Comparison of some Reduced Representation Approximations

In the field of numerical approximation, specialists considering highly complex problems have recently proposed various ways to simplify their underlying problems. In this field, depending on the problem they were tackling and the community that are at work, different approaches have been developed with some success and have even gained some maturity, the applications can now be applied to information analysis or for numerical simulation of PDE's. At this point, a crossed analysis and effort for understanding the similarities and the differences between these approaches that found their starting points in different backgrounds is of interest. It is the purpose of this paper to contribute to this effort by comparing some constructive reduced representations of complex functions. We present here in full details the Adaptive Cross Approximation (ACA) and the Empirical Interpolation Method (EIM) together with other approaches that enter in the same category

Cohort Profile: Pregnancy And Childhood Epigenetics (PACE) Consortium.

Development Psychopathology in context: famil

Multi-scale analysis of soil erosion dynamics in Kwazulu-natal, South Africa

For a case study area in the Okhombe catchment in the province of KwaZulu-Natal, South Africa, a multi-scale analysis of soil erosion dynamics was performed. At sub-catchment level, the dynamics of erosional features were investigated by means of aerial photographs. At site level, the changes in soil physical and chemical properties were investigated by means of a fence-line contrast study. Attention was paid to both surface and subsurface erosion phenomena. The number of erosional features in the study area in 2000 was not substantially different from the number of features in 1945. At sub-catchment level, an increase in the number of gullies was observed from 1975 to 2000 but this followed a substantial inactivation of most erosional features from 1962 to 1975. Increases in erosional activity in 1962 compared to 1945 were mainly related to abandoned cultivated fields. At site level, a significant decrease in soil C/N ratio was observed within the fenced site within three years. For the same site, total carbon, saturated hydraulic conductivity and bulk density were not significantly different for the topsoil inside the fenced area compared with outside. Subsurface erosion phenomena mainly occur in the communal grazing areas and are mostly related to transitions between permeable and less permeable layers. The complex relationships between soil erosion, land use change and climate might further be understood by involving local people in the development, monitoring and evaluation of alternative types of land use, which is also likely to facilitate future steps in controlled grazing management