In this paper, the Partition of Unity (PU) method is performed by blending Radial Basis Functions (RBFs) as local approximants and using locally supported weights. In particular, we present a new multidimensional data structure which makes use of an integer-based scheme. This approach allows to perform an optimized space-partitioning structure. Moreover, because of its flexibility, it turns out to be extremely meaningful in the reconstruction of the attraction basins in dynamical systems.
In this paper, basing our considerations on kernel-based approaches, we propose a new strategy allowing to approximate the prostate cancer dynamics. In particular, starting from several measure- ments of a specific biomarker, we estimate the tumor growth rate. To achieve this aim, we pre-process data via Radial Basis Function (RBF) interpolation. A careful choice of the basis function and of its shape parameter enables us to obtain reliable approximations of the cancer evolution. Numerical evidence supports our findings.
}, issn = {20356803}, doi = {10.14658/pupj-drna-2016-Special_Issue-3}, url = {http://drna.padovauniversitypress.it/2016/specialissue/3}, author = {Emma Perracchione and Ilaria Stura} }