The stochastic Klausmeier system and a stochastic Schauder-Tychonoff type theorem

On the one hand, we investigate the existence and pathwise uniqueness of a nonnegative martingale solution to the stochastic evolution system of nonlinear advection-diffusion equations proposed by Klausmeier with Gaussian multiplicative noise. On the other hand, we present and verify a general stochastic version of the Schauder-Tychonoff fixed point theorem, as its application is an essential step for showing existence of the solution to the stochastic Klausmeier system. The analysis of the system is based both on variational and semigroup techniques. We also discuss additional regularity properties of the solution.Comment: 52 pages, 74 reference

A pragmatic approach to semantic repositories benchmarking

The aim of this paper is to benchmark various semantic repositories in order to evaluate their deployment in a commercial image retrieval and browsing application. We adopt a two-phase approach for evaluating the target semantic repositories: analytical parameters such as query language and reasoning support are used to select the pool of the target repositories, and practical parameters such as load and query response times are used to select the best match to application requirements. In addition to utilising a widely accepted benchmark for OWL repositories (UOBM), we also use a real-life dataset from the target application, which provides us with the opportunity of consolidating our findings. A distinctive advantage of this benchmarking study is that the essential requirements for the target system such as the semantic expressivity and data scalability are clearly defined, which allows us to claim contribution to the benchmarking methodology for this class of applications

VAMP: semantic validation for MPEG-7 profile descriptions

MPEG-7 can be used to create complex and comprehensive metadata descriptions of multimedia content. Since MPEG-7 is defined in terms of an XML schema, the semantics of its elements has no formal grounding. In addition, certain features can be described in multiple ways. MPEG-7 profiles are subsets of the standard that apply to specific application areas and that aim to reduce this syntactic variability, but they still lack formal semantics. We propose an approach for expressing the semantics explicitly

Weak convergence of finite element approximations of linear stochastic evolution equations with additive noise II. Fully discrete schemes

We present an abstract framework for analyzing the weak error of fully discrete approximation schemes for linear evolution equations driven by additive Gaussian noise. First, an abstract representation formula is derived for sufficiently smooth test functions. The formula is then applied to the wave equation, where the spatial approximation is done via the standard continuous finite element method and the time discretization via an I-stable rational approximation to the exponential function. It is found that the rate of weak convergence is twice that of strong convergence. Furthermore, in contrast to the parabolic case, higher order schemes in time, such as the Crank-Nicolson scheme, are worthwhile to use if the solution is not very regular. Finally we apply the theory to parabolic equations and detail a weak error estimate for the linearized Cahn-Hilliard-Cook equation as well as comment on the stochastic heat equation

Numerical Schemes for Rough Parabolic Equations

This paper is devoted to the study of numerical approximation schemes for a class of parabolic equations on (0, 1) perturbed by a non-linear rough signal. It is the continuation of [8, 7], where the existence and uniqueness of a solution has been established. The approach combines rough paths methods with standard considerations on discretizing stochastic PDEs. The results apply to a geometric 2-rough path, which covers the case of the multidimensional fractional Brownian motion with Hurst index H \textgreater{} 1/3.Comment: Applied Mathematics and Optimization, 201

Stochastic Reaction-diffusion Equations Driven by Jump Processes

We establish the existence of weak martingale solutions to a class of second order parabolic stochastic partial differential equations. The equations are driven by multiplicative jump type noise, with a non-Lipschitz multiplicative functional. The drift in the equations contains a dissipative nonlinearity of polynomial growth.Comment: See journal reference for teh final published versio

dbrec — Music Recommendations Using DBpedia

Abstract. This paper describes the theoretical background and the im-plementation of dbrec, a music recommendation system built on top of DBpedia, offering recommendations for more than 39,000 bands and solo artists. We discuss the various challenges and lessons learnt while build-ing it, providing relevant insights for people developing applications con-suming Linked Data. Furthermore, we provide a user-centric evaluation of the system, notably by comparing it to last.fm