Related papers: Some preliminary results on relation between tripl…
A new class of distances appropriate for measuring similarity relations between sequences, say one type of similarity per distance, is studied. We propose a new ``normalized information distance'', based on the noncomputable notion of…
The paper concerns clustering with respect to the shape and size of 2D contours that are boundaries of cross-sections of 3D objects of revolution. We propose a number of similarity measures based on combined disparate Procrustes analysis…
I present here a review of Large-Scale Structure (LSS) studies using clusters of galaxies. First, I re-evaluate the `pros' and `cons' of using clusters for such studies, especially in this era of large galaxy redshift surveys. Secondly, I…
The quaternion Bingham distribution has been used to model preferred crystallographic orientation, or crystallographic texture, in polycrystalline materials in the materials science and geological communities. A primary difficulty in…
I review the status of large-scale structure studies based on redshift surveys of galaxies and clusters of galaxies. In particular, I compare recent results on the power spectrum and two-point correlation correlation function from the 2dF…
In this paper, we review or introduce several differential structures on manifolds in the general setting of real and complex differential geometry, and apply this study to Teichm\"uller theory. We focus on bi-Lagrangian i.e. para-K\"ahler…
We propose a new approach for clustering DNA features using array CGH data from multiple tumor samples. We distinguish data-collapsing: joining contiguous DNA clones or probes with extremely similar data into regions, from clustering:…
Complementary one-, two-, and three-dimensional tests for detecting the presence of substructure in clusters of galaxies are applied to recently obtained data from the 2dF Galaxy Redshift Survey. The sample of 25 clusters used in this study…
The traditional method of morphological classification, by visual inspection of images of uniform quality and by reference to standards for each type, is critically examined. The rate of agreement among traditional morphologists on the…
Deep learning has proven to successfully learn variations in tissue and cell morphology. Training of such models typically relies on expensive manual annotations. Here we conjecture that spatially resolved gene expression, e.i., the…
Previous studies using numerical simulations have demonstrated that the shape of the cosmic web can be described by studying the Lagrangian displacement field. We extend these analyses, showing that it is now possible to perform a…
The crystallographic texture is a key organization feature of many technical and biological materials. In these materials, especially hierarchically structured ones, the preferential alignment of the nano constituents is heavily influencing…
In the field of population health research, understanding the similarities between geographical areas and quantifying their shared effects on health outcomes is crucial. In this paper, we synthesise a number of existing methods to create a…
This thesis focuses on characterizing the distribution of points and galaxies using multifractal analysis. In this attempt the main emphasis is on calculating the Minkowski-Bouligand fractal dimension (Dq) of the distribution of points over…
Many young star clusters appear to be fractal, i.e. they appear to be concentrated in a nested hierarchy of clusters within clusters. We present a new algorithm for statistically analysing the distribution of stars to quantify the level of…
We study local algebras, which are structures similar to $\mathbb{Z}$-graded algebras concentrated in degrees $-1,0,1$, but without a product defined for pairs of elements at the same degree $\pm1$. To any triple consisting of a Kac-Moody…
The upcoming XMM Large Scale Structure Survey (XMM-LSS) will ultimately provide a unique mapping of the distribution of X-ray sources in a contiguous 64 sq. deg. region. In particular, it will provide the 3-dimensional location of about 900…
Recent advancements in spatial transcriptomics technologies allow researchers to simultaneously measure RNA expression levels for hundreds to thousands of genes while preserving spatial information within tissues, providing critical…
We have used the ROSAT All-Sky Survey around the North Ecliptic Pole to construct a complete sample of galaxy clusters. The deep and contiguous nature of the survey affords us the opportunity to examine large-scale structure in the Universe…
We introduce a density-based clustering method called skeleton clustering that can detect clusters in multivariate and even high-dimensional data with irregular shapes. To bypass the curse of dimensionality, we propose surrogate density…