The purpose of MAA205 is to use computer science and programming to solve problems in discrete mathematics, and vice versa. Topics include: graphs and their matrices, combinatorics and generating functions, elementary probability, sorting algorithms. The course consists of lectures and practical labs in python.
When you want to design and simulate a real issue (be a question of population dynamism in ecology, tumor growth in biomedical engineering, combustion dynamics in new-generation rocket engines - for example at SpaceX, prediction of solar storms and magnetic reconnection phenomena in solar physics, simulation of turbulence and turbulent combustion in fluid mechanics) the engineer or the researcher in applied mathematics or in "computational science" has to use a range of digital methods and must be able to analyze it mathematically, assess in terms of quality and computational efficacity, and finally, implement.
This course offers an introduction to numerical analysis, starting with the mathematical foundations on which numerical methods are based through to the implementation and the use of these methods on Jupyter notebooks (an active field at the Ecole Polytechnique), including their stability in relation to mathematical conditioning of the problems posed. The link is made with applications to understand the extent to which this type of method can be used from a practical point of view. Implementations of these methods in existing digital libraries are also documented.
Every class sessions include an analysis of the mathematical foundations on which a numerical method class is built, a description and analysis of the digital method (with a historical perspective). Those two aspects are covered during the course. The PC offers a review and an in-depth look at some concepts of the course, use of the method in the context of Jupyter notebooks and a description of how students can implement the method in a notebook to be handed in for the next class session.
The aim of this project is to propose methods for solving the resulting optimization issues, implement these methods and test them.
Topic 1(Frédéric Meunier): the organization of the production line in "Bucket Brigades" ensures great flexibility, while often having a production rate that is close to optimal. For order-picking lines, this type of organization presents a number of difficulties, and Pyung-Hoi Koo (Operations Research Spectrum, 2009) proposed ways to offset them while leaving several aspects open to further optimization.
Topic 2 (Frédéric Meunier): it is considered a workshop production issue, in which employees have a variety of qualifications. Products arrive according to a Poisson process, and each must visit a subset of the machines in a specific order. The arrival rate being quite high, queues can be formed in front of machines. As the employees are less numerous than the machines, the challenge is to pick which machine will be sent to an employee who has just completed a task. The aim of the project is to find the assignment rules that will keep the average stay time as low as possible.
Topic 3 (Eric Gourdin): We're interested in routing in Internet networks, which we'll first simulate and then optimize. The network is modeled by a graph whose links (edges/arcs) are equipped with capacities. We also have a set of requests, each request is defined by a source node, a destination node, and a volume of traffic to be handled. It is assumed that the network uses a shortest-path routing protocol: each link is assigned a (presumably given) administrative metric value, and traffic between the source and destination nodes is routed along the shortest paths (as defined by these administrative metrics). If there is more than one shortest path, traffic is distributed over the paths in accordance with the ECMP protocol. Link load is the ratio of traffic flow and capacity. Routing "quality" is measured by calculating the load of the fullest link. We'll take an interest in routing protocol evolution called "Segment Routing" where a request can be routed on a continuation of segments, the routing within each segment being by itself managed by the shortest paths.
Topic 4 (Eric Gourdin): in an Internet network, we're seeking to calculate a "robust" routing called "oblivious routing". The general context is similar to the previous topic: a graph with links provided with capacities, a set of requests to be handled. Unlike the previous topic, the routing to be calculated is totally free (traffic can be split over as many paths as you like, as long as you satisfy the flow conservation on each intermediate vertex). It is assumed that request volumes are unknown. We are looking for a routing that is valid for all possible requests and such the maximum overall request sets of the ratio between the max load with this single routing and the ratio obtained with a routing that would be optimized for this request set be as small as possible (oblivious routing). The modal approach consists in offering ways of calculating (or approximating) this "oblivious" routing.
Machine learning is a scientific discipline that is concerned with the design and development of algorithms that allow computers to learn from data. A major focus of machine learning is to automatically learn complex patterns and to make intelligent decisions based on them.
This course focuses on the methodology underlying supervised and unsupervised learning, with a particular emphasis on the mathematical formulation of algorithms, and the way they can be implemented and used in practice. We will therefore describe some necessary tools from optimization theory, and explain how to use them for machine learning.
Proofs will not be made during the lectures: some will be made during the labs others could be found in a document. Finally, each lab will finish with a numerical lab in Python
Validation
Objectives
The objective of this course is to introduce linear. Regression plays a key role in many problems and it is absolutely essential for a datascientist to understand the theory and the practice of regression analysis. It is also an important vehicle to address the statistical challenges in statistical learning : model selection, penalisation, resampling (bootstrap, cross-validation) robustness, detection of outliers, and also methods to detect deviations from an assumed model. The course will also serve as a motivation to sharpen the understanding of statistical techniques, covering both estimation and tests.
Syllabus
1. Introduction to statistical learning
Regression: Learning objectives and applications
Linear models : interpretation, examples
Least-Square estimators properties (bias, variance)
Case study: univariate and multivariate regression
Multivariate Linear Regression: Parametric casee
Construction of least-square estimators
2. Parametric true model
Distribution of least-squares estimatorsAsymptotic properties
Gaussian case (distribution of the parameters, confidence regions)
Confidence intervals and tests
Classical regression diagnostic (leverage points)
Case studyAlgo: understanding multiple linear regression with R (lm summary, detecting outliers, understanding classical regression diagnosis)
3. Residual analysis (homoscedasticity, non-linear dependence)
Outlier detection (leverage effects, influence, introduction to robsut statistics)
Functional modelintroduction to non-parametric regression : from parameters to functions
Multiple models for a single problemFunction classes, model selection
Variable choice / Basis / Spline
Bias / Variance (Approximation error / Estimation Error)
Case study : Spline regression
4. Model Selection and Resampling
Approximation Error / Estimation Error
Learning Error / Generalization Error
Resampling based method: jacknife, bootstrap, and Cross Validation
Case study: model selection with CV
5. Model Selection and Unbiased Risk Estimation
Unbiased Risk Estimation
AIC/BIC Penalization and Exhaustive Exploration
Forward / Backward and Stochastic Exploration
Multiple tests
6. Model Selection and Penalization
Restricted Model and Penalization
Ridge and Lasso
Numerical algorithm: Gradient Descent and Coordinate Descent
Case study: Coordinate Descent and Lasso
Langue du cours : Anglais
Objectifs :
Students will put their basic machine learning and data analysis knowledge to test for solving practical data science problems in scientific or industrial applications. Typically, we will treat two/three concrete problems coming from scientific or industrial applications (e.g., brain imaging, astrophysics, biology/chemistry, ad placement, insurance pricing). We describe and formalize the motivating problem, discuss the possible solutions, choose one, and assist the students in solving the problem. We will provide data, advise students on their choice of tools, and set up a challenge environment where students can submit their solutions. Evaluation will be based on homework assignments and performance in the challenges.
Validation :
Evaluation at the end of each data camp
This a Data Camp based on the challenges proposed by the ENS: https://challengedata.ens.fr/
You can choose any of the proposed challenges. You will have to work in groups in groups of three to four students and have to provide a solution by the end of march. To help you, we will organize non mandatory coaching sessions.
Professors in charge of the option:
Ludovic Goudenège
Email: ludovic.goudenege@polytechnique.edu
Secretariat of the Applied Mathematics Department
Tel.: 01 69 33 46 07.
Fax: 01 69 33 46 46.
Email: nathalie.rodrigues@polytechnique.edu
Modeling is a process that formalizes a concrete issue in terms of accessible mathematics to analyze and to digital calculation.
Scientific calculation is the interdisciplinary field that brings together methods and algorithms enabling to conduct - with computer - digital simulations based on a scientific approach. Most of the models involve equations (differential or partial derivative) too complicated to be solved through basic methods or with techniques of formal calculation. Scientific calculation offers to give to these models. The development of scientific calculation is related to the steady increase of the computer power. It is therefore a sector in continuous evolution.
Companies using and developing the modelisation and scientific calculation are just as large state or private companies charged to conceive and develop complex systems as little companies or Internet startups specialized in software development. They intervene in all business lines: aeronautics and spatial, energy and environment, automobile, services and telecommunications, civil engineering. Reserved not so long ago to dimensioning and verification of complex systems, digital simulation is widespread as it allows to save important times on design cycles and production of new products more basic. The design of objects or systems is often responding to general specifications is formalized as a stressed optimization issue. Modeling and scientific calculation are therefore often used in combination with optimization methods.
Internships from April to July:
The "Modeling and Scientific Computing" option is designed for students searching a training in this speciality, either to address an industrial issue, or to initiate research, regardless of their future career choices. For those who wish to take the "mathematics of modalization" option of the master of Ecole Polytechnique (in co-supervision with Sorbonne University) or the master Analysis, Modelization, and Simulation, the internship can be a first major step. For the motivated student who want to go abroad during their research internship, it is possible to find subjects of internships in foreign universities.
Example of internships of the earlier years:
Host organizations:
Required level: Have taken the digital analysis and/or optimization courses
Evaluation modalities: Written report and defense
Course language: French or English
Credits ECTS : 20
Responsables de l'option:
Stéphane Gaubert
gaubert@cmapx.polytechnique.fr
Frédéric Meunier
frederic.meunier@enpc.fr
mail générique : map593@meslistes.polytechnique.fr
Coordinatrice des enseignement du Département de Mathématiques Appliquées
Tél: 01 69 33 46 07
Fax: 01 69 33 46 46.
mail : nathalie.rodrigues@polytechnique.edu
Cette option regroupe deux disciplines complémentaires : l'automatique, art de la commande de systèmes dynamiques, et la recherche opérationnelle, qui met en œuvre les techniques d'optimisation continue et discrète.
Ces deux secteurs connaissent une demande soutenue. L'automatique est très utilisée depuis longtemps en aéronautique et dans les processus de production (chimie, cimenteries, laminage, biotechnologies). Avec l'invasion de l’électronique elle devient un élément-clé dans de nouveaux secteurs comme l'automobile. Elle intervient aussi dans la commande de grands systèmes. Elle comprend des sujets d’interface avec plusieurs domaines, comme l’ingéniérie quantique ou l’écologie. La recherche opérationnelle est la technique fondamentale de résolution des problèmes de gestion complexes : plans de production, horaires de transport, affectation de moyens, conception de réseaux, investissements. Ces deux disciplines sont présentes dans les grandes entreprises mais aussi dans de petites sociétés. Elles occupent une place importante dans les universités françaises comme étrangères.
L'option "Automatique et Recherche Opérationnelle" est conçue pour des élèves qui cherchent une formation dans cette spécialité, soit pour aborder un problème industriel, soit pour s'initier à la recherche et ce, quel que soit le choix ultérieur de leur carrière. Pour les élèves très motivés qui veulent s'expatrier durant leur stage d'option, il est possible de trouver des sujets de stages dans des universités ou des petites sociétés étrangères.
Exemples de stages effectués les années passées :
Automatique :
Recherche opérationnelle :
Organismes d'accueil proposant des stages :
Professors in charge of the option:
Stéphane Gaubert
gaubert@cmapx.polytechnique.fr
Frédéric Meunier
frederic.meunier@epnc.fr
map593@meslistes.polytechnique.fr
Secretariat of the Applied Mathematics Department:
Tel: 01 69 33 46 07
Nathalie Rodrigues
nathalie.rodrigues@polytechnique.edu
This option brings together two complementary disciplines: automatic, the art of controlling dynamic systems, and operational research, executing continuous and discrete optimization techniques. Thes sectors experience a sustained demand.
Automatic is very used in aeronautics and in production processes (chemistry, cement, lamination, biotechnologies). With the electronical invasion, it becomes a key element in the new sectors such as automobile, it also intervenes in the control of large system. It includes interface with several fields, such as quantum engineering or ecology. Operational research is the fundamental problem-solving technique for complex management: production plans, transport schedule, ressource allocations, network design, investments. These two disciplines are present in large and small companies, and they play an important role in French and foreign universities.
The "Automation and Operational Research" option is designed for students searching a training in this speciality, either to address an industrial issue, or to initiate research, regardless of their future career choices. For the motivated student who want to go abroad during their research internship, it is possible to find subjects of internships in foreign universities or small societies.
Example of internships of the earlier years:
Automatic:
Operational research:
Host organizations offering internships:
Professors in charge of the option:
Vincent Bansaye - Probabilités
Email: bansaye@cmap.polytechnique.fr
Eric Moulines - Statistics
Email: eric.moulines@polytechnique.edu
Aymeric Dieuleveut - Machine Learning
Email: aymeric.dieuleveut@polytechnique.edu
Secretariat of the Applied Mathematics Department
Tel: 01 69 33 46 07
Fax: 01 69 33 46 46
Email: leyla.marzuk@polytechnique.edu
"Probability Modeling and Statistics" internships are generally about building and studying probabilistic models designed to describe and analyse physics, biological, computing or economy phenomena. Depending on the intended goals, models can be from machine learning (statistical learning), used as a tool to analysing data and proposing predictions (estimation, tests, prediction...), or to be analysed with probabilistical mehtods in order to grasp their behaviors and limits. Note that with the global rise of AI, big data or not, and the design of macine learning algorithms adapted are at the center of many intenships proposed.
The range of applications of these methods is very broad: biology (population dynamics, genetic heritage transmission, phylogenetic selection, biological regulation network...), communication network (traffic characterization, probabilistic analysis of protocols, congestion control), insurance (pricing, prediction of reserves), economy (analysis and prediction of macroeconomic aggregates...), etc.
These internships are particularly designed to students who have taken the Applied Mathematics PA (notably the course of "Process and estimate", "Communication network, algorithms and probabilities", "Statistical learning", "Random models in ecology and evolution").
Example of internships of the earlier years:
IN FRANCE
ABROAD
Course language: French
Responsables d'option :
Eduardo Abi-Jaber
Mail : map595@meslistes.polytechnique.fr
Charles-Albert Lehalle
Mail : map595@meslistes.polytechnique.fr
Huyên Pham
Mail : map595@meslistes.polytechnique.fr
Coordinatrice des Enseignement du Département de Mathématiques Appliquées
Nathalie Rodrigues
T. +33 (0)169334607 – nathalie.rodrigues@polytechnique.edu
Les stages proposés en Mathématiques financières se passent en général dans les centres de recherche des salles de marché des banques ou d’autres organismes, tels des fonds d'investissement. Pour certains stages, il est indispensable d’avoir suivi le cours "Modèles stochastiques en finance" de troisième année. Les stages à l’étranger se déroulent soit dans la banque, soit dans des centres de recherche académiques.
Certains stages nécessitent plusieurs entretiens avec différentes équipes.
Exemples de stages proposés les années précédentes :
En France
AXA
Optimisation de stratégie tarifaire
CMAP
Principal-Agent à plusieurs agents et à une dynamique de sauts. Applications à la structuration et la tarification des contrats d'électricité
CREDIT SUISSE
Méthodes génétiques pour l'optimisation de portefeuilles
KEPLER CHEVREUX
Dynamiques de données de carnet d'ordres et détection d'algorithmes
SOCIETE GENERALE
Pricing de produits structurés très long terme
UNIVERSITE PARIS 7
Modèles financiers avec arbitrage, application à la gestion actif-passif long terme
A l'étranger
BLOOMBERG LP
Calibration of a Path Dependent Volatility model to the VIX and S&P markets*
BNP PARIBAS London Branch
Models for Overnight indexed swap rates and Libor dynamics, and related Market risk
BRITISH PETROLEUM
Application de techniques de Machine Learning à la méthode de Monte-Carlo des moindres carrés
Professors in charge of the option:
Eduardo Abi-Jaber
Mail : map595@meslistes.polytechnique.fr
Charles-Albert Lehalle
Mail : map595@meslistes.polytechnique.fr
Huyên Pham
Mail : map595@meslistes.polytechnique.fr
Teaching coordinator of the Applied Mathematics Department
Nathalie Rodrigues
T. +33 (0)169334607 – nathalie.rodrigues@polytechnique.edu
Internships offered in Financial mathematics generally take place in centers of research of banks or other organisms, such as investment funds. For some internships, it is mandatory to have taken the Year-3 course of "Stochastic models in finance". Internships abroad take place either in the bank or in academical centers of research.
Some internships require several interviews with different teams.
Example of internships of the earlier years:
En France
AXA
Optimization of pricing strategy
CMAP
Principal-Agent to several agents and to a jump dynamic. Applications to the structuing and pricing of electricity contracts
CREDIT SUISSE
Genetical methods for portfolio optimization
SOCIETE GENERALE
Pricing de produits structurés très long terme
UNIVERSITE PARIS 7
Financial models with arbitraging, application to long-term asset and liability management
Abroad
BLOOMBERG LP
Calibration of a Path Dependent Volatility model to the VIX and S&P markets
BNP PARIBAS London Branch
Models for Overnight indexed swap rates and Libor dynamics, and related Market risk
BRITISH PETROLEUM
Application de techniques de Machine Learning à la méthode de Monte-Carlo des moindres carrés
DEUTSCHE BANK Londres
Pricing and risk management of interest rate derivatives
GOLDMAN SACHS
Predictive flow Analytics & inventory optimization
JANE STREET
The volume synchronized probability of informed trading
JP MORGAN
Capital optimization, funding optimization, derivates clearing businesses, credit value adjustement
JUMP TRADING INTERNATIONAL
Latent order book in the context of market impact and liquidity drought
MONASH UNIVERSITY
Option pricing with linear market impact
SQUAREPOINT CAPITAL
Multi-period portfolio optimization to manage tail risk in equities
UNIVERSITY OF OXFORD
Numerics for the robust pricing and hedging problem in discrete time
Weekly seminar in biology, ecology and medicine: discovery of the major current themes in life sciences and the associated mathematical challenges. Guest lecture, followed by individual debriefing.
Day 1: Data wrangling
- Advanced course on Pandas
- Tidy data
- Lab on MovieLens dataset
- Challenge and getting started with RAMP
Day 2: ML Pipelines and hyperparameter search
- Column transformer and pipelines
- Bayesian optimization and hyper parameter search
- Learning curves
Day 3: Metrics and dealing with unbalanced data
- Presentation of the different ML metrics
- Problem of the metric with unbalanced data
- ML approaches to deal with imbalanced data
Day 4: Ensemble methods and feature engineering
- Gradient Boosting
- Stacking
- feature engineering
Day 5: Model inspection
- partial dependence plots
- feature importance
Challenges
Besides the students will compete during the week on a data challenge.
Partial differential equations are often used in biology to model spatially structured systems: forest propagation, inflammation dynamics, cell polarization... These models can be used, for example, to accurately simulate the behavior of an organ. In other cases, particularly when dealing with less well understood biological systems, partial differential equations can offer a qualitative description of complex phenomena.
In this course, we will focus on two ecological issues, through the study of recent work. First, we will look at propagation phenomena described by non-linear parabolic equations. We will then see that a good understanding of linear equations (elliptical or parabolic) enables us to study the behavior of non-linear models. In the second part of the course, we will study the dynamics of collective movements described by kinetic equations. To understand the dynamics of this second type of partial differential equation, we will identify a fast time scale (which will be local in space) and a slow time scale (which will govern the spatial dynamics of the system).
We will then be able to describe the solutions using macroscopic models.
The two ecological issues discussed in this course will enable us to understand a diversity of questions that can arise around partial differential equation models in biology: modeling, links with other models (in particular stochastic models), numerical simulations. We will also discuss the possible roles of mathematical analysis in the study of biological problems. The mathematical methods covered (linear/non-linear models, slow/fast dynamics) are relevant to many mathematical problems in biology.
Moreover, these methods have links with arguments used in probability and the study of dynamic systems.
Teaching supervisor: Arnaud Echard
This course lets you discover a core scientific discipline, biology, and prepares you for several other 2nd year biology courses, as well as for more advanced, 3rd year programs offered by the Biology department of Biology. This is a basic biology course, designed for students from all scientific origins.
It will reveal the logic of the living world and will show how biology, an expanding scientific discipline, is developing more and more at the interface with physics, chemistry, informatics, mathematics and engineering sciences.
The course will show the distinctive features and the informative molecules (DNA, RNA and proteins) shared by all living organisms. The main regulations controlling RNA and protein production will be detailed. This will enable us to understand how cells regulate their gene expression to answer their needs and adapt to environmental changes. It presents, in a progressive and sometimes deliberately simplified way, the major advances in the biological sciences of the 20th and 21st centuries. The course also provides an understanding of the major contemporary societal issues linked to the life sciences.
Course Language : French.
Experimentation is central to progress in biology. It enables working hypotheses to be tested. Thanks to cycles of hypothesis verification and refinement, we end up with predictive models, despite the great complexity of the objects studied: living beings.
We cannot guarantee that a student will be registered for a specific theme. The distribution of students is based on supply and demand. The following themes are likely to be opened:
- Bioluminescence:
The chemical energy extracted from organic molecules by living beings can be transformed into thermal energy, mechanical energy, electrical energy, and even light energy. This last property is more widespread than we think since it exists in several hundred species as diverse as bacteria, fungi and animals. We will study the green fluorescent protein (GFP) of the jellyfish Aequorea victoria. We will use the tools of genetic engineering, biochemistry and biophysics to understand the origin of this fluorescence and how to exploit it in various biotechnological fields. Firefly tail luciferin will also be discussed to understand the origin and mechanism of its bioluminescence.
-Antibodies: from immune defense to clinical diagnosis:
Antibodies, central molecules in the humoral immune response, play an essential role in the prevention of infections. Moreover, thanks to their precise characterization, they have also become essential tools for research, medical diagnosis and therapy, in particular anti-cancer. This Modal aims to characterize the biochemical properties of antibodies as well as to illustrate several examples of the use of antibodies in research and medical diagnosis. The use of a large number of classical techniques of biochemistry and biology also make this Modal an excellent introduction to laboratory work.
- Intracellular imaging:
The organization and dynamics of the cytoskeleton play an essential role in many eukaryotic cell life processes, such as migration, division or intracellular transport. The objective of this Modal is to observe the different components of the cytoskeleton (microtubule and actin filaments) inside human cells. It is an opportunity to introduce multiple techniques in cell biology (culture of human cells, immunocytochemistry, transfection), microscopy and digital modeling.
- Cloning:
This modal allows you to discover the key tools and techniques used daily in laboratories. Baker's yeast dihydrofolate reductase (DHFR) is an essential protein conserved in all eukaryotes. Thanks to its key role in cell growth and metabolism, DHFR is of pharmacological interest. It is the target of the few drugs that are used for the treatment of a wide spectrum of diseases. We will clone the gene coding for the eukaryotic DHFR in a bacterium, we will induce its expression and we will purify the protein produced. Finally, an enzymatic test will make it possible to functionally characterize the purified protein.
-Synthetic biology: design and construction of synthetic genetic oscillators:
Synthetic biology aims to design and build artificial life forms that perform a given function. Gene regulatory networks are sets of genes that interact with each other and with other molecules, via their expression products, allowing mutual control of their expression levels. One possible approach to synthetic biology is to modify existing genetic networks or design new ones, opening the way to the design of new biological functions. This is a very active area of research with many potential applications. The purpose of this Modal is the study and fabrication of synthetic genetic oscillators, that is to say networks of unnatural genes with an oscillating behavior. It uses the following methods and techniques: modeling of gene networks, genetic engineering, cell culture, fluorescence microscopy, image analysis.
Experimentation is central to progress in biology. It enables working hypotheses to be tested. Thanks to cycles of hypothesis verification and refinement, we end up with predictive models, despite the great complexity of the objects studied: living beings.
We cannot guarantee that a student will be registered for a specific theme. The distribution of students is based on supply and demand. The following themes are likely to be opened:
- Bioluminescence:
The chemical energy extracted from organic molecules by living beings can be transformed into thermal energy, mechanical energy, electrical energy, and even light energy. This last property is more widespread than we think since it exists in several hundred species as diverse as bacteria, fungi and animals. We will study the green fluorescent protein (GFP) of the jellyfish Aequorea victoria. We will use the tools of genetic engineering, biochemistry and biophysics to understand the origin of this fluorescence and how to exploit it in various biotechnological fields. Firefly tail luciferin will also be discussed to understand the origin and mechanism of its bioluminescence.
-Antibodies: from immune defense to clinical diagnosis:
Antibodies, central molecules in the humoral immune response, play an essential role in the prevention of infections. Moreover, thanks to their precise characterization, they have also become essential tools for research, medical diagnosis and therapy, in particular anti-cancer. This Modal aims to characterize the biochemical properties of antibodies as well as to illustrate several examples of the use of antibodies in research and medical diagnosis. The use of a large number of classical techniques of biochemistry and biology also make this Modal an excellent introduction to laboratory work.
- Intracellular imaging:
The organization and dynamics of the cytoskeleton play an essential role in many eukaryotic cell life processes, such as migration, division or intracellular transport. The objective of this Modal is to observe the different components of the cytoskeleton (microtubule and actin filaments) inside human cells. It is an opportunity to introduce multiple techniques in cell biology (culture of human cells, immunocytochemistry, transfection), microscopy and digital modeling.
- Cloning:
This modal allows you to discover the key tools and techniques used daily in laboratories. Baker's yeast dihydrofolate reductase (DHFR) is an essential protein conserved in all eukaryotes. Thanks to its key role in cell growth and metabolism, DHFR is of pharmacological interest. It is the target of the few drugs that are used for the treatment of a wide spectrum of diseases. We will clone the gene coding for the eukaryotic DHFR in a bacterium, we will induce its expression and we will purify the protein produced. Finally, an enzymatic test will make it possible to functionally characterize the purified protein.
-Synthetic biology: design and construction of synthetic genetic oscillators:
Synthetic biology aims to design and build artificial life forms that perform a given function. Gene regulatory networks are sets of genes that interact with each other and with other molecules, via their expression products, allowing mutual control of their expression levels. One possible approach to synthetic biology is to modify existing genetic networks or design new ones, opening the way to the design of new biological functions. This is a very active area of research with many potential applications. The purpose of this Modal is the study and fabrication of synthetic genetic oscillators, that is to say networks of unnatural genes with an oscillating behavior. It uses the following methods and techniques: modeling of gene networks, genetic engineering, cell culture, fluorescence microscopy, image analysis.
This course illustrates some pathologies and current methods to take charge of them. The pathologies chosen are those that represent the greatest challenges for our developed societies. This biomedical course highlights the biological substrate of pathologies and treatments as well as the economy of health.
The 10 blocks are:
It is suggested to have assimilated the courses of Molecular Biology and genetic information and Cell Biology and Development that precede this course.
These are not mandatory prerequisites, fundamental notions will be reviewed and the course aspires to be followed by any student who has an interest in biology and medicine. It should be pointed out that this course requires a lot of personal investment for those who have not done biology beforehand.
Course Language: French
Optional Year 3 project for both periods.
Alone or in pairs projects will be the subject of discussions between students and teachers and will be assiociate to one of the followed units.
The proposed projects by the Biology Department will be available in the BioInformatics PA.
The project ca be carried out according to one of the three following options with the teachers during the starting PA lecture hall: P1 or P1 and P2
- BIO511
Research project: the first option involves a research activity in laboratory. In most projects of this option, a part of data production will be followed by an analysis and modeling part.
It is a first introduction and a personal initial contact with the research world.
- Bibliographic project: This option involves developing a bibliographic in-depth research on a specific subject related with one of the year 3 course.
The purpose is to be capable of presenting this topics in a concise, understandable and instructive way in the form of a course presentation with a written document.
- Project development: This option involves developing a funding request for a research project. The purpose will be to define a scientific project innovative and ambitious on one of the topics proposed in year 3, to write and present it orally.
For all this options, exchanges between teachers in the department and between departments are highly encouraged. All these topics can also be developed in engineering perspective, incuding the developement of methods, tools, software, databases and genetically modified organisms.
The purpose of the year 3 project is to start a personal project on a biology research topic by combining reflection, bibliographic analysis and/or experiments and data analases. The project is to be realized alone or in pairs (possibly more but a clear division of tasks will be required). It will be attached to one of the year 3 teachers that you have chosen so you can discuss your progress and interogations regurarly with your teachers. In order that your projects are succesful, a real engagement is required, both in terms of working time you will devote to it in the first weeks and in terms of openness and maturity you must demonstrate, to collect sources of information from your teachers but also from teachers in other departments or regional researchers. You will learn the most by keeping the project alive.
Schedule:
A list of projects and subjects will be presented at the lecture hall 0 in September.
At the end of the day, each student must have defined a project, a subject and/or chosen a referent teacher. The projects and subjects presented remain open and are intended to give you a starting point and to show you the different fields of expertise of the biology department's teachers. Feel free to develop these projects or to discuss with the teachers to bring out new ones that are important to you, our only goal is to make sure that these projects are coherent and realizable, so you can develop your full potential. You can also choose an article analysis with a unit of P1, especially BIO571.
Evaluation modality:
A 10 minutes oral presentation (15 minutes for a duo) will be followed by a 15 minutes discussion with coordinators and project tutors. We do not ask for a written report but we encourage you to deliver a report to your renferent so they can keep a record of your work. Check with them for the expected form.
Course language: French
