BURA Collection:
http://bura.brunel.ac.uk/handle/2438/234
2014-12-22T19:16:48Z
2014-12-22T19:16:48Z
Mutual selection in time-varying networks
Hoppe, K
Rodgers, GJ
http://bura.brunel.ac.uk/handle/2438/9186
2014-11-01T11:19:32Z
2013-01-01T00:00:00Z
Title: Mutual selection in time-varying networks
Authors: Hoppe, K; Rodgers, GJ
Abstract: Time-varying networks play an important role in the investigation of the stochastic processes that occur on complex networks. The ability to formulate the development of the network topology on the same time scale as the evolution of the random process is important for a variety of applications, including the spreading of diseases. Past contributions have investigated random processes on time-varying networks with a purely random attachment mechanism. The possibility of extending these findings towards a time-varying network that is driven by mutual attractiveness is explored in this paper. Mutual attractiveness models are characterized by a linking function that describes the probability of the existence of an edge, which depends mutually on the attractiveness of the nodes on both ends of that edge. This class of attachment mechanisms has been considered before in the fitness-based complex networks literature but not on time-varying networks. Also, the impact of mutual selection is investigated alongside opinion formation and epidemic outbreaks. We find closed-form solutions for the quantities of interest using a factorizable linking function. The voter model exhibits an unanticipated behavior as the network never reaches consensus in the case of mutual selection but stays forever in its initial macroscopic configuration, which is a further piece of evidence that time-varying networks differ markedly from their static counterpart with respect to random processes that take place on them. We also find that epidemic outbreaks are accelerated by uncorrelated mutual selection compared to previously considered random attachment.
Description: Copyright @ 2013 American Physical Society
2013-01-01T00:00:00Z
Percolation on fitness-dependent networks with heterogeneous resilience
Hoppe, K
Rodgers, GJ
http://bura.brunel.ac.uk/handle/2438/9185
2014-11-01T11:19:31Z
2014-01-01T00:00:00Z
Title: Percolation on fitness-dependent networks with heterogeneous resilience
Authors: Hoppe, K; Rodgers, GJ
Abstract: The ability to understand the impact of adversarial processes on networks is crucial to various disciplines. The objects of study in this article are fitness-driven networks. Fitness-dependent networks are fully described by a probability distribution of fitness and an attachment kernel. Every node in the network is endowed with a fitness value and the attachment kernel translates the fitness of two nodes into the probability that these two nodes share an edge. This concept is also known as mutual attractiveness. In the present article, fitness does not only serve as a measure of attractiveness, but also as a measure of a node's robustness against failure. The probability that a node fails increases with the number of failures in its direct neighborhood and decreases with higher fitness. Both static and dynamic network models are considered. Analytical results for the percolation threshold and the occupied fraction are derived. One of the results is that the distinction between the dynamic and the static model has a profound impact on the way failures spread over the network. Additionally, we find that the introduction of mutual attractiveness stabilizes the network compared to a pure random attachment. © 2014 American Physical Society.
Description: Copyright @ 2014 American Physical Society
2014-01-01T00:00:00Z
Mixed-state evolution in the presence of gain and loss
Brody, DC
Graefe, E-M
http://bura.brunel.ac.uk/handle/2438/8067
2014-11-01T13:14:49Z
2012-01-01T00:00:00Z
Title: Mixed-state evolution in the presence of gain and loss
Authors: Brody, DC; Graefe, E-M
Abstract: A model is proposed that describes the evolution of a mixed state of a quantum system for which gain and loss of energy or amplitude are present. Properties of the model are worked out in detail. In particular, invariant subspaces of the space of density matrices corresponding to the fixed points of the dynamics are identified, and the existence of a transition between the phase in which gain and loss are balanced and the phase in which this balance is lost is illustrated in terms of the time average of observables. The model is extended to include a noise term that results from a uniform random perturbation generated by white noise. Numerical studies of example systems show the emergence of equilibrium states that suppress the phase transition.
Description: Copyright @ 2012 American Physical Society
2012-01-01T00:00:00Z
Network growth model with intrinsic vertex fitness
Smolyarenko, IE
Hoppe, K
Rodgers, GJ
http://bura.brunel.ac.uk/handle/2438/7770
2014-11-01T11:33:13Z
2013-01-01T00:00:00Z
Title: Network growth model with intrinsic vertex fitness
Authors: Smolyarenko, IE; Hoppe, K; Rodgers, GJ
Abstract: We study a class of network growth models with attachment rules governed by intrinsic node fitness. Both the individual node degree distribution and the degree correlation properties of the network are obtained as functions of the network growth rules. We also find analytical solutions to the inverse, design, problems of matching the growth rules to the required (e.g., power-law) node degree distribution and more generally to the required degree correlation function. We find that the design problems do not always have solutions. Among the specific conditions on the existence of solutions to the design problems is the requirement that the node degree distribution has to be broader than a certain threshold and the fact that factorizability of the correlation functions requires singular distributions of the node fitnesses. More generally, the restrictions on the input distributions and correlations that ensure solvability of the design problems are expressed in terms of the analytical properties of their generating functions.
Description: © 2013 American Physical Society
2013-01-01T00:00:00Z