**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 |