Coronary vasospasm is one of the main reasons for atypical chest pain in patients with clinical signs of myocarditis and biopsy-proven PVB19 myocarditis in the absence of significant CAD.

The multivariate central limit theorems (CLT) for the volumes of excursion sets of stationary quasi-associated random fields on R d are proved. Special attention is paid to Gaussian and shot noise fields. Formulae for the covariance matrix of the limiting distribution are provided. A statistical version of the CLT is considered as well. Some numerical results are also discussed.

We consider two integral transforms which are frequently used in integral geometry and related fields, namely the cosine and the spherical Radon transform. Fast algorithms are developed which invert the respective transforms in a numerically stable way. So far, only theoretical inversion formulas or algorithms for atomic measures have been derived, which are not so important for applications. We focus on the two and threedimensional case, where we also show that our method leads to a regularization. Numerical results are presented and show the validity of the resulting algorithms. First, we use synthetic data for the inversion of the Radon transform. Then we apply the algorithm for the inversion of the cosine transform to reconstruct the directional distribution of line processes from finitely many intersections of their lines with test lines (2D) or planes (3D), respectively. Finally we apply our method to analyze a series of microscopic two-and three-dimensional images of a fibre system.

For parallel neighborhoods of the paths of the d-dimensional Brownian motion, so-called Wiener sausages, formulae for the expected surface area are given for any dimension d ≥ 2. It is shown by means of geometric arguments that the expected surface area is equal to the first derivative of the mean volume of the Wiener sausage with respect to its radius.

Main characteristics of stationary anisotropic Poisson processes of cylinders (dilated k-dimensional flats) in d-dimensional Euclidean space are studied. Explicit formulae for the capacity functional, the covariance function, the contact distribution function, the volume fraction, and the intensity of the surface area measure are given which can be used directly in applications.