Relation reconstruction is a broad family of algorithmic problems. It ranges from solving linear systems which have particular patterns, to computing polynomials in several variables which satisfy approximation or interpolation constraints. The patterns and variables bring structure to the equations which implicitly define the sought relations. Relation reconstruction, as a core computational task, arises naturally in many areas of computer science, e.g. in path combinatorics, cryptography and error-correcting codes, where one commonly reconstructs algebraic relations from objects that hide them through implicit descriptions. The design and the implementation of highly efficient algorithms for this task is then of first importance and with high impact. This project combines a complexity driven approach, through the lens of the algebraic structures underlying relation reconstruction, and the design of dedicated data representations and algorithmic techniques. The core goals are, first, to design the next generation of disruptive algorithms of quasi optimal complexity; second, to produce optimized open-source implementations; and lastly, to popularize and increase their impact by solving targeted instances arising in the aforementioned areas of computer science. This project builds on recent results which allowed us to break through long-standing complexity barriers, for the moment on a restricted set of relations. It is organized around three grand objectives. The first two will bring the foundational algorithmic innovations, which will then be deployed and exploited in the last one to solve challenging instances of relation reconstruction. The key innovative ideas developed in this project are efficient reductions to optimized subroutines such as matrix multiplication and polynomial multiplication in one variable, dimension reduction of the space where such relations are computed, and the exploitation of non-linear algebraic structures which arise in this algorithmic problem.

The AMORNET Network aims at training a world-class cohort of doctoral researchers (DRs) who will invent and implement the next generation of mathematical algorithms solving geometric problems arising in robotics. We aim to build strong lasting links between strategically selected industry and academic partners, combining a wide range of mathematical expertise with advanced expertise on robotics design and geometry. The research programme targets, in particular, computational problems arising from soft robotics, a topical area where robotics manipulators are no more rigid but designed with flexible bodies. Soft robots are expected to be more secure when interacting with their environment and to enjoy more mobility properties. Hence, robotics applications of soft robots are numerous and appealing but, to let the Industry adopt them, there is an urgent need to sharpen their geometric designs, models, and identify their mobility properties. This gives rise to challenging and stimulating problems in computational mathematics, especially since these are non-linear but algebraic. The planned training network will provide research and training opportunities to a new generation of DRs, who, in the long-run, shall address the Grand Challenge of making computational mathematics efficient and accurate enough to solve these algebraic problems arising in robotics. This will enable the design of robotics manipulators which will be safer, more reliable and more efficient. The AMORNET Network involves a number of industrial partners and academic facilities that will be used to validate experimentally the theoretical achievements brought by the DRs. The AMORNET Network will deliver more efficient and accurate mathematical methods, algorithms for solving algebraic problems, and their particular applications to issues robotics combined with experimental validation will accelerate the adoption of soft robotics by the EU Industry.

The year 2022 has witnessed the advent of the first supercomputer able to perform over 10^18 floating-point operations per second, officially launching the exascale computing era. While exascale computing holds promises of unprecedented computational power, it also brings numerous significant challenges. Supercomputers have grown larger, more heterogeneous, and more power hungry, and so it has become much harder for complex numerical algorithms to achieve high performance and scalability. This project, MixHPC, confronts these challenges by harnessing the power of lower precision arithmetics, whose recent emergence on modern hardware represents one of the most significant developments of the High Performance Computing (HPC) landscape of the last few years. Reducing the precision makes computations faster, communications lighter, and power consumption greener. However, reducing the precision is also a risky approach that requires major algorithmic innovations in order to avoid compromising the accuracy and robustness of the algorithms. With MixHPC I propose to tackle this challenge by rethinking the role of precision in HPC: rather than viewing it as a fixed, static parameter, MixHPC will dynamically and adaptively employ multiple precisions, strategically mixing them to obtain novel mixed precision algorithms. This research encompasses both fundamental and applied science, spanning the fields of HPC, numerical linear algebra, data science, and numerical analysis. Indeed, I believe that the key to develop effective mixed precision algorithms is to combine knowledge and skills from all these fields. I aim to leverage my double experience both as a numerical analyst and an HPC practitioner to develop innovative algorithms that are fast, numerically sound, provably robust, and able to scale on large problems and on exascale computers with modern hardware.

Motivated by recent works showing significant untapped potential in the design of variation operators for randomized search heuristics, we take up the challenge of analyzing the power and limits of generalizing their design. Randomized search heuristics are general-purpose optimization algorithms, designed to provide good solutions for problems that cannot be solved by exact approaches---for example, because the quality of the solution candidates can only be assessed through simulations or physical experiments or because we lack the time or the knowledge to design a problem-tailored solution. Such situations are ubiquitous in our everyday lives, so that much scientific and industrial progress depends on efficient search heuristics. Variation operators are a key component of randomized search heuristics. They determine how new solution candidates are generated from previously evaluated ones. Variation operators differ in how they balance the trade-off between small local moves with decent probability of improving over the current-best solution and riskier sampling at larger distances, with the hope to identify more promising areas of the search space. Recent works, partially driven by the PI, indicate that state-of-the-art variation operators are too risk-averse, with severe effects on the overall performance of randomized search heuristics. The goal of the VARIATION project is to identify optimal variation operators with proven performance guarantees. To this end, we will formulate their design as a meta-optimization problem, which we analyze through rigorous algorithm analysis and complexity-theoretic approaches. We will use our theoretical insights to derive variation operators whose performance gains will be empirically validated on diverse sets of common optimization and machine learning benchmarks as well as on real-world applications from systems biology and from the automotive industry.

The ICI-Lab joint laboratory, a partnership between LIP6 and the company BodyCAP, aims to study and develop smart biomedical electronic devices to aid in the diagnosis of diseases of the intestinal tract. The ICI-Lab benefits from scientific expertise in AI and in embedded systems for biomedical devices of LIP6 and from the know-how and patents in the design and production of "Capsule" type medical devices of BodyCAP. The work carried out within the ICI-Lab involves the integration of digital processing, from low to high level, within video-endoscopic capsules to produce a new generation of medical devices which will allow: i. a multimodal analysis (image, pH, temperature, gas) within an endoscopic capsule; ii. an interpretation of the data for the explicability of the algorithms; iii. the improvement and automation of procedures for analyzing and interpreting images of the intestinal tract; iv. support to the medical teams in establishing a diagnosis; v. the improvement of the follow-up and care of gastroenterology patients. Images acquired by a capsule can sometimes show obstruction of the lumen of the intestine due to the presence of fluid and / or feces. The multi-modality will make it possible upstream to have additional information to the image and to reinforce the discriminatory nature in the detection of polyps. The treatments will be dedicated to the acquisition of the characteristics of the various data (images, pH, temperature, gas) and on their interpretation for the recognition of pathology markers. These will be based on artificial intelligence algorithms, including deep learning, vector support machines and decision trees. The study, design and validation of intelligent endoscopic video capsules are the purpose of this joint laboratory. The pooling of industrial resources and the assets of the 2 stakeholders will make it possible to develop a platform for in-vitro testing and validation using a bio-mechanical intestinal simulator. These tools will make it possible to create a unique test environment to validate the designed devices on a real life scale, in an artificial environment. Thanks to the partnerships already set up by BodyCAP with various technical platforms, validations will be continued on an animal model and in humans, with the aim of bringing innovative devices to the market in 2025 in order to support diagnosis and improve the effectiveness of screening for bowel pathologies.