Related papers: Lattices of coarse structures
We announce various results concerning the structure of compactly generated simple locally compact groups. We introduce a local invariant, called the structure lattice, which consists of commensurability classes of compact subgroups with…
We investigate the representation of lattices as sublattices of the lattice of all convex subsets (intervals) of a linearly ordered set $(X,\le)$. We introduce the purely lattice-theoretic notion of a \textit{loc-lattice} and prove that…
Moire lattices consist of two identical periodic structures overlaid with a relative rotation angle. Present even in everyday life, moire lattices have been also produced, e.g., with coupled graphene-hexagonal boron nitride monolayers,…
For a presentation $\mathcal{A}$ of a transversal matroid $M$, we study the set $T_{\mathcal{A}}$ of single-element transversal extensions of $M$ that have presentations that extend $\mathcal{A}$; we order these extensions by the weak…
This note aims at obtaining a variational characterization of complex structures by means of a calculus of variations for real vector bundle valued differential forms, and outlines a perspective to study existence questions via functionals…
Suppose $G$ is a locally solid lattice group. It is known that there are non-equivalent classes of bounded homomorphisms on $G$ which have topological structures. In this paper, our attempt is to assign lattice structures on them. More…
We describe a 3D percolation-type approach to modeling of the processes of aging and certain other properties of tissues analyzed as systems consisting of interacting cells. Lattice sites are designated as regular (healthy) cells, senescent…
The intrinsic connection between lattice theory and topology is fairly well established, For instance, the collection of open subsets of a topological subspace always forms a distributive lattice. Persistent homology has been one of the…
Colloidal systems offer unique opportunities for the study of phase formation and structure since their characteristic length scales are accessible to visible light. As a model system the two dimensional assembly of colloidal magnetic and…
Developments in QCD at finite density are reviewed. I begin by discussing some new algorithms which have been applied to other theories with sign problems. Then I discuss the method of analytic continuation in QCD using a series expansion…
We describe a "cellular" approach to the computation of the cohomology of a poset with coefficients in a presheaf. A cellular cochain complex is constructed, described explicitly and shown to compute the cohomology under certain…
I review some recent lattice results on studying chiral and deconfinement transition in QCD at finite temperature and density, as well as properties of strongly interacting matter at high temperatures. I discuss lattice results on the…
Diversities are a generalization of metric spaces, where instead of the non-negative function being defined on pairs of points, it is defined on arbitrary finite sets of points. Diversities have a well-developed theory. This includes the…
The set of space-time short-distance structures which can be described through linear operators is limited to a few basic cases. These are continua, lattices and a further short-distance structure which implies an ultraviolet cut-off. Under…
A well-known conjecture states that the Whitney numbers of the second kind of a geometric lattice (simple matroid) are logarithmically concave. We show this conjecture to be equivalent to proving an upper bound on the number of new copoints…
We obtain structure results for locally conformally symplectic Lie algebras. We classify locally conformally symplectic structures on four-dimensional Lie algebras and construct locally conformally symplectic structures on compact quotients…
The natural topological, differentiable and geometrical structures on the space of light rays of a given spacetime are discussed. The relation between the causality properties of the original spacetime and the natural structures on the…
We aim at studying collections of algebraic structures defined over a commutative ring and investigating the complexity of significant constructions carried out on these objects. The assignment of measures of size, via a multiplicity…
Lattice simulations of hadronic structure are now reaching a level where they are able to not only complement, but also provide guidance to current and forthcoming experimental programmes at, e.g. Jefferson Lab, COMPASS/CERN and FAIR/GSI.…
This paper investigates the structure-property relations of thin-walled lattices under dynamic longitudinal compression, characterized by their cross-sections and heights. These relations elucidate the interactions of different geometric…