Marked point processes with a view to the minicolumn hypothesis

Mærkede punktprocesser anvendt på minisøjlehypotesen

Christoffersen, Andreas Dyreborg ; Christensen, Heidi Søgaard

4. term

Mathematics, Master

2016

This thesis examines the minicolumn hypothesis—i.e., columnar organization of neurons in the cerebral cortex—using spatial marked point processes. The data consist of three-dimensional locations of pyramidal-cell nucleoli and their orientations. The analysis proceeds hierarchically: the unmarked point pattern (locations) is modeled first, supported by Palm theory, functional summary statistics, and global envelope tools, and a Strauss hardcore point process is found to suitably describe the nucleolus locations. The marked component (orientations) is then investigated. To link orientation to potential columnar structure, a new summary statistic—a modified (mark-weighted) cylindrical K-function—is introduced alongside mark correlation functions and the mark-weighted K-measure. These tools are used to test for independent marking, which does not appear to be an appropriate model for the data. The thesis closes with a discussion of implications and directions for future work.

Dette speciale undersøger minisøjlehypotesen om kolonnær organisering af neuroner i hjernebarken ved hjælp af rumlige, mærkede punktprocesser. Datagrundlaget er tredimensionelle positioner af pyramidecellers nukleoler samt cellernes orienteringer. Analysen er hierarkisk: Først modelleres det umærkede punktmønster (lokationerne), hvor vi med støtte i Palm-teori, funktionelle summary-statistikker og globale envelopes finder, at en Strauss hardcore punktproces giver en passende beskrivelse af nukleoleplaceringerne. Dernæst analyseres de tilhørende mærker (orienteringerne). For at koble orientering til mulig søjlestruktur introduceres en ny summary-statistik, en modificeret (mærke-vægtet) cylindrisk K-funktion, suppleret af mark-korrelationsfunktioner og det mærke-vægtede K-mål. Disse værktøjer anvendes til at teste for uafhængig mærkning, hvilket ikke fremstår som en egnet model for data. Afslutningsvis diskuteres implikationer og mulige veje for fremtidige analyser.

[This apstract has been generated with the help of AI directly from the project full text]

Download PDF
View record in AAU Student Projects

Christoffersen, Andreas Dyreborg:

• Marked point processes with a view to the minicolumn hypothesis of neuroscience (2016)

Christensen, Heidi Søgaard:

• Marked point processes with a view to the minicolumn hypothesis of neuroscience (2016)