**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**

**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, notes | |

01.23.2018 | Linear algebra: vector, inner product, system of equations | MATLAB tutorial2, lecture1, LinAlgNotes, notes | PS1 |

01.25.2018 | Linear algebra: vector space, basis, matrix product, rank | MATLAB tutorial3, lecture2 | |

01.30.2018 | Linear least-squares regression. Overfitting and cross-validation. | lecture3 | PS2 |

02.01.2018 | Variance, covariance, and the Pearson correlation coefficient. | lecture4 | |

02.06.2018 | Time-series: cross- and auto-correlation. | lecture5 | PS3, c1p8.mat , gridcell_halfmsbins.mat |

02.8.2018 | Analyzing temporal structure in spike trains. | lecture6 | |

02.13.2018 | Convolution and applications: Mach bands, edge-detection in the retina. | lecture7 | PS4, generate_STAdata.m |

02.15.2018 | Convolution and applications: smoothing, generating rates from spike trains. | lecture8 | |

02.20.2018 | Wiener-Hopf equations (reverse correlation) and the spike-triggered average | lecture9 | PS5, plant.mat |

02.22.2018 | System of linear equations. Decoding the cercal system response. | ||

02.27.2018 | Under/over-determined systems: 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. | ||

03.22.2018 | Dimensionality reduction, denoising with PCA. Intro to probability. | ||

03.27.2018 | Discrete probability distributions. Bayes Rule. | ||

03.29.2018 | Common probability distrubtions and densities in Neuroscience. | ||

04.03.2018 | |||

04.05.2018 | Maximum likelihood estimation. | ||

04.10.2018 | Introduction to information theory. | ||

04.12.2018 | Nernst potential and subthreshold neural dynamics. | ||

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. | ||

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. |