# Modelling columnarity of pyramidal cells in the human cerebral cortex

Australian & New Zealand Journal of Statistics

Published On 2021/3

For modelling the location of pyramidal cells in the human cerebral cortex, we suggest a hierarchical point process in that exhibits anisotropy in the form of cylinders extending along the z‐axis. The model consists first of a generalised shot noise Cox process for the xy‐coordinates, providing cylindrical clusters, and next of a Markov random field model for the z‐coordinates conditioned on the xy‐coordinates, providing either repulsion, aggregation or both within specified areas of interaction. Several cases of these hierarchical point processes are fitted to two pyramidal cell data sets, and of these a final model allowing for both repulsion and attraction between the points seem adequate. We discuss how the final model relates to the so‐called minicolumn hypothesis in neuroscience.

Journal

Australian & New Zealand Journal of Statistics

Published On

2021/3

Volume

63

Issue

1

Page

33-54

## Authors

#### Jesper Møller

##### Aalborg Universitet

Position

Professor in Statistics

H-Index(all)

46

H-Index(since 2020)

23

I-10 Index(all)

0

I-10 Index(since 2020)

0

Citation(all)

0

Citation(since 2020)

0

Cited By

0

Research Interests

Mathematical Statistics

Probability Theory

University Profile Page

### Other Articles from authors

Jesper Møller

Aalborg Universitet

arXiv preprint arXiv:2404.09525

##### Coupling results and Markovian structures for number representations of continuous random variables

A general setting for nested subdivisions of a bounded real set into intervals defining the digits of a random variable with a probability density function is considered. Under the weak condition that is almost everywhere lower semi-continuous, a coupling between and a non-negative integer-valued random variable is established so that have an interpretation as the ``sufficient digits'', since the distribution of conditioned on does not depend on . Adding a condition about a Markovian structure of the lengths of the intervals in the nested subdivisions, becomes a Markov chain of a certain order . If then are IID with a known distribution. When and the Markov chain is uniformly geometric ergodic, a coupling is established between and a random time so that the chain after time is stationary and follows a simple known distribution. The results are related to several examples of number representations generated by a dynamical system, including base- expansions, generalized L\"uroth series, -expansions, and continued fraction representations. The importance of the results and some suggestions and open problems for future research are discussed.

*2024/4/15*

Jesper Møller

Aalborg Universitet

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##### The asymptotic distribution of the scaled remainder for pseudo golden ratio expansions of a continuous random variable

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*2024/4/12*

Jesper Møller

Aalborg Universitet

Methodology and Computing in Applied Probability

##### How many digits are needed?

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*2024/3*

Jesper Møller

Aalborg Universitet

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##### The asymptotic distribution of the remainder in a certain base- expansion

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*2023/12/15*

Jesper Møller

Aalborg Universitet

Proceedings of the London Mathematical Society

##### Realizability and tameness of fusion systems

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*2023/12*

Jesper Møller

Aalborg Universitet

ACM Transactions on Spatial Algorithms and Systems

##### Stochastic Routing with Arrival Windows

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*2023/11/21*

Jesper Møller

Aalborg Universitet

Spatial Statistics

##### Fitting the grain orientation distribution of a polycrystalline material conditioned on a Laguerre tessellation

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*2023/6/1*

Jesper Møller

Aalborg Universitet

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##### Singular distribution functions for random variables with stationary digits

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*2023/3*

Jesper Møller

Aalborg Universitet

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*2022/12/16*

Jesper Møller

Aalborg Universitet

Stat

##### Determinantal shot noise Cox processes

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*2022/12*

Jesper Møller

Aalborg Universitet

Journal of Applied Probability

##### Characterization of random variables with stationary digits

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*2022/12*

Jesper Møller

Aalborg Universitet

Spatial Statistics

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*2022/10/1*

Jesper Møller

Aalborg Universitet

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*2022/9/5*

Jesper Møller

Aalborg Universitet

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Jesper Møller

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*2022/4/3*

Jesper Møller

Aalborg Universitet

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Jesper Møller

Aalborg Universitet

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*2021/11*

Jesper Møller

Aalborg Universitet

Communications Biology

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*2021/9/2*

Jesper Møller

Aalborg Universitet

AMERICAN MATHEMATICAL SOCIETY

##### THE NUMBER OF p-ELEMENTS IN FINITE GROUPS OF LIE TYPE OF CHARACTERISTIC p

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*2021/7/1*

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