Related papers: Eden model for Pentagons
Other than vector representations, the direct objects of human cognition are generally high-order tensors, such as 2D images and 3D textures. From this fact, two interesting questions naturally arise: How does the human brain represent…
Graphene, the new wondrous material, is a perfect example of a two-dimensional hexagonal crystal unlike any other. Here we exhibit some of the characteristic directional features associated with hexagonal cells, emphasising the sixfold…
Solidification is an important process in many alloy processing routes. The solidified microstructure of alloys is usually made up of dendrites, eutectics or a combination of both. The evolving morphologies are largely determined by the…
Vertex models have been extensively used for simulating the evolution of multicellular systems, and have given rise to important global properties concerning their macroscopic rheology or jamming transitions. These models are based on the…
The enduring legacy of Euclidean geometry underpins classical machine learning, which, for decades, has been primarily developed for data lying in Euclidean space. Yet, modern machine learning increasingly encounters richly structured data…
We consider certain point patterns of an Euclidean space and calculate the Ellis enveloping semigroup of their associated dynamical systems. The algebraic structure and the topology of the Ellis semigroup, as well as its action on the…
We consider an age-size structured cell population model based on the cell cycle length. The model is described by a first order partial differential equation with initial-boundary conditions. Using the theory of semigroups of positive…
The purpose of this paper is to study the shapes and stabilities of bio-membranes within the framework of exterior differential forms. After a brief review of the current status in theoretical and experimental studies on the shapes of…
We establish some new theorems on pentagon and pentagram.
We discuss the theoretical predictions for the two photon decay width of the pseudoscalar etab meson. Predictions from potential models are examined. It is found that various models are in good agreement with each other. Results for etab…
A powerful experimental approach for investigating computation in networks of biological neurons is the use of cultured dissociated cortical cells grown into networks on a multi-electrode array. Such preparations allow investigation of…
We measure different contributions to entropy production in a living functional epithelial tissue. We do this by extracting the functional dynamics of development while at the same time quantifying fluctuations. Using the translucent…
This paper investigates several distinct attempts to generalize in higher dimension the standard 2-dimensional phyllotaxy set construction. We first recall known contructions for these sets on $2D$ manifolds of constant curvature (the…
Constructive-deductive method for plane Euclidean geometry is proposed and formalized within Coq Proof Assistant. This method includes both postulates that describe elementary constructions by idealized geometric tools (pencil, straightedge…
Modern spatial microscopy has provided developmental biology with powerful research tools. However, the recent significant technological breakthroughs have inevitably led to technical "bottlenecks" for the application of the new procedures…
Processes of random tessellations of the Euclidean space $\mathbb{R}^d$, $d\geq 1$, are considered which are generated by subsequent division of their cells. Such processes are characterized by the laws of the life times of the cells until…
Voronoi tessellations have been used to model the geometric arrangement of cells in morphogenetic or cancerous tissues, however so far only with flat hypersurfaces as cell-cell contact borders. In order to reproduce the experimentally…
We propose a two-scale model to resolve essential features of developmental tissue deformations. The model couples individual cellular behavior to the mechanics at tissue scale. This is realized by a multiphase-field model addressing the…
How do mammalian cells that share the same genome exist in notably distinct phenotypes, exhibiting differences in morphology, gene expression patterns, and epigenetic chromatin statuses? Furthermore how do cells of different phenotypes…
We investigate several topics of triangle geometry in the elliptic and in the extended hyperbolic plane, such as: centers based on orthogonality, centers related to circumcircles and incircles, radical centers and centers of similitude,…