Related papers: Linking systems of difference sets
Random intersection graphs model networks with communities, assuming an underlying bipartite structure of groups and individuals, where these groups may overlap. Group memberships are generated through the bipartite configuration model.…
The standard assumptions that underlie many conceptual and quantitative frameworks do not hold for many complex physical, biological, and social systems. Complex systems science clarifies when and why such assumptions fail and provides…
Agglomerative hierarchical clustering can be implemented with several strategies that differ in the way elements of a collection are grouped together to build a hierarchy of clusters. Here we introduce versatile linkage, a new infinite…
It was recently shown that arbitrary first-order models canonically extend to models (of the same language) consisting of ultrafilters. The main precursor of this construction was the extension of semigroups to semigroups of ultrafilters, a…
The flow of contracting systems contracts 1-dimensional polygons (i.e. lines) at an exponential rate. One reason for the usefulness of contracting systems is that many interconnections of contracting sub-systems yield an overall contracting…
Networked dynamical systems are common throughout science in engineering; e.g., biological networks, reaction networks, power systems, and the like. For many such systems, nonlinearity drives populations of identical (or near-identical)…
Predicting missing links in complex networks requires algorithms that are able to explore statistical regularities in the existing data. Here we investigate the interplay between algorithm efficiency and network structures through the…
We claim that networks are created according to the priority attachment mechanism and we show a simple model which uses the priority attachment to generate both synthetic and close to empirical networks. Priority attachment is a mechanism…
As a generalization of the linking number, we construct a set of invariant numbers for two-component handlebody-links. These numbers are elementary divisors associated with the natural homomorphism from the first homology group of a…
The core group is an invariant of unoriented virtual links. We introduce a peripheral structure for the core group, in which the longitudes are sensitive to orientations. We show that the combination of the core group and its peripheral…
Relational structures are emerging as ubiquitous mathematical machinery in the semantics of open systems of various kinds. Cartesian bicategories are a well-known categorical algebra of relations that has proved especially useful in recent…
The background of this paper is the following: search of the minimal systems of generators for this class of group which still was not founded also problem of representation for this class of group, exploration of systems of generators for…
In this paper a variant of the classical hierarchical cluster analysis is reported. This agglomerative (bottom-up) cluster technique is referred to as the Adaptive Mean-Linkage Algorithm. It can be interpreted as a linkage algorithm where…
The structure of transformation semigroups on a finite set is analyzed by introducing a hierarchy of functions mapping subsets to subsets. The resulting hierarchy of semigroups has a corresponding hierarchy of minimal ideals, or kernels.…
We consider a generic configuration of regions, consisting of a collection of distinct compact regions $\{\Omega_i\}$ in $\mathbb{R}^{n+1}$ which may be either smooth regions disjoint from the others or regions which meet on their piecewise…
We define and study the link prediction problem in bipartite networks, specializing general link prediction algorithms to the bipartite case. In a graph, a link prediction function of two vertices denotes the similarity or proximity of the…
We introduce a technique that is capable to filter out information from complex systems, by mapping them to networks, and extracting a subgraph with the strongest links. This idea is based on the Minimum Spanning Tree, and it can be applied…
Link prediction is one of the fundamental problems in computational social science. A particularly common means to predict existence of unobserved links is via structural similarity metrics, such as the number of common neighbors; node…
The local minima (inherent structures) of a system and their associated transition links give rise to a network. Here we consider the topological and distance properties of such a network in the context of spin glasses. We use steepest…
In complex networks the rich nodes are the subset of nodes with high degree. These well connected nodes tend to dominate the organisation of the network's structure. In non-evolving networks, a reference network has been used to detect if…