THIS LEARNING PATH HAS BEEN DEFINITIVELY CLOSED SINCE 2019-2020.
CMB is an international Master of science dedicated to the analysis and the modelling of complex biological systems, created as a part of the graduate school of the Turing Center of living systems (CENTURI).
This Master is shared by the departments of computer science, mathematics and biology, and aims at gathering students with a high potential coming from different backgrounds and at benefiting from the interdisciplinary synergies between training experts in that scientific area on the rise.
CMB offers a program by and for scientific research, with many opportunities for pursuing studies towards a PhD or obtaining a job in numerous companies having a research department.
On the computer science side, the main courses are dedicated to theoretical aspects of the discipline, in order for students to master advanced and essential concepts for the modelling of natural phenomena (models of computation, complexity, dynamical systems). Other courses allow in parallel to develop skills in mathematics and biology.
This Master of science relies on the activities and skills of the laboratories that compose the Turing center of living systems (CENTURI).
As this Master is a research-focused study path, a BSc in Computer Science obtained with Honors is required.
Group projects and internships in research laboratories will lead students to apply interdisciplinary approaches and interact directly with researchers from the institutes of the Turing Center for Living Systems (CENTURI).
The Master Computational and Mathematical Biology, entirely taught in English, combines theoretical and practical courses of mathematics, computer sciences and biology. It provides an interdisciplinary training oriented towards modelling of complex biological systems.
This course Fundamentals in biology is divided in 2 parts taught during the 1st and 2nd semester of CMB. In the first semester, we will give 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.
Below are some topics covered during the lectures :
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.
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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.
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 :
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).
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 :
Some biological examples of applications could concern the probability of patterns in genomic sequences, the detection of differentially expressed genes.
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.
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The course is in conitnuity with the course Fundamentals of biology 1. This module will show how these molecular mechanisms underlie the development and functioning of tissues and organisms. It will be structured around four areas :
Some examples topics covered during the lectures :
This specialization course on discrete modelling deals with the following :
This specialization course helps the student to deepen his knowledge on problems on graphs and their solutions :
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 :
This course 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”. The following notions will be investigated :
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.
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.
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Following the module Research project and scientific communication, the students will do a short internship in laboratory. They will have to propose a modelling or data processing problem at the math-info-bio interface. They will be asked to synthesize their results in a dissertation and an oral presentation.
Following the module Centuri seminars 2, the students will attend all the Centuri seminars of this semester. For two of them, they will be asked to broaden their knowledges on the subject and present an oral and written synthese. The work will be done in collaboration.
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