Course content and aim
This course will provide a broad introduction to basic mathematical and computational tools for a quantitative analysis of neural systems. Integrated lectures, MATLAB sessions, and homework sets will introduce techniques and help us learn to apply them. We will cover a range of topics, including neural encoding and decoding, population codes, filtering, correlation, convolution, spike-triggered averaging (reverse correlation), deconvolution, and dimensionality reduction, clustering, and spike-sorting through principal components analysis, as well as some probability and Bayesian inference, as used in neuroscience. The goal is to help develop a level of intuitive and practical comfort with quantitative methods and visualization of complex data.
Time & Place
Tuesday/Thursday 11:00 a.m. 12:30 p.m. GDC 5.304, 3:30 p.m. 5:00 p.m. WEL 2.128.
Office hours
Tuesday 5:00p.m.-6:00p.m. and Thursday 12:30p.m.-13.30p.m. @ NHB 4.344.
Syllabus
Tutorials
MathWorks – Tutorial
Matlab – Primer
Course Schedule
| Date | Topics | Ressources | Homework |
|---|---|---|---|
| 01.21.2020 | Preliminaries: introduction to course aims. | Cercal System Review, MATLAB tutorial1, NR_movie, NRiter1, NRiter2, NRiter3, NRiter4, NRiter5, ComplexGrid, MatlabIntro | |
| 01.24.2020 | Linear algebra: vector, inner product, system of equations | MATLAB tutorial2, LinAlgNotes1 | PS1 |
| 01.28.2020 | Linear algebra: vector space, basis, matrix product, rank | MATLAB tutorial3, LinAlgSlide1, linAlgNotes2 | |
| 01.30.2020 | Overfitting and cross-validation. | FittingSlides | |
| 02.04.2020 | Variance, covariance, and the Pearson correlation coefficient. | StatSlides | PS2 |
| 02.06.2020 | Time-series: cross- and auto-correlation. | CorrSlides1 | |
| 02.11.2020 | Analyzing temporal structure in spike trains. | CorrSlides2 | PS3, c1p8.mat , gridcell_halfmsbins.mat |
| 02.13.2020 | Spike-triggered average | STA_Slides | |
| 02.18.2020 | Convolution and applications: Mach bands, edge-detection in the retina. | ConvSlides | MarrHildreth80 |
| 02.20.2020 | Wiener-Hopf equations. | WH_Slides1 | PS4, generate_STAdata.mt |
| 02.25.2020 | Reverse correlation analysis. | WH_Slides2 | |
| 02.27.2020 | No class. | ||
| 03.03.2020 | Linear least-squares regression. | LSR_Notes | |
| 03.05.2020 | Eigenvalues, eigenvectors, and the spectral theorem. | ||
| 03.10.2020 | Review, more examples, Q&A for midterm. | ||
| 03.12.2020 | In-class midterm. | ||
| 03.17.2020 | Spring Break. | ||
| 03.19.2020 | Spring Break. | ||
| 03.24.2020 | Online troubleshooting | ||
| 03.26.2020 | Review on eigenvalues, eigenvectors, and the spectral theorem. | ||
| 03.31.2020 | PCA: theory. | PCA1_Notes | PS5, clusters_generate_fake_3d.m |
| 04.02.2020 | PCA: application (dimensionality reduction, denoising) | PCA2_Notes | PCATutorial_Shlens |
| 04.07.2020 | Intro to Probability | Probability_Notes |
PS6, SpikeSortingData.mat, HandwrittenDigits.mat, plotImage.m |
| 04.09.2020 | Bayes rules | ||
| 04.14.2020 | Maximum Likelihood | PS7, linearneuron1.mat,linearneuron2.mat | |
| 04.16.2020 | Final project discussion | Moreno-Bote | |
| 04.21.2020 | Modeling: Dynamical system | Dynamics_Notes | |
| 04.23.2020 | Modeling: Noisy dynamics | Noise_Notes | |
| 04.28.2020 | Modeling: Simulation | ||
| 04.30.2020 | Fourier analysis: theory | Fourier_Notes | |
| 05.05.2020 | Fourier analysis: application | ||
| 05.07.2020 | Final_Project, switch_time_recording.m, Necker_cube_stimulus |