Related papers: The topological structure of 2D disordered cellula…
We investigate the statistical properties of two dimensional random cellular systems (froths) in term of their shell structure. The froth is analyzed as a system of concentric layers of cells around a given central cell. We derive exact…
Various structures in human physiology follow a treelike morphology, which often expresses complexity at very fine scales. Examples of such structures are intrathoracic airways, retinal blood vessels, and hepatic blood vessels. Large…
Different cell types aggregate and sort into hierarchical architectures during the formation of animal tissues. The resulting spatial organization depends (in part) on the strength of adhesion of one cell type to itself relative to other…
Topologically stable cellular partitions of D dimensional spaces are studied. A complete statistical description of the average structural properties of such partition is given in term of a sequence of D/2-1 (or (D-1)/2) variables for D…
The organization of cells within tissues plays a vital role in various biological processes, including development and morphogenesis. As a result, understanding how cells self-organize in tissues has been an active area of research. In our…
To insight the relationships between the self-organizing structures of cells, such as the cell clusters, and the properties of biotissues is helpful in revealing the function and designing biomaterial. Traditional random foam model neglects…
Structural cellular materials in nature, such as wood, trabecular bone, corals, and dentin combine complex biological functions with structural roles, such as skeletal support and impact protection1,2. They feature complex structural…
A computation of the dynamical structure factor of topologically disordered systems, where the disorder can be described in terms of euclidean random matrices, is presented. Among others, structural glasses and supercooled liquids belong to…
We describe the topological structure and the underlying organization principles of the directories created by users of a computer cluster when storing his/her own files. We analyze degree distributions, average distance between files,…
Rapid advance of experimental techniques provides an unprecedented in-depth view into complex developmental processes. Still, little is known on how the complexity of multicellular organisms evolved by elaborating developmental programs and…
We consider causal 3-dimensional triangulations with the topology of $S^2\times [0,1]$ or $D^2\times [0,1]$ where $S^2$ and $D^2$ are the two-dimensional sphere and disc, respectively. These triangulations consist of slices and we show that…
Physical systems are frequently modeled as sets of points in space, each representing the position of an atom, molecule, or mesoscale particle. As many properties of such systems depend on the underlying ordering of their constituent…
Voronoi tessellations of Poisson point processes are widely used for modeling many types of physical and biological systems. In this paper, we analyze simulated Poisson-Voronoi structures containing a total of 250,000,000 cells to provide…
Disordered systems like liquids, gels, glasses, or granular materials are not only ubiquitous in daily life and in industrial applications but they are also crucial for the mechanical stability of cells or the transport of chemical and…
Much information about a graph can be obtained by studying its spanning trees. On the other hand, a graph can be regarded as a 1-dimensional cell complex, raising the question of developing a theory of trees in higher dimension. As observed…
Cellular patterns formed by self-organization of dislocations are a most conspicuous feature of dislocation microstructure evolution during plastic deformation. To elucidate the physical mechanisms underlying dislocation cell structure…
The topology and form finding of tensegrity structures have been studied extensively since the introduction of the tensegrity concept. However, most of these studies address topology and form separately, where the former represented a…
Many systems in nature and the synthetic world involve ordered arrangements of units on two-dimensional surfaces. We review here the fundamental role payed by both the topology of the underlying surface and its detailed curvature. Topology…
Disordered systems like liquids, gels, glasses, or granular materials are not only ubiquitous in daily life and in industrial applications but they are also crucial for the mechanical stability of cells or the transport of chemical and…
We use Topological Data Analysis tools for studying the inner organization of cells in segmented images of epithelial tissues. More specifically, for each segmented image, we compute different persistence barcodes, which codify lifetime of…