This paper introduces the general framework, concepts, and procedures of anatomically informed basis functions (AIBF), a new method for the analysis of functional magnetic resonance imaging (fMRI) data. In contradistinction to existing voxel-based univariate or multivariate methods the approach described here can incorporate various forms of prior anatomical knowledge to specify sophisticated s...

Radial basis function methods are modern ways to approximate multivariate functions, especially in the absence of grid data. They have been known, tested and analysed for several years now and many positive properties have been identified. This paper gives a selective but up-to-date survey of several recent developments that explains their usefulness from the theoretical point of view and contr...

Radial basis function networks (RBF) are efficient general function approximators. They show good generalization performance and they are easy to train. Due to theoretical considerations RBFs commonly use Gaussian activation functions. It has been shown that these tight restrictions on the choice of possible activation functions can be relaxed in practical applications. As an alternative differ...

In this thesis, a method is presented that incorporates anatomical information into the statistical analysis of functional neuroimaging data. Available anatomical information is used to explicitly specify spatial components within a functional volume that are assumed to carry evidence of functional activation. After estimating the activity by fitting the same spatial model to each functional vo...

Recently renewed interest in the Lobachevsky-type integrals and interesting identities involving cardinal sine motivate an extension of classical Parseval formula both periodic non-periodic functions. We develop a version that is often more practical applications illustrate its use by extending recent results on integrals. Some previously known, are re-proved transparent manner new formulas for...