Pathwise optimal transport bounds between a one-dimensional diffusion and its Euler scheme

In the present paper, we prove that the Wasserstein distance on the space of continuous sample-paths equipped with the supremum norm between the laws of a uniformly elliptic one-dimensional diffusion process and its Euler discretization with $N$ steps is smaller than $O(N^{-2/3+\varepsilon})$ where $\varepsilon$ is an arbitrary positive constant. This rate is intermediate between the strong error estimation in $O(N^{-1/2})$ obtained when coupling the stochastic differential equation and the Euler scheme with the same Brownian motion and the weak error estimation $O(N^{-1})$ obtained when comparing the expectations of the same function of the diffusion and of the Euler scheme at the terminal time $T$. We also check that the supremum over $t\in[0,T]$ of the Wasserstein distance on the space of probability measures on the real line between the laws of the diffusion at time $t$ and the Euler scheme at time $t$ behaves like $O(\sqrt{\log(N)}N^{-1})$.Comment: Published in at http://dx.doi.org/10.1214/13-AAP941 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Propagation of chaos for rank-based interacting diffusions and long time behaviour of a scalar quasilinear parabolic equation

We study a quasilinear parabolic Cauchy problem with a cumulative distribution function on the real line as an initial condition. We call 'probabilistic solution' a weak solution which remains a cumulative distribution function at all times. We prove the uniqueness of such a solution and we deduce the existence from a propagation of chaos result on a system of scalar diffusion processes, the interactions of which only depend on their ranking. We then investigate the long time behaviour of the solution. Using a probabilistic argument and under weak assumptions, we show that the flow of the Wasserstein distance between two solutions is contractive. Under more stringent conditions ensuring the regularity of the probabilistic solutions, we finally derive an explicit formula for the time derivative of the flow and we deduce the convergence of solutions to equilibrium.Comment: Stochastic partial differential equations: analysis and computations (2013) http://dx.doi.org/10.1007/s40072-013-0014-

New Analytical Methods for Camera Trap Data

Density estimation of terrestrial mammals has become increasingly important in ecology, and robust analytical tools are required to provide results that will guide wildlife management. This thesis concerns modelling encounters between unmarked animals and camera traps for density estimation. We explore Rowcliffe et al. (2008) Random Encounter Model (REM) developed for estimating density of species that cannot be identified to the individual level from camera trap data. We demonstrate how REM can be used within a maximum likelihood framework to estimate density of unmarked animals, motivated by the analysis of a data set from Whipsnade Wild Animal Park (WWAP), Bedfordshire, south England. The remainder of the thesis focuses on developing and evaluating extended Random Encounter Models, which describe the data in an integrated population modelling framework. We present a variety of approaches for modelling population abundance in an integrated Random Encounter Model (iREM), where complicating features are the variation in the encounters and animal species. An iREM is a more flexible and robust parametric model compared with a nonparametric REM, which produces novel and meaningful parameters relating to density, accounting for the sampling variability in the parameters required for density estimation. The iREM model we propose can describe how abundance changes with diverse factors such as habitat type and climatic conditions. We develop models to account for induced-bias in the density from faster moving animals, which are more likely to encounter camera traps, and address the independence assumption in integrated population models. The models we propose consider a functional relationship between a camera index and animal density and represent a step forward with respect to the current simplistic modelling approaches for abundance estimation of unmarked animals from camera trap data. We illustrate the application of the models proposed to a community of terrestrial mammals from a tropical moist forest at Barro Colorado Island (BCI), Panama

Wafer-level packaged RF-MEMS switches fabricated in a CMOS fab

Reports on wafer-level packaged RF-MEMS switches fabricated in a commercial CMOS fab. Switch fabrication is based on a metal surface micromachining process. A novel wafer-level packaging scheme is developed, whereby the switches are housed in on-chip sealed cavities using benzocyclobutene (BCB) as the bonding and sealing material. Measurements show that the influence of the wafer-level package on the RF performance can be made very small.\ud \u

Diffuse emission measurement with INTEGRAL/SPI as indirect probe of cosmic-ray electrons and positrons

Significant advances have been made in the understanding of the diffuse Galactic hard X-ray continuum emission using data from the INTEGRAL observatory. The diffuse hard power-law component seen with the INTEGRAL/SPI spectrometer has been identified with inverse-Compton emission from relativistic (GeV) electrons on the cosmic microwave background and Galactic interstellar radiation field. In the present analysis, SPI data from 2003 to 2009, with a total exposure time of ~ 10^8 s, are used to derive the Galactic ridge hard X-ray spatial distribution and spectrum between 20 keV and 2.4 MeV. Both are consistent with predictions from the GALPROP code. The good agreement between measured and predicted emission from keV to GeV energies suggests that the correct production mechanisms have been identified. We discuss the potential of the SPI data to provide an indirect probe of the interstellar cosmic-ray electron distribution, in particular for energies below a few GeV.Comment: 39 pages, 11 figures. Accepted for publication in The Astrophysical Journa

3-200 keV spectral states and variability of the INTEGRAL Black Hole binary IGR J17464-3213

On March 2003, IBIS, the gamma-ray imager on board the INTEGRAL satellite, detected an outburst from a new source, IGR J17464-3213, that turned out to be a HEAO-1 transient, H1743-322. In this paper we report on the high energy behaviour of this BHC studied with the three main instruments onboard INTEGRAL. The data, collected with unprecedented sensitivity in the hard X-Ray range, show a quite hard Comptonised emission from 3 keV up to 150 keV during the rising part of the source outburst, with no thermal emission detectable. A few days later, a prominent soft disk multicolour component appears, with the hard tail luminosity almost unchanged: 10-9 erg*cm-2*s-1. Two months later, during a second monitoring campaign near the end of the outburst, the observed disk component was unchanged. Conversely, the Comptonised emission from the central-hot part of the disk reduced by a factor of 10. We present here its long term behaviour in different energy ranges and the combined JEM-X, SPI and IBIS wide band spectral evolution of this source.Comment: 12 pages, 4 figures, accepted for pubblication in AP

Spatial Separation of the 3.29 micron Emission Feature and Associated 2 micron Continuum in NGC 7023

We present a new 0.9" resolution 3.29 micron narrowband image of the reflection nebula NGC 7023. We find that the 3.29 micron IEF in NGC 7023 is brightest in narrow filaments NW of the illuminating star. These filaments have been seen in images of K', molecular hydrogen emission lines, the 6.2 and 11.3 micron IEFs, and HCO+. We also detect 3.29 micron emission faintly but distinctly between the filaments and the star. The 3.29 micron image is in contrast to narrowband images at 2.09, 2.14, and 2.18 micron, which show an extended emission peak midway between the filaments and the star, and much fainter emission near the filaments. The [2.18]-[3.29] color shows a wide variation, ranging from 3.4-3.6 mag at the 2 micron continuum peak to 5.5 mag in the filaments. We observe [2.18]-[3.29] to increase smoothly with increasing distance from the star, up until the filament, suggesting that the main difference between the spatial distributions of the 2 micron continuum and the the 3.29 micron emission is related to the incident stellar flux. Our result suggests that the 3.29 micron IEF carriers are likely to be distinct from, but related to, the 2 micron continuum emitters. Our finding also imply that, in NGC 7023, the 2 micron continuum emitters are mainly associated with HI, while the 3.29 micron IEF carriers are primarily found in warm molecular hydrogen, but that both can survive in HI or molecular hydrogen. (abridged)Comment: to appear in ApJ, including 1 table and 8 figures, high resolution figures available at http://www.ast.cam.ac.uk/~jin/n7023