Repeated games for eikonal equations, integral curvature flows and non-linear parabolic integro-differential equations

The main purpose of this paper is to approximate several non-local evolution equations by zero-sum repeated games in the spirit of the previous works of Kohn and the second author (2006 and 2009): general fully non-linear parabolic integro-differential equations on the one hand, and the integral curvature flow of an interface (Imbert, 2008) on the other hand. In order to do so, we start by constructing such a game for eikonal equations whose speed has a non-constant sign. This provides a (discrete) deterministic control interpretation of these evolution equations. In all our games, two players choose positions successively, and their final payoff is determined by their positions and additional parameters of choice. Because of the non-locality of the problems approximated, by contrast with local problems, their choices have to "collect" information far from their current position. For integral curvature flows, players choose hypersurfaces in the whole space and positions on these hypersurfaces. For parabolic integro-differential equations, players choose smooth functions on the whole space

Existence of solutions for a higher order non-local equation appearing in crack dynamics

In this paper, we prove the existence of non-negative solutions for a non-local higher order degenerate parabolic equation arising in the modeling of hydraulic fractures. The equation is similar to the well-known thin film equation, but the Laplace operator is replaced by a Dirichlet-to-Neumann operator, corresponding to the square root of the Laplace operator on a bounded domain with Neumann boundary conditions (which can also be defined using the periodic Hilbert transform). In our study, we have to deal with the usual difficulty associated to higher order equations (e.g. lack of maximum principle). However, there are important differences with, for instance, the thin film equation: First, our equation is nonlocal; Also the natural energy estimate is not as good as in the case of the thin film equation, and does not yields, for instance, boundedness and continuity of the solutions (our case is critical in dimension $1$ in that respect)

Magnetic Interactions and Transport in (Ga,Cr)As

The magnetic, transport, and structural properties of (Ga,Cr)As are reported. Zincblende Ga$_{1-x}$Cr$_{x}$As was grown by low-temperature molecular beam epitaxy (MBE). At low concentrations, x$\sim$0.1, the materials exhibit unusual magnetic properties associated with the random magnetism of the alloy. At low temperatures the magnetization M(B) increases rapidly with increasing field due to the alignment of ferromagnetic units (polarons or clusters) having large dipole moments of order 10-10$^2$$\mu_B$. A standard model of superparamagnetism is inadequate for describing both the field and temperature dependence of the magnetization M(B,T). In order to explain M(B) at low temperatures we employ a distributed magnetic moment (DMM) model in which polarons or clusters of ions have a distribution of moments. It is also found that the magnetic susceptibility increases for decreasing temperature but saturates below T=4 K. The inverse susceptibility follows a linear-T Curie-Weiss law and extrapolates to a magnetic transition temperature $\theta$=10 K. In magnetotransport measurements, a room temperature resistivity of $\rho$=0.1 $\Omega$cm and a hole concentration of $\sim10^{20}$ cm$^{-3}$ are found, indicating that Cr can also act as a acceptor similar to Mn. The resistivity increases rapidly for decreasing temperature below room temperature, and becomes strongly insulating at low temperatures. The conductivity follows exp[-(T$_1$/T)$^{1/2}$] over a large range of conductivity, possible evidence of tunneling between polarons or clusters.Comment: To appear in PRB 15 Mar 200

Goos-H\"{a}nchen and Imbert-Fedorov shifts of polarized vortex beams

We study, analytically and numerically, reflection and transmission of an arbitrarily polarized vortex beam on an interface separating two dielectric media and derive general expressions for linear and angular Goos-Hanchen and Imbert-Fedorov shifts. We predict a novel vortex-induced Goos-Hanchen shift, and also reveal direct connection between the spin-induced angular shifts and the vortex-induced linear shifts.Comment: 4 pages, 2 figures, to appear in Optics Letter

Spontaneous splenic rupture in an active duty Marine upon return from Iraq: a case report

<p>Abstract</p> <p>Introduction</p> <p>Atraumatic splenic rupture is a rare event that has been associated with several infectious disease processes. In the active duty military population, potential exposure to these pathogens is significant. Here we discuss the case of an active duty Marine with spontaneous splenic rupture upon return from a six-month deployment in Iraq.</p> <p>Case presentation</p> <p>A previously healthy 30-year-old Caucasian male active duty Marine presented with abdominal pain, fever and diarrhea after deployment to Iraq in support of Operation Iraqi Freedom. Based on clinical and radiographic evidence, a diagnosis of spontaneous splenic rupture was ultimately suspected. After exploratory laparotomy with confirmation of rupture, splenectomy was performed, and the patient made a full, uneventful recovery. Histopathologic examination revealed mild splenomegaly with a ruptured capsule of undetermined cause.</p> <p>Conclusion</p> <p>Spontaneous splenic rupture is a rare event that may lead to life-threatening hemorrhage if not diagnosed and treated quickly. Although the cause of this patient's case was unknown, atraumatic splenic rupture has been associated with a variety of infectious diseases and demonstrates some risks the active duty military population may face while on deployment. Having an awareness of these pathogens and their role in splenic rupture, clinicians caring for military personnel must be prepared to recognize and treat this potentially fatal complication.</p

Coordinated optimization of visual cortical maps (II) Numerical studies

It is an attractive hypothesis that the spatial structure of visual cortical architecture can be explained by the coordinated optimization of multiple visual cortical maps representing orientation preference (OP), ocular dominance (OD), spatial frequency, or direction preference. In part (I) of this study we defined a class of analytically tractable coordinated optimization models and solved representative examples in which a spatially complex organization of the orientation preference map is induced by inter-map interactions. We found that attractor solutions near symmetry breaking threshold predict a highly ordered map layout and require a substantial OD bias for OP pinwheel stabilization. Here we examine in numerical simulations whether such models exhibit biologically more realistic spatially irregular solutions at a finite distance from threshold and when transients towards attractor states are considered. We also examine whether model behavior qualitatively changes when the spatial periodicities of the two maps are detuned and when considering more than 2 feature dimensions. Our numerical results support the view that neither minimal energy states nor intermediate transient states of our coordinated optimization models successfully explain the spatially irregular architecture of the visual cortex. We discuss several alternative scenarios and additional factors that may improve the agreement between model solutions and biological observations.Comment: 55 pages, 11 figures. arXiv admin note: substantial text overlap with arXiv:1102.335

Rotation, activity, and lithium abundance in cool binary stars

We have used two robotic telescopes to obtain time-series high-resolution spectroscopy and V I and/or by photometry for a sample of 60 active stars. Orbital solutions are presented for 26 SB2 and 19 SB1 systems with unprecedented phase coverage and accuracy. The total of 6,609 R=55,000 echelle spectra are also used to systematically determine effective temperatures, gravities, metallicities, rotational velocities, lithium abundances and absolute H{\alpha}-core fluxes as a function of time. The photometry is used to infer unspotted brightness, V - I and/or b - y colors, spot-induced brightness amplitudes and precise rotation periods. Our data are complemented by literature data and are used to determine rotation-temperature-activity relations for active binary components. We also relate lithium abundance to rotation and surface temperature. We find that 74% of all known rapidly-rotating active binary stars are synchronized and in circular orbits but 26% are rotating asynchronously of which half have Prot > Porb and e > 0. Because rotational synchronization is predicted to occur before orbital circularization active binaries should undergo an extra spin-down besides tidal dissipation. We suspect this to be due to a magnetically channeled wind with its subsequent braking torque. We find a steep increase of rotation period with decreasing effective temperature for active stars. For inactive, single giants with Prot > 100 d, the relation is much weaker. Our data also indicate a period-activity relation for H{\alpha} of the form RH{\alpha} \propto P - 0.24 for binaries and RH{\alpha} \propto P -0.14 for singles. Lithium abundances in our sample increase with effective temperature. On average, binaries of comparable effective temperature appear to exhibit 0.25 dex less surface lithium than singles. We also find a trend of increased Li abundance with rotational period of form log n(Li) \propto - 0.6 log Prot

SEIS: Insight's Seismic Experiment for Internal Structure of Mars.

By the end of 2018, 42 years after the landing of the two Viking seismometers on Mars, InSight will deploy onto Mars' surface the SEIS (Seismic Experiment for Internal Structure) instrument; a six-axes seismometer equipped with both a long-period three-axes Very Broad Band (VBB) instrument and a three-axes short-period (SP) instrument. These six sensors will cover a broad range of the seismic bandwidth, from 0.01&nbsp;Hz to 50&nbsp;Hz, with possible extension to longer periods. Data will be transmitted in the form of three continuous VBB components at 2 sample per second (sps), an estimation of the short period energy content from the SP at 1&nbsp;sps and a continuous compound VBB/SP vertical axis at 10&nbsp;sps. The continuous streams will be augmented by requested event data with sample rates from 20 to 100 sps. SEIS will improve upon the existing resolution of Viking's Mars seismic monitoring by a factor of ∼ 2500 at 1&nbsp;Hz and ∼ 200 000 at 0.1&nbsp;Hz. An additional major improvement is that, contrary to Viking, the seismometers will be deployed via a robotic arm directly onto Mars' surface and will be protected against temperature and wind by highly efficient thermal and wind shielding. Based on existing knowledge of Mars, it is reasonable to infer a moment magnitude detection threshold of M w ∼ 3 at 40 ∘ epicentral distance and a potential to detect several tens of quakes and about five impacts per year. In this paper, we first describe the science goals of the experiment and the rationale used to define its requirements. We then provide a detailed description of the hardware, from the sensors to the deployment system and associated performance, including transfer functions of the seismic sensors and temperature sensors. We conclude by describing the experiment ground segment, including data processing services, outreach and education networks and provide a description of the format to be used for future data distribution.Electronic supplementary materialThe online version of this article (10.1007/s11214-018-0574-6) contains supplementary material, which is available to authorized users

CD8+ T Cells from Human Neonates Are Biased toward an Innate Immune Response

To better understand why human neonates show a poor response to intracellular pathogens, we compared gene expression and histone modification profiles of neonatal naive CD8+ T cells with that of their adult counterparts. We found that neonatal lymphocytes have a distinct epigenomic landscape associated with a lower expression of genes involved in T cell receptor (TCR) signaling and cytotoxicity and a higher expression of genes involved in the cell cycle and innate immunity. Functional studies corroborated that neonatal CD8+ T cells are less cytotoxic, transcribe antimicrobial peptides, and produce reactive oxygen species. Altogether, our results show that neonatal CD8+ T cells have a specific genetic program biased toward the innate immune response. These findings will contribute to better diagnosis and management of the neonatal immune response.This project was specifically supported by a joint EcosNord-Anuies-SEP-Con-acyt project (M11S01). Work in the M.A.S. laboratory is supported by grantsfrom Consejo Nacional de Ciencia y Tecnologı ́a(CONACYT; CB-2011-01168182) and Programa de Mejoramiento del Profesorado (PROMEPSI-UAEM/13/342). Work in the S.S. laboratory is supported by recurrent fundingfrom the Inserm and Aix-Marseille University and by specific grants from theEuropean Union’s FP7 Program (agreement 282510-BLUEPRINT), the Associ-ation pour la Recherche contre le Cancer (ARC) (project SFI20111203756), andthe Aix-Marseille initiative d’excelence (A*MIDEX) project ANR-11-IDEX-0001-02. We thank Centro Estatal de la Transfusio ́n Sanguı ́nea in Cuernavaca for thedonation of leukocyte concentrates and the mothers and babies of HospitalGeneral Parres in Cuernavaca for the donation of cord blood. This study makesuse of data generated by the Blueprint and Roadmap consortia. A full list of theinvestigators who contributed to the generation of the data is availablefromwww.blueprint-epigenome.euandhttp://www.roadmapepigenomics.org/. Funding for the Blueprint project was provided by the European Union’sSeventh Framework Program (FP7/2007-2013) under grant agreement282510 – BLUEPRINT. The Roadmap consortium is financed by the NIH. Weare grateful to Professor C.I. Pogson for critical reading of the manuscript.S