Related papers: Self-similar shapes under Errera division rule on …
The mechanical behaviour and symmetry-breaking shape deformation of red blood cells subjected to shear flows is used to demonstrate that far from being random fluids, both the membrane and cytoplasm of every biological cell undergo…
The two pillars of Algebraic topology - Homology and homotopy theory rely on the availability of basic building blocks called cells. Cells take the form of simplexes, and have properties such as faces, sub-cells, convexity and…
We study the vertex model for epithelial tissue mechanics extended to include coupling between the cell shapes and tensions in cell-cell junctions. This coupling represents an active force which drives the system out of equilibrium and…
Heterogeneous growth plays an important role in the shape and pattern formation of thin elastic structures ranging from the petals of blooming lilies to the cell walls of growing bacteria. Here we address the stability and regulation of…
New expansionary and rotational quadratic forms are constructed for $E^n$-endomorphisms. Relations amongst the various eigenvalues, eigendirections and matrix invariants are established, including propositions on complexity and geometric…
In this paper, we study a reverse isoperimetric inequality for planar convex bodies whose radius of curvature is between two positive numbers 0 < $\alpha$ < $\beta$, called ($\alpha$, $\beta$)--convex bodies. We show that among planar…
While the shape equations describing the equilibrium of an unstretchable thin sheet that is free to bend are known, the boundary conditions that supplement these equations on free edges have remained elusive. Intuitively, unstretchability…
Cell deformability is an essential determinant for tissue-scale mechanical nature, such as fluidity and rigidity, and is thus crucial for understanding tissue homeostasis and stable developmental processes. However, numerical simulations…
In this note we describe a discrete dynamical system acting on the similarity classes of a plane convex body within the affine class of the body. We find invariant elements in all affine classes, and describe the orbits of bodies in some…
The balance between stretching and bending deformations characterizes shape transitions of thin elastic sheets. While stretching dominates the mechanical response in tension, bending dominates in compression after an abrupt buckling…
We study the mathematical properties of a general model of cell division structured with several internal variables. We begin with a simpler and specific model with two variables, we solve the eigenvalue problem with strong or weak…
This study focuses on an extended model of a standard cellular automaton (CA) that includes an extra index consisting of a radius that defines a perception area for each cell in addition to the radius defined by the CA rule. Extended…
How can dense biological tissue maintain sharp boundaries between coexisting cell populations? We explore this question within a simple vertex model for cells, focusing on the role of topology and tissue surface tension. We show that the…
We find explicit subdivision rules for all special cubulated groups. A subdivision rule for a group produces a sequence of tilings on a sphere which encode all quasi-isometric information for a group. We show how these tilings detect…
One-dimensional cellular automata are discrete dynamical systems that operate on an infinite lattice of sites and are characterized by the locality and uniformity of their update rule. Permutations of the state set and isometric…
The shape of a cell influences and it is influenced by interactions with its neighbouring partners. Here, we introduce a coarse-grained model of non-reciprocal interactions between single-cell organisms to study emergent morphologies during…
This work sets the non isotropic noncentral elliptical shape distributions via QR decomposition in the context of zonal polynomials, avoiding the invariant polynomials and the open problems for their computation. The new shape distributions…
Biological cells are able to generate intricate structures and respond to external stimuli, sculpting their membrane from within. Simplified biomimetic systems can aid in understanding the principles which govern these shape changes and…
We study kernel quadrature rules with convex weights. Our approach combines the spectral properties of the kernel with recombination results about point measures. This results in effective algorithms that construct convex quadrature rules…
Motivated by models in engineering and also biology we determine in closed form the probability density function of the angle shaped by two random chords in a fixed disc. Our main result focus on the event in which the intersection locates…