Algebraic Structures and Stochastic Differential Equations driven by Levy processes

We construct an efficient integrator for stochastic differential systems driven by Levy processes. An efficient integrator is a strong approximation that is more accurate than the corresponding stochastic Taylor approximation, to all orders and independent of the governing vector fields. This holds provided the driving processes possess moments of all orders and the vector fields are sufficiently smooth. Moreover the efficient integrator in question is optimal within a broad class of perturbations for half-integer global root mean-square orders of convergence. We obtain these results using the quasi-shuffle algebra of multiple iterated integrals of independent Levy processes.Comment: 41 pages, 11 figure

Recurrent approach to effective material properties with application to anisotropic binarized random fields

Building on the foundation work of Brown, Milton and Torquato, we present a tractable approach to analyse the effective permittivity of anisotropic two-phase structures. This methodology accounts for successive dipolar interactions, providing a recurrent series expansion of the effective permittivity to arbitrary order. Within this framework, we also demonstrate a progressive method to determine tight bounds that converge towards the exact solution. We illustrate the utility of these methods by using ensemble averaging to determine the micro-structural parameters of anisotropic level-cut Gaussian fields. We find that the depolarization factor of these structures is equivalent to that of an isolated ellipse with the same stretchingratio, and discuss the contribution of the fourth order term to the exact anisotropy

Geometrical-based algorithm for variational segmentation and smoothing of vector-valued images

An optimisation method based on a nonlinear functional is considered for segmentation and smoothing of vector-valued images. An edge-based approach is proposed to initially segment the image using geometrical properties such as metric tensor of the linearly smoothed image. The nonlinear functional is then minimised for each segmented region to yield the smoothed image. The functional is characterised with a unique solution in contrast with the Mumford–Shah functional for vector-valued images. An operator for edge detection is introduced as a result of this unique solution. This operator is analytically calculated and its detection performance and localisation are then compared with those of the DroGoperator. The implementations are applied on colour images as examples of vector-valued images, and the results demonstrate robust performance in noisy environments

Dispersion of Magnetic Fields in Molecular Clouds. III

We apply our technique on the dispersion of magnetic fields in molecular clouds to high spatial resolution Submillimeter Array polarization data obtained for Orion KL in OMC-1, IRAS 16293, and NGC 1333 IRAS 4A. We show how one can take advantage of such high resolution data to characterize the magnetized turbulence power spectrum in the inertial and dissipation ranges. For Orion KL we determine that in the inertial range the spectrum can be approximately fitted with a power law k^-(2.9\pm0.9) and we report a value of 9.9 mpc for {\lambda}_AD, the high spatial frequency cutoff presumably due to turbulent ambipolar diffusion. For the same parameters we have \sim k^-(1.4\pm0.4) and a tentative value of {\lambda}_AD \simeq 2.2 mpc for NGC 1333 IRAS 4A, and \sim k^-(1.8\pm0.3) with an upper limit of {\lambda}_AD < 1.8 mpc for IRAS 16293. We also discuss the application of the technique to interferometry measurements and the effects of the inherent spatial filtering process on the interpretation of the results.Comment: 25 pages, 9 figures; accepted for publication in The Astrophysical Journa