## basics of probability theory¶

In the context of a course in Computational Neuroscience, I am teaching a basic introduction in Probabilities, Bayes and the Free-energy principle.

Let's learn to use probabilities in practice by generating some "synthetic data", that is by using the computer's number generator.

## 2017-01-15 Bogacz (2017) A tutorial on free-energy

I enjoyed reading "A tutorial on the free-energy framework for modelling perception and learning" by Rafal Bogacz, which is freely available here. In particular, the author encourages to replicate the results in the paper. He is himself giving solutions in matlab, so I had to do the same in python all within a notebook...

## generating databases¶

A set of bash code to resize images to a fixed size.

Problem statement: we have a set of images with heterogeneous sizes and we want to homogenize the database to avoid problems when classifying them. Solution: ImageMagick.

We first identify the size and type of images in the database. The database is a collection of folders containing each a collection of files. We thus do a nested recursive loop:

## 2016-11-24 Using generators in Python

Let's explore generators and the yield statement in the python language...

## 2016-11-17 Finding extremal values in a nd-array

Sometimes, you need to pick up the $N$-th extremal values in a mutli-dimensional matrix.

Let's suppose it is represented as a nd-array (here, I further suppose you are using the numpy library from the python language). Finding extremal values is easy with argsort but this function operated on 1d vectors... Juggling around indices is sometimes not such an easy task, but luckily, we have the unravel_index function.

Let's unwrap an easy solution combining these functions:

## 2016-11-15 Saving and displaying movies and dynamic figures

It is insanely useful to create movies to illustrate a talk, blog post or just to include in a notebook:

In [1]:
from IPython.display import HTML
HTML('<center><video controls autoplay loop src="../files/noise.mp4" width=61.8%/></center>')

Out[1]:

For years I have used a custom made solution made around saving single frames and then calling ffmpeg to save that files to a movie file. That function (called anim_save had to be maintained accross different libraries to reflect new needs (going to WEBM and MP4 formats for instance). That made the code longer than necessary and had not its place in a scientific library.

Here, I show how to use the animation library from matplotlib to replace that

## 2016-10-01 A pi-pie named Monte Carlo

A lively community of people including students, researchers and tinkerers from Marseille (France) celebrate the so-called "π-day" on the 3rd month, 14th day of each year. A nice occasion for general talks on mathematics and society in a lively athmosphere and of course to ... a pie contest!

I participated last year (in 2016) with a pie called "Monte Carlo". Herein, I give the recipe by giving some clues on its design... This page is a notebook - meaning that you can download it and re-run the analysis I do here at home (and most importantly comment or modify it and correct potential bugs...).

## 2016-10-01 Une tarte au pi nommée Monte Carlo

Une active communauté d'étudiants, chercheurs et bidouilleurs célèbrent à Marseille la "journée π" le 3ème mois, 14ème jour de chaque année. Une occasion de rêve pour en apprendre plus sur les mathématiques et la science dans une ambiance conviviale... Mais c'est aussi l'occasion d'un concours de tartes!

J'ai eu l'opportunité d'y participer l'an dernier (soit pour l'édition 2016) avec une tarte appelée "Monte Carlo". Je vais donner ici la "recette" de ma tarte, le lien avec le nombre π et quelques digressions mathématiques (notament par rapport à la présence incongrue d'un éléphant mais aussi par rapport à la démarche scientifique)... Cette page est un "notebook" - vous pouvez donc la télécharger et relancer les analyses et figures (en utilisant python + jupyter). C'est aussi un travail non figé - prière de me suggérer des corrections!

When studying a multi-dimensional random variable, if these are guassian the norm if the vector follows a $\chi$ distribution (see http://en.m.wikipedia.org/wiki/Chi_distribution).