The Stability of the Minkowski space for the Einstein-Vlasov system

We prove the global stability of the Minkowski space viewed as the trivial solution of the Einstein-Vlasov system. To estimate the Vlasov field, we use the vector field and modified vector field techniques developed in [FJS15; FJS17]. In particular, the initial support in the velocity variable does not need to be compact. To control the effect of the large velocities, we identify and exploit several structural properties of the Vlasov equation to prove that the worst non-linear terms in the Vlasov equation either enjoy a form of the null condition or can be controlled using the wave coordinate gauge. The basic propagation estimates for the Vlasov field are then obtained using only weak interior decay for the metric components. Since some of the error terms are not time-integrable, several hierarchies in the commuted equations are exploited to close the top order estimates. For the Einstein equations, we use wave coordinates and the main new difficulty arises from the commutation of the energy-momentum tensor, which needs to be rewritten using the modified vector fields.Comment: 139 page

A vector field method for relativistic transport equations with applications

We adapt the vector field method of Klainerman to the study of relativistic transport equations. First, we prove robust decay estimates for velocity averages of solutions to the relativistic massive and massless transport equations, without any compact support requirements (in $x$ or $v$) for the distribution functions. In the second part of this article, we apply our method to the study of the massive and massless Vlasov-Nordstr\"om systems. In the massive case, we prove global existence and (almost) optimal decay estimates for solutions in dimensions $n \geq 4$ under some smallness assumptions. In the massless case, the system decouples and we prove optimal decay estimates for the solutions in dimensions $n \geq 4$ for arbitrarily large data, and in dimension $3$ under some smallness assumptions, exploiting a certain form of the null condition satisfied by the equations. The $3$-dimensional massive case requires an extension of our method and will be treated in future work.Comment: 72 pages, 3 figure

From constructive field theory to fractional stochastic calculus. (I) An introduction: rough path theory and perturbative heuristics

Let $B=(B_1(t),..,B_d(t))$ be a $d$-dimensional fractional Brownian motion with Hurst index $\alpha\le 1/4$, or more generally a Gaussian process whose paths have the same local regularity. Defining properly iterated integrals of $B$ is a difficult task because of the low H\"older regularity index of its paths. Yet rough path theory shows it is the key to the construction of a stochastic calculus with respect to $B$, or to solving differential equations driven by $B$. We intend to show in a forthcoming series of papers how to desingularize iterated integrals by a weak singular non-Gaussian perturbation of the Gaussian measure defined by a limit in law procedure. Convergence is proved by using "standard" tools of constructive field theory, in particular cluster expansions and renormalization. These powerful tools allow optimal estimates of the moments and call for an extension of the Gaussian tools such as for instance the Malliavin calculus. This first paper aims to be both a presentation of the basics of rough path theory to physicists, and of perturbative field theory to probabilists; it is only heuristic, in particular because the desingularization of iterated integrals is really a {\em non-perturbative} effect. It is also meant to be a general motivating introduction to the subject, with some insights into quantum field theory and stochastic calculus. The interested reader should read in a second time the companion article \cite{MagUnt2} (or a preliminary version arXiv:1006.1255) for the constructive proofs

Observations of the 18-cm OH lines of comet 103P/Hartley 2 at Nan\c{c}ay in support to the EPOXI and Herschel missions

The 18-cm radio lines of the OH radical were observed in comet 103P/Hartley 2 with the Nan\c{c}ay radio telescope in support to its flyby by the EPOXI mission and to observations with the Herschel Space Observatory. The OH lines were detected from 24 September to 15 December 2010. These observations are used to estimate the gas expansion velocity within the coma to 0.83 \pm 0.08 km/s in October 2010. The water production increased steeply but progressively before perihelion, and reached 1.9 \pm 0.3 X 10E28 s-1 just before the EPOXI flyby.Comment: Accepted for publication in Icarus (6 pages, 4 figures

The chemical diversity of comets

A fundamental question in cometary science is whether the different dynamical classes of comets have different chemical compositions, which would reflect different initial conditions. From the ground or Earth orbit, radio and infrared spectroscopic observations of a now significant sample of comets indeed reveal deep differences in the relative abundances of cometary ices. However, no obvious correlation with dynamical classes is found. Further results come, or are expected, from space exploration. Such investigations, by nature limited to a small number of objects, are unfortunately focussed on short-period comets (mainly Jupiter-family). But these in situ studies provide "ground truth" for remote sensing. We discuss the chemical differences in comets from our database of spectroscopic radio observations, which has been recently enriched by several Jupiter-family and Halley-type comets.Comment: In press in Earth, Moon and Planets (proceedings of the workshop "Future Ground-based Solar System Research: Synergies with Space Probes and Space Telescopes", Portoferraio, Isola d'Elba, Livorno (Italy), 8-12 September 2008). 6 pages with 2 figure

Asymptotic Stability of Minkowski Space-Time with Non-compactly Supported Massless Vlasov Matter.

We prove the global asymptotic stability of the Minkowski space for the massless Einstein-Vlasov system in wave coordinates. In contrast with previous work on the subject, no compact support assumptions on the initial data of the Vlasov field in space or the momentum variables are required. In fact, the initial decay in v is optimal. The present proof is based on vector field and weighted vector field techniques for Vlasov fields, as developed in previous work of Fajman, Joudioux, and Smulevici, and heavily relies on several structural properties of the massless Vlasov equation, similar to the null and weak null conditions. To deal with the weak decay rate of the metric, we propagate well-chosen hierarchized weighted energy norms which reflect the strong decay properties satisfied by the particle density far from the light cone. A particular analytical difficulty arises at the top order, when we do not have access to improved pointwise decay estimates for certain metric components. This difficulty is resolved using a novel hierarchy in the massless Einstein-Vlasov system, which exploits the propagation of different growth rates for the energy norms of different metric components

B cell-activating factor of the tumor necrosis factor family (BAFF) is expressed under stimulation by interferon in salivary gland epithelial cells in primary Sjögren's syndrome

B cell-activating factor (BAFF) has a key role in promoting B-lymphocyte activation and survival in primary Sjögren's syndrome (pSS). The cellular origin of BAFF overexpression in salivary glands of patients with pSS is not fully known. We investigated whether salivary gland epithelial cells (SGECs), the main targets of autoimmunity in pSS, could produce and express BAFF. We used quantitative RT-PCR, ELISA and immunocytochemistry in cultured SGECs from eight patients with pSS and eight controls on treatment with IL-10, tumor necrosis factor α (TNF-α), IFN-α and IFN-γ. At baseline, BAFF expression in SGECs was low in pSS patients and in controls. Treatment with IFN-α, IFN-γ and TNF-α + IFN-γ increased the level of BAFF mRNA in pSS patients (the mean increases were 27-fold, 25-fold and 62-fold, respectively) and in controls (mean increases 19.1-fold, 26.7-fold and 17.7-fold, respectively), with no significant difference between patients and controls. However, in comparison with that at baseline, stimulation with IFN-α significantly increased the level of BAFF mRNA in SGECs of pSS patients (p = 0.03) but not in controls (p = 0.2), which suggests that SGECs of patients with pSS are particularly susceptible to expressing BAFF under IFN-α stimulation. Secretion of BAFF protein, undetectable at baseline, was significantly increased after IFN-α and IFN-γ stimulation both in pSS patients (40.8 ± 12.5 (± SEM) and 47.4 ± 18.7 pg/ml, respectively) and controls (24.9 ± 8.0 and 9.0 ± 3.9 pg/ml, respectively), with no significant difference between pSS and controls. Immunocytochemistry confirmed the induction of cytoplasmic BAFF expression after stimulation with IFN-α and IFN-γ. This study confirms the importance of resident cells of target organs in inducing or perpetuating autoimmunity. Demonstrating the capacity of SGECs to express and secrete BAFF after IFN stimulation adds further information to the pivotal role of these epithelial cells in the pathogenesis of pSS, possibly after stimulation by innate immunity. Our results suggest that an anti-BAFF therapeutic approach could be particularly interesting in pSS

Gas and dust productions of Comet 103P/Hartley 2 from millimetre observations: Interpreting rotation-induced time variations

Comet 103P/Hartley 2 made a close approach to the Earth in October 2010. It was the target of an extensive observing campaign including ground- and orbit-based observatories and was visited by the Deep Impact spacecraft in the framework of its mission extension EPOXI. We present observations of HCN and CH_3OH emission lines conducted with the IRAM Plateau de Bure interferometer on 22–23, 28 October and 4, 5 November 2010 at 1.1, 1.9 and 3.4 mm wavelengths. The thermal emission from the dust coma and nucleus is detected simultaneously. Interferometric images with unprecedented spatial resolution of ∼100 to ∼500 km are obtained. A sine–wave like variation of the thermal continuum is observed in the 23 October data, that we associate with the nucleus thermal light curve. The nucleus contributes up to 30–55% of the observed continuum emission. The dust thermal emission is used to measure the dust production rate. The inferred large dust-to-gas ratio (in the range 2–6) can be explained by the unusual activity of the comet for its size, which allows decimeter size particles and large boulders to be entrained by the gas due to the small nucleus gravity. The rotational temperature of CH_3OH is measured with beam radii from ∼150 km to ∼1500 km. We attribute the increase from ∼35 K to ∼46 K with increasing beam size to radiative processes. The HCN production rate displays strong rotation-induced temporal variations, varying from ∼0.3 × 10^(25) s^(−1) to ∼2.0 × 10^(25) s^(−1) in the 4–5 November period. The HCN production curve, as well as the CO_2 and H_2O production curves measured by EPOXI, are interpreted with a geometric model which takes into account the complex rotational state of 103P/Hartley 2 and its shape. The HCN and H_2O production curves are in phase, showing that these molecules have common sources. The ∼1.7 h delay, in average, of the HCN and H_2O production curves with respect to the CO_2 production curve suggests that HCN and H_2O are mainly produced by subliming icy grains. The scale length of production of HCN is determined to be on the order of 500–1000 km, implying a mean velocity of 100–200 m s^(−1) for the icy grains producing HCN. From the time evolution of the insolation of the nucleus, we show that the CO_2 production is modulated by the insolation of the small lobe of the nucleus. The three-cycle pattern of the production curves reported earlier is best explained by an overactivity of the small lobe in the longitude range 0–180°. The good correlation between the insolation of the small lobe and CO_2 production is consistent with CO_2 being produced from small depths below the surface. The time evolution of the velocity offset of the HCN lines, as well as the displacement of the HCN photocenter in the interferometric maps, are overall consistent with this interpretation. Other localized sources of gas on the nucleus surface are also suggested

Ethyl alcohol and sugar in comet C/2014 Q2 (Lovejoy)

The presence of numerous complex organic molecules (COMs; defined as those containing six or more atoms) around protostars shows that star formation is accompanied by an increase of molecular complexity. These COMs may be part of the material from which planetesimals and, ultimately, planets formed. Comets represent some of the oldest and most primitive material in the solar system, including ices, and are thus our best window into the volatile composition of the solar protoplanetary disk. Molecules identified to be present in cometary ices include water, simple hydrocarbons, oxygen, sulfur, and nitrogen-bearing species, as well as a few COMs, such as ethylene glycol and glycine. We report the detection of 21 molecules in comet C/2014 Q2 (Lovejoy), including the first identification of ethyl alcohol (ethanol, C_2H_5OH) and the simplest monosaccharide sugar glycolaldehyde (CH_2OHCHO) in a comet. The abundances of ethanol and glycolaldehyde, respectively 5 and 0.8% relative to methanol (0.12 and 0.02% relative to water), are somewhat higher than the values measured in solar-type protostars. Overall, the high abundance of COMs in cometary ices supports the formation through grain-surface reactions in the solar system protoplanetary disk

Increased levels of circulating microparticles in primary Sjögren's syndrome, systemic lupus erythematosus and rheumatoid arthritis and relation with disease activity

INTRODUCTION: Cell stimulation leads to the shedding of phosphatidylserine (PS)-rich microparticles (MPs). Because autoimmune diseases (AIDs) are characterized by cell activation, we investigated level of circulating MPs as a possible biomarker in primary Sjögren's syndrome (pSS), systemic lupus erythematosus (SLE) and rheumatoid arthritis (RA). METHODS: We measured plasma levels of total, platelet and leukocyte MPs by prothrombinase capture assay and flow cytometry in 43 patients with pSS, 20 with SLE and 24 with RA and in 44 healthy controls (HCs). Secretory phospholipase A2 (sPLA2) activity was assessed by fluorometry. Soluble CD40 ligand (sCD40L) and soluble P-selectin (sCD62P), reflecting platelet activation, were measured by ELISA. RESULTS: Patients with pSS showed increased plasma level of total MPs (mean +/- SEM 8.49 +/- 1.14 nM PS equivalent (Eq), P < 0.0001), as did patients with RA (7.23 +/- 1.05 n PS Eq, P = 0.004) and SLE (7.3 +/- 1.25 nM PS Eq, P = 0.0004), as compared with HCs (4.13 +/- 0.2 nM PS Eq). Patients with AIDs all showed increased level of platelet MPs (P < 0.0001), but only those with pSS showed increased level of leukocyte MPs (P < 0.0001). Results by capture assay and flow cytometry were correlated. In patients with high disease activity according to extra-glandular complications (pSS), DAS28 (RA) or SLEDAI (SLE) compared with low-activity patients, the MP level was only slightly increased in comparison with those having a low disease activity. Platelet MP level was inversely correlated with anti-DNA antibody level in SLE (r = -0.65; P = 0.003) and serum beta2 microglobulin level in pSS (r = -0.37; P < 0.03). The levels of total and platelet MPs were inversely correlated with sPLA2 activity (r = -0.37, P = 0.0007; r = -0.36, P = 0.002, respectively). sCD40L and sCD62P concentrations were significantly higher in pSS than in HC (P </= 0.006). CONCLUSIONS: Plasma MP level is elevated in pSS, as well as in SLE and RA, and could be used as a biomarker reflecting systemic cell activation. Level of leukocyte-derived MPs is increased in pSS only. The MP level is low in case of more severe AID, probably because of high secretory phospholipase A2 (sPLA2) activity, which leads to consumption of MPs. Increase of platelet-derived MPs, sCD40L and sCD62P, highlights platelet activation in pSS