This proposal focuses on the first thematic axis: complex systems modeling, and closely respond to the modeling of environmental sciences thematic of the call for proposal, specifically oceanography. The ocean, coupled with other components (atmosphere, continent, and ice) is a building block of the earth system. Recent events have raised questions on social and economic implications of anthropic alterations of the earth system, i.e. both its long-term evolution and extreme events. A better understanding of the ocean system is a key ingredient for improving our prediction of such implications. Ocean models are essential tools to understand key processes, simulate and forecast events of various space and time scales. The whole French ocean modeling community has been recently assembled under the group name COMODO (COmmunauté de Modélisation Océanique). This community is diverse and offers a variety of applications and numerical approaches for ocean modeling; it also relies at various degrees on the international community. For the first time, this proposal reflects a global effort of the French community to strengthen interactions between its members. This common effort will be directed towars two main objectives: improvement of existing models and numerical methods, guidelines for the development of future generation ocean models. Existing ocean models suffers from a number of well-identified issues that will be addressed during this project. To improve on those issues, the present proposal suggests an innovative evaluation of dissipation mechanisms especially in the context of submesoscale modelling and an improvement of advection-diffusion schemes for the reduction of spurious diapycnal mixing for the accurate representation of active and passive tracers. The second part of the proposal is based on recent advances of our community on vertical coordinate systems, unstructured meshes and non-hydrostatic modelling. The objective is here both to continue fundamental research in these topics and to contribute to the design of future generation models involving their system of equations and numerical methods. The proposed developments will be evaluated thanks to a benchmark suite that covers both idealized test cases design to assess basic important properties of numerical schemes and more complex test cases that will be set-up for a thorough evaluation of progresses made during this project. This benchmark suite, accompanied with the results of the different models, will be made publicly available so as to provide elements for future model developments as well as an opportunity for more theoretical work on numerical schemes to be evaluated in the context of ocean modeling.

The overall goal of the project is to provide representations and algorithms for the real-time navigation, on consumer hardware, in a realistic and plausible virtual Earth model. We target the rendering of terrain, vegetation, water surfaces and clouds (we exclude human artefacts), all highly detailed at all scales from ground to space, with physically based motion and illumination at all scales, and without visible transitions between scales. We do not target the best possible physical accuracy as in radiative transfer models or computational fluid dynamics methods (like for instance in remote sensing, climate modelization, meteorology, etc). Instead, we target visual quality and physical plausibility, i.e., shape, illumination and motion models that look realistic and are efficient enough for real-time applications. These goals are ambitious, as several scientific locks must be unlocked to reach them. Solving these hard problems, even for some specific cases only, would be important scientific breakthroughs: - Scalable shape models are hard to design, especially when they must scale on several orders of magnitude. And providing seamless transitions between scales greatly complicates the problem. These goals have been reached only in few cases. - Scalable illumination models is an even harder problem. Indeed averaging the shapes inside a pixel is much easier than averaging the illumination contribution of all these shapes, which can have different orientation, visibility (due to self occlusions), incoming light (due to self shadowing and inter-reflections) and reflection properties. - Scalable motion models for fluids (water and clouds) is also a hard problem, especially when seamless transitions are needed across several orders of magnitude. Although multi-resolution techniques have been proposed for grid-based and particle-based methods, providing real-time fluid motions on large domains remains difficult. Our results will be published in scientific conferences and journals. We also plan to integrate them in the Proland [Pro09] platform, our Virtual Earth browser prototype that integrates our preliminary results on terrain, atmosphere, ocean and rivers. We made demonstrations of Proland to the public at the « Fête de la science » in 2009, and plan to do it again in the future. We also sold a license of Proland to a planetarium company and we use it in an industrial project for flight simulations. Its source code is not public, and we do not plan to release it as Open Source software. This project involves two academic researchers of the same laboratory who work in neighbor teams, plus students hired on the project (one PhD plus short term students). The project tasks and sub-tasks are well separated and independent. The project management is therefore trivial.

All the three partners of this proposal work at developing formal techniques to smoothly define, statically analyze, efficiently implement and optimize, transformations of documents in XML format. To reach its objectives each partner uses a different approach (in which they have a world renowned expertise): a logical approach based on solvers for WAM, a programming language (PL) approach for PPS, and a data-oriented approach for LRI. Each approach achieves different goals and interestingly, though not surprisingly, the strengths of the one are often the weaknesses (or the “future work” issues) of the other. The objective of this project is to produce a paradigm shift for the manipulation of XML data. In order to achieve this goal we will mutualize experiences and know-how of each group and use them first to improve, by cross-fertilization, the research in each specific domain, and then to integrate them into a unique framework. Accordingly, we plan to use functional languages techniques to enrich the µ-calculus of our solver with polymorphic variables and to statically analyze (in order to efficiently materialize) transformations in XML engines. We will reengineer the techniques we developed for the solver to handle backward axes so as to enrich with upward moves the automata used to efficiently query native XML engines. We will modify the solver to fit the resolution of constraint systems generated in the type inference of the application of polymorphic functions. We will use the automata theories developed for querying XML systems to define iterators and study the parallelization of functional languages to manipulate XML. We will adapt the techniques used for typing XML programming languages to enrich the solver (or its meta-theory) with higher-order polymorphic transformations. We will transpose the PL techniques developed for static analysis of programs. to standard processing languages for XML data. We will use the Coq proof assistant to develop formal specifications for XPath, tree automata, and µ-calculus (the core tools of our project), verify the implementations of the solver and of the query engine against these specifications, and formally guarantee their efficiency. The highly ambitious and final goal of this project is to produce a new generation of XML programming languages stemming from the synergy of integrating the three approaches into a unique framework. Languages whose constructions are inspired by the latest results in the PL research; with precise and polymorphic type systems that merge PL typing techniques with logical-solver-based type inference; with efficient implementations issued by latest researches on tree automata and formally certified by latest theorem prover technologies; with optimizations directly issued from their types systems and the logical formalizations and whose efficiency will be formally guaranteed; with the capacity to specify and formally verify invariants, business rules, and data integrity. Languages with a direct and immediate impact on standardization processes.

A major goal of Computer Graphics algorithms is to create images of virtual scenes that are as close as possible to what the scenes would look like in reality. This is called photorealistic rendering, and is commonly used in virtual prototyping, e.g., in the automotive industry or in architecture. Such photorealistic rendering implies accurate computation of the effects of light transport and reflection in the scene, which is a very computationally expensive process. The process is expensive partly because illumination behaves in a highly complex manner: in some places, it varies very rapidly, while in others it changes smoothly. However, through a complete and thorough analysis of the equations of light transport, we believe that we can extract information about this behaviour, and use it for more efficient computations. We will analyze light transport using three different approaches: frequency analysis, dimensionality analysis and 1st-order analysis. Each will be used for two different applications of lighting simulation: either offline, high-quality simulation or interactive simulations. The key novelty of our approach stems from the extraction of compact and efficient quantities from the above analysis, which are used to design innovative algorithms, with significant gains in both time and storage. In what follows, we will present examples of both the analysis and its application, e.g., the use of the covariance matrix to encode frequency properties of light transport and its potential to dramatically improve the speed of Monte-Carlo path-tracing.

The VIMAD project has two main goals: - (technological) build a robust and reliable perception system, only based on visual and inertial measurements, to enhance the navigation capabilities of fully autonomous micro aerial drones; - (scientific) acquire a deep comprehension of the problem of fusing visual and inertial measurements (from now on the Visual-Inertial structure from motion, VISfM). The perception system will be embedded on micro drones to make them able to safely and autonomously navigate in GPS denied and unknown environments and even to perform aggressive manoeuvres. In particular, with unknown environments, we mean environments that are not equipped with motion capture systems or any external sensor. Perception is still the main problem for high-performance robotics. Once the perception problem is assumed solved, for example by the use of external motion-capture systems, then established control techniques allow for highly performing systems [19,28]. A perception system suitable for a micro aerial vehicle must satisfy sever constraints, due to the small size and, consequently, the low allowed payload. This imposes the employment of low weight sensors and low computational complexity algorithms. In this context inertial sensors and monocular cameras, thanks to their complementary characteristics, low weight, low cost and widespread use, represent an interesting sensor suite. On the other hand, current technologies for navigation only based on visual and inertial sensors have the following strong limitations: - The localization task is achieved via recursive algorithms which need initialization. This means that they are not fully autonomous and, more importantly, they are not robust against any unmodeled event (e.g. system failure) which requires the algorithm to be re-initialized; - They are not enough precise in order to allow a micro aerial vehicle to undertake aggressive manoeuvres and, more in general, to accomplish sophisticated tasks. To overcome these limitations our perception system will be developed by relying on the following three new paradigms: - Use of the closed-form solution to the visual-inertial structure from motion problem introduced in [23,24]; - Exploitation of the information contained in the dynamics of the drones; - Use of the observability tool developed in [22] The first paradigm will allow the perception system to be able to initialize (or reinitialize) the localization task, without external support. In other words, it will make the localization task fully autonomous and robust against any unmodeled event like a kidnapping. Additionally, it can be used to introduce a low-cost data association method. The second paradigm will enhance the perception capabilities in terms of precision. This is important in order to accomplish aggressive manoeuvres. Finally, the third paradigm will allow us both to acquire a deeper comprehension of the VISfM and hopefully to design new and more effective sensor arrangements. This scientific topic deserves in our opinion a deep theoretical investigation since the perception system of most mammals relies precisely on visual and vestibular signals. A deep scientific comprehension of this problem could allow the robotics community to introduce new technologies for navigation. Specifically, we will approach this fundamental problem by proceeding in two main steps. In the former we will investigate an open problem in the framework of control theory, which is the Unknown Input Observability (UIO), namely the observability analysis in the case of unknown inputs; the latter is the use of the results obtained for UIO to investigate the observability properties of the VISfM in the case of missing inertial inputs and eventually to design new sensor arrangements.