The rapid improvement of computer hardware and physical simulation capabilities has revolutionized science and engineering, placing computational simulation on an equal footing with theoretical analysis and physical experimentation. This rapidly increasing reliance on the predictive capabilities has created the need for rigor- ous control of numerical errors which strongly impact these predictions. A rigorous control of the numerical error can be only achieved through mesh adaptivity. In this context, the role of mesh adaptation is prominent, as the quality of the mesh, its refinement, and its alignment with the physics are major contributions to these numerical errors. The IMPACTS project aims at pushing the envelope in mesh adaptation in the context of large size, very high fidelity simulations by proposing a new adaptive mesh generation framework. This framework will extensively used the Riemmannian metric-field and will be based on a unique cavity-operator coupled with advancing-point techniques to produce high quality hybrid, curved and adapted meshes.

Fault-tolerant distributed data structures are at the core distributed systems. Due to the multiple sources of non-determinism, their development is challenging. The project aims to increase the confidence we have in distributed implementations of data structures. We think that the difficulty does not only come from the algorithms but from the way we think about distributed systems. We will investigate partially synchronous programming abstractions that reduce the number of interleavings, simplifying the reasoning about distributed systems and their proof arguments. We will use partial synchrony to define reduction theorems from asynchronous semantics to partially synchronous ones, enabling the transfer of proofs from the synchronous world to the asynchronous one. Moreover, we will define a domain specific language, that allows the programmer to focus on the algorithm task, it compiles into efficient asynchronous code, and it is equipped with automated verification engines.

One of the great challenges of imaging sciences is to recover high resolution images from incomplete and possibly noisy measurements. A common practice when tackling such inverse problems is to define a pixel grid on which to reconstruct an image that accounts for the observations, for instance by minimizing an energy. There are many drawbacks to that approach: discretization artifacts, large problem sizes, difficulties to analyze the properties of the model... With CIPRESSI, we propose to develop novel discretization methods which respect the continuous nature of imaging problems. By leveraging the properties of continuous models, we will design fast algorithms which produce artifact-free images. Besides laying the foundation of this next generation of imaging methods, we will apply them to two real problems, in meteorology and microscopy.

The virtualisation of financial transactions is ubiquitous. While payment cards do not offer anonymity, electronic cash does, but despite extensive research it has hardly ever been deployed. Instead, users are increasingly turning to ``crypto\-currencies" like Bitcoin, which provide online payments and promise users privacy. This is undesirable from an ecological point of view, as Bitcoin's security relies on wasting electricity; but even more so from an economical point of view, since taking the control over the money supply out of the hands of central banks is not a viable economic model. Cryptographic e-cash aims at mimicking the properties of physical cash. A bank issues coins which can be withdrawn by users and then spent in a completely anonymous way. So far, all proposed schemes that are practical lack one property of physical cash, which Bitcoin lacks as well, namely the possibility to exchange coins without involving the bank nor requiring users to be online. While classical e-cash must be deposited at the bank once spent, transferable e-cash goes one step further in emulating physical cash. However, achieving the desirable anonymity properties has turned out challenging and so far no practical schemes have been proposed; changing this is one of the goals of the EfTrEC proposal for the ANR JCJC Award. In more detail, we will first (i) revisit the formal model for transferable e-cash, as currently all formal security definitions are of considerable complexity, which makes them hard to work with. We will introduce simple clean definitions and analyse their relations to existing notions; our model can then serve as the basis for analysing proposed schemes. Next we will (ii) develop new and more efficient tools based on which we will construct transferable e-cash schemes with practical efficiency, which we will then analyse by giving rigorous security proofs. We will also aim at reducing the necessary trust by proposing the first schemes that do not require a trusted setup. Our most long-term goal is (iii) the development of schemes that go beyond current techniques in order to counter attacks even on quantum computers. Therefor we will first port tools and techniques from elliptic-curve cryptography that have proved useful for constructing privacy-preserving protocols to the lattice-based world.

This project is motivated by current and projected needs of a power grid with significant renewable energy integration. Renewable energy sources such as wind and solar have a high degree of unpredictability and time variation, which makes balancing demand and supply challenging. There is an increased need for ancillary services to smooth the volatility of renewable power. In the absence of large, expensive batteries, we may have to increase our inventory of responsive fossil-fuel generators, negating the environmental benefits of renewable energy. The proposed approach addresses this challenge by harnessing the inherent flexibility in demand of many types of loads. The objective of the project is to develop decentralized control for automated demand dispatch, %based on probabilistic algorithms and control theory, that can be used by grid operators as ancillary service to regulate demand-supply balance at low cost. We call the resource obtained from these techniques virtual energy storage (VES). Our goal is to create the necessary ancillary services for the grid that are environmentally friendly, that have low cost and that do not impact the quality of service (QoS) for the consumers. Besides respecting the needs of the loads, the aim of the project is to design local control solutions that require minimal communications from the loads to the centralized entity. %, with the aim of respecting the privacy of users. This is possible through a systems architecture that includes the following elements: i) local control at each load based on local measurements combined with a grid-level signal; ii) frequency decomposition of the regulation signal based on QoS and physical constraints for each class of loads.