Methodologically, the ODISSE project is at the crossroads of inverse problems for partial differential equations (PDE) and observer theory. These two disciplines have a long and rich history of interactions between them and their overlap is becoming more and more important. The ODISSE project proposes fundamental/theoretical contributions in observer design to reconstitute online missing parameters in some dynamical systems described by PDE. Indeed, to analyze, monitor, control or understand physical or biological phenomena, the first step is to provide a mathematical modeling in the form of mathematical equations that describe the evolution of the system variables. Some of these variables are accessible through measurement and others are not. One of the problems in control engineering is that of designing algorithms to provide real time estimates of the unmeasured data from other measured variables. These estimation algorithms are called state observers and are used in many devices. The implementation of such estimators in the context of hyperbolic PDE systems, which are infinite-dimensional systems in the sense that the system's state belongs to a functional space of infinite dimension, is a topic of great interest both from the practical and theoretical points of view. Systems modeled by hyperbolic PDE, that can be of order one or two, correspond to propagation phenomena and appear in many physical contexts and industrial applications. The ODISSE project aims at developing rigorous methodological tools for the design of estimating algorithms for infinite-dimensional systems governed by hyperbolic PDE, with a particular focus on two typical equations: transport equations (hyperbolic PDE of order one) and wave equations (order two). For this purpose, observability properties of this type of PDE systems will be investigated and novel tools for analyzing their estimations will be developed. Based on the peculiarities of each field, we try several challenges that could help in solving some observation problems for hyperbolic PDEs: 1- Find a way to connect the notion of identifiability in inverse problems and that of observability in observer design. 2- For identifiable parameters in the sense of inverse problems, find a way to synthesize a robust and online estimation algorithm (an observer). 3- Find means to incorporate recent advances in the field of observer designs for nonlinear finite dimensional systems. Conversely, study the possibility of using tools from infinite dimensional systems for observer synthesis for finite dimensional systems. 4- Implement the proposed algorithms and perform convergence analysis of the discretized (finite dimensional) systems toward the continuous initial (infinite dimension) systems. These challenges will be addressed in the ODISSE project through a close collaboration between researchers in applied mathematics and control theory from the community of inverse problems and observers design. Several control applications will serve as a test bed to evaluate practical relevance of the theoretical tools to be developed. More specifically, we will work out analysis and design of observers for the concrete processes : batch crystallization processes, polymerization processes and transient elastography.

The mission of the CRYPTECS project is to make privacy-preserving computing (PPC) technology readily available for industrial use by leveraging the broad expertise of a strong transnational Franco-German consortium. Our main innovation will be an open source cloud platform that promotes the adoption of PPC technology by offering a broad spectrum of business-ready PPC techniques (Secure Multiparty Computation, Homomorphic Encryption, Trusted Execution Environments, and methods of Statistical Disclosure Control) as reusable and composable services. The CRYPTECS solution will implement efficient techniques with comprehensive and provable end-to-end security and privacy guarantees. The main scientific challenges addressed in the CRYPTECS project are the elimination of shortcomings of individual PPC techniques, like performance of MPC and FHE or limited utility for DP, the removal of barriers to the integration of different PPC techniques into secure and privacy-preserving machine learning and data analytics services, and the fusion of PPC techniques and cloud native technology to address prerequisites for production use in an industrial context, like scalability. The CRYPTECS consortium, consisting of renowned scientific institutes, multinational companies, and innovative SMBs from both France and Germany, covers the expertise for today's most important PPC techniques and allows us to tackle challenges along the entire innovation chain, from basic research and industrial implementation to field trials with real customers in the IoT and the automotive domain. This breadth allows us to systematically investigate not only individual techniques in isolation but also the interactions between them at all relevant levels. This integrated approach requires intensive cooperation, which is supported by regular face-to-face meetings and the exchange of researchers between partners from Germany and France. We expect that CRYPTECS will have a lasting impact on the successful development and deployment of PPC technologies in Europe, so that privacy protection will be an enabler rather than an obstacle to new innovative applications. For European companies, this is an opportunity to improve their services and to conquer market shares with privacy-friendly GDPR-compliant products. By making PPC techniques suitable for large-scale industrial use, CRYPTECS will help to pave the way for a future in which empowered customers will be able to share their personal data for processing with companies that have earned trust through the use of state-of-the-art privacy-friendly technology. People's concerns about emerging technologies such as Autonomous Driving, Industry 4.0 and Big Data can be alleviated and their development can become a European success story. Obviously, this will have a beneficial impact on the lives of European citizens and societies as a whole.

Hilbert geometry, defined on any convex body in a real affine space, is a rich source of examples of metric spaces and has had numerous applications since its description by Hilbert in 1895. The members of this consortium are contributing to various generalizations of this concept and its applications to different contexts, of affine spaces over other field than the real numbers. The objective of this project is threefold: - to develop a unified approach to these generalizations: unified definitions, common generalization of Benzecri's results and of notions of volumes; - to explore the interplay between the different contexts, through numerous examples; - to obtain meaningful applications of Hilbert geometry in each specific case. Applications include projects around: - the study of the metrics of minimal entropy for symmetric spaces; - degeneracy of convex projective structures on surfaces; - around the frontier of the set of Anosov representations in complex hyperbolic geometry; - new linear programming algorithms, with Smale's 9th problem in mind.

Current evolutions in medical practices induce a change of paradigm with the convergence of diagnosis and therapy, going to personalized medicine and “theranostics”. One can observe the new role of biomarkers in biomedical and therapeutic applications, for instance in the development of molecular multiplex biosensors (nucleic acid, proteins, and metabolites). In addition this is supported by the explosion of point-of-care (POC) technologies and of home monitoring/testing devoted to probe patient parameters in his direct environment. In this context, synthetic biology provides new opportunities to develop a novel generation of biological biosensors able to perform multiplex biomarker detection, simple computation and return of a useful result. However, in order to design robust circuits and to be reliable in a clinical context, synthetic biological biosensor systems must progress in their biochemical implementation of logical tasks and simple operations. While for the biologist, as well as for the mathematician, the sizes of the biological networks and the number of elementary interactions constitute a complexity barrier, for the computer scientist the difficulty is not that much in the size of the networks than in the unconventional nature of biochemical computation. Unlike most programs, biochemical computation involve transitions that are stochastic rather than deterministic, continuous-time rather than discrete-time, poorly insulated in compartments instead of well-structured in modules, and created by evolution instead of by rational design. Although designing biochemical systems is in several ways similar to designing electronic systems, there are fundamental differences that require novel solutions. For example, an asynchronous design approach (in contrast to the standard synchronous approach to electronic system design) is more natural for biochemical reactions, which may vary in a wide spectrum of time scales. Signal integrity and modularity have to be carefully considered since molecules without confining to local compartments may have undesirable global interference. Moreover, available molecular species can be very limited and should be reused whenever possible. These difficulties await new design automation and robustness analysis tools for engineering biochemical systems. The scientific challenge proposed in this project is to master the complexity of biochemical computation and biochemical programming, by working on four fronts: • development of a compiler of behaviour specifications into biochemical reactions, • use of chemical reaction networks (CRNs) as a programming language suitable for mapping into biochemical system design, • implementation of biochemical biosensor programs in microfluidic reactors, • formal verification methods to assess what a circuit can and cannot do.

Bell’s theorem shows that quantum correlations are nonlocal, that is fundamentally nonclassical. It had a profound impact on our understanding of what quantum correlations are or allow for, both for foundational reasons, and for concrete applications in certification of quantum devices and protocols such as randomness generation and cryptography. Often, corresponding experimental demonstrations involve elementary quantum networks, along which several independent quantum states are distributed and measured. It was very recently understood that beyond Bell theorem itself, the correlations emerging from these quantum network structures offered very promising new possibilities in terms of foundational understanding of quantum theory and its applications. LINKS main objective is to take into account quantum network causal structures in order to reinvent the study of quantum nonlocality, from foundations to applications. LINKS will (A) lay the foundations of the study of correlations in network causal structure in order to (B) reveal foundational and applicational consequences of quantum network correlations and (C) enable the implementation of concrete quantum protocols in the lab. LINKS will result in a metamorphosed visibility of the application of quantum theory in the context of quantum networks. It will have a significate impact toward researchers, which could result with a consequent boost in quantum technology and have a concrete impact toward technological companies and start-ups. LINKS will be conducted by a consortium of three researchers: the coordinator, a recognised expert in the very young field of quantum nonlocality in causal network structures, and two internationally recognised experts in the field of nonlocality, certification of quantum devices and the mathematical aspects of quantum information theory. This team will be completed by a 3-year PhD (funded by other means) and a 3-year postdoc (for whom we request the funding).