We perturb the simple cubic (SC), body-centered cubic (BCC), and face-centered cubic (FCC) structures with a spatial Gaussian noise whose adimensional strength is controlled by the parameter α and analyze the statistical properties of the cells of the resulting Voronoi tessellations. We concentrate on topological properties, such as the number of faces, and on metric properties, such as the are...

We analyze the problem of tessellating an n-sided patch with ideal, maximally-regular internal quadrangulation, featuring a single irregular vertex (or none, for n=4). derive, in closed-form, necessary and sufficient conditions that boundary must meet it to admit quadrangulation this kind, and, if so, provide full description resulting tessellation(s), as functions number edges subdividing side...

The role of specific structural patterns in keratin filament networks for regulating biophysical properties of epithelial cells is poorly understood. This is at least partially due to a lack of methods for the analysis of filament network morphology. We have previously developed a statistical approach to the analysis of keratin filament networks imaged by scanning electron microscopy. The segme...

Mixed elements meshes based on the modified octree approach contain several co-spherical point configurations. While generating Delaunay tessellations to be used together with the finite volume method, it is not necessary to partition them into tetrahedra; co-spherical elements can be used as final elements. This paper presents a study of all co-spherical elements that appear while tessellating...

We adapt a construction of Guth and Lubotzky [GL14] to obtain a family of quantum LDPC codes with non-vanishing rate and minimum distance scaling like n where n is the number of physical qubits. Similarly as in [GL14], our homological code family stems from tessellated hyperbolic 4-manifolds. The main novelty of this work is that we consider a regular tessellation consisting of hypercubes. We e...