This project is aimed to providing a new tool to chemists in laboratory or industrial production: a highly efficient regio- and / or enantioselective biocatalysed Baeyer-Villiger oxidation in high concentration. In a first step, a set of new enzymes displaying complementary activities will be proposed to face up to the weakness of the current offer of Baeyer-Villigerases (a dozen available enzymes in laboratory and only one commercialised). The genes of putative BVases will be identified in genomic data banks by comparison of sequences then introduced into host microorganism via a high throughput cloning. High and medium throughput screenings intended to report respectively the activity and enantioselectivity profiles of these enzymes will be set up and carried out in order to develop a tool for making easier and faster the choice of the catalyst On the other hand, productivity often reaches limits because of inhibition (or toxicity) phenomena. To move closer to industrial benchmarks, a process based on adsorbent resins will be implemented to increase concentrations. Besides their "green" and sustainable aspect, Baeyer-Villiger biooxidations present an enzymatic version more efficient in terms of enantioselectivity than the chemical version. In order to harness these features, Dynamic Kinetic Resolution (DKR) process associating in situ substrate racemisation simultaneously with microbiological Baeyer-Villiger oxidation (to overcome the maximal 50 % of yield inherent to classic resolutions) will be developed. Various chemical and enzymatic racemisation conditions will be investigated. DKR and resin-based process will be finally brought together in a Dynamic Kinetic Resolution process at High Concentration, which should lead to a significant increase in productivity. The approach proposed in this project will be validated by the industrial scale production of molecules of interest in the field of flavours or synthesis intermediates.

The concept of digital expansion is fundamental to various branches of mathematics and computer science. Beside the instances of so-called q-ary numeration systems (binary, hexadecimal etc.), there are plenty of other digital systems which have been studied in recent years. Mention, for instance, digital expansions with respect to a base which satisfies a linear recursion. For a given numeration system there are plenty of digit functionals which are worth studying, both from a theoretical and practical point of view. We mention, for instance, the sum-of-digits function, the digit or block-counting functions, or more generally, so-called q-additive functions. Digital expansions have a variety of applications. For example, the construction of pseudo-random sequences is crucial in cryptography and intimately related to digital expansions. The aim of this project is to make progress on several fundamental questions which interrelate digital expansions and its functionals (most prominently, the sum-of-digits function and q-additive functions) to classical objects of number theory (integer multiples, prime numbers, polynomials, recurrences). While each of these topics is well investigated, there is still lack of knowledge regarding the interplay between them. The project can be subdivided into three main parts, which are closely connected in terms of the phenomenon of « interaction ». The first part is concerned with studying distribution properties of digital functionals on polynomials or quasi-polynomials in arithmetic progressions. A famous open problem of A. O. Gelfond (1968) regards the distribution of the sum of digits function of special sparse sequences (primes, polynomials) in arithmetic progressions. The cases of primes and squares have recently effectively been treated by C. Mauduit and J. Rivat, using a wealth of techniques from Fourier analysis, exponential sums and combinatorics. The aim is to pursue further this question for higher degree polynomials, where only lower density estimates are known. Also, we want to treat other open conjectures in this area, where the approach could be useful. The appropriate methodological machinery comes from analytic number theory in conjunction with thorough considerations of the arithmetics behind the notion of « digits ». The second part is concerned with studying local distribution properties and oscillation phenomena of error terms of digital functions on integer multiples. Newman (1969) showed that the multiples of three have more often an even number of binary ones than an odd number. In recent years, similar « drifting phenomena » have been shown for many other different multiples, but a characterization is still unavailable. We aim for such a result. A related problem is to find asymptotic approximations of the number of n’s whose multiples (with an arbitrary multiplicative factor) have a given sum of digits. J. Schmid (1984) has obtained such a formula in the case of fixed multiplicative factor. It is a an open and demanding problem to provide such formulae for a large range of multiplicative factors. The third part is concerned with studying the behaviour and distribution of friable integers (« entiers friables »). Friable integers have only small prime divisors and a thorough understanding of their properties is crucial for the quality and complexity of modern factorization algorithms. Recent progress has been made on studying the friable integers among polynomial sequences. The tools to attack such kind of problems of « interaction » stem from probabilistic models. One can refine the notion of friable integers to almost-friable integers, where the friable multiplicative part is large. Another point of interest is to study random multiplicative functions on friable integers, an area of considerable importance in recent years. Finally, it would be interesting to investigate the digital behaviour of friable numbers.

VIRAGE in French means turn/change of direction. Galaxies are evolving systems that experience transformations during their lifetime: their orbits, mass accretion and star formation histories and finally morphology all change. This happens in the context of a living Universe in which structures assemble by the gravitational growth of initial dark matter fluctuations to create the massive galaxy clusters we observe today. How much galaxy transformations are driven by the physics of this gravitational assembly and how much by the physics of baryons is one of the most hotly debated questions today. The underlying key question is whether the dominant processes are internal to galaxies (nature) or due to their interactions with the environment (nurture). We address this question by a detailed characterization of environmental effects within the densest environment of the nearby Universe, the Virgo galaxy cluster. We aim to examine in greater detail than ever before the galaxies in this system, their interactions and the interaction with their surrounding medium in the core of the cluster as well as its peripheral regions. Our goal is to provide a reference analysis of galaxies in these different cluster environments that is statistically complete in range of galaxy mass and multi-wavelength coverage. This is only possible because of its proximity, which makes of Virgo the only galaxy cluster in which baryonic structures can be studied in such great detail, from the brightest to the very faintest galaxies, and including the extremely faint tidal structures around them. Over the next few years, a wealth of surveys of this cluster will revolutionize the way we study it, because of their unprecedented depth, spatial and wavelength coverage. They will discover new objects and expand our insight on the star formation and interacting history of galaxies in this remarkable system. The strength of our team lies in our involvement in all of these major surveys, as either PIs or Co-Is . Our collaboration will therefore have the access, resources and expertise to fully capitalize on this outstanding data set. Our analysis will primarily draw on three surveys: the Next Generation Virgo Survey, the NGVS-IR, and GUViCS, combined with complementary data when needed for our scientific goals. We propose to combine the unique data from these three surveys to characterize the effects of environment on galaxy star formation histories, spatial distribution, and on the intragalactic medium. Our analysis will: -discover new faint galaxies and low surface brightness features (tidal tails, stellar streams) -produce a distance catalog of Virgo galaxies and examine environmental signatures as a function of local (instead of projected) galaxy density -enable spectro-chemical modeling of environmental effects on galaxy spectral energy distributions, and the reconstruction of galaxy star formation histories from the brightest to the faintest objects When completed, our results will be used for decades as benchmarks in the characterization of galaxies changing in a dense environment, from the most massive to the very faintest, and a reference for future comparison of galaxies in the field.

The aim of proposed research is to study various models of non-Markovian random walks modeling the dynamical properties of disordered media. Among these models, the focus is on random walks in random environments, random walks on random graphs like percolation clusters or random trees, reinforced random walks, and random walks in random sceneries. These models have different origins and motivations, but all have natural applications in physics, biology or engineering (see for instance [AH], [BDG], [BTDA], [CM], [dG], [MM], [lD], [St], ...) . All of these models exhibit strong dependence on the past, either by definition of the model itself, or as a consequence of averaging with respect to the random environment. This feature leads to a number of interesting questions, about recurrence/transience of these processes, limit theorems, or large deviations properties that we wish to address in the present project.