Related papers: Inferring a Cell Structure on the Space of Cyclooc…
The accidental degeneracy appearing in cycloacenes as triplets and quadruplets is explained with the concept of segmentation, introduced here with the aim of describing the effective disconnection of $\pi$ orbitals on these organic…
We present a computational study of the electronic properties of amorphous SiO2. The ionic configurations used are the ones generated by an earlier molecular dynamics simulations in which the system was cooled with different cooling rates…
The tight-span of a finite metric space is a polytopal complex that has appeared in several areas of mathematics. In this paper we determine the polytopal structure of the tight-span of a totally split decomposable (finite) metric. Totally…
We investigate the mechanical interplay between the spatial organization of the actin cytoskeleton and the shape of animal cells adhering on micropillar arrays. Using a combination of analytical work, computer simulations and in vitro…
With the help of a mathematical model, the metabolic process of the Krebs cycle is studied. The autocatalytic processes resulting in both the formation of the self-organization in the Krebs cycle and the appearance of a cyclicity of its…
We develop the Lorentzian geometry of a crooked halfspace in 2+1-dimensional Minkowski space. We calculate the affine, conformal and isometric automorphism groups of a crooked halfspace, and discuss its stratification into orbit types,…
In this paper, we list several interesting structures of cyclotomic polynomials: specifically relations among blocks obtained by suitable partition of cyclotomic polynomials. We present explicit and self-contained proof for all of them,…
X-shaped liquid crystalline molecules (XLCMs) are obtained by tethering two flexible end A-blocks and two flexible side B-blocks to a rigid backbone (R). A rich array of ordered structures can be formed from XLCMs, driven by the competition…
The topological organisation of cells in a model of living tissue (the crypt of intestinal epithelium) is identical to the topological organisation of atoms in carbon nanotubes. The existing models of growth of these two structures contain…
We discuss $\mathcal{N}=1$ Klein and Klein-Conformal superspaces in $D=(2,2)$ space-time dimensions, realizing them in terms of their functor of points over the split composition algebra $\mathbb{C}_{s}$. We exploit the observation that…
Previously, a seven-cluster pattern claiming to be a universal one in bacterial genomes has been reported. Keeping in mind the most popular theory of chloroplast origin, we checked whether a similar pattern is observed in chloroplast…
The cell cortex, a thin film of active material assembled below the cell membrane, plays a key role in cellular symmetry breaking processes such as cell polarity establishment and cell division. Here, we present a minimal model of the…
We demonstrate the emergence of the conformal group SO(4,2) from the Clifford algebra of spacetime. The latter algebra is a manifold, called Clifford space, which is assumed to be the arena in which physics takes place. A Clifford space…
This thesis proposes a framework based on a notion of combinatorial cell complex (cc) whose cells are defined simply as finite sets of vertices. The cells of a cc are subject to four axioms involving a rank function that assigns a rank (or…
Carbon is the most important chemical element and the theoretical study of its new allotropes can be of great interest. In this study, regular dodecahedron (dodecahedrane) oligomers (n = 1, 3, 5, 7, 9, 11, 13) by extending the dodecahedrane…
We model the electronic properties of thin films of binary compounds with stacked layers where each layer is a two-dimensional honeycomb lattice with two atoms per unit cell. The two atoms per cell are assigned different onsite energies in…
The possibility of realizing topological insulators by spontaneous formation of electronic superstructure is theoretically investigated in a minimal two-orbital model including both the spin-orbit coupling and electron correlations on a…
Spatial organisation is a hallmark of all living cells, and recreating it in model systems is a necessary step in the creation of synthetic cells. It is therefore of both fundamental and practical interest to better understand the basic…
Metabolism displays striking and robust regularities in the forms of modularity and hierarchy, whose composition may be compactly described. This renders metabolic architecture comprehensible as a system, and suggests the order in which…
In this paper we consider the classification of minimal cellular structures of spaces of topological complexity two under some hypotheses on there graded cohomological algebra. This continues the method used by M.Grant et al. in [1].