Institut Camille Jordan

It has been difficult to establish whether we are limited to the heart muscle cells we are born with or if cardiomyocytes are generated also later in life. We have taken advantage of the integration of carbon-14, generated by nuclear bomb tests during the Cold War, into DNA to establish the age of cardiomyocytes in humans. We report that cardiomyocytes renew, with a gradual decrease from 1% turning over annually at the age of 25 to 0.45% at the age of 75. Fewer than 50% of cardiomyocytes are exchanged during a normal life span. The capacity to generate cardiomyocytes in the adult human heart suggests that it may be rational to work toward the development of therapeutic strategies aimed at stimulating this process in cardiac pathologies.

OBJECTIVE: Adipose tissue may contain few large adipocytes (hypertrophy) or many small adipocytes (hyperplasia). We investigated factors of putative importance for adipose tissue morphology. RESEARCH DESIGN AND METHODS: Subcutaneous adipocyte size and total fat mass were compared in 764 subjects with BMI 18-60 kg/m(2). A morphology value was defined as the difference between the measured adipocyte volume and the expected volume given by a curved-line fit for a given body fat mass and was related to insulin values. In 35 subjects, in vivo adipocyte turnover was measured by exploiting incorporation of atmospheric (14)C into DNA. RESULTS: Occurrence of hyperplasia (negative morphology value) or hypertrophy (positive morphology value) was independent of sex and body weight but correlated with fasting plasma insulin levels and insulin sensitivity, independent of adipocyte volume (beta-coefficient = 0.3, P < 0.0001). Total adipocyte number and morphology were negatively related (r = -0.66); i.e., the total adipocyte number was greatest in pronounced hyperplasia and smallest in pronounced hypertrophy. The absolute number of new adipocytes generated each year was 70% lower (P < 0.001) in hypertrophy than in hyperplasia, and individual values for adipocyte generation and morphology were strongly related (r = 0.7, P < 0.001). The relative death rate (approximately 10% per year) or mean age of adipocytes (approximately 10 years) was not correlated with morphology. CONCLUSIONS: Adipose tissue morphology correlates with insulin measures and is linked to the total adipocyte number independently of sex and body fat level. Low generation rates of adipocytes associate with adipose tissue hypertrophy, whereas high generation rates associate with adipose hyperplasia.

The current standard model of cosmology successfully describes a variety of measurements, but the nature of its main ingredients, dark matter and dark energy, remains unknown. Euclid is a medium-class mission in the Cosmic Vision 2015–2025 programme of the European Space Agency (ESA) that will provide high-resolution optical imaging, as well as near-infrared imaging and spectroscopy, over about 14 000 deg 2 of extragalactic sky. In addition to accurate weak lensing and clustering measurements that probe structure formation over half of the age of the Universe, its primary probes for cosmology, these exquisite data will enable a wide range of science. This paper provides a high-level overview of the mission, summarising the survey characteristics, the various data-processing steps, and data products. We also highlight the main science objectives and expected performance.

The hematopoietic system seeds the CNS with microglial progenitor cells during the fetal period, but the subsequent cell generation dynamics and maintenance of this population have been poorly understood. We report that microglia, unlike most other hematopoietic lineages, renew slowly at a median rate of 28% per year, and some microglia last for more than two decades. Furthermore, we find no evidence for the existence of a substantial population of quiescent long-lived cells, meaning that the microglia population in the human brain is sustained by continuous slow turnover throughout adult life.

Going beyond the linearized study has been a longstanding problem in the theory of Landau damping. In this paper we establish exponential Landau damping in analytic regularity. The damping phenomenon is reinterpreted in terms of transfer of regularity between kinetic and spatial variables, rather than exchanges of energy; phase mixing is the driving mechanism. The analysis involves new families of analytic norms, measuring regularity by comparison with solutions of the free transport equation; new functional inequalities; a control of non-linear echoes; sharp “deflection” estimates; and a Newton approximation scheme. Our results hold for any potential no more singular than Coulomb or Newton interaction; the limit cases are included with specific technical effort. As a side result, the stability of homogeneous equilibria of the non-linear Vlasov equation is established under sharp assumptions. We point out the strong analogy with the KAM theory, and discuss physical implications. Finally, we extend these results to some Gevrey (non-analytic) distribution functions.

Recent articles have shown the connection between representation theory of quivers and the theory of cluster algebras. In this article, we prove that some cluster algebras of type A-D-E can be recovered from the data of the corresponding quiver representation category. This also provides some explicit formulas for cluster variables.

We study the local equation of energy for weak solutions of three-dimensional incompressible Navier-Stokes and Euler equations. We define a dissipation term D ( u ) which stems from an eventual lack of smoothness in the solution u . We give in passing a simple proof of Onsager's conjecture on energy conservation for the three-dimensional Euler equation, slightly weakening the assumption of Constantin et al . We suggest calling weak solutions with non-negative D ( u ) `dissipative'.

Activation of naive CD8 T-cells can lead to the generation of multiple effector and memory subsets. Multiple parameters associated with activation conditions are involved in generating this diversity that is associated with heterogeneous molecular contents of activated cells. Although naive cell polarisation upon antigenic stimulation and the resulting asymmetric division are known to be a major source of heterogeneity and cell fate regulation, the consequences of stochastic uneven partitioning of molecular content upon subsequent divisions remain unclear yet. Here we aim at studying the impact of uneven partitioning on molecular-content heterogeneity and then on the immune response dynamics at the cellular level. To do so, we introduce a multiscale mathematical model of the CD8 T-cell immune response in the lymph node. In the model, cells are described as agents evolving and interacting in a 2D environment while a set of differential equations, embedded in each cell, models the regulation of intra and extracellular proteins involved in cell differentiation. Based on the analysis of \textit{in silico} data at the single cell level, we show that immune response dynamics can be explained by the molecular-content heterogeneity generated by uneven partitioning at cell division. In particular, uneven partitioning acts as a regulator of cell differentiation and induces the emergence of two coexisting sub-populations of cells exhibiting antagonistic fates. We show that the degree of unevenness of molecular partitioning, along all cell divisions, affects the outcome of the immune response and can promote the generation of memory cells.

18 pages, 6 figures

A pre-Lie algebra is a vector space L endowed with a bilinear product ⋅:L×L→L satisfying the relation (x⋅y)⋅z−x⋅(y⋅z)=(x⋅z)⋅y−x⋅(z⋅y), ∀ x,y,z∈L⁠. We give an explicit combinatorial description in terms of rooted trees of the operad associated to this type of algebras and prove that it is a Koszul operad.

We study a new monoid structure for Artin groups associated with finite Coxeter systems. Like the classical positive braid monoid, the new monoid is a Garside monoid. We give several equivalent constructions: algebraically, the new monoid arises when studying Coxeter systems in a “dual” way, replacing the pair (W,S) by (W,T), with T the set of all reflections; geometrically, it arises when looking at the reflection arrangement from a certain basepoint. In the type A case, we recover the monoid constructed by Birman, Ko and Lee. Nous étudions une nouvelle structure de monoı̈de pour les groupes d'Artin associés aux systèmes de Coxeter finis. Ce nouveau monoı̈de est, tout comme le classique monoı̈de des tresses positives, un monoı̈de de Garside. Nous en donnons différentes constructions : algébriquement, le nouveau monoı̈de apparaı̂t quand on étudie les systèmes de Coxeter avec un point de vue “dual”, qui consiste à remplacer la paire (W,S) par (W,T), où T est l'ensemble de toutes les réflexions ; géométriquement, il apparaı̂t quand on observe l'arrangement de réflexions depuis un point-base particulier. Pour les systèmes de type A, nous retrouvons le monoı̈de construit par Birman, Ko et Lee.

In some recent studies, a view emerged that stochastic dynamics governing the switching of cells from one differentiation state to another could be characterized by a peak in gene expression variability at the point of fate commitment. We have tested this hypothesis at the single-cell level by analyzing primary chicken erythroid progenitors through their differentiation process and measuring the expression of selected genes at six sequential time-points after induction of differentiation. In contrast to population-based expression data, single-cell gene expression data revealed a high cell-to-cell variability, which was masked by averaging. We were able to show that the correlation network was a very dynamical entity and that a subgroup of genes tend to follow the predictions from the dynamical network biomarker (DNB) theory. In addition, we also identified a small group of functionally related genes encoding proteins involved in sterol synthesis that could act as the initial drivers of the differentiation. In order to assess quantitatively the cell-to-cell variability in gene expression and its evolution in time, we used Shannon entropy as a measure of the heterogeneity. Entropy values showed a significant increase in the first 8 h of the differentiation process, reaching a peak between 8 and 24 h, before decreasing to significantly lower values. Moreover, we observed that the previous point of maximum entropy precedes two paramount key points: an irreversible commitment to differentiation between 24 and 48 h followed by a significant increase in cell size variability at 48 h. In conclusion, when analyzed at the single cell level, the differentiation process looks very different from its classical population average view. New observables (like entropy) can be computed, the behavior of which is fully compatible with the idea that differentiation is not a "simple" program that all cells execute identically but results from the dynamical behavior of the underlying molecular network.

In this paper, we analyze the impact of the cavitation model on the numerical assessment of lubricated journal bearings. We compare results using the classical Reynolds model and the so-called p-θ model proposed by Elrod and Adams [1974, “A Computer Program for Cavitation and Saturation Problems,” Proceedings of the First LEEDS-LYON Symposium on Cavitation and Related Phenomena in Lubrication, Leeds, UK] to fix the lack of mass conservation of Reynolds’ model. Both models are known to give quite similar predictions of load-carrying capacity and friction torque in nonstarved conditions, making Reynolds’ model the preferred model for its better numerical behavior. Here, we report on numerical comparisons of both models in the presence of microtextured bearing surfaces. We show that in the microtextured situation, Reynolds’ model largely underestimates the cavitated area, leading to inaccuracies in the estimation of several variables, such as the friction torque. This dictates that only mass-conserving models should be used when dealing with microtextured bearings.

In the acyclic case, we establish a one-to-one correspondence between the tilting objects of the cluster category and the clusters of the associated cluster algebra. This correspondence enables us to solve conjectures on cluster algebras. We prove a multiplicativity theorem, a denominator theorem, and some conjectures on properties of the mutation graph. As in the previous article, the proofs rely on the Calabi–Yau property of the cluster category. Pour le cas des carquois acycliques, nous établissons une correspondance biunivoque entre les objets basculants de la catégorie amassée et les amas de l'algèbre amassée associée. Cette correspondance nous permet de résoudre des conjectures sur les algèbres amassées. Nous prouvons un théorème de multiplication, un théorème de dénominateurs, ainsi que certaines conjectures sur les propriétés du graphe de mutation. Comme dans l'article précédent, les démonstrations reposent sur la propriété de Calabi–Yau de la catégorie amassée.

We give a necessary and sufficient condition on the cost function so that the map solution of Monge’s optimal transportation problem is continuous for arbitrary smooth positive data. This condition was first introduced by Ma, Trudinger and Wang [24], [30] for a priori estimates of the corresponding Monge–Ampère equation. It is expressed by a socalled cost-sectional curvature being non-negative. We show that when the cost function is the squared distance of a Riemannian manifold, the cost-sectional curvature yields the sectional curvature. As a consequence, if the manifold does not have non-negative sectional curvature everywhere, the optimal transport map cannot be continuous for arbitrary smooth positive data. The non-negativity of the cost-sectional curvature is shown to be equivalent to the connectedness of the contact set between any cost-convex function (the proper generalization of a convex function) and any of its supporting functions. When the cost-sectional curvature is uniformly positive, we obtain that optimal maps are continuous or Hölder continuous under quite weak assumptions on the data, compared to what is needed in the Euclidean case. This case includes the quadratic cost on the round sphere.

The vanishing viscosity limit is considered for the incompressible 2D Navier-Stokes equations in a bounded domain. Motivated by studies of turbulent flow we suppose Navier's friction condition in the tangential direction, i.e. the creation of a vorticity proportional to the tangential velocity. We prove the existence of the regular solutions for the Navier-Stokes equations with smooth compatible data and of the solutions with bounded vorticity for initial vorticity being only bounded. Finally, we establish a uniform -bound for the vorticity and convergence to the incompressible 2D Euler equations in the inviscid limit.

The sharing economy is a new phenomenon considered to stimulate sustainable practices. It is viewed as the synergy between technology, information and marketing that promotes a new culture where customers favor access over ownership enabling them to use resources more efficiently. Therefore, it represents an innovative business model that can act as a potential pathway to sustainable economic development and energy efficiency. However, economic, and ecological impacts of the sharing economy remain controversial and need further investigation. In fact, sharing economy has disrupted the prevailing economic paradigm soliciting questions about the advantages and the risks of this new behavior. This study aims to fill this gap in the literature and quantitatively assesses the potential implications that the sharing economy has on sustainable economic development and energy efficiency. It builds a proxy indicator for the annual level of sharing economy use per country using internet search data from Google Trends. In addition, it uses annual secondary data for a balanced panel of 18 OECD countries for the period 2014–2018 to test the proposed models’ hypotheses. The positive impacts of the sharing economy on sustainable economic development and energy efficiency are supported by the results of the fixed effect regressions with Driscoll-Kraay standard errors. The findings suggest that the sharing economy represents a socio-economic trend that has the potential to stimulate sustainable economic development and energy efficiency. Therefore, they highlight the power of the sharing economy and offer important theoretical and practical implications for researchers, individuals, and policy makers.

Cluster algebras were introduced by S. Fomin and A. Zelevinsky in connection with dual canonical bases. Let U U be a cluster algebra of type A n A_n . We associate to each cluster C C of U U an abelian category C C \mathcal {C}_C such that the indecomposable objects of C C \mathcal {C}_C are in natural correspondence with the cluster variables of U U which are not in C C . We give an algebraic realization and a geometric realization of C C \mathcal {C}_C . Then, we generalize the “denominator theorem” of Fomin and Zelevinsky to any cluster.

This paper is devoted mainly to the global existence problem for the two-dimensional parabolic-parabolic Keller-Segel system in the full space.We derive a critical mass threshold below which global existence is ensured.Carefully using energy methods and ad hoc functional inequalities, we improve and extend previous results in this direction.The given threshold is thought to be the optimal criterion, but this question is still open.This global existence result is accompanied by a detailed discussion on the duality between the Onofri and the logarithmic Hardy-Littlewood-Sobolev inequalities that underlie the following approach.

We study a reaction-diffusion equation with an integral term describing nonlocal consumption of resources in population dynamics. We show that a homogeneous equilibrium can lose its stability resulting in appearance of stationary spatial structures. They can be related to the emergence of biological species due to the intra-specific competition and random mutations. Various types of travelling waves are observed.