Related papers: Extraordinary variability and sharp transitions in…
Recently, we introduced dynamic networks with preferred degrees, showing that interesting properties are present in a single, homogeneous system as well as one with two interacting networks. While simulations are readily performed, analytic…
Since their inception about a decade ago, dynamic networks which adapt to the state of the nodes have attracted much attention. One simple case of such an adaptive dynamics is a model of social networks in which individuals are typically…
In common descriptions of phase transitions, first order transitions are characterized by discontinuous jumps in the order parameter and normal fluctuations, while second order transitions are associated with no jumps and anomalous…
Unlike typical phase transitions of first and second order, a system displaying the Thouless effect exhibits characteristics of both at the critical point (jumps in the order parameter and anomalously large fluctuations). An $extreme$…
If a system undergoing phase transitions exhibits some characteristics of both first and second order, it is said to be of 'mixed order' or to display the Thouless effect. Such a transition is present in a simple model of a dynamic social…
We consider a toy model of interacting extrovert and introvert agents introduced earlier by Liu et al [Europhys. Lett. {\bf 100} (2012) 66007]. The number of extroverts, and introverts is $N$ each. At each time step, we select an agent at…
In a recent work \cite{LiuJoladSchZia13}, we introduced dynamic networks with preferred degrees and presented simulation and analytic studies of a single, homogeneous system as well as two interacting networks. Here, we extend these studies…
We study the dynamical properties of a finite dynamical network composed of two interacting populations, namely; extrovert ($a$) and introvert ($b$). In our model, each group is characterized by its size ($N_a$ and $N_b$) and preferred…
We study a simple model of dynamic networks, characterized by a set preferred degree, $\kappa$. Each node with degree $k$ attempts to maintain its $\kappa$ and will add (cut) a link with probability $w(k;\kappa)$ ($1-w(k;\kappa)$). As a…
The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…
Random walk on discrete lattice models is important to understand various types of transport processes. The extreme events, defined as exceedences of the flux of walkers above a prescribed threshold, have been studied recently in the…
We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…
We explore the dependence structure in the sampled sequence of large networks. We consider randomized algorithms to sample the nodes and study extremal properties in any associated stationary sequence of characteristics of interest like…
Dynamic systems characterized by diversified evolutions are not only more flexible, but also more resilient to attacks, failures and changing conditions. This article addresses the quantification of the diversity of non-linear transient…
We study a model for a statistical network formed by interactions between its nodes and links. Each node can be in one of two states (Ising spin up or down) and the node-link interaction facilitates linking between the like nodes. For high…
Extreme events are emergent phenomena in multi-particle transport processes on complex networks. In practice, such events could range from power blackouts to call drops in cellular networks to traffic congestion on roads. All the earlier…
Highly-diverse ecosystems exhibit a broad distribution of population sizes and species turnover, where species at high and low abundances are exchanged over time. We show that these two features generically emerge in the fluctuating phase…
The control and risk assessment in complex information systems require to take into account extremes arising from nodes with large node degrees. Various sampling techniques like a Page Rank random walk, a Metropolis-Hastings Markov chain…
Extreme events have low occurrence probabilities and display pronounced deviation from their average behaviour, such as earthquakes or power blackouts. Such extreme events occurring on the nodes of a complex network have been extensively…
We study rare events in networks with both internal and external noise, and develop a general formalism for analyzing rare events that combines pair-quenched techniques and large-deviation theory. The probability distribution, shape, and…