Related papers: The topological structure of 2D disordered cellula…

Here we would like to discuss the light transmission modulation by periodic and disordered one dimensional (1D) photonic structures. In particular, we will present some theoretical and experimental findings highlighting the peculiar optical…

Disordered proteins and nucleic acids play key roles in cellular function and disease. Here we review recent advances in the computational exploration of the conformational dynamics of flexible biomolecules. We focus on hierarchical chain…

The spatial structure of the cell is highly organized at all levels: from small complexes and assemblies, to local nano- and micro-clusters, to global, micrometer scales across and between cells. We suggest that this multiscale spatial cell…

The purpose of this present paper is to investigate the geometric structure of regular overdetermined systems of second order with two independent and one dependent variables from the point of view of rank 2 prolongations. Utilizing this…

We present a general computational theory of stem cell networks and their developmental dynamics. Stem cell networks are special cases of developmental control networks. Our theory generates a natural classification of all possible stem…

Biologically inspired pressure actuated cellular structures can alter their shape through pressure variations. Previous work introduced a computational framework for pressure actuated cellular structures which was limited to two cell rows…

Topological and geometrical properties and the associated topological defects find a rapidly growing interest in studying the interplay between mechanics and the collective behavior of cells on the tissue level. We here test if well studied…

In this paper we will present a way of examining the Stokes structure of certain irregular singular $\mathcal D$-modules, namely the direct image of exponentially twisted regular singular meromorphic connections, in a topological point of…

This work targets the influence of disorder on the relaxed structure and macroscopic mechanical properties of elastic networks. We construct network classes of different types of disorder (length, topology and stiffness), which are…

Cells forming various epithelial tissues have a strikingly universal distribution for the number of their edges. It is generally assumed that this topological feature is predefined by the statistics of individual cell divisions in growing…

Topological defects, which are singular points in a director field, play a major role in shaping active systems. Here, we experimentally study topological defects and the flow patterns around them, that are formed during the highly rapid…

We define 2-calibrated structures, which are analogs of symplectic structures in odd dimensions. We show the existence of differential topological constructions compatible with the structure.

In many areas of applied geometric/numeric computational mathematics, including geo-mapping, computer vision, computer graphics, finite element analysis, medical imaging, geometric design, and solid modeling, one has to compute incidences,…

Biological systems exploit self-assembly to create complex structures whose arrangements are finely controlled from molecular to mesoscopic level. Herein we report an example of using fully synthetic systems that mimic two levels of…

Unlike other tissue types, like epithelial tissue, which consist of cells with a much more homogeneous structure and function, the nervous tissue spans in a complex multilayer environment whose topographical features display a large…

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…

The shell map is a very simple representation of the structure of foams, combining the geometrical (random tiling) and dynamical (loss of information from an arbitrary cell out) aspects of disorder. The structure is built from the central…

Geometry of networks endowed with a causal structure is discussed using the conventional framework of equilibrium statistical mechanics. The popular growing network models appear as particular causal models. We focus on a class of tree…

Open cellular solids usually possess random microstructures that may contain a characteristic length scale, such as the cell size. This gives rise to size dependent mechanical properties where large systems behave differently from small…

We investigate cosmological structure formation seeded by topological defects which may form during a phase transition in the early universe. First we derive a partially new, local and gauge invariant system of perturbation equations to…