The face of Internet has dramatically changed over the last few years, from a small community of specialists with research and engineering needs to a space with billions of users using it in their daily life. Jupiter research expects the number of users to attain up to 1.5 billions in 2008 from 1.1 in 2006, representing a growth of 36% in only 2 years. At the same time, new applications appear, like social networking (e.g. Facebook) to share, keep the contact with friends, family or people with common interests. This new usages make network traffic drastically grows, with an expected acceleration of this trend in the near future [7,8]. For example, a recent note on clubic.com evokes the multiplication by four of the peer to peer traffic in the five next years. This increasing number of users with new needs and ways of being connected to the Internet modifies the characteristics of the network and the dynamic of traffic in the following ways: o New traffic concentrated on huge data centers: the development of search engines, large systems of video on demand (e.g. youtube), and of cloud computing, make that a large part of the traffic is concentrated on huge data centers. This phenomenon changes the topology of the Internet. This change depends on the applications deployed and used in the network with opposite effects between P2P and data center applications. o Mobility of users: the usage of mobile devices like laptops and cellular phones spreads and operators are developing multimedia applications for the new smartphones. Their users more and more require to be able to use these applications without experiencing any disruption, e.g. video streaming in a train. o Strong variation of users traffic: the video streaming of popular events and the development of social sharing create communities of users wanting to access a multimedia content. Hence, a large number of users may try to connect to the same resource at the same time. This leads to a highly dynamic traffic load and possible sharp peaks in traffic rates. Therefore new solutions have to be invented for network design and management to take into accounts these new constraints and needs. These changes have to been done in a society facing specific new challenges. A new context. With the increased cost of energy and the sharp growth of demand, the need of energy-aware solutions has appeared as an imperative for governments, companies and individuals. This thematic is also particularly relevant for the networking community. For example, as of 2006, the electricity usage attributable to the servers and data centers in the US is estimated at about 61 billion kilowatt-hours (kWh), or also 1.5% of total U.S. electricity consumption. Between 2000 and 2006, this usage more than doubled, amounting to about $4.5 billion in electricity costs. It's poised to double again by 2011. Hence a very important objective is the reduction of the energy consumption to operate and manage the existing networks, especially with the development of demanding new applications. To reduce the power consumption induced by Internet, several techniques can be studied: 1. At the hardware level: the overall consumption of the network can be reduced by technological progresses in the creation of network equipments, e.g. more efficient cooling systems or the introduction of different hardware states depending on the level of activity. 2. At the network design level: the networks need to be conceived to suite the new needs and applications of users. For example, changes in topologies and well distributed replications of the data are a way to reduce the resources used by the networks. 3. At the network management level: when the network has been already designed, new routing policies taking the power consumption into account can be introduced. During this project, we will focus mainly on the design and management of networks, as there plainly are in the scope of our competences. Finally, the main objectives of this project will be to introduce and analyze energy-aware networks. This will lead to increasing the life-span of telecommunication hardware and to reducing the energy consumption together with the electricity bill. In order to achieve the main goal of the project, we plan to propose: o New cost functions for the network devices (e.g. routers) via measures and models of their consumption in function of their load and other hardware constraints. o New tools for designing energy efficient networks, based on the analysis of the new changes of network topology. o Efficient routing policies, that takes into account the new characteristics of Internet traffic, e.g. the strong variation of user traffic.

In the past few years, all of the major processor vendors adopted multi-core architectures as the main way to improve the processor performance. Within the context of Grid, cloud and other high performance computing infrastructures that traditionally used parallel and concurrent programming, the use of multi-core architectures introduces an additional level of complexity: the intra-node parallelism. The currently available multi-core architectures rely on the well-known SMP model, but the new trends in processor development target asymmetric multi-core architectures (cores with the same instruction set, but different performance in terms of clock speeds, CPUs versus GPUs, etc). In this MCorePHP project, we would like to investigate certain methods and techniques that help simplify the parallel programming without sacrificing performance. Some of the main areas we would like to touch are scheduling, synchronization and proper use of the multi-core architecture features. This requires new programming models, in particular for managing concurrency and memory sharing within the processor architecture. But achieving good performance isn’t our only goal. Multi-core systems tend to become harder to handle as the number of cores per chip increases. Therefore, we need a safe, dependable, autonomic way of developping applications on multi-core processors, but also on multilevel infrastructures including multi-core, clusters, and large scale grid/cloud resources. We will ensure the compatibility of the new programming model with the China Grid specifications, and will assess the viability and efficiency of the approach on a large example from the area of bioinformatics.

Research on fusion energy has entered a new era with the decision to build ITER in Cadarache, France. The success of this international endeavour is crucial for all partners, the host country, as well as for the PACA region where Cadarache is located. The association of several laboratories in the PACA region to focus on outstanding open questions for ITER is one element in the means to respond to such a challenge. Among the open questions, the issue of plasma-wall interaction is a matter of growing concern since it associates a broad range of problems: safety, engineering of the wall components and the future performance of the device. Most important among the latter is the ability to reach the main ITER objective, namely the operation of burning plasmas. We are concerned here by a simulation effort of the plasma wall interaction based on first principle physics. This issue is particularly important since the design of components dedicated to the control of the edge plasma-wall interaction stems from an extrapolation procedure based on an ad-hoc transport code with no embedded scaling properties from present experiments to ITER conditions. This ad-hoc transport is local and linear and cannot account for the known properties of the plasma turbulent transport. Furthermore, it removes all the non linear effects and their enhancement via the coupling to atomic physics, erosion of material or bifurcations of the plasma properties, such as the turbulence transport capability. Our project named ESPOIR, for Edge Simulation of the Physics Of ITER Relevant turbulent transport, is based on the development of two main simulation codes. The long-term goal is to build the new generation of codes dedicated to the analysis of the edge and divertor physics and thus replace the present codes based on as-hoc diffusive plasma transport. Although a kinetic description of the plasma turbulence would be more appropriate, we have chosen a fluid description that is in itself a challenge regarding our goal of providing a routine simulation tool prior to ITER experiments. With this challenge in mind we have organised the ESPOIR project as an interdisciplinary effort including physicists specialised in plasma physics and fluid turbulence simulation codes, applied mathematicians in charge of large code developments and applied mathematicians specialised numerical analysis of novel numerical schemes including asymptotic limits and boundary conditions. All three partners have an internationally recognised expertise and more than 10 years continuous experience in turbulence simulations. Furthermore, one participant is an internationally recognised expert in the field of Plasma-Wall Interaction including theory and experiments. A first effort is dedicated to the development of a versatile simulation tool (TOKAM-3D) that will address the physics in a simplified cylindrical geometry and will also be used as a test bed to implement novel numerical schemes developed with the mathematicians participating to the project. The second effort aims at developing the code ESPOIR in full ITER geometry. Given the importance of the computer resources required by such a simulation, first runs will be achieved within framework of the project but routine operation of the ESPOIR code can only be envisaged just prior to ITER operation. Among the key physics to be addressed in the project are the width of the heat channel at the plasma edge, the plasma fuelling and density limit (related to the so-called Greenwald density), the bifurcations of the edge plasma state such as the H-mode as well as radiative bifurcations and the interaction of the plasma with the main chamber wall and consequent erosion problems. Each of these issues is crucial for ITER and benefit from a significant experimental investigation including that from circular cross section tokamaks such as Tore Supra. Furthermore, these non-linear physics problems strongly depend on the turbulent transport and thus require a proper first principle description to achieve reliable predictive capability. The present specific contribution aims at developing a tool with accurate understanding and knowledge of its numerics and physics as well as a properly defined architecture that will also enable an efficient coupling to the neutral particle source term as generated by the Monte Carlo code EIRENE, the reference neutral particle code for ITER. The joint effort between French partners is therefore completed by a European collaboration with the team in charge of EIRENE as well as with the two European task forces for fusion, respectively in charge of the Integrated Tokamak Modelling and of the Plasma-Wall Interaction. The ESPOIR project will allow us to address key physics issue for ITER with advanced simulation tools. This will provide the basis for new theoretical insight into the problem of plasma wall interaction as well as the renewed means for the crucial collaboration with experimentalists.

GIGA stands for Geometric Inference and Geometric Approximation. GIGA aims at designing mathematical models and algorithms for analyzing, representing and manipulating discretized versions of continuous sub-manifolds or compact subsets of, possibly high dimensional, Riemannian manifolds without losing their topological and geometric properties. Depending on the context, geometric shapes can be represented in three different way: the physical representation (the shape is known only through measurements), the mathematical representation (abstract and continuous), and the computerized representation (inherently discrete). This proposal aims at studying the transitions from one type to the other, as well as the associated discrete data structures. It is divided into tasks which have Geometric Inference and Geometric Approximation as a common thread. Some tasks are motivated by problems coming from data analysis, which can be found when studying data sets in high dimensional spaces. They are dedicated to the development of mathematically well-founded models and tools for the robust estimation of topological and geometric properties of data sets sampled around an unknown compact set in Euclidean spaces or around Riemannian manifolds. Some tasks are motivated by problems coming from data generation, which can be found when studying data sets in lower dimensional spaces (Euclidean spaces of dimension 2 or 3). The proposed research activities aim at leveraging some concepts from computational geometry and harmonic forms to provide novel algorithms for generating discrete data structures either from mathematical representations (possibly deriving from an inference process) or from ''raw'' discrete data. Emphasis will be put on surface reconstruction and mesh generation for data sampled from the physical world. For surface reconstruction our goal is high resilience to noise and outliers as well as reconstruction of stratified objects. For mesh generation we target both isotropic and anisotropic meshes, and simplicial as well as quadrangle and hexahedral meshes. As for surface reconstruction we assume that the input domain boundary is the output of an inference process.

Andre Raspaud launched in 2005 a fruitful cooperation with the Department of Applied Mathematics of the Sun Yat-Sen University of Kaohsiung, Taiwan. This proposal takes its roots from this three years cooperation (including one PhD student in double doctoral degree scheme). The priority scienti'c theme ?Telecommunications' is a well-known key application area of graph theory. The scienti'c aim of this proposal is to tackle telecommunications problems, especially wireless communications problems, with the help of graph colorings and polyhedral graph theory. A key tool which appears in various related context is graph coloring: wavelength division multiplexing (WDM) networks where colors represent wavelengths, radio networks where colors represent frequencies, fault tolerance where colors represent shared resource risk groups, scheduling problems ... In this project, we intend to study new trends of graph colorings, such as list L(p,q)-colorings, and their implications in telecommunications, especially for channel assignments problems (Task 2, subsection 3.3.3). Clustering introduces a hierarchy that is useful to facilitate routing of information through the network. For dynamic networks such as wireless networks, ef'cient resource management, routing and better throughput performance can be achieved through adaptive clustering of these mobile nodes. Dominating sets and their variants are key graph structures to design clusters, and will be studied in subtask 1.1 (subsection 3.3.2). Stable sets are widely used to model in a so-called con'ict graph, mutually non-con'icting nodes in a network, with respect to some shared ressource. In channel assignment problems, the interference graph is such a con'ict graph. Besides con'ict graphs, computing the maximum size of a stable set does have natural translations in telecommunications issues: the maximum stable set problem on a connectivity graph yields the maximum broadcasting set in a TDMA framework or an activation set in a multihop radio network. In a broadcast schedule for TDMA, different time slots correspond to different colors of a suitable graph coloring: in subtask 1.3, we will investigate this further (subsection 3.3.2, again). The core of our projet is devoted to variations of graph colorings that allow to capture speci'cities of channel assignments problems (subsection 3.3.3). A meaningful example is L(p, q)- labelling which models channel assignment problem in radio networks. Because of their theoretical and practical interests L(p, q)-labellings have received considerable attention. We will study list L(p, q)-labellings, as they are suitable to model channel assignments problems such that the list of available frequencies depends on the transmitter. With the emergence of new technologies like optical technologies, it is necessary to design cheap networks that are reliable. A usual technique to guarantee the survivability of a network in case of failure is to impose the existence of a certain number of disjoint paths between the endnodes of the traf'c demands. Another issue is about the quality of the routing in case of failure. It often happens that the secondary path used to route traf'c between two terminals can be much longer than the usual one, increasing the delay of transmission. To avoid this, it is possible to impose some bound on the paths used for routing informations, depending on the type of rerouting strategy. Polyhedral graph theory turned out to be very helpful to provide ef'cient linear programming based algorithms, for problems with a unique rerouting demand. We will extend this approach to handle several rerouting demands (Task 3, subsection 3.3.4). All participants to this project have a strong commitment to graph theory and will bene't from the expertise of the team Mascotte in telecommunication network design and from the expertise of the team RealOpt in mathematical programming. This project will be especially a great opportunity to establish a collaborative research action between the two INRIA teams RealOpt and Mascotte. It will build a strong research network between french researchers in graph theory (from Bordeaux, Grenoble and Sophia-Antipolis) and the Taiwanese discrete mathematic research community (from the Sun Yat-sen University, the National Taiwan University and Academia Sinica).