Counting Figures in Planar Random Configurations

Random configurations are considered that are generated by a Poisson process of figures in the plane, and a recent result is used to derive formulae for the estimation of the number of figures, and their mean area and perimeter. The formulae require merely the determination of the area, the perimeter, and the Euler-Poincaré characteristic of the random configurations in a fixed field of view. There are no similar formulae for the standard deviations of the estimates; their magnitudes in typical cases are therefore assessed by Monte Carlo simulations

Concepts of microdosimetry

This is the first part of an investigation of microdosimetric concepts relevant to numerical calculations. The definitions of the microdosimetric quantities are reviewed and formalized, and some additional conventions are adopted. The common interpretation of the quantities in terms of energy imparted to spherical sites is contrasted with their interpretation as the result of a diffusion process applied to the initial spatial pattern of energy transfers in the irradiated medium