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, spiketriggered averaging (reverse correlation), deconvolution, and dimensionality reduction, clustering, and spikesorting 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 6.202, 3:30 p.m. 5:00 p.m. WEL 2.128.
Office hours
Tu 12:30p.m.1:30p.m. and Wed 12:00p.m.12.30p.m. @ NHB 3.128.
Syllabus
Tutorials
MathWorks – Tutorial
Matlab – Primer
Course Schedule
Date  Topics  Ressources  Homework 

01.18.2018  Preliminaries: introduction to course aims.  Cercal System Review, MATLAB tutorial1, NR_movie, NRiter1, NRiter2, NRiter3, NRiter4, NRiter5, ComplexGrid, MatlabIntro  
01.23.2018  Linear algebra: vector, inner product, system of equations  MATLAB tutorial2, lecture_LinAlg1, LinAlgNotes, notes  PS1 
01.25.2018  Linear algebra: vector space, basis, matrix product, rank  MATLAB tutorial3, lecture_LinAlg2  
01.30.2018  Linear leastsquares regression. Overfitting and crossvalidation.  lecture_Mod  PS2 
02.01.2018  Variance, covariance, and the Pearson correlation coefficient.  lecture_Corr  
02.06.2018  Timeseries: cross and autocorrelation.  lecture_XCorr  PS3, c1p8.mat , gridcell_halfmsbins.mat 
02.8.2018  Analyzing temporal structure in spike trains.  lecture_STA  
02.13.2018  Convolution and applications: Mach bands, edgedetection in the retina.  lecture_Conv  PS4, generate_STAdata.m 
02.15.2018  Convolution and applications: smoothing, generating rates from spike trains.  lecture_Stat  
02.20.2018  WienerHopf equations (reverse correlation) and the spiketriggered average  lecture_WH  PS5, plant.mat 
02.22.2018  System of linear equations. Under/overdetermined systems.  lecture_LSR  
02.27.2018  Pseudoinverse solution.  
03.01.2018  Eigenvalues, eigenvectors and the spectral theorem.  
03.06.2018  Review, more examples, Q&A for midterm.  
03.08.2018  Inclass midterm.  
03.13.2018  Spring Break.  
03.15.2018  Spring Break.  
03.20.2018  Change of basis. PCA and applications.  lecturePCA  PS6, clusters_generate_fake_3d.m 
03.22.2018  Dimensionality reduction, denoising with PCA. Intro to probability.  PCA_Shlens, PCA.m 

03.27.2018  Common probability distrubtions and densities in Neuroscience.  PS7, SpikeSortingData.mat, HandwrittenDigits.mat, plotImage.m 

03.29.2018  Bayes Rule.  
04.03.2018  
04.05.2018  Maximum likelihood estimation.  PS8  
04.10.2018  Introduction to information theory.  
04.12.2018  Nernst potential and subthreshold neural dynamics.  PS9, linearneuron1.mat, linearneuron2.mat, linearneuronBernoulli.m 

04.17.2018  Analytical and numerical integration of the membrane voltage equation. PROJECTS.  
04.19.2018  The leaky integrateandfire model, spikefrequency adaptation. PROJECTS.  
04.24.2018  Dynamical systems. Stability of fixed points. Graphical stability analysis. PROJECTS.  
04.26.2018  Fourier series: sines and cosines as a basis set for periodic functions. Filtering and denoising. PROJECTS.  
05.01.2018  Fourier transforms. Identifying frequency content of a signal. Convolution as product. PROJECTS.  
05.03.2018  Course evaluations. PROJECTS. 