society for Neuroscience Meeting | ||
| Nov 19 |
Estimation II: MAP, Bayes Examples |
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| Nov 21 |
Estimation III: Statistical tests, Bootstrapping |
DRAFT: Probability and Statistics (hc) Efron Bootstrapping (hc) |
HW5 (pdf) (due Dec 3) mkGaussian (m), blackBox (m) |
| Nov 26 |
Bootstrapping example: Basics of Statistical Decision Theory |
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| Nov 28 | Signal Detection Theory [Rubin] | ||
| Dec 3 |
More on ROC Decisions with Neurons |
HW6 (pdf) (due Dec 17) Nava's SDT problem (MS-word) neurometricData (mat), simulateSNL (m), makeWhiteNoise (m) |
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| Dec 5 |
BREAK: Neural Information Processing Systems (NIPS) Meeting |
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| Dec 7 |
Simple neural models: linear/nonlinear, Poisson White noise analysis |
Chichilnisky article (pdf) | |
| Dec 10 |
Reading spike trains PSTH, JPSTH, Correlograms |
Brody article (pdf) |
Electronic:
- Sam Roweis' Tutorial notes
- On-line Glossary of Statistical Pattern Recognition
- Wolfram Research World of Mathematics
Dead Trees:
- Computationa/Theoretical Neuroscience:
Theoretical Neuroscience , by Peter Dayan and Larry Abbott. MIT Press, 2001.
- Linear Algebra / Least Squares:
Linear Algebra Appendix from PDP series, by Michael Jordan.
Linear Algebra and Its Applications, by Gilbert Strang. Academic Press, 1980.- Linear (shift-invariant) Systems
Discrete-time Signal Processing, by Alan Oppenheim and Ron Schafer. Prentice Hall, 1989.- Probability/Statistics:
Fundamentals of Applied Probability Theory , by Alvin Drake. McGraw-Hill, 1988.- Decision Theory:
Biology: Signal Detection Theory and Psychophysics, by David Green & John Swets. Peninsula Publishing, 1988.
Math: Statistical Decision Theory, by James O. Berger. Springer-Verlag, 1980.- Bootstrap/Resampling:
An Intoduction to the Bootstrap, by Bradley Efron and Robert Tibshirani. Chapman & Hall, 1998.
Resampling Methods: A practical guide to data analysis, by Phillip Good. Birkhäuser, 1999.- Spikes, Neural Coding, Reverse Correlation:
Spikes: Exploring the Neural Code, by Fred Rieke, David Warland, Rob De Ruyter, & Bill Bialek. MIT Press, 1997.
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| Revised: 10 December 2001. |
Feedback/comments to: eero AT cns.nyu.edu |
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