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International audience; We consider an offshore wind farm defined by the location of the wind turbines and the amount of energy supplied per turbine, as well as the location of the central station responsible for redistributing the collected energy to users on the power grid. Knowing the power injected at each node, the capacities, susceptance and costs of the cables that can be used, the goal is to determine the least expensive cabling to route the energy supplied by the wind turbines to the central station. This cabling must respect the capacity constraints on the cables as well as the electrical constraints of Load Flow defined at each node of the network. In a second step, we look for a cabling that is also robust in case of failure of a cable, the notion of robustness being seen here as the protection again the worst case of failure. This work was carried out in collaboration with EDF Energies renouvelables. We give a mathematical model of the problem taking into account all the constraints of capacity, connectivity, load flow, cable types and incompatibility between edges, in the form of a mixed integer quadratic program that can be linearized and solved using a MIP solver. We then propose two mathematical models for the robust problem, formulation inspired by the previous one and a bi-level program where the second level is a max min program. Finally we present the results of our tests which provide solutions for real data up to about 50 nodes, before concluding.

International audience

International audience; Discrete tomography deals with the reconstruction of discrete homogenous objects from their projections. The reader is referred to the book of Hermann and Kuba [2] for an overview on discrete tomography. The image reconstruction problem is important since its solution is required for developing efficient procedures in image processing, data bases, crystallography, statistics, data compressing,... It can be formulated as follows: given a rectangular array where entries represent the pixels of a digitalized image coloured with k different colors, we consider the problem of reconstructing an image from the number of occurrences of each colour in every column and in every row. The problem is known to be polynomial for k=1, NP-complete for k=3 [1] and its complexity is still open for k=2. Here, we shall consider a graph colouring problem which generalizes both the well known basic graph colouring problem and the above image reconstruction problem. We are given a graph G=(V,E) and a collection P of p subsets Pi of vertices of G. We are also given a set of colours 1, 2, ..,k as well as a collection of p vectors h(Pi) of integers. The problem is to find a k-partition, i.e. a k-colouring, of V such that the number of vertices of Pi coloured with colour j is equal to the jth entry of the vector h(Pi), for all j=1,..,k and all i=1,..,p. The basic graph colouring problem deals with different colour assigned to adjacent vertices: we will call this a "proper" k-colouring otherwise we will call this simply a k-colouring. In this talk, we will consider colouring as well as proper colouring. Let us consider the special case where the graph G is a grid graph, the vertices, denoted by Xrs, are located on row r and column s, r=1,..,m and s=1,..,n, and P is the collection of the m+n chains corresponding to the rows and columns: the problem of finding a k-colouring of G corresponds exactly to the image reconstruction problem. In this talk we will consider some extensions by taking more general classes of graphs such as trees or bipartite graphs. We will restrict our attention to the case where each Pi is a chain in G. We call "cover index" of P, c(P), the maximum number of members of P which may cover a single element of V, i.e. which have a non empty intersection. We call "nested" a family P such that, for any pair of subsets, either one subset is included in the other or they are disjoint; then, the "nesticity" of P, nest(P), is the smallest number of nested families in a partition of P into nested families. First we will give several basic conditions for a solution to exist. Then, we will classify the problems according to the number of colours, the values of c(P) and nest(P), the class of the graph, the diameter of the graph, and so on. For each problem, either we will propose a polynomial time algorithm or we will give complexity results. For instance, we will prove that when G is a tree, the 2-colouring problem and the proper 3-colouring problems are NP-complete even if the maximum degree of G is bounded by 3; but we will propose a polynomial time algorithm solving the k-colouring problem when G is a tree and when any two Pi intersect in at most one vertex. All our results will be summarized in a table.

International audience; BACKGROUND:Coffee intake has been shown to modulate both the effect of ethanol on serum GGT activities in some alcohol consumers and the risk of alcoholic cirrhosis in some patients with chronic diseases. This study aimed to analyze the impact of coffee intake and alcohol consumption on advanced liver fibrosis (ALF) in HIV-HCV co-infected patients.METHODS:ANRS CO13-HEPAVIH is a French, nationwide, multicenter cohort of HIV-HCV-co-infected patients. Sociodemographic, behavioral, and clinical data including alcohol and coffee consumption were prospectively collected using annual self-administered questionnaires during five years of follow-up. Mixed logistic regression models were performed, relating coffee intake and alcohol consumption to ALF.RESULTS:1019 patients were included. At the last available visit, 5.8% reported high-risk alcohol consumption, 27.4% reported high coffee intake and 14.5% had ALF. Compared with patients with low coffee intake and high-risk alcohol consumption, patients with low coffee intake and low-risk alcohol consumption had a lower risk of ALF (aOR (95% CI) 0.24 (0.12⁻0.50)). In addition, patients with high coffee intake had a lower risk of ALF than the reference group (0.14 (0.03⁻0.64) in high-risk alcohol drinkers and 0.11 (0.05⁻0.25) in low-risk alcohol drinkers).CONCLUSIONS:High coffee intake was associated with a low risk of liver fibrosis even in HIV-HCV co-infected patients with high-risk alcohol consumption.

We are interested in the design of robust (or resilient) capacitated rooted Steiner networks in case of terminals with uniform demands. Formally, we are given a graph, capacity and cost functions on the edges, a root, a subset of nodes called terminals, and a bound k on the number of edge failures. We first study the problem where k = 1 and the network that we want to design must be a tree covering the root and the terminals: we give complexity results and propose models to optimize both the cost of the tree and the number of terminals disconnected from the root in the worst case of an edge failure, while respecting the capacity constraints on the edges. Second, we consider the problem of computing a minimum-cost survivable network, i.e., a network that covers the root and terminals even after the removal of any k edges, while still respecting the capacity constraints on the edges. We also consider the possibility of protecting a given number of edges. We propose three different formulations: a cut-set based formulation, a flow based one, and a bilevel one (with an attacker and a defender). We propose algorithms to solve each formulation and compare their efficiency.

International audience; Introduction Alcohol use disorder (AUD) is a major public health concern worldwide. In France, only 10% of people with AUD (PWAUD) receive medical care. General practitioners (GP) are one of the main entry points for AUD care. The present ongoing study, entitled ASIA (Access to Care and Indifference toward Alcohol, Acces aux Soins et Indifference a l'Alcool in French), aims to improve knowledge about factors associated with access to care for AUD by exploring related GP and PWAUD practices, experiences and perceptions. Methods and analysis The ASIA project is an ongoing cross-sectional multisite study based on a complementary mixed-method approach (quantitative and qualitative) using a convergent parallel design. The double-perspective design of the study will enable us to collect and compare data regarding both PWAUD and GP points of view. For the PWAUD quantitative study, 260 PWAUD will be interviewed using a telephone-based questionnaire. For the qualitative study, 36 PWAUD have already been interviewed. The GP quantitative study will include 100 GP in a 15min survey. Fifteen GP have already participated in semistructured interviews for the qualitative study. Logistic regression will be used to identify predictors for access to care. With respect to data analyses, qualitative interviews will be analysed using semantic analysis while quantitative logistic regression will be used for quantitative interviews. Ethics and dissemination This study was approved by the CNIL (French National Commission on Informatics and Liberties) (approval reference number: C16-10, date of approval: 17 July 2017), the CCTIRS (Advisory Committee on Information Processing in Material Research in the Field of Health) and the CEEI (Evaluation and Ethics Committee) (approval reference number: 16-312, date of approval: 8 July 2016) of INSERM (French National Institute of Health and Medical Research). Results from ASIA will be disseminated in peer-reviewed publications, conference presentations, reports and in a PhD thesis.

In a graph G = (V, E) a subset F of V is a d-extensible set if for any stable set Sof F with |S|= d it exists a stable set S' of V-FF such that SUS' is a maximum stable set of G.We say that S can be extended to a maximum stable set with vertices outside of F, shortly S can be extended. We present a characterization of the d-extensible sets for the class of bipartite graphs and we determine, for some values of d, the maximum cardinality of a d-extensible set.We also determine the maximum cardinality of a d-extensible set for a subclass of arborescenceswhere any vertex x of V belongs to a maximum stable set. This problem has some applicationsin reliability where we consider vertex failures in the graph G : a d-extensible set is the set ofvertices that are not protected.

Nous étudions la résolution d'un programme linéaire mixte (MILP) en présence d'incertitudes sur les coefficientsdes contraintes (à droite et à gauche) lorsque la somme des variations de ces coefficients est bornée. Le problèmerobuste se modélise par un programme en deux étapes, les variables de première étape sont entières ou continues,celles du programme de recours (de deuxième étape) sont continues. Nous montrons que le programme de recours,dans lequel les variables de première étape sont fixées, s'écrit comme un nouveau programme linéairemixte. Le programme robuste se résout ensuite à l?aide d?un algorithme de génération de contraintes. Nous montronsque la méthode s'applique lorsque l?hypothèse de recours complet n?est pas satisfaite et lorsque l?ensembledes incertitudes est un polytope dont les points extrêmes sont connus.

International audience; Due to the emergence of bandwidth-requiring services, telecommunication operators are being compelled to renew their fix access network, most of them favoring the Fiber To The Home (FTTH) technology. This paper focuses on the optimization of FTTH deployment, which is of prime importance due to the economic stakes. The key design issue here is locating splitters and routing fi bers in an existing network infrastructure to which is associated a graph with given capacities on the edges. No assumption is made on the structure of the graph. First we propose a mixed integer formulation for this decision problem. Then, valid inequalities and problem size reduction schemes are presented. Finally efficiency of solving approaches is assessed through extensive numerical tests performed on Orange real-life data

Due to the recent increase in bandwidth requirements, telecommunication operators have to support it with the deployment of optical fiber networks through Fiber-To-The-Home Gigabit Passive Optical Network technology (FTTH GPON). One great challenge, in a deregulated context, is to design this network while not knowing who and where the future subscribers will be.We focus on the problem of the robust optical fiber network deployment under demand uncertainty. A two-stage robust optimization model is proposed for this problem, as well as two robust solution methods extending classical results from Ben-Tal et al. and Babonneau et al. in order to be compliant with our uncertainty set.

A general formulation of the problems we are going to consider may be sketched as follows: we are given a system S which is operated by an actor A; this actor tries to choose among several optimal actions which may be represented by subsets of S.An opponent O wants to prevent actor A from operating S in an optimum way by destroying some part P of S. O may in particular wish to find a part P of S as small as possible whose removal will reduce the efficiency of the operation of the system S by a given amount. Another way for O would be to determine a smallest possible part P (the most vital elements) which hits in a sufficient amount every possible optimal action of A.This kind of problem occurs in various situation related to safety or reliability or even in game theoretic contexts.Such problems have been studied from a theoretical point of view in very special cases for which combinatorial optimization models may give an acceptable represen- tation of S. It leads to challenging optimization problems; the goal of this chapter is to give a partial survey of such situations while focusing on simple models based on graphs and other (hopefully tractable) combinatorial structures.

We are concerned with matchings and stable sets in bipartite graphs