Ph.d.-forelæsning/PhD Defense, Andreas Dyreborg Christoffersen

Title:
Iterated and Anisotropic Marked Point Processes with a view to the Minicolumn Hypothesis  

Abstract:
Finding patterns in data consisting of randomly scattered data points is of interest in many scientific fields such as ecology, stereology, neurology, and astronomy. For instance, in neurology the organisation of neurons in human brains is investigated for patterns and is of great interest, because different patterns are linked to different neurological diseases. Obviously, each brain has a unique neuronal structure and is, from a statistical point of view, a realisation of an underlying random mechanism. This random mechanism is referred to as a point processes, that is generally defined as a random and countable collection of points, and its realisations are called point patterns. Point patterns for which additional information is attributed to each of the points are called marked point patterns. This additional information could for instance be the type of neuron, the neuron size, or the orientation of the neuron.

The thesis deals with marked point processes, with a specific focus on modelling the neuronal structure of the human brain, where the points are the locations of so-called pyramidal cells and the marks are the orientations of these cells. It further deals with some theoretical detail of Markov chains of point processes, and the behaviour of these Markov chains in the limit.