## Quantitative Methods for Neuroscience

#### 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

NEU466_Syllabus_2020

#### Course Schedule

Date Topics Ressources Homework
01.21.2020  Preliminaries: introduction to course aims.  Cercal System ReviewMATLAB tutorial1NR_movie, NRiter1, NRiter2, NRiter3, NRiter4, NRiter5, ComplexGrid,  MatlabIntro
01.24.2020  Linear algebra: vector, inner product, system of equations MATLAB tutorial2LinAlgNotes1  PS1
01.28.2020  Linear algebra: vector space, basis, matrix product, rank MATLAB tutorial3LinAlgSlide1linAlgNotes2
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
02.25.2020 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  PS5clusters_generate_fake_3d.m
04.02.2020  PCA: application (dimensionality    reduction, denoising) PCA2_Notes  PCATutorial_Shlens
04.07.2020  Intro to Probability  Probability_Notes

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_Projectswitch_time_recording.mNecker_cube_stimulus