Related papers: Geometry of Morphogenesis
Let $M$ denote a two-dimensional Moore space (so $H_2(M; \Z) = 0$), with fundamental group $G$. The $M$-cellular spaces are those one can build from $M$ by using wedges, push-outs, and telescopes (and hence all pointed homotopy colimits).…
The study of the morphology of galaxies is important in order to understand the formation and evolution of galaxies and their sub-components as a function of luminosity, environment, and star-formation and galaxy assembly over cosmic time.…
We describe the geometry of conjugation within any split subgroup $H$ of the full isometry group $G$ of $n$-dimensional Euclidean space. We prove that for any $h \in H$, the conjugacy class $[h]_H$ of $h$ is described geometrically by the…
In a previous work [J. Chem. Phys. 155, 244111 (2021)], we found counterexamples to the fundamental Hohenberg-Kohn theorem from density-functional theory in finite-lattice systems represented by graphs. Here, we demonstrate that this only…
The ordering dynamics of the Higgs field is studied, using techniques inspired by the study of phase ordering in condensed matter physics, as a first step to understanding the evolution of cosmic structure through the formation of…
We here define a cell structure for real, complex and quaternionic flag manifolds in a unified way. Our method is geometric in nature and is inspired from a method due to Milnor and Stasheff, which they used to define a cell structure for…
The phenomenological model for cell shape deformation and cell migration (Chen et.al. 2018; Vermolen and Gefen 2012) is extended with the incorporation of cell traction forces and the evolution of cell equilibrium shapes as a result of cell…
We study non-equilibrium bacterial colony growth using a geometry-first, time-resolved analysis of morphology. From time-lapse microscopy data, we track the coupled evolution of area, perimeter, and boundary-sensitive shape descriptors…
This study develops an equation for describing three-dimensional membrane transformation through proliferation of its component cells regulated by morphogen density distributions on the membrane. The equation is developed in a…
Several orders of magnitude typically separate the contour length of eukaryotic chromosomes and the size of the nucleus where they are confined. The ensuing topological constraints can slow down the relaxation dynamics of genomic filaments…
The theory of geometric structures on a surface with nonempty boundary can be developed by using a decomposition of such a surface into hexagons, in the same way as the theory of geometric structures on a surface without boundary is…
In this paper we argue that the pattern of cell movements in the morphogenetic process known as convergent extension can be understood as a energy minimization process, provided the cell-cell adhesive energy has a certain kind of…
Cell shape has long been used to discern cell phenotypes and states, but the underlying premise has not been quantitatively tested. Here, we show that a single cell image can be used to discriminate its migration behavior by analyzing a…
The Voronoi-based cellular model is highly successful in describing the motion of two-dimensional confluent cell tissues. In the homogeneous version of this model, the energy of each cell is determined solely by its geometric shape and…
The optimal shapes attained by contractile cells on adhesive substrates are determined by the interplay between intracellular forces and adhesion with the extracellular matrix. We model the cell as a contractile film bounded by an elastic…
Geometrical analysis of a new type of Unified Field Theoretical models follow the guidelines of previous works of the authors is presented. These new unified theoretical models are characterized by an underlying hypercomplex structure, zero…
Although cell shape can reflect the mechanical and biochemical properties of the cell and its environment, quantification of 3D cell shapes within 3D tissues remains difficult, typically requiring digital reconstruction from a stack of 2D…
We investigate morphologies of proliferating cellular tissue using a newly developed numerical simulation model for mechanical cell division. The model reproduces structures of simple multi-cellular organisms via simple rules for selective…
In this work, major principles of the mathematical constitution of space and the principles of construction of the physical space are presented. Generalized conceptions of distances and dimensionality evaluation are proposed, together with…
Tumor growth has a number of features in common with a physical process known as molecular beam epitaxy. Both growth processes are characterized by the constraint of growth development to the body border, and surface diffusion of…