Epidemiology of Schistosoma mansoni infection in Ituri Province, north-eastern Democratic Republic of the Congo.

Background: Schistosomiasis, caused by Schistosoma mansoni, is of great significance to public health in sub-Saharan Africa. In the Democratic Republic of Congo (DRC), information on the burden of S. mansoni infection is scarce, which hinders the implementation of adequate control measures.

Solving 3-D PDEs by Tensor B-Spline Methodology: A High Performance Approach Applied to Optical Diffusion Tomography.

Solutions of 3-D elliptic PDEs form the basis of many mathematical models in medicine and engineering. Solving elliptic PDEs numerically in 3-D with fine discretization and high precision is challenging for several reasons, including the cost of 3-D meshing, the massive increase in operation count, and memory consumption when a high-order basis is used, and the need to overcome the "curse of dimensionality." This paper describes how these challenges can be either overcome or relaxed by a Tensor B-spline methodology with the following key properties: 1) the tensor structure of the variational formulation leads to regularity, separability, and sparsity, 2) a method for integration over the complex domain boundaries eliminates meshing, and 3) the formulation induces high-performance and memory-efficient computational algorithms.

A Tensor B-Spline Approach for Solving the Diffusion PDE With Application to Optical Diffusion Tomography.

Optical Diffusion Tomography (ODT) is a modern non-invasive medical imaging modality which requires mathematical modelling of near-infrared light propagation in tissue. Solving the ODT forward problem equation accurately and efficiently is crucial. Typically, the forward problem is represented by a Diffusion PDE and is solved using the Finite Element Method (FEM) on a mesh, which is often unstructured.

Reconstruction of large, irregularly sampled multidimensional images. A tensor-based approach.

Many practical applications require the reconstruction of images from irregularly sampled data. The spline formalism offers an attractive framework for solving this problem; the currently available methods, however, are hard to deploy for large-scale interpolation problems in dimensions greater than two (3-D, 3-D+time) because of an exponential increase of their computational cost (curse of dimensionality). Here, we revisit the standard regularized least-squares formulation of the interpolation problem, and propose to perform the reconstruction in a uniform tensor-product B-spline basis as an alternative to the classical solution involving radial basis functions.