The Quantum Information and Computing course is organized at the interface of physics and computer science, and is equally accessible to students with a background in computer science or physics. We first introduce the basic concepts of quantum information, focusing on the pivotal notions of superposition of states, entanglement, measurement processes, qubits, as well as quantum gates, and circuits. We also introduce the Bloch sphere picture and the density matrix formalism. Landmark applications and abilities of quantum processes to overcome classical approaches are illustrated around Bell's inequalities, quantum teleportation, and super-dense coding. We then discuss quantum computing via the quantum gate model. This model allows quantum algorithms to efficiently solve problems believed to be hard in the classical world, like factorization (Shor's algorithm). This is a significant threat against many currently deployed cryptographic systems. After presenting the main quantum algorithms we will cover the foundations of quantum information theory. Ultimately, we will present cryptographic systems whose security is based on the very nature of quantum mechanics.
- Teaching coordinator: Ayral Thomas
- Teaching coordinator: Debris Thomas
- Teaching coordinator: Sanchez-Palencia Laurent
Quantum mechanics has led to the emergence of new concepts in various mathematical fields (in analysis: Hilbert spaces formalized by von Neumann; in algebra: representation theory according to Cartan and Weyl). In return, these concepts have led to better formalizations in fundamental physics, as well as important discoveries, such as the standard model of elementary particles (Glashow, Weinberg, Salam). For this EA, the mathematics considered will be based on group theory and the physics targeted will essentially be that of the infinitely small.
In physics, whether at the classical or quantum level, the analysis of the symmetries of a system makes it possible to simplify its study because they generally imply the existence of retained quantities, selection rules, etc. The symmetry groups at play are part of the daily tools of many areas of fundamental physics. Some mathematical subtleties of abstract group theory are strikingly embodied in physics: for example, the difference between the SU(2) and SO(3) groups corresponds to the existence of half-entire spin particles, objects that do not have a classical interpretation. Extensions of orthogonal groups, the Lorentz and Poincaré groups, are interpreted as symmetry groups of relativistic physical systems. It so happens that the unit groups, SU(2) as well as U(1) and SU(3), also appear as "internal" symmetry groups of elementary particles: this discovery led to the formulation of the standard model of particle physics mentioned above. This theory classifies the elementary bricks of matter and describes their interactions, and its many predictions have passed all experimental tests to date.
The mathematical notion of linear representation of a group is central to quantum mechanics, and is a beautiful illustration of the interaction between mathematics and physics that we propose to present: it is a notion that pre-existed in quantum mechanics, but the directions in which it developed have sometimes been very strongly determined by physical considerations (E. Wigner). It is in this spirit that the basics of this theory will be presented (weight diagrams, character representations, tables and Young's diagrams).
The sessions are led alternately by a mathematician teacher and a physics teacher.
In parallel to the teaching, the students prepare a bibliographic project on a subject of their choice, leading to the writing of a report and an oral defense at the end of the period.
Language of the course: French or English, depending on the audience
ECTS credits: 5
- Teaching coordinator: De Suzzoni Anne-Sophie
- Teaching coordinator: Munier Stéphane
Ever since Bachelier’s PhD thesis in 1900, a theory of Brownian motion 5 years before Einstein, our understanding of financial markets has reasonably progressed. Over the past decades, financial engineering has grown tremendously and has regrettably outgrown our understanding. The inadequacy of the models used to describe financial markets is often responsible for the worst financial crises, with significant impact on everyday economy. From a physicist’s perspective, understanding the price for- mation mechanisms – namely how markets absorb and process information of thousands of individual agents to come up to a "fair" price – is a truly fascinating and challenging problem. Fortunately, modern financial markets provide enormous amounts of data that can now be used to test scientific theories at levels of precision comparable to those achieved in physical sciences.
This course presents the approach adopted by physicists to analyse and model financial markets. Our analysis shall, insofar as this is possible, always be grounded on the real financial data. Rather than sticking to a rigorous mathematical formalism, we will seek to foster critical thinking and develop intuition on the "mechanics" of financial markets, the orders of magnitude, and certain open problems.
- Teaching coordinator: Benzaquen Michael
- Teaching coordinator: Zakine Ruben
This course is organized with both Applied Mathematics and Mathematics departments and is also referenced MAT567.
The aim of this course is to present models of transport and particle diffusion used in various relevent application fields on the energy plan. The chain reaction mechanism in nuclear sectors, greenhouse effect in climatology, radiative transfer in thermics or astrophysics, some models of structured population dynamics in biology, to quote only a few examples, involves this type of models.
After a mathematical presentation of these models, we will show that diffusion is the limit of transport in a strongly collisional , and we will explain the critical mass or size notio. We will introduce finite-differences and Monte-Carlo digital resolution methods.
Bibliography:
- Dautray R., (1989). Méthodes probabilistes pour les équations de la physique, Eyrolles, Paris
- Dautray R., Lions J.-L., (1988). Analyse mathématique et calcul numérique pour les sciences et les techniques, Masson, Paris
- Perthame B., (2007). Transport equations in biology, Birkhäuser, Bâle
- Planchard J. (1995). Méthodes mathématiques en neutronique. Collection de la Direction des Études et Recherches d'EDF, Eyrolles.
- Pomraning G., (1973). The equations of radiation hydrodynamics, Pergamon Press. Oxford, New-York
- Teaching coordinator: Golse François
- Teaching coordinator: Pichard Teddy
- Teaching coordinator: Raoul Gael
Medicines and the molecules that will interest us during this teaching journey are able to modulate biological processes, all of which are governed by chemical interactions between biomolecules. Responses to these interactions take place at various scales ranging from the molecule (e.g. conformational change) to the cell (e.g. cell death), the body (e.g. lower body temperature) or even the environment (e.g. new antibiotic resistance). These effects can be caused and influenced by small organic or inorganic molecules, peptides, proteins and antibodies interacting with biological macromolecules (e.g. membrane or intracellular receptor, enzyme, DNA...). This is the basis of the development of drugs and of any molecule that can modulate or correct a biological process. This course aims to teach how we can study and design drugs, and more generally any compound capable of interacting with the body.
This course is jointly offered by the Department of Biology and the Department of Chemistry. The aim of this course is not only to introduce students to the sciences of drugs, but also to deepen their knowledge of the different stages of drug discovery and development.
This course requires some knowledge in chemistry and biology, but not to be already a specialist in these fields. The following topics and key notions will be covered:
- Identification and validation of therapeutic targets
- Mechanism of action of drugs
- Ligand - receptor interactions, enzyme inhibitors
- Drug modalities: organic and inorganic small molecules, peptides, proteins, antibodies, gene and cell therapies, new modalities
- Target-based and phenotypic drug discovery
- Compound libraries and high-throughput screening
- Medicinal chemistry, synthetic strategies for drug conception
- Chemoinformatics, molecular docking and structure-activity relationships (SAR)
- Molecular and cellular pharmacology, animal models
- Efficacy, selectivity, safety, bioavailability and metabolism of drugs.
Language: English
- Teaching coordinator: Formstecher Etienne
- Teaching coordinator: Gasser Gilles
- Teaching coordinator: Nay Bastien
Biomechanics in health and disease
Biomechanics is the application of mechanics to biological and/or biomedical systems. Over the last twenty years, mechanical stresses have been identified as a key player in the regulation of physiological functioning and in the development of several pathologies such as cardiovascular diseases, cancers, glaucoma and diabetes. Mechanical considerations are also essential for the design and development of devices and therapies that target these pathologies. The role of mechanics extends from the molecular scale to the whole-tisuue scale. This course will present fundamental aspects of macroscopic and microscopic biomechanics and will discuss the role of mechanics in physiology and pathology.
The course consists of lectures and research projects conducted by students. The lectures will focus on the following topics: 1) tissue-scale mechanics with emphasis on fluid mechanics, solid mechanics, and mass transport; 2) mechanics at the cellular level with a focus on cell behavior patterns and cell mechanotransduction; 3) the role of mechanics in the development and progression of diseases such as cardiovascular disease, cancer, and glaucoma; and 4) mechanical considerations in the design and development of medical devices and therapeutic approaches. Student-led projects will be research projects that will advance knowledge in a field related to the role of mechanics in physiology and pathology. These projects may be of a theoretical, numerical or experimental nature. Students will present their results at the end of the term. They will also have the opportunity to visit laboratories in the Paris region working in these fields.
Prerequisites: Basic knowledge in fluid and solid mechanics. There is no biology prerequisite.
Evaluation modality: Students are evaluated on the basis of the research projects and the final oral presentations
Course language: English
- Teaching coordinator: Barakat Abdul
Understanding and use of Life Cycle Assessment for ecodesign
The aim of Life Cycle Assessment (LCA) course is to describe this main environmental management methodology to assess and improve environmental performances of technologies. It provides the fundamental notions required to perform LCA, to use LCA software and to interpret and use LCA results in decision-making process. A focus will be made on LCA and advanced practices as uncertainty and sensitivity analysis. Students will have to carry out a LCA of a specific case study (wastewater treatment plant and sludge recovery).
Teaching staff
- Lynda Aissani, Research Engineer, INRAE
- Marilys Pradel, Research Engineer, INRAE
- Amir Nafi, University Lecturer, ENGEES
- Anne Ventura, Researcher, IFSTTAR
- Tristan Senga Kiessé, Researcher, INRAE
Course outline
- Concepts about environment
- Definition of some concepts as “environment”, “anthroposystem” and “ecosystem”
- Definition and description of environmental impacts
- Case study presentation
- Concepts of life cycle assessment (LCA)
- LCA steps description
- Focus on methodological key points
- Beginning of case study modeling
- LCA software training
- Getting started with the software
- Case study modeling thanks to the software
- Introduction to uncertainty and sensitivity analyses and matrix calculation in LCA
- Concepts and methods to consider uncertainty and sensitivity analyses
- Matrix calculation
- Identification of sensitive parameters of the case study
- Sensitive analysis: scenario and Monte Carlo approaches
- Presentation of scenario and Monte Carlo approaches
- Application of these approaches through case study
- LCA results interpretation and decision-making
- Principles of LCA results interpretation
- Understanding of the use of LCA results in decision-making process
- Application of these approaches through case study
- Oral presentation of case study resolution
- Students present the LCA of the case study
The module includes 22 hours of courses and 18 hours of practical work.
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Level required: Basic knowledge of environmental management
Language: English
Credits ECTS: 6
Supervisor: Lynda Aissani
- Teaching coordinator: Aissani Lynda
Modeling approaches are increasingly applied to living systems. These approaches are used to test whether a set of hypotheses is sufficient to explain the functioning of a system, to design methods to act on this system or to supplement experimentation when it is impossible. Thus, the majority of the fields of life sciences and bioengineering are concerned with modelling.
This module will give students an overview of the field, through lectures and the study of research articles, and lead them to carry out a modeling project in small groups. Each group defines a topic, proposes hypotheses from experimental data, formulates the corresponding model, solves numerically and discusses how to test the experimental model.
This course provides a hands-on experience in the modelling of living systems, based on short lectures, on the study of research papers, and on a project.
- Teaching coordinator: Boudaoud Arezki
Bioinformatics Project
This module corresponds to an individual or joint research project carried out in association with a researcher. Students discover a biological problem through modeling or simulation work.
They acquire new knowledges while putting into practice the concepts of courses.
The Python programming language is used, in particular the Biopython library.
Required level: At least one biology module in year 2.
Course language: French
- Teaching coordinator: Gaillard Thomas
- Teaching coordinator: Will Sebastian