A semi-Lagrangian scheme for Hamilton–Jacobi–Bellman equations with oblique derivatives boundary conditions

We investigate in this work a fully-discrete semi-Lagrangian approximation of second order possibly degenerate Hamilton–Jacobi–Bellman (HJB) equations on a bounded domain O⊂ RN (N= 1 , 2 , 3) with oblique derivatives boundary conditions. These equations appear naturally in the study of optimal control of diffusion processes with oblique reflection at the boundary of the domain. The proposed scheme is shown to satisfy a consistency type property, it is monotone and stable. Our main result is the convergence of the numerical solution towards the unique viscosity solution of the HJB equation. The convergence result holds under the same asymptotic relation between the time and space discretization steps as in the classical setting for semi-Lagrangian schemes on O= RN. We present some numerical results, in dimensions N=1,2, on unstructured meshes, that confirm the numerical convergence of the scheme

Mixture of Kernels and Iterated Semidirect Product of Diffeomorphisms Groups

In the framework of large deformation diffeomorphic metric mapping (LDDMM), we develop a multi-scale theory for the diffeomorphism group based on previous works. The purpose of the paper is (1) to develop in details a variational approach for multi-scale analysis of diffeomorphisms, (2) to generalise to several scales the semidirect product representation and (3) to illustrate the resulting diffeomorphic decomposition on synthetic and real images. We also show that the approaches presented in other papers and the mixture of kernels are equivalent.Comment: 21 pages, revised version without section on evaluatio

Robust Estimators in Generalized Pareto Models

This paper deals with optimally-robust parameter estimation in generalized Pareto distributions (GPDs). These arise naturally in many situations where one is interested in the behavior of extreme events as motivated by the Pickands-Balkema-de Haan extreme value theorem (PBHT). The application we have in mind is calculation of the regulatory capital required by Basel II for a bank to cover operational risk. In this context the tail behavior of the underlying distribution is crucial. This is where extreme value theory enters, suggesting to estimate these high quantiles parameterically using, e.g. GPDs. Robust statistics in this context offers procedures bounding the influence of single observations, so provides reliable inference in the presence of moderate deviations from the distributional model assumptions, respectively from the mechanisms underlying the PBHT.Comment: 26pages, 6 figure

Thermal activation between Landau levels in the organic superconductor β′′\beta''-(BEDT-TTF)2_{2}SF5_{5}CH2_{2}CF2_{2}SO3_{3}

We show that Shubnikov-de Haas oscillations in the interlayer resistivity of the organic superconductor $\beta''$-(BEDT-TTF)$_{2}$SF$_{5}$ CH$_{2}$CF$_{2}$SO$_{3}$ become very pronounced in magnetic fields $\sim$~60~T. The conductivity minima exhibit thermally-activated behaviour that can be explained simply by the presence of a Landau gap, with the quasi-one-dimensional Fermi surface sheets contributing negligibly to the conductivity. This observation, together with complete suppression of chemical potential oscillations, is consistent with an incommensurate nesting instability of the quasi-one-dimensional sheets.Comment: 6 pages, 4 figure

Superconductivity in a Ferromagnetic Layered Compound

We examine superconductivity in layered systems with large Fermi-surface splitting due to coexisting ferromagnetic layers. In particular, the hybrid ruthenate-cuprate compound RuSr_2GdCu_2O_8 is examined on the coexistence of the superconductivity and the ferromagnetism, which has been observed recently. We calculate critical fields of the superconductivity taking into account the Fulde-Ferrell-Larkin-Ovchinnikov state in a model with Fermi-surfaces which shapes are similar to those obtained by a band calculation. It is shown that the critical field is enhanced remarkably due to a Fermi-surface effect, and can be high enough to make the coexistence possible in a microscopic scale. We also clarify the direction of the spatial oscillation of the order parameter, which may be observed by scanning tunneling microscope experiments.Comment: 4 pages, 4 figures, (Latex, revtex.sty, epsf.sty

Response Inhibition and ADHD Traits: Correlates and Heritability in a Community Sample

Endophenotypes or intermediate phenotypes are of great interest in neuropsychiatric genetics because of their potential for facilitating gene discovery. We evaluated response inhibition, latency and variability measures derived from the stop task as endophenotypes of ADHD by testing whether they were related to ADHD traits in the general population, heritable and shared genetic risk with ADHD traits. Participants were 16,099 children and adolescents, ages 6 to 18æyears who visited a local science center. We measured ADHD traits using the Strengths and Weaknesses of ADHD-symptoms and Normal-Behavior (SWAN) rating scale and performance on the stop signal task (SST)?response inhibition (SSRT), response latency (GoRT), and response variability (GoRTSD). Regression analysis was used to assess the relationship of cognitive measures and ADHD traits while controlling for family, age, sex, ethnicity, socioeconomic status and treatment status. Heritability of ADHD and cognitive traits was estimated using SOLAR in 7,483 siblings from 3,507 families that included multiple siblings. Bivariate relationships between pairs of variables were examined. Individuals with greater ADHD trait scores had worse response inhibition, slower response latency, and greater variability. Younger participants and girls had inferior performance although the gender effects were minimal and evident in youngest participants. Inhibition, latency, variability, total ADHD traits, inattention and hyperactivity-impulsivity scores were significantly heritable. ADHD traits and inhibition, but not latency or variability were coheritable. In the largest study in the general population, we found support for the validity of response inhibition as an endophenotype of ADHD. Electronic supplementary material The online version of this article (doi:10.1007/s10802-012-9693-9) contains supplementary material, which is available to authorized users

Metal-insulator transitions in anisotropic 2d systems

Several phenomena related to the critical behaviour of non-interacting electrons in a disordered 2d tight-binding system with a magnetic field are studied. Localization lengths, critical exponents and density of states are computed using transfer matrix techniques. Scaling functions of isotropic systems are recovered once the dimension of the system in each direction is chosen proportional to the localization length. It is also found that the critical point is independent of the propagation direction, and that the critical exponents for the localization length for both propagating directions are equal to that of the isotropic system (approximately 7/3). We also calculate the critical value of the scaling function for both the isotropic and the anisotropic system. It is found that the isotropic value equals the geometric mean of the two anisotropic values. Detailed numerical studies of the density of states for the isotropic system reveals that for an appreciable amount of disorder the critical energy is off the band center.Comment: 6 pages RevTeX, 6 figures included, submitted to Physical Review

Phase Fluctuations and Vortex Lattice Melting in Triplet Quasi-One-Dimensional Superconductors at High Magnetic Fields

Assuming that the order parameter corresponds to an equal spin triplet pairing symmetry state, we calculate the effect of phase fluctuations in quasi-one-dimensional superconductors at high magnetic fields applied along the y (b') axis. We show that phase fluctuations can destroy the theoretically predicted triplet reentrant superconducting state, and that they are responsible for melting the magnetic field induced Josephson vortex lattice above a magnetic field dependent melting temperature Tm.Comment: 4 pages (double column), 1 eps figur

The nanoscale phase separation in hole-doped manganites

A macroscopic phase separation, in which ferromagnetic clusters are observed in an insulating matrix, is sometimes observed, and believed to be essential to the colossal magnetoresistive (CMR) properties of manganese oxides. The application of a magnetic field may indeed trigger large magnetoresistance effects due to the percolation between clusters allowing the movement of the charge carriers. However, this macroscopic phase separation is mainly related to extrinsic defects or impurities, which hinder the long-ranged charge-orbital order of the system. We show in the present article that rather than the macroscopic phase separation, an homogeneous short-ranged charge-orbital order accompanied by a spin glass state occurs, as an intrinsic result of the uniformity of the random potential perturbation induced by the solid solution of the cations on the $A$-sites of the structure of these materials. Hence the phase separation does occur, but in a more subtle and interesting nanoscopic form, here referred as ``homogeneous''. Remarkably, this ``nanoscale phase separation'' alone is able to bring forth the colossal magnetoresistance in the perovskite manganites, and is potentially relevant to a wide variety of other magnetic and/or electrical properties of manganites, as well as many other transition metal oxides, in bulk or thin film form as we exemplify throughout the article.Comment: jpsj2 TeX style (J. Phys. Soc. Jpn); 18 pages, 7 figure