Related papers: Lattice Structure of Variable Precision Rough Sets
Many generalized set models have the same basic form: they assign a value to each object, and the main difference lies in the kind of values that are allowed. This paper studies that common form through scale-valued sets (SV-sets), defined…
The failure of mechanical metamaterials is a function of the interplay between the properties of the base material and the microstructural geometry. Stochastic failure properties of the base material and disordered microstructural…
A pluri-Lagrangian structure is an attribute of integrability for lattice equations and for hierarchies of differential equations. It combines the notion of multi-dimensional consistency (in the discrete case) or commutativity of the flows…
Models which allow an explicit application to structurally modulated substances are reviewed within the frame of a symmetry-based approach starting from discrete lattice theory. Focus is set on models formulated in terms of local variables…
I propose a mathematical framework for embedding an unshaped discrete lattice $L$ on a smooth manifold $M$. This framework simplifies complex concepts in pure mathematics and physics by connecting discrete lattice structures with continuous…
High dimensional integrals are abundant in many fields of research including quantum physics. The aim of this paper is to develop efficient recursive strategies to tackle a class of high dimensional integrals having a special product…
The problem of detecting variance breaks in the case of smooth time-varying variance structure is studied. It is highlighted that the tests based on (piecewise) constant specification of the variance are not able to distinguish between…
This survey presents a necessarily incomplete (and biased) overview of results at the intersection of arithmetic circuit complexity, structured matrices and deep learning. Recently there has been some research activity in replacing…
The class of skew lattices can be seen as an algebraic category. It models an algebraic theory in the category of Sets where the Green's relation D is a congruence describing an adjunction to the category of Lattices. In this paper we will…
The lifetime of a system of connected units under some natural assumptions can be represented as a random variable Y defined as a weighted lattice polynomial of random lifetimes of its components. As such, the concept of a random variable Y…
We study the variance of the random variable that counts the number of lattice points in some shells generated by a special class of finite type domains in $\mathbb R^d$. The proof relies on estimates of the Fourier transform of indicator…
Rough sets are efficient for data pre-processing in data mining. As a generalization of the linear independence in vector spaces, matroids provide well-established platforms for greedy algorithms. In this paper, we apply rough sets to…
This paper studies the structure of Lax pairs associated with integrable lattice systems (where space is a one-dimensional lattice, and time is continuous). It describes a procedure for generating examples of such systems, and emphasizes…
In this manuscript the idea of soft convex structures is given and some of their properties are investigated. Also, soft convex sets, soft concave sets and soft convex hull operator are defined and their properties are studied. Moreover,…
The reduction of covering decision systems is an important problem in data mining, and covering-based rough sets serve as an efficient technique to process the problem. Geometric lattices have been widely used in many fields, especially…
Flexible mechanical metamaterials possess repeating structural motifs that imbue them with novel, exciting properties including programmability, anomalous elastic moduli and nonlinear and robust response. We address such structures via…
In order to better understand the structure of closed collections of reversible gates, we investigate the lattice of closed sets and the maximal members of this lattice. In this note, we find the maximal closed sets over a finite alphabet.…
As new experimental data arrive from the LHC the prospect of indirectly detecting new physics through precision tests of the Standard Model grows more exciting. Precise experimental and theoretical inputs are required to test the unitarity…
We study geometric rigidity of a class of fractals, which is slightly larger than the collection of self-conformal sets. Namely, using a new method, we shall prove that a set of this class is contained in a smooth submanifold or is totally…
Recent advances in lattice field theory, in computer technology and in chiral perturbation theory have enabled lattice QCD to emerge as a powerful quantitative tool in understanding hadron structure. I describe recent progress in the…