Related papers: Cumulative Merging Percolation: A long-range perco…
The use of machine learning techniques in classical and quantum systems has led to novel techniques to classify ordered and disordered phases, as well as uncover transition points in critical phenomena. Efforts to extend these methods to…
Complex network theory provides a powerful framework to statistically investigate the topology of local and non-local statistical interrelationships, i.e. teleconnections, in the climate system. Climate networks constructed from the same…
We offer a solution to a long-standing problem in the physics of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity -- the propensity for two neighbors of a network node also to be…
In this paper we introduce a contact process on a dynamical long range percolation (CPDLP) defined on a complete graph $(V,\mathcal{E})$. A dynamical long range percolation is a Feller process defined on the edge set $\mathcal{E}$, which…
Coupling is a widely used technique in the theoretical study of interacting stochastic processes. In this paper I present an example demonstrating its usefulness also in the efficient computer simulation of such processes. I first describe…
A substantial share of the Earth's land surface is managed by humans, with cities representing the most extreme form of anthropogenic land use. There are zillion ways in which settlements can be arranged across a given area, and their…
Realistic network-like systems are usually composed of multiple networks with interacting relations such as school-enterprise research and development collaboration networks. Here we study the percolation properties of a special kind of…
Percolation clusters are random fractals whose geometrical and transport properties can be characterized with the help of probability distribution functions. Using renormalized field theory, we determine the asymptotic form of various of…
We investigate the behavior of extended urban traffic networks within the framework of percolation theory by using real and synthetic traffic data. Our main focus shifts from the statistical properties of the cluster size distribution…
We present percolation strategies based on multipartite measurements to propagate entanglement in quantum networks. We consider networks spanned on regular lattices whose bonds correspond to pure but non-maximally entangled pairs of qubits,…
In this work, we explore the analogy between entanglement and secret classical correlations in the context of large networks, more precisely the question of percolation of secret correlations in a network. It is known that entanglement…
In this paper we introduce a novel description of the equilibrium state of a bond percolation process on random graphs using the exact method of generating functions. This allows us to find the expected size of the giant connected component…
This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the…
Coalescent theory is the study of random processes where particles may join each other to form clusters as time evolves. These notes provide an introduction to some aspects of the mathematics of coalescent processes and their applications…
Clustering methods group a set of data points into a few coherent groups or clusters of similar data points. As an example, consider clustering pixels in an image (or video) if they belong to the same object. Different clustering methods…
This paper studies growth, percolation, and correlations in disordered fiber networks. We start by introducing a 2D continuum deposition model with effective fiber-fiber interactions represented by a parameter $p$ which controls the degree…
We consider a class of random, weighted networks, obtained through a redefinition of patterns in an Hopfield-like model and, by performing percolation processes, we get information about topology and resilience properties of the networks…
Coordinated Multi-Point (CoMP) is known to be a key technology for next generation mobile communications systems, as it allows to overcome the burden of inter-cell interference. Especially in the uplink, it is likely that interference…
The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, Percolation in…
Percolation offers acknowledged models of random media when the relevant medium characteristics can be described as a binary feature. However, when considering habitat modeling in ecology, a natural constraint comes from nearest-neighbor…