Related papers: Robust Morphological Measures for Large-Scale Stru…
We construct a set of shape-finders which determine shapes of compact surfaces (iso-density surfaces in galaxy surveys or N-body simulations) without fitting them to ellipsoidal configurations as done earlier. The new indicators arise from…
The paper discusses local porosity theory and its relation with other geometric characterization methods for porous media such as correlation functions and contact distributions. Special emphasis is placed on the charcterization of…
Experiments on fracture surface morphologies offer increasing amounts of data that can be analyzed using methods of statistical physics. One finds scaling exponents associated with correlation and structure functions, indicating a rich…
We present a novel method for computing the Minkowski Functionals from isodensity surfaces extracted directly from the Delaunay tessellation of a point distribution. This is an important step forward compared to the previous cosmological…
This article discusses how the individual morphological properties of basic objects (e.g. neurons, molecules and aggregates), jointly with their particular spatial distribution, can determine the connectivity and dynamics of systems…
The Brunn-Minkowski theory in convex geometry concerns, among other things, the volumes, mixed volumes, and surface area measures of convex bodies. We study generalizations of these concepts to Borel measures with density in…
Upon a consistent topological statistical theory the application of structural statistics requires a quantification of the proximity structure of model spaces. An important tool to study these structures are Pseudo-Riemannian metrices,…
This paper reviews selected aspects of the growth of cosmological structure, covering the following general areas: (1) expected characteristics of linear density perturbations according to various candidate theories for the origin of…
Many tools and techniques measure local structure in materials in contexts ranging from biology to geology. We provide a survey of those tools and metrics that are especially useful for analyzing particulate soft matter. The metrics we…
We develop technique concerning statistical analyses of the large-scale structure of the universe in the presence of biasing in the structure formation. We formulate the diagrammatic method to calculate the correlation functions of the…
A theory for studying the dynamic scaling properties of branes and relativistic topological defect networks is presented. The theory, based on a relativistic version of the level set method, well-known in other contexts, possesses…
This paper develops goodness of fit statistics that can be used to formally assess Markov random field models for spatial data, when the model distributions are discrete or continuous and potentially parametric. Test statistics are formed…
Hyperuniformity, the suppression of density fluctuations at large length scales, is observed across a wide variety of domains, from cosmology to condensed matter and biological systems. Although the standard definition of hyperuniformity…
The paper is devoted to the study of Gromov-Hausdorff convergence and stability of irreversible metric-measure spaces, both in the compact and noncompact cases. While the compact setting is mostly similar to the reversible case developed by…
This report introduces and investigates a family of metrics on sets of pointed Kripke models. The metrics are generalizations of the Hamming distance applicable to countably infinite binary strings and, by extension, logical theories or…
Cities are complex products of human culture, characterised by a startling diversity of visible traits. Their form is constantly evolving, reflecting changing human needs and local contingencies, manifested in space by many urban patterns.…
To the families of geometric measures of convex bodies (the area measures of Aleksandrov-Fenchel-Jessen, the curvature measures of Federer, and the recently discovered dual curvature measures) a new family is added. The new family of…
This paper reviews several Riemannian metrics and evolution equations in the context of diffeomorphic shape analysis. After a short review of of various approaches at building Riemannian spaces of shapes, with a special focus on the…
The surgery technique of Gromov and Lawson may be used to construct families of positive scalar curvature metrics which are parameterised by Morse functions. This has played an important role in the study of the space of metrics of positive…
Minkowski functionals (MFs) quantify the topological properties of a given field probing its departure from Gaussianity. We investigate their use on lensing convergence maps in order to see whether they can provide further insights on the…