Computational Neuroscience Crash Course (2020)
Given the increasing complexity of neural data and the generalized use of theoretical models in neuroscience, more and more neuroscientists rely on computationnal tools for modelling or data analysis. We would like to offer the possibility to those who feel that their maths / informatics background is a bit short to update their maths and to get familiar with basic techniques for data analysis/modelling using the Python language. The Computational Neuroscience Crash Course (CNCC) will span over two years, with a first part focusing on the maths and programming pre-requisites, and a second part next year on data analysis (and possibly modelling to follow).
For all courses (maths and programming), we'll provide some theoretical background, propose small exercices for participant to work on their own and then solve the exercices together and make sure everybody has acquired the related concepts and techniques. Courses will be taught in English.
Contact
- Arthur Leblois: [email protected]
- Nicolas Rougier: [email protected]
Important dates
This year and ue to the pandemic, the whole course will be online and this means you'll have to read the different lessons before each session, following the proposed schedule below:
Monday 15 June 2020
Make sure to have read (see below):
- Math: Linear Algebra
- Prog: Installation + Introduction
Tuesday 16 June 2020
Make sure to have read (see below):
- Math: Signal Processing + Fourier transform
- Prog: Numerical computing
Wednesday 17 June
Make sure to have read (seel below):
- Math: Fourier transform
- Prog: Scientific computing
Each morning (Monday, Tuesday and Wednesday), from 9am to 10am, we'll try to quickly highlight the main points on each lesson (15mn) and we'll take 45mn to answer any questions you may have on the lessons or the project.
The (mini) project
The goal of the project is to sort (automatically) audio files that
correspond to the recording of adult or juvenile songbirds. If you
listen to the audio files, you will hear that the sound is quite
different between an adult (song) and a juvenile (babbling). This
means we can probably process the audio files in order to decide if it
corresponds to an adult or a juvenile and the goal is thus to write a
function songsort(directory) that will automatically sort
all the files present in some-path and label them accordingly.
For the project, you'll need to team with someone else such as to work together at one computer (pair programming). When one is typing, the other is reading an commenting and for maximum efficiency, you'll have to switch roles frequently. This can be done online by sharing the screen of someone.
For the project, we'll use Jupyter notebook and we'll start with the project/introduction.ipynb notebook.
Data is available here: https://filesender.renater.fr/?s=download&token=77a5fac3-ee68-40af-baab-4b34ab09d6b8
Mathematical lessons
Linear Algebra
This course will introduce vectors and matrices, how to peform operations such as addition & multiplication on these objects. The correspondence with geometry and the resolution of a system of linear equations will be explained.
Prerequisites: None
On-line courses:
Mathematics for Computational Neuroscience: only Part 1, Chapter 2, 1-3 (ignore the least square approx in 4).
Ch4 Linear Algebra (Owen&Corrado, Stanford U)
Exercices: PDF link: https://drive.google.com/file/d/1i2xM37M35iSrTbXoNOX5qQFARRrH2MTn/view?usp=sharing
Signal Processing
We'll explain first what is the Fourier transform that is ubiquituous in signal processing, what is spectral analysis and how to compute correlation in order to reveal similarity between signals.
Prerequisites: None
On-line courses:
What is signal processing, and why ? https://www.youtube.com/watch?v=YmSvQe2FDKs
Autocorrelation and crosscorrelation : https://en.wikipedia.org/wiki/Autocorrelation & https://en.wikipedia.org/wiki/Cross-correlation (in both pages, focus on the case of ‘deterministic signals’ and ignore the case of random vectors)
Video explanation and demo : https://www.youtube.com/watch?v=_r_fDlM0Dx0
The case of neurons and spikes : https://www.med.upenn.edu/mulab/analysis.html
Fourier transforms :
https://en.wikipedia.org/wiki/Fourier_transform (up to 5.1 basic properties)
I ntuitive definition : https://sites.northwestern.edu/elannesscohn/2019/07/30/developing-an-intuition-for-fourier-transforms/ More complete definition : https://physiology.med.cornell.edu/people/banfelder/qbio/resources_2016/S.2_fourier.pdf
A video course on the basics of Fourier transform : https://www.ibiology.org/talks/fourier-transform/
To go beyond, the history and many applications of Fourier transforms : http://www.yalescientific.org/2010/12/fourier-transform-natures-way-of-analyzing-data/
Differential Equations (optional)
We'll cover first-order differential equations (that can for example describe the evolution of a membrane potential). We'll see how to analyze and solve such equation.
Prerequisites: None
See also:
Wikipedia | Differential Equations &
Mathematics for Computational Neuroscience
Programming lessons
Installation
This lesson aims at providing the student with a clean development environment, including Python installation and essential packages, a decent text editor, and a shell. We'll also introduce the Python & IPython shells, the Jupyter notebook and explains how to run a python script from the command line.
Prerequisites: None
See also: Anaconda installation
Introduction
We introduce here Python, a powerful and easy to learn programming language. It has efficient high-level data structures and a simple but effective approach to object-oriented programming (Python website). However, we'll only cover the strict minimum necessary for getting started with numerical computing.
Prerequisites: Installation
See also: Official Python tutorial & Dive into Python
Numerical computing
This lesson gives an overview of NumPy, the core library for performant numerical computing, with support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays.
Prerequisites: Introduction
See also: Scipy Lecture Notes, Numpy for Matlab users & From Python to Numpy
Data Visualization
We'll explore the matplotlib library which is a Python 2D plotting library which produces publication quality figures in a variety of hardcopy formats and interactive environments across platforms. Matplotlib can be used in Python scripts, the Python and IPython shells, the Jupyter notebook, web application servers, and four graphical user interface toolkits.
Prerequisites: Numerical computing
See also: Matplotlib tutorial, Ten Simple Rules for Better Figures
Scientific computing
This lesson, from the scipy mlecture notes, will cover scipy which is a scientific-computing libraries, such as the GSL (GNU Scientific Library for C and C++), or Matlab’s toolboxes. Scipy is the core package for scientific routines in Python; it is meant to operate efficiently on numpy arrays, so that numpy and scipy work hand in hand.
Prerequisites: Numerical computing
See also: Elegant Scipy, Python Data Science Handbook
Computational Neuroscience Crash Course (CNCC 2020)
Copyright © 2020 Arthur Leblois & Nicolas P. Rougier – CC-BY 4.0 International license.