Related papers: Geometry of Morphogenesis
A computational theory and model of the ontogeny and development of bilateral symmetry in multicellular organisms is presented. Understanding the origin and evolution of bilateral organisms requires an understanding of how bilateral…
The spatial organization of bacteria in dense biofilms is key to their collective behaviour, and understanding it will be important for medical and technological applications. Here we study the morphology of a compact biofilm that undergoes…
Collective cell motions underlie structure formation during embryonic development. Tissues exhibit emergent multicellular characteristics such as jamming, rigidity transitions, and glassy dynamics, but there remain questions about how those…
We introduce a generic, purely mechanical model for environment sensitive motion of mammalian cells that is applicable to chemotaxis, haptotaxis, and durotaxis as modes of motility. It is able to theoretically explain all relevant…
Coordination geometries describe how the neighbours of a central particle are arranged around it. Such geometries can be thought to lie in an abstract topological space; a model of this space could provide a mathematical basis for…
We study the morphology of a fluid membrane in spherical confinement. When the area of the membrane is slightly larger than the area of the outer container, a single axisymmetric invagination is observed. For higher area, self-contact…
In a previous effort [arXiv:1708.05492] we have created a framework that explains why topological structures naturally arise within a scientific theory; namely, they capture the requirements of experimental verification. This is…
It is shown how the coherent states permit to find different geometrical objects as the geodesics, the conjugate locus, the cut locus, the Calabi's diastasis and its domain of definition, the Euler-Poincar\'e characteristic, the number of…
The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a similarity space and concepts are represented by convex regions in this space. After pointing…
Cell invasion and spatial pattern formation are two distinct manifestations of cellular self-organisation in development, regeneration, and disease. Here, we develop and analyse a unified theoretical framework that links these two seemingly…
We report the existence of a single plane in the space of global photometric parameters describing elliptical galaxies and the bulges of early type spiral galaxies. The three parameters which define the plane are obtained by fitting the…
The evolution of multicellularity involved the transformation of a simple cell wall of unicellular ancestors into a complex, multifunctional extracellular matrix (ECM). A suitable model organism to study the formation and expansion of an…
In this paper, we define a new metric structure on the shape space of a high genus surface. We introduce a rigorous definition of a shape of a surface and construct a metric based on two energies measuring the area distortion and the angle…
We show that Euclidean geometry in suitably high dimension can be expressed as a theory of orthogonality of subspaces with fixed dimensions and fixed dimension of their meet.
We suggest a concept of generalized `angles' in arbitrary real normed vector spaces. We give for each real number a definition of an `angle' by means of the shape of the unit ball. They all yield the well known Euclidean angle in the…
We present a model, based on symmetry and geometry, for proteins. Using elementary ideas from mathematics and physics, we derive the geometries of discrete helices and sheets. We postulate a compatible solvent-mediated emergent pairwise…
Three different representation of the proper Euclidean geometry are considered. They differ in the number of basic elements, from which the geometrical objects are constructed. In E-representation there are three basic elements (point,…
In this paper we present a definition of oriented Lagrangian symplectic matroids and their representations. Classical concepts of orientation and this extension may both be thought of as stratifications of thin Schubert cells into unions of…
Recent advances in spatial omics technologies have revolutionized our ability to study biological systems with unprecedented resolution. By preserving the spatial context of molecular measurements, these methods enable comprehensive mapping…
Rod-like bacteria maintain their cylindrical shapes with remarkable precision during growth. However, they are also capable to adapt their shapes to external forces and constraints, for example by growing into narrow or curved confinements.…