## 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 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

NEU466 – Syllabus

#### Course Schedule

Date Topics Ressources Homework
01.18.2018  Preliminaries: introduction to course aims.  Cercal System ReviewMATLAB tutorial1NR_movie, NRiter1, NRiter2, NRiter3, NRiter4, NRiter5, ComplexGrid,  MatlabIntro
01.23.2018  Linear algebra: vector, inner product, system of equations MATLAB tutorial2lecture_LinAlg1, LinAlgNotes, notes  PS1
01.25.2018  Linear algebra: vector space, basis, matrix product, rank MATLAB tutorial3, lecture_LinAlg2
01.30.2018 Linear least-squares regression. Overfitting and cross-validation.  lecture_Mod  PS2
02.01.2018 Variance, covariance, and the Pearson correlation coefficient.  lecture_Corr
02.06.2018 Time-series: cross- and auto-correlation.  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, edge-detection 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 Wiener-Hopf equations (reverse correlation) and the spike-triggered average  lecture_WH  PS5,
plant.mat
02.22.2018  System of linear equations. Under/over-determined systems.  lecture_LSR
02.27.2018  Pseudo-inverse solution.
03.01.2018 Eigenvalues, eigenvectors and the spectral theorem.
03.06.2018 Review, more examples, Q&A for midterm.
03.08.2018  In-class 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 integrate-and-fire model, spike-frequency adaptation. PROJECTS.
04.24.2018  Dynamical systems. Stability of fixed points. Graphical stability analysis. PROJECTS. final_project, moreno-bote-jnphys,
switch_time_recording.mNecker_cube_stimulus
04.26.2018  Fourier series: sines and cosines as a basis set for periodic functions. Filtering and denoising. PROJECTS. adapt_script.m ,
noise_script.m
05.01.2018  Fourier transforms. Identifying frequency content of a signal. Convolution as product. PROJECTS.
05.03.2018  Course evaluations. PROJECTS.