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Spreading broadly refers to the notion of an entity propagating throughout a networked system via its interacting components. Evidence of its ubiquity and severity can be seen in a range of phenomena, from disease epidemics to financial…
We discuss two cases that can be connected to the dynamics of interacting populations: (I.) density waves for the case or negligible random fluctuations of the populations densities, and (II.) probability distributions connected to the…
We present a model in which we investigate the structure and evolution of a random network that connects agents capable of exchanging wealth. Economic interactions between neighbors can occur only if the difference between their wealth is…
Dynamic network data have become ubiquitous in social network analysis, with new information becoming available that captures when friendships form, when corporate transactions happen and when countries interact with each other. Flexible…
Condensation phenomenon is often observed in social networks such as Twitter where one "superstar" vertex gains a positive fraction of the edges, while the remaining empirical degree distribution still exhibits a power law tail. We…
In this communication, some economic models given by functional mappings are addressed. These are models for random markets where agents trade by pairs and exchange their money in a random and conservative way. They display the exponential…
Virtually all real-world networks are dynamical entities. In social networks, the propensity of nodes to engage in social interactions (activity) and their chances to be selected by active nodes (attractiveness) are heterogeneously…
This article examines how diseases on random networks spread in time. The disease is described by a probability distribution function for the number of infected and recovered individuals, and the probability distribution is described by a…
We analyze random networks that change over time. First we analyze a dynamic Erdos-Renyi model, whose edges change over time. We describe its stationary distribution, its convergence thereto, and the SI contact process on the network, which…
Neutral models for the dynamics of a system of competing species are used, nowadays, to describe a wide variety of empirical communities. These models are used in many situations, ranging from population genetics and ecological biodiversity…
We report an innovative model for predicting entanglement distribution between end parties of a quantum network using our in-house simulation algorithm. Our implementation is based on stochastic methods that are built upon a unique global…
Effectively capturing the joint distribution of all agents in a scene is relevant for predicting the true evolution of the scene and in turn providing more accurate information to the decision processes of autonomous vehicles. While new…
A predictive distribution over a sequence of $N+1$ events is said to be "frequency mimicking" whenever the probability for the final event conditioned on the outcome of the first $N$ events equals the relative frequency of successes among…
The cover-time problem, i.e., time to visit every site in a system, is one of the key issues of random walks with wide applications in natural, social, and engineered systems. Addressing the full distribution of cover times for random walk…
We propose a model of multiagent systems whose agents have a tendency to balance their decisions in time. We find phase transitions to oscillatory behavior, explainable by the aggregation of agents into two groups. On a longer time scale,…
Evolving networks with a constant number of edges may be modelled using a rewiring process. These models are used to describe many real-world processes including the evolution of cultural artifacts such as family names, the evolution of…
We study the distributions of money in a simple closed economic system for different types of monetary transactions. We know that for arbitrary and random sharing but locally conserving money transactions, the money distribution goes to the…
We model a system of networking agents that seek to optimize their centrality in the network while keeping their cost, the number of connections they are participating in, low. Unlike other game-theory based models for network evolution,…
The eigenvalue spectrum of a random matrix often only depends on the first and second moments of its elements, but not on the specific distribution from which they are drawn. The validity of this universality principle is often assumed…
The analysis of social networks, in particular those describing face-to-face interactions between individuals, is complex due to the intertwining of the topological and temporal aspects. We revisit them both, using public data recorded by…