Our project deals with the restoration and the enhancement of moving pictures. More precisely, it aims at the suppression of occluding defects, the restoration of radiometric impairments and the development of super-resolution techniques. Objectives: Develop fast and automatic algorithms yielding visually satisfying results, in particular when coping with high definition sequences. Originality: Our team has a background both in image processing and applied mathematics. We believe that recent mathematical tools (variational methods, a contrario methods, topographic map, transportation theory, geometry-texture decomposition) will allow significant progresses toward our goals. Expected results: Flicker correction Reliable motion estimation, even with complex motions Automatic detection of instantaneous defects (blotches) and persistent defects (scratches) Variational restoration of fine artefacts Inpainting techniques adapted to high resolution and complex motions Super-resolution for moving pictures We plan to implement algorithms developed by our team as plug-ins for classical and/or specialised softwares.

Bone materials take an important place among prehistoric materials as they record, as biomatérials, a wealth of information on the past way of life in their aspect, structure as well as in their chemical and isotopic composition. Therefore, many physico-chemical studies are devoted to the investigation of archaeological bone as well as their alteration phenomena. It is also important to note that a large quantity of art objects in our museums is at least partly constituted of bone, ivory or antler. They were used from prehistoric times to the Middle Ages to manufacture, among others, sculptures and book covers. However, curators are often at a loss for the conservation of the bone material which is often integrated in complex assemblages with other materials or it has been surface treated. To consolidate its fragile structure, consolidation treatments have been applied without any systematic control and testing of interaction with the different materials. The treatment is generally achieved with a polymer to reinforce the bone structure. However, the consolidation agent can have negative effects on the remaining bone material. It can cause additional alteration processes linked with the degradation of the consolidation agent. To our knowledge, there is no conservation method available today which is adapted to the degree of preservation and to the archaeological conservation purpose (museum, excavation field, DNA analysis…) and which fully respects the preservation criteria required in the archaeological and museum context. The aim of this programme is to develop the knowledge, the methods and the conserveration treatments that correspond to these needs. The proposed programme comprises two parts: an analytical part on the characterisation of model and archaeological bone material and a second one on the application of consolidates to bone material as well as the evaluation of the effects caused by consolidation treatments on the structure, the chemical composition and the mechanical properties at different hierarchical levels. An analytical strategy using complementary analytical micro- and nanotechniques is needed. In former studies, a methodology for the characterisation of the bone mineral phase has been developed. It is now necessary to elaborate a complementary procedure for the characterisation of the organic phase at different levels and of the interface between the mineral and the organic phases at nanoscale in bone material. PIXE, XRF and nano-SIMS, SEM-EDX are used for the analysis of the chemical composition. Structural investigations are mainly realised by means of XRD, microFT-IR, synchrotron based methods such as microtomography and SAXS/WAXS and morphological observations using SEM and TEM. In addition, analysis of the state of preservation of the organic phase is developed by means of microFT-IR, HPLC, LC-MS, STXM-NEXAFS and DSC analyses. A crucial step will be the sample preparation for these analyses. Indeed, the preparation procedure will comprise microtomy and ultramicrotomy in order to keep all information on the structure at micro- and nanoscale and on the texture of the material. Last but not least, measurements of the mechanical properties of the bone material are necessary. In the second part of the programme different treatment procedures using model polymers and currently used restoration polymers are tested. In order to test their efficiency, the bone material has to be analysed concerning its composition, structure and mechanical properties before and after treatment using the newly established analytical procedure. The comparison of the analytical results will allow us to evaluate the effect of the treatments on the bone material and their efficiency. The next step of the research consists in the study of the durability of the applied treatments. The treated material has to be submitted to different accelerated aging tests (under UV light, under changing relative humidity and temperature conditions, in the presence of SO2, NOx and other atmospheric gases …). In parallel, microbiological analyses will be performed to evaluate the contribution of bacteria and other microorganisms to the decomposition of bone in soils. Studies on the conservation of ancient DNA and the effects of treatments on its preservation are also very interesting and necessary. First archaeological samples are non consolidated and consolidated pieces of Palaeolithic reindeer antlers originating from the Musée National de Préhistoire, les Eyzies-de-Tayac, Magdalenian period, Dordogne, France and of archaeological ivory from Jinsha site, 1300BC-550BC, Chengdu (Sichuan province, China). These two study sites allow us to dispose of the two cases generally found in archaeology: on one hand dry samples in a museum and on the other hand wet fragments coming from field excavations. Additionally, modern bone, ivory and antler samples are investigated in order to provide an adequate reference.

Recently a group of European scientists proposed an homonymous ESF project on Collective behaviour & diffusion (CBDif). French mathematicians were associated to the preparation the scientific project. This proposal is intended to fund the French participation to the project. French and other European participants have a long track of active and successful collaborations, through joint research project, bilateral contracts and networks. More specifically, the goal of this proposal is to • cover travel expenses for early stage researchers visiting French groups (1-2 months per visit), • cover travel expenses for French mathematicians participating to workshops organized in the framework of the ESF project, visiting a group of the ESF project or for invitations, • organize one workshop, in coordination with the ESF project. Although very strong, the ESF project is under evaluation and may eventually not be selected. In that case, the present project, CBDif-Fr, would have an even more important role, as it would structure the forces at the European level. The ESF project on 'Collective behaviour & Diffusion: mathematical models and simulations' (CBDif) aims at creating a multinational and multidisciplinary research network at the interface of mathematics with sociology, economy, life sciences, physics and engineering sciences. All partners feature a modern, application-oriented approach to ordinary and partial differential equations (ODEs and PDEs), incorporating core areas of physics and engineering, as well as emerging fields in social, economic and life sciences: asymptotic analysis is used for deriving and understanding hierarchies of models, while sound numerical analysis provides efficient predictive computer simulations for the targeted applications. Mathematical modelling using PDEs plays an increasing role in the aforementioned fields: multidimensional computations of complex multi-scale phenomena are now with-in reach; sophisticated nonlinear analysis deepens our understanding of increasingly complex models; computational results feed back into the modelling process, giving insight to detailed mechanisms which often cannot be studied by real life experiments. Among the numerous areas of applications, we will concentrate particularly on those examples which can be identified, at the modelling stage, as systems made out of a large number of 'individuals' which show a 'collective behaviour' and how to obtain from them 'averaged' information. The behaviour of the individuals can be typically modelled via stochastic ODEs or 'kinetic' type PDEs, while the average dynamics is usually described via continuum model systems of 'diffusion' or 'hydrodynamic' type. The interplay between the aggregate behaviour, (nonlocal, nonlinear) transport phenomena and nonlinear diffusion, is the main issue in the asymptotic analysis of these models. We emphasize that the mathematical methodologies described here serve to investigate important scientific problems sharing the common (PDE) modelling framework of this proposal. At the European level, the participants of CBDif were carefully chosen for their proven track record in successful participations and collaborations in projects of previous international and national framework programmes. French mathematicians have played an important role in the past collaborations among participants. This CBDif-Fr proposal covers the French contribution to the project and is proposed to the ANR in close coordination with the promoters of the ESF project (J. Carrillo, M. Burger and L. Pareschi).

Predicates of natural language like 'red', 'rich' or 'young' are vague, in the sense that they have borderline cases: for instance, we readily admit that an 18 year old is young, and that a 90 year old is not young, but it seems hardly possible to specify the precise age at which an individual would cease to be young. The phenomenon of vagueness has given rise to a large body of literature since the 1970s, in the domains of philosophical logic, cognitive psychology and natural language semantics. While most of the literature in philosophical logic deals with the semantic resolution of sorites paradoxes induced by vague predicates, increasing attention has been given in recent years to the sources of vagueness, both semantic and epistemological. Is vagueness due fundamentally to our ignorance of the limits of applicability of natural language predicates, as argued by proponents of the epistemic account of vagueness (Williamson, Sorensen)? Or rather, does vagueness fundamentally originate in the fact that some stimuli are ambiguous and that this ambiguity cannot be resolved on purely objective grounds, as suggested by the semantic and contextualist accounts of vagueness (Raffman, Shapiro)? The project aims at settling the debate, by investigating the cognitive origins of vagueness into more detail. While the project is led by philosophers and is mostly theoretical, one ambition of the project will be to promote new perspectives on the problem of vagueness, giving in particular emphasis to psychological aspects of the problem in semantics and in perception, but also to foundational issues in the epistemology of vagueness more generally. The project will be led by philosophers with complementary interests and backgrounds, competent in the areas of philosophy of science (Anouk Barberousse), philosophy of language (Pascal Ludwig, Paul Egré), philosophy of mind and perception (Jérôme Dokic, Pascal Ludwig) psychology (Jérôme Sackur), and formal semantics and philosophical logic (Denis Bonnay, Paul Egré). The project is articulated on the investigation of 5 main issues: (1) What is the link between vagueness, context-dependence, and ambiguity? This part of the project will rely on the semantic literature of vagueness. We will discuss work on the typology of vague predicates and on the different forms of context-dependence at stake in the phenomenon of vagueness. (2) How is vagueness semantically and perceptually resolved? Our perception of phonemes is essentially categorical, leaving little room for ambiguity, even when stimuli are made to vary continuously. The project will discuss the scope of categorical perception, and examine the relative status of semantic indeterminacy. Experiments will be made to see how subjects actually behave in situation of forced semantic choice in front of soritical series. (3) What is the scope of judgments of uncertainty characteristic of vagueness? Vagueness in the epistemic account of vagueness is referred to the non-transitivity of perceptual indiscriminability. Williamson's logic of inexact knowledge, in particular, makes crucial use of the intransivity of indiscriminability to model higher-order vagueness. Experiments will be made to test for higher-order uncertainty in semantic judgments, in particular to delimit the scope of higher-order vagueness in a more precise way. (4) What are the epistemological foundations of fuzzy-logic and degree-theoretic treatments of vagueness? This part of the project will rely on the historical and critical assessment of the probabilistic account of vagueness put forward by Emile Borel in the beginning of the 20th century. We propose to clarify the foundation of the notion of degree of truth on the basis of Borel's account, as well as the articulation between modern fuzzy logic and probability theory. (5) What is the incidence of vagueness in decision-theory? Vagueness is not only manifest in explicit linguistic judgments, but is implicit in scenarios in which subjects have to make practical decisions that depend on their implicit estimation of how large or small a quantity is. An instance of this problem is the characterization of 'almost common knowledge' in situations of mutual uncertainty. Decision-theoretic aspects of the phenomenon of vagueness will be investigated. The research will rely on the continuation of work and collaborations in progress on each of these issues. The project relies on the association of members of the Logos group in Barcelona (Prof. M. Kölbel and M. Garcia-Carpintero in particular). It involves the organization of several international conferences and its aim is to foster collaboration with groups active on this topic in other places in Europe in particular (Oxford, St Andrews, Prague).

Les expériences à venir d'observation du fond diffus cosmologique (Planck) et des répartition de masse dans l'univers (catalogues de galaxies et astigmatisme cosmique, en particulier le projet DUNE) vont produire des volumes de données importants qui permettront en plus de réaliser un inventaire détaillé du contenu matériel actuel de l'univers, d'en étudier aussi la physique et l'évolution à des époques très anciennes non accessibles par l'expérimentation directe. La communauté scientifique dispose à l'heure actuelle de nombreux outils numériques grace auxquels on connaît très précisément l'évolution des structures dans l'univers depuis la nucléosynthèse. Par contre, si l'évolution de l'univers à des époques plus reculées a déjà abondamment été étudiée par diverses méthodes limitées à des cas solubles analytiquement mais peu réalistes, elle n'a pas encore fait l'objet d'investigations comparables au niveau numérique pour des modèles physiquement plus plausibles. Le domaine d'étude concerné comprend, en plus des modèles d'inflation, des modèles motivés par la théorie des cordes ou d'autres théories quantiques de la gravitation par l'intermédiaire de la phénoménologie (théorie de champs effective). Il s'agira par exemple du pré big-bang, des cosmologies non singulières, des modèles à dimensions supplémentaires et autres branes, voire de la physique transplanckienne. Des expériences de haute précision comme Planck et DUNE ne permettront de tester les prédictions de ces modèles d'univers primordial que par l'intermédiaire d'effets fins qui nécessitent une approche numérique. Il n'existe pas encore d'équipes spécialisées dans ce domaine, pourtant appelé à se développer dans un futur proche, mais toutes les compétences requises sont déjà présentes en France, en particulier à l'Institut d'Astrophysique de Paris où des composantes importantes des projets expérimentaux sont développées. Cette demande a donc pour objectif d'utiliser cette occasion unique de former le premier groupe de pointe dans le domaine au niveau international.