307 research outputs found
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 â 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
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