Quantitative methods in neuroscience

Neuro 545/PBIO 545

M/Th 12:30-1:50, G328 HSB

Date Topic and Handouts

Reading and Discussion topics


Linear Algebra

some logistics

linear algebra primer from Eero Simoncelli

Dean Pospisil's primer

Linear transformations on Wikipedia

Column space demo from class (note: requires some files from linear algebra tutorial - get those first)


Linear Algebra part 2

link to videos


linear algebra tutorial normrnd PlotVector Plot3DVector statsizechk

note: you need all five files; make sure they are all on Matlab's path. You may already have normrnd and statsizechk if you have the statistics toolbox.

Markov chain slides (optional part of tutorial)

ColorSpace HW: script cone spectra monitor spectra


Journal club




Wandell, Foundations of Vision, Chapter 4 (good intro) or here: https://foundationsofvision.stanford.edu/chapter-4-wavelength-encoding/

Baylor, Nunn and Schnapf (1987) J Physiol 390:145-160. (primary paper)

http://graphics.stanford.edu/courses/cs178/applets/colormatching.html (introduction to color matching)


Introduction to the Theory of Stochastic Processes

Howard Berg, Random Walks in Biology, Appendix A
Koch, Chapter 15
Duda, Hart and Stork, Pattern Classification (2nd edition), Appendix 4

probability basics tutorial


Introduction to the Theory of Stochastic Processes: Discussion

Stochastic Processes Tutorial

accessory files (note: make sure they are all on Matlab's path)

Moment generating functions tuturial (you need both files in folder)

Kemeny and Snell, Finite Markov Chains




Journal club:


Shadlen et al (primary paper for discussion)

de la Rocha et al. (supplement re how correlated activity is shaped)


Fourier Analysis, Filters and Convolution

link to videos

Press et al., Numerical Recipes, pages 496-508 (2nd edition, this is beginning of Ch. 12); Ch. 13
Koch, Biophysics of Computation, Appendix B
Wandell, Foundations of Vision, Appendix A (a mix of linear algebra and linear systems stuff).

graphical convolution tutorial


Fourier Analysis, Filters and Convolution: Discussion

Fourier analysis tutorial

linear systems primer from Eero Simoncelli (note this is not the same as the linear algebra one above - has a lot of Fourier stuff in it).

linear systems primer from David Heeger

Partha Mitra’s open source Matlab code for spectral analysis, with links to online tutorials: http://chronux.org/home/

spectral analysis notes from Kleinfeld


Journal club:



methods paper (read first): Betzig

discussion paper: Dani

supplementary: Xu


Class Discussion and module wrapup





Differential equations and neural dynamics

notes on integrating linear differential equations

link to videos

Howard Berg, Random Walks in Biology, Appendix B
Hugh Wilson, Spikes, Decisions and Actions, Chapters 1, 2, 3
Wilson, Chapter 5 (numerical methods)


Differential equations and neural dynamics: Discussion


Simulink tutorial (optional)


Journal club:


Robinson (primary paper)

Fuchs, Scudder and Kaneko (physiological counterpart to Robinson paper)


Supplementary material:

Vilis material part 1

Vilis material part 2

2/27 PCA and Dimensional Reduction

PCA tutorial

Shlens PCA review

rgc spike data

single photon response data

3/2 PCA and Dimensional Reduction: Discussion

Journal club:




Rust et al (primary discussion paper)

Yang Dan complex cell paper

Simoncelli chapter (good intro to PCA and friends)

Golomb LGN paper

Horwitz V1 paper


Class Discussion and module wrapup


Instructors and contact info:

Adrienne Fairhall fairhall@uw.edu
Fred Rieke rieke@uw.edu
Wyeth Bair wyeth.bair@gmail.com
Abhishek De abhisd@uw.edu


Course project:

suggested projects

Computers, etc:

Computers with MATLAB are available in the PBIO computer room and the Neuroscience office.

Contact one of us if you are having problems finding a machine you can use.

Useful links:

site for Theoretical Neuroscience, Dayan and Abbott (see Exercises)

Vilis web site

Mathematical details of Fourier analysis from Wolfram Research

Fourier transform primer (vision centered)