Related papers: Multi-granular Perspectives on Covering
Cloud computing is an emerging concept combining many fields of computing. The foundation of cloud computing is the delivery of services, software and processing capacity over the Internet, reducing cost, increasing storage, automating…
Consider the following variant of the set cover problem. We are given a universe $U=\{1,...,n\}$ and a collection of subsets $\mathcal{C} = \{S_1,...,S_m\}$ where $S_i \subseteq U$. For every element $u \in U$ we need to find a set $\phi(u)…
Percolation problems appear in a large variety of different contexts ranging from the design of composite materials to vaccination strategies on community networks. The key observable for many applications is the percolation threshold.…
While machine learning can accurately model process systems, models for decision making should also be structurally simple and physically interpretable. In process control, for example, (nearly) linear models are favored than nonlinear…
We propose a new model for the description of complex granular particles and their interaction in molecular dynamics simulations of granular material in two dimensions. The grains are composed of triangles which are connected by deformable…
Rendering realistic cloth has always been a challenge due to its intricate structure. Cloth is made up of fibers, plies, and yarns, and previous curved-based models, while detailed, were computationally expensive and inflexible for large…
Many complex networks are only a part of larger systems, where a number of coexisting topologies interact and depend on each other. We introduce a layered model to facilitate the description and analysis of such systems. As an example of…
Hypergraphs, which belong to the family of higher-order networks, are a natural and powerful choice for modeling group interactions in the real world. For example, when modeling collaboration networks, which may involve not just two but…
The majority of model-based clustering techniques is based on multivariate Normal models and their variants. In this paper copulas are used for the construction of flexible families of models for clustering applications. The use of copulas…
Thin coverings are a method of constructing graded-simple modules from simple (ungraded) modules. After a general discussion, we classify the thin coverings of (quasifinite) simple modules over associative algebras graded by finite abelian…
Covering problems are fundamental classical problems in optimization, computer science and complexity theory. Typically an input to these problems is a family of sets over a finite universe and the goal is to cover the elements of the…
Computational multiscale modeling encompasses a wide range of end-products and a great number of technological applications. This paper provides an overview of the computational multiscale modeling approach based on the utilization of MBN…
We study the set of all pseudoline arrangements with contact points which cover a given support. We define a natural notion of flip between these arrangements and study the graph of these flips. In particular, we provide an enumeration…
We propose a new model for the description of complex granular particles and their interaction in molecular dynamics simulations of granular material in two dimensions. The grains are composed of triangles which are connected by deformable…
Overlapping clusters are common in models of many practical data-segmentation applications. Suppose we are given $n$ elements to be clustered into $k$ possibly overlapping clusters, and an oracle that can interactively answer queries of the…
Granular convergence is a property of a granular pack as it is repeatedly sheared in a cyclic, quasistatic fashion, as the packing configuration changes via discrete events. Under suitable conditions the set of microscopic configurations…
We present a detailed study of the combinatorial interpretation of matrix integrals, including the examples of tessellations of arbitrary genera, and loop models on random surfaces. After reviewing their methods of solution, we apply these…
Limit and Pseudotopological spaces are two generalizations of topological spaces which are defined by indicating what filters converge under some axioms. In this article, we introduce covering spaces and set forth some necessary conditions…
Many real-world phenomena are naturally modeled by graphs and networks. However, classical graph models are often limited to pairwise interactions and may not adequately capture the richer structures that arise in practice. Higher-order…
Generalized topological spaces are not necessarily closed under finite intersections. Moreover, the whole universe does not need to be open. We use modified version of this framework to establish certain models for non-normal modal logics.…