Related papers: Network Models in Class C on Arbitrary Graphs
We derive properties of Latent Variable Models for networks, a broad class of models that includes the widely-used Latent Position Models. These include the average degree distribution, clustering coefficient, average path length and degree…
We prove that for the Activated Random Walks model on transitive unimodular graphs, if there is fixation, then every particle eventually fixates, almost surely. We deduce that the critical density is at most 1. Our methods apply for much…
Deterministic equilibrium flows in transport networks can be investigated by means of Markov's processes defined on the dual graph representations of the network. Sustained movement patterns are generated by a subset of automorphisms of the…
In this work, we study some statistical properties of the extreme eigenstates of the randomly-weighted adjacency matrices of random graphs. We focus on two random graph models: Erd\H{o}s-R\'{e}nyi (ER) graphs and random geometric graphs…
The quantum Hall ferromagnet at filling fraction $\nu = 1$ has some unusual properties due to the remarkable identity between the topological density of a spin distortion and the associated electrical charge density. We investigate the…
We study the propagation of stress waves through ordered 2D networks of granular chains. The quasi-particle continuum theory employed captures the acoustic pulse splitting, bending, and recombination through the network and is used to…
We consider the anomalous sub-diffusion of a class of Gaussian processes that can be expressed in terms of sums of Ornstein-Uhlenbeck processes. As a generic class of processes, we introduce a single parameter such that for any $\nu \in…
The paper contains a simplified and improved version of the results obtained by the authors earlier. Wave propagation is discussed in a network of branched thin wave guides when the thickness vanishes and the wave guides shrink to a one…
Proximity networks are time-varying graphs representing the closeness among humans moving in a physical space. Their properties have been extensively studied in the past decade as they critically affect the behavior of spreading phenomena…
We investigate the one-dimensional propagation of waves in the Anderson localization regime, for a single-mode, surface disordered waveguide. We make use of both an analytical formulation and rigorous numerical simulation calculations. The…
With the wide-spread availability of complex relational data, semi-supervised node classification in graphs has become a central machine learning problem. Graph neural networks are a recent class of easy-to-train and accurate methods for…
Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools…
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 study the mean traversal time for a class of random walks on Newman-Watts small-world networks, in which steps around the edge of the network occur with a transition rate F that is different from the rate f for steps across small-world…
The growing complexity of wireless systems has accelerated the move from traditional methods to learning-based solutions. Graph Neural Networks (GNNs) are especially well-suited here, since wireless networks can be naturally represented as…
Within the scattering matrix approach to electronic transport, the scattering and transport properties of tight-binding random graphs are analyzed. In particular, we compute the scattering matrix elements, the transmission, the…
Wave propagation through waveguides, quantum wires or films with a modest amount of disorder is in the semi-ballistic regime when in the transversal direction(s) almost no scattering occurs, while in the long direction(s) there is so much…
We study a class of symmetric quantum walks on Hamming graphs, where the distance between vertices specifies the transition probability. A special model is the simple quantum walk on the hypercube, which has been discussed in the…
It is well known that many real world networks have the power-law degree distribution (scale-free property). However there are no rigorous results for continuous-time quantum walks on such realistic graphs. In this paper, we analyze…
We study hierarchical network models which have recently been introduced to approximate the Chalker-Coddington model for the integer quantum Hall effect (A.G. Galstyan and M.E. Raikh, PRB 56 1422 (1997); Arovas et al., PRB 56, 4751 (1997)).…