Related papers: Full Connectivity: Corners, edges and faces
We introduce a new percolation model to describe and analyze the spread of an epidemic on a general directed and locally finite graph. We assign a two-dimensional random weight vector to each vertex of the graph in such a way that the…
We study expanding circle maps interacting in a heterogeneous random network. Heterogeneity means that some nodes in the network are massively connected, while the remaining nodes are only poorly connected. We provide a probabilistic…
Recently the problem of classes of vulnerable vertices (represented by colors) in complex networks has been discussed, where all vertices with the same vulnerability are prone to fail together. Utilizing redundant paths each avoiding one…
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…
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 study aggregation as a mechanism for the creation of complex networks. In this evolution process vertices merge together, which increases the number of highly connected hubs. We study a range of complex network architectures produced by…
We study a natural model of random 2-dimensional cubical complex which is a subcomplex of an n-dimensional cube, and where every possible square $2$-face is included independently with probability p. Our main result is to exhibit a sharp…
Nodes are randomly distributed within an annulus (and then a shell) to form a point pattern of communication terminals which are linked stochastically according to the Rayleigh fading of radio-frequency data signals. We then present…
The analytical characterization of coverage probability in finite three-dimensional wireless networks has long remained an open problem, hindered by the loss of spatial independence in finite-node settings and the coupling between link…
We introduce an evolving network model in which a new node attaches to a randomly selected target node and also to each of its neighbors with probability $p$. The resulting network is sparse for $p<\frac{1}{2}$ and dense (average degree…
We introduce a method to estimate continuum percolation thresholds and illustrate its usefulness by investigating geometric percolation of non-interacting line segments and disks in two spatial dimensions. These examples serve as models for…
In order to clarify how the percolation theory governs the conductivities in real materials which consist of small conductive particles, e.g., nanoparticles, with random configurations in an insulator, we numerically investigate the…
The density distribution of the one-dimensional Hubbard model in a harmonic trapping potential is investigated in order to study the effect of the confining trap. Strong superimposed oscillations are always present on top of a uniform…
We derive an exact, simple relation between the average number of clusters and the wrapping probabilities for two-dimensional percolation. The relation holds for periodic lattices of any size. It generalizes a classical result of Sykes and…
We provide a framework for modeling social network formation through conditional multinomial logit models from discrete choice and random utility theory, in which each new edge is viewed as a "choice" made by a node to connect to another…
The study of complex networks has been one of the most active fields in science in recent decades. Spectral properties of networks (or graphs that represent them) are of fundamental importance. Researchers have been investigating these…
We prove that uniformly random packings of copies of a certain simply-connected figure in the plane exhibit global connectedness at all sufficiently high densities, but not at low densities.
We study entanglement and other correlation properties of random states in high-dimensional bipartite systems. These correlations are quantified by parameters that are subject to the "concentration of measure" phenomenon, meaning that on a…
First principle network models are crucial to make sense of the intricate topology of real complex networks. While modeling efforts have been quite successful in undirected networks, generative models for networks with asymmetric…
Convolutional neural networks (CNN) exhibit unmatched performance in a multitude of computer vision tasks. However, the advantage of using convolutional networks over fully-connected networks is not understood from a theoretical…