Adaptive sparse grids

Sparse grids, as studied by Zenger and Griebel in the last 10 years have been very successful in the solution of partial differential equations, integral equations and classification problems. Adaptive sparse grid functions are elements of a function space lattice. Such lattices allow the generalisation of sparse grid techniques to the fitting of very high-dimensional functions with categorical and continuous variables. We have observed in first tests that these general adaptive sparse grids allow the identification of the ANOVA structure and thus provide comprehensible models. This is very important for data mining applications. Perhaps the main advantage of these models is that they do not include any spurious interaction terms and thus can deal with very high dimensional data

Identification and classification of interesting variable stars in the MACHO database

The MACHO database is an astronomical database of the intensities of about 20 million stars, recorded approximately every night for several years. About one percent of these stars are classified as ``variable stars''. These variable stars are generally roughly periodic and can have periods ranging from less than one day to hundreds or thousands of days. We investigate the application of computationally simple features in order to classify these stars. We present a methodology for extracting potentially interesting stars based on their location in feature-space, and methods for using human interaction to group these interesting stars

Spatial and temporal rainfall approximation using additive models

We investigate the approximation of Rainfall data using additive models . In our model, space and elevation are treated as the predictor variables. The multi-dimensional approximation problem is demonstrated using rainfall data collected by ACTEW Corporation

Small-scale fisheries access to fishing opportunities in the European Union: is the common fisheries policy the right step to SDG14b?

The profile of small-scale fisheries has been raised through a dedicated target within the United Nations Sustainable Development Goals (SDG14b) that calls for the provision of ‘access of small-scale artisanal fishers to marine resources and markets’. By focusing on access to fisheries resources in the context of European Union, in this article we demonstrate that the potential for small-scale fishing sectors to benefit from fishing opportunities remains low due to different mechanisms at play including legislative gaps in the Common Fisheries Policy, and long-existing local structures somewhat favouring the status quo of distributive injustice. Consequently, those without access to capital and authority are faced by marginalizing allocation systems, impacting the overall resilience of fishing communities. Achieving SDG14b requires an overhaul in the promulgation of policies emanating from the present nested governance systems.info:eu-repo/semantics/publishedVersio

Smolyak's algorithm: A powerful black box for the acceleration of scientific computations

We provide a general discussion of Smolyak's algorithm for the acceleration of scientific computations. The algorithm first appeared in Smolyak's work on multidimensional integration and interpolation. Since then, it has been generalized in multiple directions and has been associated with the keywords: sparse grids, hyperbolic cross approximation, combination technique, and multilevel methods. Variants of Smolyak's algorithm have been employed in the computation of high-dimensional integrals in finance, chemistry, and physics, in the numerical solution of partial and stochastic differential equations, and in uncertainty quantification. Motivated by this broad and ever-increasing range of applications, we describe a general framework that summarizes fundamental results and assumptions in a concise application-independent manner

Iteratively regularized Newton-type methods for general data misfit functionals and applications to Poisson data

We study Newton type methods for inverse problems described by nonlinear operator equations $F(u)=g$ in Banach spaces where the Newton equations $F'(u_n;u_{n+1}-u_n) = g-F(u_n)$ are regularized variationally using a general data misfit functional and a convex regularization term. This generalizes the well-known iteratively regularized Gauss-Newton method (IRGNM). We prove convergence and convergence rates as the noise level tends to 0 both for an a priori stopping rule and for a Lepski{\u\i}-type a posteriori stopping rule. Our analysis includes previous order optimal convergence rate results for the IRGNM as special cases. The main focus of this paper is on inverse problems with Poisson data where the natural data misfit functional is given by the Kullback-Leibler divergence. Two examples of such problems are discussed in detail: an inverse obstacle scattering problem with amplitude data of the far-field pattern and a phase retrieval problem. The performence of the proposed method for these problems is illustrated in numerical examples