Related papers: Lattice Structure of Variable Precision Rough Sets
Rough sets are efficient for data pre-processing in data mining. Matroids are based on linear algebra and graph theory, and have a variety of applications in many fields. Both rough sets and matroids are closely related to lattices. For a…
A definition of structural diversity, adapted from the biodiversity literature, is introduced to provide a general characterization of structures of condensed matter. Using the Favored Local Structure (FLS) lattice model as a testbed, the…
In a way similar to the continuous case formally, we define in different but equivalent manners the difference discrete connection and curvature on discrete vector bundle over the regular lattice as base space. We deal with the difference…
There is a deformation of the ordinary differential calculus which leads from the continuum to a lattice (and induces a corresponding deformation of physical theories). We recall some of its features and relate it to a general framework of…
We define and study structural properties of hypergraphs of models of a theory including lattice ones. Characterizations for the lattice properties of hypergraphs of models of a theory, as well as for structures on sets of isomorphism types…
The synthesis of porous, lattice, or microstructure geometries has captured the attention of many researchers in recent years. Implicit forms, such as triply periodic minimal surfaces (TPMS) has captured a significant attention, recently,…
Rough sets were proposed to deal with the vagueness and incompleteness of knowledge in information systems. There are may optimization issues in this field such as attribute reduction. Matroids generalized from matrices are widely used in…
The purpose of this paper is to study convex bodies $C$ for which there exists no convex body $C^\prime\subsetneq C$ of the same lattice width. Such bodies shall be called ``lattice reduced'', and they occur naturally in the study of the…
While there is a well developed theory of locally solid topologies, many important convergences in vector lattice theory are not topological. Yet they share many properties with locally solid topologies. Building upon the theory of…
The lattice size of a lattice polytope is a geometric invariant which was formally introduced in the context of simplification of the defining equation of an algebraic curve, but appeared implicitly earlier in geometric combinatorics.…
This is a survey of characterizations and relationships between some properties of lattices, particularly the modular, Arguesian, linear, and distributive properties, but also some other related properties. The survey emphasizes finite and…
Lattice models or structures are geometrical objects with mathematical forms, that are used to represent physical systems. They have been used widely in diverse fields, namely, in condensed matter physics, to study degrees of freedom of…
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…
The use of lattice QCD to understand hadron structure is described, with particular emphasis on exploring the role of glue.
The first part of this paper surveys several results on the lattice structure of variable exponent Lebesgue function spaces (or Nakano spaces) $\lpv$. In the second part strictly singular and disjointly strictly singular operators between…
Lattice structures have been widely used in various applications of additive manufacturing due to its superior physical properties. If modeled by triangular meshes, a lattice structure with huge number of struts would consume massive…
This paper explores the embedding of lattice structures $L \subseteq \mathbb{R}^n$ into smooth manifolds $M \subseteq \mathbb{R}^n$ through a rigorous mathematical framework. Building upon the foundational results established in "Embedding…
This paper is devoted to the study of the dynamics of a discrete system related to some self stabilizing protocol on a ring of processors.
We discuss how lattice calculations can be a useful tool for the study of structure functions. Particular emphasis is given to the perturbative renormalization of the operators.
We study the joint variability of structural information in a hard sphere fluid biased to avoid crystallisation and form fivefold symmetric geometric motifs. We show that the structural covariance matrix approach, originally proposed for…