Abstract:
We consider stochastic flow on n-dimensional Euclidean space driven by fractional Brownian motion with Hurst parameter H greater than half, and study tangent flow and the growth of the Hausdorff measure of sub-manifolds of the ambient n-dimensional Euclidean space, as they evolve under the flow. The main result is a bound on the rate of (global) growth in terms of the (local) Holder norm of the flow.

Abstract:
Coupling separately developed codes offers an attractive method for increasing the accuracy and fidelity of the computational models. Examples include the earth sciences and fusion integrated modeling. This paper describes the Framework Application for Core-Edge Transport Simulations (FACETS).

Abstract:
In this article we present an example of a random oriented tree model on d-dimensional lattice, that is a forest in d=3 with positive probability. This is in contrast with the other random tree models in the literature which are a forest only when d strictly greater than 3.

Abstract:
In this note, we investigate the behaviour of suprema for band-limited spherical random fields. We prove upper and lower bound for the expected values of these suprema, by means of metric entropy arguments and discrete approximations; we then exploit the Borell-TIS inequality to establish almost sure upper and lower bounds for their fluctuations. Band limited functions can be viewed as restrictions on the sphere of random polynomials with increasing degrees, and our results show that fluctuations scale as the square root of the logarithm of these degrees.

Abstract:
In this paper, we shall be concerned with geometric functionals and excursion probabilities for some nonlinear transforms evaluated on Fourier components of spherical random fields. In particular, we consider both random spherical harmonics and their smoothed averages, which can be viewed as random wavelet coefficients in the continuous case. For such fields, we consider smoothed polynomial transforms; we focus on the geometry of their excursion sets, and we study their asymptotic behaviour, in the high-frequency sense. We put particular emphasis on the analysis of Euler-Poincar\'e characteristics, which can be exploited to derive extremely accurate estimates for excursion probabilities. The present analysis is motivated by the investigation of asymmetries and anisotropies in cosmological data.

Abstract:
This paper discusses the bathymetric mapping technologies by means of satellite remote sensing (RS) with special emphasis on bathymetry derivation models, methods, accuracies, advantages, limitations, and comparisons. Traditionally, bathymetry can be mapped using echo sounding sounders. However, this method is constrained by its inefficiency in shallow waters and very high operating logistic costs. In comparison, RS technologies present efficient and cost-effective means of mapping bathymetry over remote and broad areas. RS of bathymetry can be categorised into two broad classes: active RS and passive RS. Active RS methods are based on active satellite sensors, which emit artificial radiation to study the earth surface or atmospheric features, e.g. light detection and ranging (LIDAR), polarimetric synthetic aperture radar (SAR), altimeters, etc. Passive RS methods are based on passive satellite sensors, which detect sunlight (natural source of light) radiation reflected from the earth and thermal radiation in the visible and infrared portion of the electromagnetic spectrum, e.g. multispectral or optical satellite sensors. Bathymetric methods can also be categorised as imaging methods and non-imaging methods. The non-imaging method is elucidated by laser scanners or LIDAR, which measures the distance between the sensor and the water surface or the ocean floor using a single wave pulse or double waves. On the other hand, imaging methods approximate the water depth based on the pixel values or digital numbers (DN) (representing reflectance or backscatter) of an image. Imaging methods make use of the visible and/or near infrared (NIR) and microwave radiation. Imaging methods are implemented with either analytical modelling or empirical modelling, or by a blend of both. This paper presents the development of bathymetric mapping technology by using RS, and discusses the state-of-the-art bathymetry derivation methods/algorithms and their implications in practical applications.

Abstract:
In this investigation, the effect of formulation variables on the release properties of timed- release press-coated tablets was studied using the Taguchi method of experimental design. Formulations were prepared based on Taguchi orthogonal array design with different types of hydrophilic polymers (X1), varying hydrophilic polymer/ethyl cellulose ratio (X2), and addition of magnesium stearate (X3) as independent variables. The design was quantitatively evalu-ated by best fit mathematical model. The results from the statistical analysis revealed that factor X1, X3 and interaction factors between X1X2 and X1X3 were found to be significant on the re-sponse lag time (Y1), where as only factor X1 was found to be significant on the response percent drug release at 8 hrs (Y2). A numerical optimization technique by desirability function was used to optimize the response variables, each having a different target. Based on the re-sults of optimization study, HPC was identified as the most suitable hydrophilic polymer and incorporation of hydrophobic agent magnesium stearate, could significantly improve the lag time of the timed-release press-coated tablet.

Abstract:
We consider global geometric properties of a codimension one manifold embedded in Euclidean space, as it evolves under an isotropic and volume preserving Brownian flow of diffeomorphisms. In particular, we obtain expressions describing the expected rate of growth of the Lipschitz-Killing curvatures, or intrinsic volumes, of the manifold under the flow. These results shed new light on some of the intriguing growth properties of flows from a global perspective, rather than the local perspective, on which there is a much larger literature.

Abstract:
In this work we consider infinite dimensional extensions of some finite dimensional Gaussian geometric functionals called the Gaussian Minkowski functionals. These functionals appear as coefficients in the probability content of a tube around a convex set $D\subset\mathbb{R}^k$ under the standard Gaussian law $N(0,I_{k\times k})$. Using these infinite dimensional extensions, we consider geometric properties of some smooth random fields in the spirit of [Random Fields and Geometry (2007) Springer] that can be expressed in terms of reasonably smooth Wiener functionals.

Abstract:
We prove a general lemma for deriving contraction rates for linear inverse problems with non parametric nonconjugate priors. We then apply it to Gaussian priors and obtain minimax rates in mildly ill-posed case. This includes, for example, Meyer wavelet basis with Gaussian priors in the {\it deconvolution problem}. The result for severely ill-posed problems is derived only when the prior is sufficiently smooth. The bases for which our method works is dense in the space of all bases in a sense which shall be described in this paper.