#
Computational Science Major

Master 1 courses

# 1st Semester

## Shared courses

**Organisation: **TD (18h)

**Lecturers: ** Julien Lefèvre

**Evaluation:** projects and oral presentation

The teaching unit consists of a presentation of the main professions involved in biological modelling. It will be carried out in two ways. First of all, some seminars will be offered with speakers from outside Aix-Marseille University in the academic and industrial field. Secondly, students will benefit from an immersion in Centuri laboratories where they will discover multidisciplinary research topics. To conclude this unit, students will be asked to present a specific problem related to data processing and modelling. The scientific aspect will also have to be integrated into a reflection on the underlying professional issues, whether in the academic or private sector

**Organisation: **Lectures (6h), TD (6h), TP (6h)

**Lecturers: ** Sylvain Sené, Elisabeth Remy

**Evaluation:** projects and final written exam

This course is an introduction to the basics of finite dynamic systems and PLC networks (definitions of local functions, global function/relationship, automata, interaction graph, transition graph) as well as the main static and dynamic properties. A part of the lecture will also focus on the parallel update mode.

The lectures should provide students the skills to implement modelling approaches (differential, logical, stochastic or deterministic equations) to develop mathematical models of a biological system, analyze mathematical models and biological data to understand complex systems, evaluate the adequacy between a biological question, available data, and mathematical formalisms and interpret and validate a study.

**Organisation: **Lectures (18h)

**Lecturers: ** Thomas Lecuit, Jacques van Helden, Michael Kopp, Laurence Röder, François Muscatelli

**Evaluation:** final written exam

This course is divided in 2 parts taught during the 1^{st} and 2^{nd} semester of CMB. The first part of this module is a presentation of the evolutionary theories that have founded modern biology (from Lamarck to Darwin), and a synthesis of the discoveries that have led to current concepts of molecular and cellular biology: the role of macromolecules in cell function (information transfer between DNA, RNA, proteins, regulation, etc.), heredity and cellular adaptation.

Examples topics covered during the lectures:

- Information, evolution causes for living organisms
- Cellular information
- Epigenetics – phenomenons, information, adaptation, mechanisms

**Organisation: **Lectures (14h), TP (16h)

**Lecturers: ** Laurent Pézard

**Evaluation:** projects and final written exam

Computational biology will introduce the biological concepts necessary to model complex systems, implement modelling approaches (differential, logical, stochastic or deterministic equations) to develop mathematical models of a biological system, analyze mathematical models and biological data to understand complex systems and assess the adequacy between a biological question.

The course is divided in 2 sections:

- computational neuroscience: dynamic models of neuron function: dynamic behavioural simulation, biological aspects, computer complexity, analytical aspects
- bioinformatics: alignment, molecular phylogeny, prediction and modelling of structural aspects of proteins, cis-regulation

**Organisation: **Lectures (12h), TD (12h), TP (12h)

**Lecturers: ** Jacques van Helden, Charlotte Perrin

**Evaluation:** projects and final written exam

*This course is divided in 2 parts.*

**Probability and statistics for modeling 1**

The first part of this course is a quick revision of the basics of probability and statistics. The concepts will be taught in relation to concrete biology exemples (genome analysis, complex systems). The following concepts will be taught:

- Combinatorial analysis
- Probabilities concepts
- Discrete laws (Bernoulli, géométrique, hypergéométrique, binomiale, Poisson)
- Quick review of the basic continuous laws (normale, Student)
- Estimation and sampling
- Hypothetical tests

**Continuous dynamical systems and modeling, examples**

The purpose of this course is to introduce some of the simplest differential equations and systems of differential equations which underlie the main continuous models used in biology (dynamics of populations or cells, biochemical processes, etc.). We will address both qualitative (long-time behavior) and quantitative (positivity, parameter dependency) properties of the considered models. In parallel to this theoretical study, numerical simulations will be performed during the computer sessions. Practicals will consist in using Python specialised libraries as scipy.integrate in order to visualise trajectories and systems behaviours.

## Computational Science courses

**Organisation: **Lectures (12h), TD (12h), TP (12h)

**Lecturers:** Kevin Perrot, Giuseppe Di Molfetta

**Evaluation:** continuous monitoring, projects and final written exam

When we define neatly and consider the set of "algorithms" (Turing machines) and the set of "things an algorithm may compute" (functions), we can notice, thanks to an argument from the 19th century (Cantor's diagonal), that there are strictly more "things to compute" than "algorithms to compute them". Then what are these things a computer cannot compute?

This course will teach the basics of computational complexity and answer to the following questions: within the set of computable things, how to define the hardness of a "thing to compute" (aka problem)? When defined neatly (again some maths), these questions raise fundamental open problems of our century, such as the famous 1,000,000 usd question mark: does P equal NP?

You will also be given the tools to say: "this problem is reasonably solvable on a computer" (in P) or "this one is not" (NP-hard).

**Organisation: **Lectures (18h), TD (18h), TP (18h)

**Lecturers:** Pablo Arrighi, Kevin Perrot, Laurent Tichit

**Evaluation:** continuous monitoring, projects and final written exam

What is useful to know in order to lead a large software project? This course will give you the answer to this question by covering the essential technical aspects (versioning with git, building with gradle, testing with Junit...); methodological aspects (pricing estimates, the phases of the V-diagram, agile project management, free software methods...) and conceptual aspects (test coverage, UML, design patterns...) of the issue. The concepts of the lectures are put in practice via concrete projects.

# 2nd Semester

## Shared courses

**Organisation: **Lectures (12h)

**Lecturers: ** Bianca Habermann, Laurent Tichit

**Evaluation:** project and continuous monitoring

Scientific seminars constitute a good way to broaden your scientific horizon. In this regard, MSc students will frequently attend CENTURI seminars. At the end of the semester, students will be asked to write a summary of two seminars they have attended.

The students will learn to work in an interdisciplinary group, to deepen a subject and to communicate on it.

**Organisation: **Lectures (12h), TD (12h)

**Lecturers: ** François Muscatelli, Thomas Lecuit, Dominique Payet, Guillaume Voisinne, Valery Matarazzo, Julie Koenig

**Evaluation:** final written exam

The second part of this module will show how these molecular mechanisms underlie the development and functioning of tissues and organisms. It will be structured around four areas: intergenerational transmission of traits; organism development; immune system and nervous system.

Examples topics covered during the lectures:

- Information and organization: intergenerational transmission (cells, organisms Information, evolution causes for living organisms)
- Organisms’ development
- Information and organization of the immune system
- Information and organization of the nervous system

**Organisation: **Lectures (12h), TD (12h), TP (12h)

**Lecturers: ** Victor Chepoi, Kolja Knauer

**Evaluation:** projects and final written exam

*This course is divided in 2 parts.*

**Statistics for biology**

Statistics for biology aims at providing students with a practical approach of the analysis of biological data with R, based on the concepts acquired in the course “Probabilities and statistics for modelling 1”. The associated mathematical foundations will be developed in the course “Advanced statistics”.

- Sampling and estimation (moments, robust estimators, confidence intervals)
- Fitting
- Quelques distributions additionnelles
- Hypothesis testing (mean comparison, goodness of fit, …)

**Graph theory and algorythms 1**

This introductory course focuses on graphs as mathematical objects and some of its uses to solve applications to biological networks. After intruducing different classes of graphs and their properties, the following points will be developped:

- Planar graphs, graphs on a surface, Euler characteristic
- Interval graphs, perfect graphs

**Organisation: **Project

**Evaluation:** project

At the end of the courses Professional perspectives for biological systems modelling, and Fundamentals of biology 1, students will choose a scientific article at the interface of several disciplines on which they will work in groups. They will have to present in a memory and an oral presentation, to explain the biological context and the related basic concepts, to explain the methods used to interpret the biological data, to synthesize the results obtained in the article. Through this lecture, students will learn to work in an interdisciplinary group, to deepen a subject and to communicate on it.

**Lecturers: ** Denis Puthier

**Evaluation:** projects and final written exam

*This course is divided in 2 parts.*

** Bioinformatic analysis : **TD (15h), TP (15h)

Analysis of omics data constitute a first approach towards omics data’s (e.g. DNA sequencing) high speed analysis. This course will first focus on introducing bioinformatics’ methods and their goal (e.g. quality check, positioning reads on a genome, searching for ChIP-seq’s spikes, etc.). Different kinds of files needed to proceed to these analysis will be presented, and more particularly those used in epigenomic sequencing (e.g. ChIP-seq, RNA-seq, etc.).

**Statistical analysis: **TD (10h), TP (20h)

During this course you will learn more about concepts of probability and statistics applied to biological models (e.g. epigenomic data sets). These biological models will be picked amongst the models presented in other courses.

Here are some examples:

- Statistical concepts: Fisher's exact test, hypergeometric distribution, multiple tests, unsupervised classification
- Biological models: detection of differentially expressed genes with counting data, functional enrichment analysis, classification of expression profiles

## Computational Science courses

**Organisation: **Lectures (9h), TD (9h)

**Lecturers: ** Sylvain Sené

**Evaluation:** final written exam

The lecture is composed of 2 parts:

**Discrete modeling of biological systems 2**

This specialization course on discrete modelling deals with the following:

- Details on non-parallel update modes (both determinists - periodic or not and non-deterministic - asynchronous or elementary)
- Presentation of "classical" models, methods and results (theorems of stability, instability and any other results that appears relevant).

**Graph theory and algorithms 2**

This specialization course helps the student to deepen his knowledge on problems on graphs and their solutions:

- Counting and enumeration: number of covering trees, number of couplings of a planar graph
- Flow algorithms
- Problems of connection, coupling, assignment, transport