Operations Research, combinatorics and optimization (ORCO)

This course provides an introduction to the basic concepts of object-oriented programming in C++: classes and encapsulation, operator overloading, generic classes (templates), STL (Standard Template Library), inheritance and derived classes, polymorphism and virtual functions.
Lab sessions illustrate these concepts, and applications for applied mathematics. 

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Contents:

• Types of equations, conservation laws
• Finite differences methods
• Laplace equation
• Parabolic equations (diffusion)
• Hyperbolic equations (propagation)
• Non linear hyperbolic equations

This course include practical sessions.

This is a two parts course, this part is the course mutualized with Ensimag 2A 4MMMEDPS.

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Contents:

• Image definition
• Fourier transform, FFT, applications
• Image digitalisation, sampling
• Image processing: convolution, filtering. Applications
• Image decomposition, multiresolution. Application to compression

This course includes practical sessions.

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This course is an introduction to the differential geometry of curves and surfaces with a particular focus on spline curves and surfaces that are routinely used in geometrical design softwares.

Content

This course includes practical sessions.

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The syllabus of the English course in M2 aims at enabling students to validate 3 competences that will be essential for their working life or for their doctoral studies in the future, at the B2 level:

1°) CAN give a clear presentation on a familiar topic, and CAN answer predictable or factual questions

2°) CAN find relevant information and essential points in written texts

3°) CAN make simple notes that are of reasonable use for essay or revision purposes, capturing most important points." (CEF, appendix D).

Reading comprehension can be validated in M1.

The course contents are linked to the students' fields of studies.

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Connaitre les notions élémentaires et indispensables de probabilités. Maitriser les calculs de lois, d'espérance; connaitre les fonctions de simulation de logiciels spécialisés; savoir utiliser ces fonctions pour illustrer les résultats
de probabilité. Chaque notion sera abordée en cours et illustrée numériquement en séance
avec les étudiants.

Connaitre les principaux estimateurs, leurs propriétés.
Être capable de programmer les différents estimateurs dans des
situations simples; savoir illustrer par simulation les propriétés des estimateurs (biais, erreur quadratique).
Chaque notion sera abordée en cours et illustrée numériquement en séance avec les étudiants.

Contenu : Lois fondamentales discrètes et continues; Variables indépendantes, lois conditionnelles.
Espérance, espérance conditionnelle. Convergence de variables aléatoires. Théorème
centrale limite, loi des grands nombres. Vecteur gaussien, théorème Cochran. Notion
de chaine de Markov illustrée dans des TP.

Estimateur, estimation. Biais, erreur quadratique, convergence. Intervalle de
confiance. Estimateur des moindres carrés. Estimateur des moments. Estimateur du maximum
de vraisemblance. Equations estimantes.

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Ce cours présente des manières géométriques de traiter et résoudre des problèmes décrits par des équations différentielles.

        - chapitre I : Introduction : généralités sur les systèmes dynamiques

        - chapitre II : Systèmes unidimensionnels : Les points fixes, linéarisation et stabilité, Exemple : le modèle logistique, Existence et unicité des solutions d'équations différentielles ordinaires

        - chapitre III :  Bifurcations : Bifurcation selle-nœud, Bifurcation transcritique, Bifurcation transcritique imparfaite, Bifurcation fourche, Bifurcation fourche supercritique, Bifurcation fourche sous-critique, Bifurcation fourche supercritique imparfaite

        - chapitre IV :  Champ de vecteur sur un cercle : Oscillateur uniforme, Oscillateur non-uniforme

        - chapitre V : Flots bidimensionnels et applications : Existence et unicité des solutions et conséquences topologiques, Systèmes linéaires, Systèmes non-linéaires : linéarisation proche des points fixes, Cycles limites, Le théorème de Poincaré-Bendixson, Systèmes Liénard, Systèmes gradients, Fonctions de Liapunov

        - chapitre VI : Bifurcations bidimensionnelles : Bifurcations selle-nœud, transcritique et fourche, Bifurcation de Hopf, Bifurcations globales de cycles

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This course presents basic notions on instabilities and turbulence. We try to be as progressive as possible and to base our presentation on analyses of real experiments and real flows. We review few mathematical methods to analyze nonlinear systems in terms of instabilities. The students have to use their new knowledge to run and analyze numerical simulations of very simple systems. We then study some of the most important physical mechanisms for fluid instabilities and the corresponding criteria. We quickly present a zoology of common fluid instabilities and discuss the mechanisms and the possible technical implications. We give a broad introduction on turbulence and describe few fundamental methods and results, in particular the Richardson cascade, the Reynolds decomposition and the Kolmogorov spectra.

Teaching program:

1. General introduction

- Instabilities and turbulence, interest?

- Reynolds experiment and Reynolds number

- Incompressible Navier-Stokes equations: diffusion and advection

- An example: the wake of a cylinder

2. Instabilities and transition to turbulence

- Systems with few degrees of freedom

- Fluid instability mechanisms and conditions

- Other flows examples

3. Effects of variable density

- Boussinesq approximation

- Unstable stratification, Rayleigh-Taylor instability

- Rayleigh-Benard instability (Ra, Nu)

- Stable stratification, Kelvin-Helmoltz instability and Richardson number

4. Turbulence

- Introduction, Richardson cascade

- Average and Reynolds decomposition

- Experimental and numerical methods to study turbulence

- Statistical descriptions

For this course, the students have to write in LaTeX a report on their practical work. Thus, we spent some time for a first gentle introduction of this tool widely used in scientific academia.

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Ce module est une introduction à la turbulence phénoménologique et statistique. On s’intéresse aux définitions et propriétés de la turbulence en terme de processus physiques et leur description dans des familles types d’écoulements cisaillés que l’on peut retrouver dans la nature et en ingénierie.

jet turbulent
jet turbulent

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Contents:

• Introduction to database
• Introduction to big data
• Introduction to high performance computing (HPC)
• Numerical solvers for HPC

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January science and/or industrial project.

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Industrial and/or research internship.

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This program combines case studies coming from real life problems or models and lectures providing the mathematical and numerical backgrounds.

Contents:

• Introduction, classification, examples.
• Theoretical results: convexity and compacity, optimality conditions, KT theorem
• Algorithmic for unconstrained optimisation (descent, line search, (quasi) Newton)
• Algorithms for non differentiable problems
• Algorithms for constrained optimisation: penalisatio, SQP methods
• Applications

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Operational Research proposes scientific methods
to help make better decisions. The idea is to develop and use mathematical and computer
tools to master complex problems. Practical applications are historically in
the direction and management of large systems of people, machines, and
materials in industry, service, humanitarian aid, environment ...

In this course, we will focus on especially on problems with a combinatorial
structure: the number of possible solutions is finite but too large to be
enumerated. The study of these problems involves a phase of modelling practical
problems and then algorithmic resolution.

At the end of this course, students will be able to propose a model and will be
able to implement practical solutions (dedicated or industrial tools) to deal
with a problem of decision or optimization.

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To acquire the main theoretical and practical notions of modern cryptography: from notions in algorithmic complexity and information theory, to a general overview on the main algorithms and protocols in symmetric and asymmetric cryptography.

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Computer Graphics covers the set of techniques enabling the synthesis of animated virtual worlds. The applications range from entertainment (special effects, 3D feature films, video games), to industrial design (modelling and visualizing prototypes) and virtual reality (flight simulator, interactive walk-trough). This course introduces the domain by presenting the bases for the creation of 3D models, their animation, and the rendering of the corresponding 3D scene. Student will be invited to practice through programming exercises in OpenGL.

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Content

This course include practical sessions.

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This course provides an introduction to the basic concepts of object-oriented programming in C++: classes and encapsulation, operator overloading, generic classes (templates), STL (Standard Template Library), inheritance and derived classes, polymorphism and virtual functions.
Lab sessions illustrate these concepts, and applications for applied mathematics. 

Visit the full page about this course

Contents:

• Types of equations, conservation laws
• Finite differences methods
• Laplace equation
• Parabolic equations (diffusion)
• Hyperbolic equations (propagation)
• Non linear hyperbolic equations

This course include practical sessions.

This is a two parts course, this part is the course mutualized with Ensimag 2A 4MMMEDPS.

Visit the full page about this course

Visit the full page about this course

Visit the full page about this course

Contents:

• Image definition
• Fourier transform, FFT, applications
• Image digitalisation, sampling
• Image processing: convolution, filtering. Applications
• Image decomposition, multiresolution. Application to compression

This course includes practical sessions.

Visit the full page about this course

This course is an introduction to the differential geometry of curves and surfaces with a particular focus on spline curves and surfaces that are routinely used in geometrical design softwares.

Content

This course includes practical sessions.

Visit the full page about this course

Connaitre les notions élémentaires et indispensables de probabilités. Maitriser les calculs de lois, d'espérance; connaitre les fonctions de simulation de logiciels spécialisés; savoir utiliser ces fonctions pour illustrer les résultats
de probabilité. Chaque notion sera abordée en cours et illustrée numériquement en séance
avec les étudiants.

Connaitre les principaux estimateurs, leurs propriétés.
Être capable de programmer les différents estimateurs dans des
situations simples; savoir illustrer par simulation les propriétés des estimateurs (biais, erreur quadratique).
Chaque notion sera abordée en cours et illustrée numériquement en séance avec les étudiants.

Contenu : Lois fondamentales discrètes et continues; Variables indépendantes, lois conditionnelles.
Espérance, espérance conditionnelle. Convergence de variables aléatoires. Théorème
centrale limite, loi des grands nombres. Vecteur gaussien, théorème Cochran. Notion
de chaine de Markov illustrée dans des TP.

Estimateur, estimation. Biais, erreur quadratique, convergence. Intervalle de
confiance. Estimateur des moindres carrés. Estimateur des moments. Estimateur du maximum
de vraisemblance. Equations estimantes.

Visit the full page about this course

The syllabus of the English course in M2 aims at enabling students to validate 3 competences that will be essential for their working life or for their doctoral studies in the future, at the B2 level:

1°) CAN give a clear presentation on a familiar topic, and CAN answer predictable or factual questions

2°) CAN find relevant information and essential points in written texts

3°) CAN make simple notes that are of reasonable use for essay or revision purposes, capturing most important points." (CEF, appendix D).

Reading comprehension can be validated in M1.

The course contents are linked to the students' fields of studies.

Visit the full page about this course

Contents:

• Introduction to database
• Introduction to big data
• Introduction to high performance computing (HPC)
• Numerical solvers for HPC

Visit the full page about this course

Visit the full page about this course

Visit the full page about this course

January science and/or industrial project.

Visit the full page about this course

Industrial and/or research internship.

Visit the full page about this course

This program combines case studies coming from real life problems or models and lectures providing the mathematical and numerical backgrounds.

Contents:

• Introduction, classification, examples.
• Theoretical results: convexity and compacity, optimality conditions, KT theorem
• Algorithmic for unconstrained optimisation (descent, line search, (quasi) Newton)
• Algorithms for non differentiable problems
• Algorithms for constrained optimisation: penalisatio, SQP methods
• Applications

Visit the full page about this course

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Operational Research proposes scientific methods
to help make better decisions. The idea is to develop and use mathematical and computer
tools to master complex problems. Practical applications are historically in
the direction and management of large systems of people, machines, and
materials in industry, service, humanitarian aid, environment ...

In this course, we will focus on especially on problems with a combinatorial
structure: the number of possible solutions is finite but too large to be
enumerated. The study of these problems involves a phase of modelling practical
problems and then algorithmic resolution.

At the end of this course, students will be able to propose a model and will be
able to implement practical solutions (dedicated or industrial tools) to deal
with a problem of decision or optimization.

Visit the full page about this course

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To acquire the main theoretical and practical notions of modern cryptography: from notions in algorithmic complexity and information theory, to a general overview on the main algorithms and protocols in symmetric and asymmetric cryptography.

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Computer Graphics covers the set of techniques enabling the synthesis of animated virtual worlds. The applications range from entertainment (special effects, 3D feature films, video games), to industrial design (modelling and visualizing prototypes) and virtual reality (flight simulator, interactive walk-trough). This course introduces the domain by presenting the bases for the creation of 3D models, their animation, and the rendering of the corresponding 3D scene. Student will be invited to practice through programming exercises in OpenGL.

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Content

This course include practical sessions.

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Description

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1. Holomorphic and analytical functions, in particular the equivalence between the two notions, exponential function and logarithm, principle of analytic continuation, principle of isolated zeros, Cauchy formula for the disc
2. Elemental properties of holomorphic functions (Cauchy inequalities, sequences and series of holomorphic functions, property of the mean, and principle of the maximum)
3. Cauchy theory (existence of primitives, Cauchy theorems)
4. Meromorphic functions (classification of isolated singularities, meromorphic functions, residue theorem, Laurent series)
5. Riemann conformal representation theorem

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This Teaching Unit proposes a discovery of research in mathematics through the study of a subject describing a result or a mathematical theory, with which the student will have to familiarize themselves in order to appropriate them and to be able to account for them in a written report and an oral presentation.

In practice, a list of subjects is proposed during the first semester. Each student selects four subjects from this list, ranked from 1 to 4, and then the person responsible for the training assigns to each student a topic as far as possible among these four. As soon as the assignments are known, each student will contact the author of their subject, who will supervise them for this work throughout the second semester. Once the supervisor has presented the subject and the details of the expected work, the student meets them regularly to report on the progress of his/her work and progress.

The Supervised Research Work leads to the writing of a written report using LaTeX software, which must include an abstract and a bibliography, and an oral defence of 20 to 30 minutes, often followed by questions, before a jury which includes the supervisor. The report and the defence jointly contribute to the evaluation of the work carried out.

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Compléments du premier semestre : principe du maximum faible pour les ÉDP elliptiques du second ordre, inégalité de Harnack

Compléments sur les espaces de Sobolev : injections de Sobolev, opérateurs d'extension, théorie des traces. Introduction aux distributions, distributions tempérées

Opérateurs maximaux monotones, théorème de Hille-Yosida

Équation de la chaleur dans Ω × ]0,+∞[, où Ω ⊂ ℝn est un domaine régulier : existence et unicité des solutions avec conditions au bord de Dirichlet et de Neumann ; principe du maximum pour les solutions de l'équation de la chaleur

Équation des ondes dans Ω × ]0,+∞[ : existence et unicité des solutions, propagation à vitesse finie

Équation de la chaleur semi-linéaire

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Introduction to curves and surfaces.

Curves: Frénet references, covariant derivatives, reference fields, connection forms, structural equations.

Surfaces: surfaces of R^3, plane tangents, differential forms, differentiable applications between surfaces.

Abstract Variety: Whitney's Theorem

Curvature: Normal curvature, Gauss curvature, Geodesics. Case of surfaces of revolution.

Geometry of the surfaces of R^3: Egregium theorem, Gauss Bonnet's theorem

 Possibility of complement: Transition to sub-varieties of ^Rn and abstract varieties

 Possibility of complement: Introduction to dynamic systems. Vector fields and dynamic systems on varieties

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Description

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Description

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Operational Research proposes scientific methods
to help make better decisions. The idea is to develop and use mathematical and computer
tools to master complex problems. Practical applications are historically in
the direction and management of large systems of people, machines, and
materials in industry, service, humanitarian aid, environment ...

In this course, we will focus on especially on problems with a combinatorial
structure: the number of possible solutions is finite but too large to be
enumerated. The study of these problems involves a phase of modelling practical
problems and then algorithmic resolution.

At the end of this course, students will be able to propose a model and will be
able to implement practical solutions (dedicated or industrial tools) to deal
with a problem of decision or optimization.

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This course presents advanced methods and technics for Operations Research.

Reminder :

Linear Programming, Dynamic Programming, MIP modelling and BB
Complexity (P, NP, Co-NP)

Advanced MIP :

formulation, cuts, bounds
applications
lagragian relaxation
column generation
Benders decomposition
Solvers

Constraint Programming

Heuristics

local search
approximation algorithms

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The aim of this course is to provide a broad knowledge of fundamental problems in Combinatorial Optimization to show their algorithmic solutions and to derive min-max results on them. In order to achieve this goal a new object called a polyhedron is introduced. This polyhedral approach helps to shed new light on some classic results of Combinatorial Optimization.

Syllabus: Study of polyhedra associated to problems of Combinatorial Optimization ; Theory of blocking polyhedra ; Connectivity: shortest paths, spanning trees and spanning arborescences of minimum weight ; Flows: Edmonds-Karp Algorithm, Goldberg-Tarjan Algorithm, minimum cost flows ; Matchings: Hungarian method, Edmonds' Algorithm, Chinese postman problem; Matroids: greedy algorithm, intersection of two matroids ; Graph coloring ; Applications coming from various areas of Operations Research.

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The objective of this course is to present different techniques to handle uncertainty in decision problems. These techniques will be illustrated on several applications e.g. inventory control, scheduling, energy, machine learning.

Syllabus : Introduction to uncertainty in optimization problems; Reminders (probability, dynamic programming, ...); Markov chains; Markov decision processes; Stochastic programming; Robust optimization

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The aim of this course is to learn how to use the structure of graphs and other discrete objects to obtain general results on them, and in particular efficient algorithms solving important problems.

We will cover the following topics:

• Structural Graph Theory: we will study the structure of important graph classes with nice algorithmic properties (planar graphs, interval graphs, comparability graphs, ...) and show several concrete problems that can be solved thanks to their structural properties.
• Graph Drawing: with the rise of Big Data, representing huge data sets is a fundamental challenge. Efficient ways to represent large graphs will be presented.
• Codes: we will see various codes (dominating, locating, identifying, ...) in graphs and their applications.
• Extremal combinatorics: the typical question in this field is "what global condition do we need to impose in some graph in order to make sure that some nice structure appears locally?" We will introduce a powerful tool called "the probabilistic method", an show how it can be applied to solve problems in this important area of research.

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This course offers the possibility for the students to gain some experience by facing open/difficult combinatorial problems.

The goal is to model and solve a combinatorial problem with direct industrial applications. We expect the students to take a variety of approaches (local search, compact/extended linear programming formulations, constraint programming, ...) and establish useful results (lower bounds, cuts, complexity,...).

The experimental results will be compared to the litterature (a known academic open benchmark will be available in this case) or will be validated by the industrial partner.

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Today, parallel computing is omnipresent across a large spectrum of computing platforms, from processor cores or GPUs up to Supercomputers and Cloud platforms. The largest Supercomputers gather millions of processing units and are heading towards Exascale (a quintillion or 10^18 flops - http://top500.org). If parallel processing was initially targeting scientific computing, it is now part of many domains like Big Data analytics and Deep Learning. But making an efficient use of these parallel resources requires a deep understanding of architectures, systems, parallel programming models, and parallel algorithms.

Overview:

The class is organized around weekly lectures, discussions and help time. The presented materials that will be available each week on the class web page. To get practical experience and good understanding of the main concepts the students are expected to develop short programs and experiments. Students will also have to prepare a presentation or a written report on research articles. Students will have access to Grid'5000 parallel machines and the SimGrid simulator for experiments.

This class is organized around 2 main blocks:

Overview of parallel systems:

1. • Introduction to parallelism from GPU to supercomputers.
   • Hardware and system considerations for parallel processing (multi-core architectures, process and thread handling, cache efficiency, remote data access, atomic instructions)
   • Parallel programming: message passing, one-sided communications, task-based programming, work stealing based runtimes (MPI, Cilk, TBB, OpenMP).
   • Modeling of parallel programs and platforms. Locality, granularity, memory space, communications.
   • Parallel algorithms, collective communications, topology aware algorithms.
   • Scheduling: list algorithms; partitioning techniques. Application to resource management (PBS, LSF, SGE, OAR).
   • Large scale scientific computing: parallelization of Lagrangian and Eulerian solvers, parallel data analytics and scientific visualization.
   • AI and HPC: how parallelism is used at different levels to accelerate machine learning and deep learning using supercomputers.

Functional parallel programming:

We propose to study a clean and modern approach to the design of parallel algorithms: functional programming. Functional languages are known to provide a different and cleaner programming experience by allowing a shift of focus from "how to do" on "what to do".
If you take for example a simple dot product between two vectors. In c language you might end up with:

unsigned int n = length(v1); double s = 0.0; for (unsigned int i = 0 ; i < n ; i++) { s += v1[i] * v2[i]; }

In python however you could write:

return sum(e1*e2 for e1, e2 in zip(v1, v2))

You can easily notice that the c language code displayed here is highly sequential with a data-flow dependence on the i variable. It intrinsically contains an ordering of operations because it tells you how to do things to obtain the final sum. On the other end the python code exhibits no dependencies at all. It does not tell you how to compute the sum but just what to compute: the sum of all products.

In this course we will study how to express parallel operations in a safe and performant way. The main point is to study parallel iterators and their uses but we will also consider classical parallel programming schemes like divide and conquer. We will both study the theoretical complexity of different parallel algorithms and practice programming and performance analysis on real machines.
All applications will be developed in the RUST programming language around the Rayon parallel programming library.
No previous knowledge of the rust language is required as we will introduce it gradually during the course. You need however to be proficient in at least one low level language (typically C or C++)

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Multi-agent systems (MAS) is a very active field of AI research, with multiple industrial and societal applications. The 2 main fields of application concern Distributed Problem Solving (DPS) and Agent-Based Modelling and Simulation (ABMS). The goal of this course is to understand the concepts of agents, multi-agent systems, models and simulations, and to learn how to design such models. 

This course introduces the field of MAS, various theoretical aspects (agent architectures, reasoning, interactions, game theory, social choice, etc), as well as practical applications from recent research. The focus is mostly on agent-based social simulation, and how to integrate psychological aspects in agents (so-called “human factors”: emotions, biases…) to make them more human-like and realistic. Applications discussed include epidemics modelling, computational economy, crisis management, urban planning, serious games, etc. The practical part of the course comprises several tutorials with various agent-based modelling platforms (in particular GAMA and Netlogo), scientific papers discussions, and analysis and/or extension of existing models. 

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Modern computing increasingly takes advantage of large amounts of distributed data and knowledge. This is grounded on theoretical principles borrowing to several fields of computer science such as programming languages, data bases, structured documentation, logic and artificial intelligence. The goal of this course is to present some of them, the problems that they solve and those that they uncover. The course considers two perspectives on data and knowledge: interpretation (what they mean), analysis (what they reveal) and processing (how can they be traversed efficiently and transformed safely).

The course offers a semantic perspective on distributed knowledge. Distributed knowledge may come from data sources using different ontologies on the semantic web, autonomous software agents learning knowledge or social robots interacting with different interlocutors. The course adopts a synthetic view on these. It first presents principles of the semantics of knowledge representation (RDF, OWL). Ontology alignments are then introduced to reduce the heterogeneity between distributed knowledge and their exploitation for answering federated queries is presented. A practical way for cooperating agents to evolve their knowledge is cultural knowledge evolution that is then illustrated. Finally, the course defines dynamic epistemic logics as a way to model the communication of knowledge and beliefs.

The course also introduces a perspective on programming language foundations, algorithms and tools for processing structured information, and in particular tree-shaped data. It consists in an introduction to relevant theoretical tools with an application to NoSQL (not only SQL) and XML technologies in particular. Theories and algorithmic toolboxes such as fundamentals of tree automata and tree logics are introduced, with applications to practical problems found for extracting information. Applications include efficient query evaluation, memory-efficient validation of document streams, robust type-safe processing of documents, static analysis of expressive queries, and static type-checking of programs manipulating structured information. The course also aims at presenting challenges, important results, and open issues in the area.

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The course aims to provide the fundamental basis for a sound scientific methodology of experimental evaluation in computer science. This lecture emphasizes on methodological aspects of measurement and on the statistics needed to analyze computer systems, human-computer interaction systems, and machine learning systems. We first sensibilize the audience to reproducibility issues related to empirical research in computer science as well as to ethical and scientific integrity aspects. Then we present tools that help address the aforementioned issues and we give the audience the basis of probabilities and statistics required to develop sound experiment designs. The content of the lecture is therefore both theoretical and practical, illustrated by a lot of case studies and practical sessions. The goal is not to provide analysis recipes or techniques that researchers can blindly apply but to make students develop critical thinking and understand some simple (and possibly not-so-simple) tools so that they can both readily use and explore later on.

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The course is divided in two complementary parts: distributed systems and data management.

Part 1: Distributed systems

Summary

Distributed systems are omnipresent. They are formed by a set of computing devices, interconnected by a network, that collaborate to perform a task. Distributed systems execute on a wide range of infrastructures: from Cloud datacenters to wireless sensor networks.

The goal of this course is to study the main algorithms used at the core of Distributed systems. These algorithms must be efficient and robust. An algorithm is efficient when it sustains a high level of performance. Performance can be measured using various metrics such as throughput, latency, response time. An algorithm is robust when it is able to operate despite the occurrence of various types of (network and/or machine) and attacks.

Content

During the course, we will cover several topics that are listed below:

• Event-driven formalisms for distributed algorithms
• Basic abstractions: processes, links
• Failure detector algorithms
• Leader election algorithms
• Broadcasting algorithms
• Distributed shared memory algorithms
• Consensus algorithms
• Epidemic algorithms
• Performance models for distributed systems

Part 2: Data management

Summary

The ability to process large amounts of data is key to both industry and research today. As computing systems are getting larger, they generate more data that need to be analyzed to extract knowledge.

Data management infrastructures are growing fast, leading to the creation of large data centers and federations of data centers. Suitable software infrastructures should be used to store and process data in this context. Big Data software systems are built to take advantage of a large set of distributed resources to efficiently process massive amounts of data while being able to cope with failures that are frequent at such a scale.

In addition to the amount of data to be processed, the other main challenge that such Big Data systems need to deal with is time. For some use cases, the earlier the results of a data analysis is obtained, the more valuable the result is. Some Big Data systems especially target stream processing where data are processed in real time.

Through lectures and practical sessions, this course provides an overview of the software systems that are used to store and process data at large scale. The following topics will be covered:

• Map-Reduce programming model
• In-memory data processing
• Stream processing (data movement and processing)
• Large scale distributed data storage (distributed file systems, NoSQL databases)

Throughout the lectures, the challenges associated with performance and fault tolerance will also be discussed.

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The course present the main cryptographic primitives and security protocols, focusing on security parameters and properties.

Pedagogical goals:

- generic cryptographic primitives: one-way, trap-door and hash functions; random generators; symmetric and assymertic cipher; interactive protocols;

- security properties : complexity and reduction proofs; undistinguidhability; non-malleability; soundness, completeness and zero-knowledge; confidentiality; authentication; privacy; non-repudiation

- use, deployment and integration of protocols in standard crypro lib (eg open-ssl)

- security proofs : fundations and verufucation based on tools (eg avispa)

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Statistical learning is about the construction and study of systems that can automatically learn from data. With the emergence of massive datasets commonly encountered today, the need for powerful machine learning is of acute importance. Examples of successful applications include effective web search, anti-spam software, computer vision, robotics, practical speech recognition, and a deeper understanding of the human genome. This course gives an introduction to this exciting field. In the first part, we will introduce basic techniques such as logistic regression, multilayer perceptrons, nearest neighbor approaches, both from a theoretical and methodological point of views. In the second part, we will focus on more advanced techniques such as kernel methods, which is a versatile tool to represent data, in combination with (un)supervised learning techniques that are agnostic to the type of data that is learned from. The learning techniques that will be covered include regression, classification, clustering and dimension reduction. We will cover both the theoretical underpinnings of kernels, as well as a series of kernels that are important in practical applications. Finally we will touch upon topics of active research, such as large-scale kernel methods and the use of kernel methods to develop theoretical foundations of deep learning models.

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Machine Learning is one of the key areas of Artificial Intelligence and it concerns the study and the development of quantitative models that enables a computer to perform tasks without being explicitly programmed to do them. Learning in this context is hence to recognize complex forms and to make intelligent decisions. Given all existing entries, the difficulty of this task lies in the fact that all possible decisions is usually very complex to enumerate. To get around that, machine learning algorithms are designed in order to gain knowledge on the problem to be addressed based on a limited set of observed data extracted from this problem. To illustrate this principle, consider the supervised learning task, where the prediction function, which infers a predicted output for a given input, is learned over a finite set of labeled training examples, where each instance of this set is a pair constituted of a vector characterizing an observation in a given vector space, and an associated desired response for that instance (also called desired output). After the training step, the function returned by the algorithm is sought to give predictions on new examples, which have not been used in the learning process, with the lowest probability of error. The underlying assumption in this case is that the examples are, in general, representative of the prediction problem on which the function will be applied. We expect that the learning algorithm produces a function that will have a good generalization performance and not the one that is able to perfectly reproduce the outputs associated to the training examples. Guarantees of learnability of this process were studied in the theory of machine learning largely initiated by Vladimir Vapnik. These guarantees are dependent on the size of the training set and the complexity of the class of functions where the algorithm searches for the prediction function. Emerging technologies, particularly those related to the development of Internet, reshaped the domain of machine learning with new learning frameworks that have been studied to better tackle the related problems. One of these frameworks concerns the problem of learning with partially labeled data, or semi-supervised learning, which development is motivated by the effort that has to be made to construct labeled training sets for some problems, while large amount of unlabeled data can be gathered easily for these problems. The inherent assumption, in this case, is that unlabeled data contain relevant information about the task that has to be solved, and that it is a natural idea to try to extract this information so as to provide the learning algorithm more evidence. From these facts were born a number of works that intended to use a small amount of labeled data simultaneously with a large amount of unlabeled data to learn a prediction function.

The intent of this course is to propose a broad introduction to the field of Machine Learning, including discussions of each of the major frameworks, supervised, unsupervised, semi-supervised and reinforcement learning.

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Causality is at the core of our vision of the world and of the way we reason. It has long been recognized as an important concept and was already mentioned in the ancient Hindu scriptures: “Cause is the effect concealed, effect is the cause revealed”. Even Democritus famously proclaimed that he would rather discover a causal relation than be the king of presumably the wealthiest empire of his time. Nowadays, causality is seen as an ideal way to explain observed phenomena and to provide tools to reason on possible outcomes of interventions and what-if experiments, which are central to counterfactual reasoning, as ‘‘what if this patient had been given this particular treatment?’’

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This course is related to mathematical and statistical methods which are very used in supervised learning.

It contains two parts.

In the first part, we will focus on parametric modeling. Starting with the classical linear regression, we will describe several families of estimators that work when considering high-dimensional data, where the classical least square estimator does not work. Model selection and model assessment will particularly be described.

In the second part, we shall focus on nonparametric methods. We will present several tools and ingredients to predict the future value of a variable. We shall focus on methods for non parametric regression from independent to correlated training dataset. We shall also study some methods to avoid the overfitting in supervised learning.

This course will be followed by practical sessions with the R software.

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The automatic processing of languages, whether written or spoken, has always been an essential part of artificial intelligence. This domain has encouraged the emergence of new uses thanks to the arrival in the industrial field of many technologies from research (spell-checkers, speech synthesis, speech recognition, machine translation, …). In this course, we present the most recent advances and challenges for research. We will discuss discourse analysis whether written or spoken, text clarification, automatic speech transcription and automatic translation, in particular recent advances with neural models.

Information access and retrieval is now ubiquitous in everyday life through search engines, recommendation systems, or technological and commercial surveillance, in many application domains either general or specific like health for instance. In this course, we will cover Information retrieval basics, information retrieval evaluation, models for information retrieval, medical information retrieval, and deep learning for multimedia indexing and retrieval

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This lecture deals with Information Systems Security and provides several facets, ranging from modeling to deployment in real applications. Information Systems Security refers to the processes and methodologies involved to keep information confidential, available, and assure its integrity. The lecture is divided in two major parts and assisted with several practical labs, allowing the students to model and configure security policies and also to be aware about several kinds of attacks and breaches.

Course content

Part 1: Access Control, or how to prevent unauthorized people from entering or accessing a system?

This part deals with:

• Cryptology for authentication and trust;
  • security needs : confidentiality, availability, integrity, non-repudiation (CAI/DICP);
  • cryptology primitives : private and public key ; trusted infrastructure (PKI and ledgers).
  • zero-knowledge protocols; secret sharing and multiparty computation / or Practical work with Open SSL
• Access control mechanisms (MAC, DAC, RBAC, ABAC) and their implementations
• The detection and remediation of security breaches such as intrusions and insider attacks
• The deployment of control filters in applications and proxies.

The presented approach is built on the model-driven security paradigm (MDS). It refers to the process of modeling security requirements at a high level of abstraction, and generating technical security implementations. Security models are transformed into enforceable security rules including the run-time security management (e.g. entitlements/authorisations). Three labs are planned:

• B4MSecure: we will apply a formal language with animation and model-checking facilities to identify security breaches in Access Control policies.
• Snort: in this practical session you will set a local environment to simulate two machines, the target machine and the attacker. You will learn how to create firewall rules, monitor your network and how to react when an attack is detected.
• Metasploit: you will discover technology intelligence for vulnerabilities through a practical session where you will reproduce an exploit to hack and take control over a web-based server.

Part 2: Overview of modern attacks on systems, protocols, and networks and countermeasures

This part is devoted to modern attacks carried out on the Internet scale, in particular attacks on the DNS system (Domain Name System), such as cache or zone poisoning attacks, reflection and amplification of DDoS attacks (Distributed Denial of Service), IP spoofing - the root cause of DDoS attacks, botnets (e.g., Mirai), domain generation algorithms used for command-and-control communications, modern malware (e.g., Emotet trojan, Avalanche), spam, phishing, and business email compromise (BEC) scams.

The module will discuss preventative measures and security protocols to fight modern attacks, such as DDoS protection services, IP source address validation (SAV) known as BCP 38, Sender Policy Framework, and DMARC protocols as the first line of defense against email spoofing and BEC fraud, and DNSSEC to prevent DNS manipulation attacks. It will also discuss large-scale vulnerability measurements (a case study of the zone poisoning attack) and the challenges of deploying current security technologies by the system and network operators.

This part will be concluded with a practical team assignment in which students will be divided into groups and will have to configure a secure system in a real-world environment. The goal is to secure their system against the various types of discussed attacks and exploit other groups' systems.

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This course presents advanced methods and technics for Operations Research.

Reminder :

Linear Programming, Dynamic Programming, MIP modelling and BB
Complexity (P, NP, Co-NP)

Advanced MIP :

formulation, cuts, bounds
applications
lagragian relaxation
column generation
Benders decomposition
Solvers

Constraint Programming

Heuristics

local search
approximation algorithms

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The aim of this course is to provide a broad knowledge of fundamental problems in Combinatorial Optimization to show their algorithmic solutions and to derive min-max results on them. In order to achieve this goal a new object called a polyhedron is introduced. This polyhedral approach helps to shed new light on some classic results of Combinatorial Optimization.

Syllabus: Study of polyhedra associated to problems of Combinatorial Optimization ; Theory of blocking polyhedra ; Connectivity: shortest paths, spanning trees and spanning arborescences of minimum weight ; Flows: Edmonds-Karp Algorithm, Goldberg-Tarjan Algorithm, minimum cost flows ; Matchings: Hungarian method, Edmonds' Algorithm, Chinese postman problem; Matroids: greedy algorithm, intersection of two matroids ; Graph coloring ; Applications coming from various areas of Operations Research.

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The objective of this course is to present different techniques to handle uncertainty in decision problems. These techniques will be illustrated on several applications e.g. inventory control, scheduling, energy, machine learning.

Syllabus : Introduction to uncertainty in optimization problems; Reminders (probability, dynamic programming, ...); Markov chains; Markov decision processes; Stochastic programming; Robust optimization

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The aim of this course is to learn how to use the structure of graphs and other discrete objects to obtain general results on them, and in particular efficient algorithms solving important problems.

We will cover the following topics:

• Structural Graph Theory: we will study the structure of important graph classes with nice algorithmic properties (planar graphs, interval graphs, comparability graphs, ...) and show several concrete problems that can be solved thanks to their structural properties.
• Graph Drawing: with the rise of Big Data, representing huge data sets is a fundamental challenge. Efficient ways to represent large graphs will be presented.
• Codes: we will see various codes (dominating, locating, identifying, ...) in graphs and their applications.
• Extremal combinatorics: the typical question in this field is "what global condition do we need to impose in some graph in order to make sure that some nice structure appears locally?" We will introduce a powerful tool called "the probabilistic method", an show how it can be applied to solve problems in this important area of research.

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This course offers the possibility for the students to gain some experience by facing open/difficult combinatorial problems.

The goal is to model and solve a combinatorial problem with direct industrial applications. We expect the students to take a variety of approaches (local search, compact/extended linear programming formulations, constraint programming, ...) and establish useful results (lower bounds, cuts, complexity,...).

The experimental results will be compared to the litterature (a known academic open benchmark will be available in this case) or will be validated by the industrial partner.

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