Dispersion for the wave equation inside strictly convex domains I: the Friedlander model case

We consider a model case for a strictly convex domain of dimension $d\geq 2$ with smooth boundary and we describe dispersion for the wave equation with Dirichlet boundary conditions. More specifically, we obtain the optimal fixed time decay rate for the smoothed out Green function: a $t^{1/4}$ loss occurs with respect to the boundary less case, due to repeated occurrences of swallowtail type singularities in the wave front set.Comment: 53 pages, 4 figures, to appear in Annals of Math. Fixed typos, added remark

The Social Medium Selection Game

We consider in this paper competition of content creators in routing their content through various media. The routing decisions may correspond to the selection of a social network (e.g. twitter versus facebook or linkedin) or of a group within a given social network. The utility for a player to send its content to some medium is given as the difference between the dissemination utility at this medium and some transmission cost. We model this game as a congestion game and compute the pure potential of the game. In contrast to the continuous case, we show that there may be various equilibria. We show that the potential is M-concave which allows us to characterize the equilibria and to propose an algorithm for computing it. We then give a learning mechanism which allow us to give an efficient algorithm to determine an equilibrium. We finally determine the asymptotic form of the equilibrium and discuss the implications on the social medium selection problem

New counterexamples to Strichartz estimates for the wave equation on a 2d model convex domain

We prove that the range of Strichartz estimates on a model 2D convex domain may be further restricted compared to the known counterexamples due to the first author. Our new family of counterexamples is now built on the parametrix construction from our earlier work. Interestingly enough, it is sharp in at least some regions of phase space.Comment: 23 pages, 1 figur

uPARAP/Endo180: a multifaceted protein of mesenchymal cells.

peer reviewedThe urokinase plasminogen activator receptor-associated protein (uPARAP/Endo180) is already known to be a key collagen receptor involved in collagen internalization and degradation in mesenchymal cells and some macrophages. It is one of the four members of the mannose receptor family along with a macrophage mannose receptor (MMR), a phospholipase lipase receptor (PLA2R), and a dendritic receptor (DEC-205). As a clathrin-dependent endocytic receptor for collagen or large collagen fragments as well as through its association with urokinase (uPA) and its receptor (uPAR), uPARAP/Endo180 takes part in extracellular matrix (ECM) remodeling, cell chemotaxis and migration under physiological (tissue homeostasis and repair) and pathological (fibrosis, cancer) conditions. Recent advances that have shown an expanded contribution of this multifunctional protein across a broader range of biological processes, including vascular biology and innate immunity, are summarized in this paper. It has previously been demonstrated that uPARAP/Endo180 assists in lymphangiogenesis through its capacity to regulate the heterodimerization of vascular endothelial growth factor receptors (VEGFR-2 and VEGFR-3). Moreover, recent findings have demonstrated that it is also involved in the clearance of collectins and the regulation of the immune system, something which is currently being studied as a biomarker and a therapeutic target in a number of cancers

Highly potent HIV inhibition: engineering a key anti-HIV structure from PSC-RANTES into MIP-1β/CCL4

The HIV coreceptor CCR5 is a validated target for both the prevention and therapy of HIV infection. PSC-RANTES, an N-terminally modified analogue of one of the natural chemokine ligands of CCR5 (RANTES/CCL5), is a potent inhibitor of HIV entry into target cells. Here, we set out to engineer the anti-HIV activity of PSC-RANTES into another natural CCR5 ligand (MIP-1β/CCL4), by grafting into it the key N-terminal pharmacophore region from PSC-RANTES. We were able to identify MIP-1β/CCL4 analogues that retain the receptor binding profile of MIP-1β/CCL4, but acquire the very high anti-HIV potency and characteristic inhibitory mechanism of PSC-RANTES. Unexpectedly, we discovered that in addition to N-terminal structures from PSC-RANTES, the side chain of Lys33 is also necessary for full anti-HIV potenc

How to evaluate nature-based solutions performance for microclimate, water and soil management issues – Available tools and methods from Nature4Cities European project results

International audienceIn the context of climate change, Nature-Based Solutions (NBSs), a recently developed concept, are increasingly considered as part of the adaptation strategies of the cities. Studies using expert models and methods (EMM) receive a great deal of scientific attention. Considering EMM increasing use, this study aims to perform an analysis of the reported evaluation results, reflecting the capability of the EMM to accurately tackle urban challenges identified within the EU Nature4Cities project. Then, we propose a set of indicators and recommendations about sixteen EMM to be used by funders, researchers and practitioners when evaluating the performance of NBSs. The coupling of the different components (climate, water and soil) is not a simple matter. The analysis relies on the definition of the range of the reported metrics and on the investigation of the relationship between the various indices, applied for the EMM evaluation. Secondly, the study assesses the existing EMM, indicating the potential of NBSs: (i) to reduce urban heat island, (ii) to limit surface warming, (iii) to increase the thermal comfort of people, (iv) to limit the overheating and runoff of surfaces due to impervious areas, (v) to increase water retention during stormy episodes, (vi) to improve storm water quality at the outlet of the sustainable urban drainage systems, (vii) to promote the filtration and epuration of storm water runoff in soil and (viii) to be a support for vegetation. The analysis reveals that EMM can be considered as helpful tools for urban microclimate, urban soil and water management analysis, provided their limitations and characteristics are taken into account by the user when choosing tools and interpreting results (e.g. application scale). With regard to the performance of NBSs, the most commonly used indicators clearly depend on the scale of the project

Aircraft Numerical "Twin": A Time Series Regression Competition

International audienceThis paper presents the design and analysis of a data science competition on a problem of time series regression from aeronautics data. For the purpose of performing predictive maintenance, aviation companies seek to create aircraft "numerical twins", which are programs capable of accurately predicting strains at strategic positions in various body parts of the aircraft. Given a number of input parameters (sensor data) recorded in sequence during the flight, the competition participants had to predict output values (gauges), also recorded sequentially during test flights, but not recorded during regular flights. The competition data included hundreds of complete flights. It was a code submission competition with complete blind testing of algorithms. The results indicate that such a problem can be effectively solved with gradient boosted trees, after preprocessing and feature engineering. Deep learning methods did not prove as efficient

Global existence for energy critical waves in 3-D domains

15 pages, 2 figuresInternational audienceWe prove that the defocusing quintic wave equation, with Dirichlet boundary conditions, is globally well posed on $H^1_0(\Omega) \times L^2(\Omega)$ for any smooth (compact) domain $\Omega \subset \mathbb{R}^3$. The main ingredient in the proof is an $L^5$ spectral projector estimate, obtained recently by Smith and Sogge, combined with a precise study of the boundary value problem