Related papers: Layer Groups of Batak Weaves
The aim of this review is to present and analyze the probabilistic models of mathematical phylogenetics which have been intensively used in recent years in biology as the cornerstone of attempts to infer and reconstruct the ancestral…
We investigate 2-dimensional Viscoelastic equations with a view of Lie groups. In this sense, we answer question of the symmetry classification. We provide the algebra of symmetry and build the optimal system of Lie subalgebras. Reductions…
This work introduces a geometric framework and a novel network architecture for creating correspondences between samples of different conditions. Under this formalism, the latent space is a fiber bundle stratified into a base space encoding…
Covering is a common type of data structure and covering-based rough set theory is an efficient tool to process this data. Lattice is an important algebraic structure and used extensively in investigating some types of generalized rough…
We provide a complete classification of groups that can be realized as isometry groups of a translation surface $M$ with non-finitely generated fundamental group and no planar ends. Furthermore, we demonstrate that if $S$ has no…
We give very flexible, concrete constructions of discrete and faithful epresentations of right-angled Artin groups into higher-rank Lie groups. Using the geometry of the associated symmetric spaces and the combinatorics of the groups, we…
We prove some conditions for the existence of higher dimensional algebraic fibering of group extensions. This leads to various corollaries on incoherence of groups and some geometric examples of algebraic fibers of type $F_n$ but not…
The point group symmetry of materials is closely related to their physical properties and quite important for material modeling. However, superlattice materials have more complex symmetry conditions than crystals due to their multilevel…
Symmetry plays a fundamental role in understanding natural phenomena and mathematical structures. This work develops a comprehensive theory for studying the persistent symmetries and degree of asymmetry of finite point configurations over…
Packings of hard polyhedra have been studied for centuries due to their mathematical aesthetic and more recently for their applications in fields such as nanoscience, granular and colloidal matter, and biology. In all these fields, particle…
We introduce a novel combinatorial structure called pointed building sets, which can be viewed as families of lattices equipped with compatibility relations. To each pointed building set $\mathsf{B}$, we associate a complete lattice…
Topological insulators in the Bi$_2$Se$_3$ family manifest helical Dirac surface states that span the topologically ordered bulk band gap. Recent scanning tunneling microscopy measurements have discovered additional states in the bulk band…
Local and global amoebas are families of labeled graphs that satisfy interpolation properties on a fixed vertex set. A labeled graph $G$ on $n$ vertices is a local amoeba (resp. global amoeba) if there exists a sequence of feasible…
We give an explicit description of character sheaves for the symmetric pairs associated to inner involutions of the special linear groups. We make use of the general strategy given in [VX1] and central character consideration. We also…
The society has a multi-layered structure, where the layers represent the different contexts. To model this structure we begin with a single-layer weighted social network (WSN) model showing the Granovetterian structure. We find that when…
We study empirical statistical and gap distributions of several important tilings of the plane. In particular, we consider the slope distributions, the angle distributions, pair correlation, squared-distance pair correlation, angle gap…
We use the automorphism group $Aut(H)$, of holes in the lattice $L_8=A_2\oplus A_2\oplus D_4$, as the starting point in the construction of sphere packings in 10 and 12 dimensions. A second lattice, $L_4=A_2\oplus A_2$, enters the…
We consider an involutive automorphism of the conformal algebra and the resulting symmetric space. We display a new action of the conformal group which gives rise to this space. The space has an intrinsic symplectic structure, a…
Symmetry in mathematical programming may lead to a multiplicity of solutions. In nonconvex optimisation, it can negatively affect the performance of the branch-and-bound algorithm. Symmetry may induce large search trees with multiple…
To any quiver with relations we associate a consistent scattering diagram taking values in the motivic Hall algebra of its category of representations. We show that the chamber structure of this scattering diagram coincides with the natural…