Coevolutionary dynamics on scale-free networks

We investigate Bak-Sneppen coevolution models on scale-free networks with various degree exponents $\gamma$ including random networks. For $\gamma >3$, the critical fitness value $f_c$ approaches to a nonzero finite value in the limit $N \to \infty$, whereas $f_c$ approaches to zero as $2<\gamma \le 3$. These results are explained by showing analytically $f_c(N) \simeq A/_N$ on the networks with size $N$. The avalanche size distribution $P(s)$ shows the normal power-law behavior for $\gamma >3$. In contrast, $P(s)$ for $2 <\gamma \le 3$ has two power-law regimes. One is a short regime for small $s$ with a large exponent $\tau_1$ and the other is a long regime for large $s$ with a small exponent $\tau_2$ ($\tau_1 > \tau_2$). The origin of the two power-regimes is explained by the dynamics on an artificially-made star-linked network.Comment: 5 pages, 5 figure

Going through Rough Times: from Non-Equilibrium Surface Growth to Algorithmic Scalability

Efficient and faithful parallel simulation of large asynchronous systems is a challenging computational problem. It requires using the concept of local simulated times and a synchronization scheme. We study the scalability of massively parallel algorithms for discrete-event simulations which employ conservative synchronization to enforce causality. We do this by looking at the simulated time horizon as a complex evolving system, and we identify its universal characteristics. We find that the time horizon for the conservative parallel discrete-event simulation scheme exhibits Kardar-Parisi-Zhang-like kinetic roughening. This implies that the algorithm is asymptotically scalable in the sense that the average progress rate of the simulation approaches a non-zero constant. It also implies, however, that there are diverging memory requirements associated with such schemes.Comment: to appear in the Proceedings of the MRS, Fall 200

Emergence of scale-free leadership structure in social recommender systems

The study of the organization of social networks is important for understanding of opinion formation, rumor spreading, and the emergence of trends and fashion. This paper reports empirical analysis of networks extracted from four leading sites with social functionality (Delicious, Flickr, Twitter and YouTube) and shows that they all display a scale-free leadership structure. To reproduce this feature, we propose an adaptive network model driven by social recommending. Artificial agent-based simulations of this model highlight a "good get richer" mechanism where users with broad interests and good judgments are likely to become popular leaders for the others. Simulations also indicate that the studied social recommendation mechanism can gradually improve the user experience by adapting to tastes of its users. Finally we outline implications for real online resource-sharing systems

Evolving the Curve

Evolutionary algorithms are used to generate personal contact networks, modelling human populations, that are most likely to match a given epidemic profile. The Susceptible-Infected-Removed (SIR) model is used and also expanded upon to allow for an extended period of infection, termed the SIIR model. The networks generated for each of these models are thoroughly evaluated for their ability to match nine different epidemic profiles. The addition of the SIIR model showed that the model of infection has an impact on the networks generated. For the SIR and SIIR models, these differences were relatively minor in most cases.Natural Sciences and Engineering Research Council of Canad

Reality Inspired Voter Models: A Mini-Review

This mini-review presents extensions of the voter model that incorporate various plausible features of real decision-making processes by individuals. Although these generalizations are not calibrated by empirical data, the resulting dynamics are suggestive of realistic collective social behaviors.Comment: 13 pages, 16 figures. Version 2 contains various proofreading improvements. V3: fixed one trivial typ

Metastability and anomalous fixation in evolutionary games on scale-free networks

We study the influence of complex graphs on the metastability and fixation properties of a set of evolutionary processes. In the framework of evolutionary game theory, where the fitness and selection are frequency-dependent and vary with the population composition, we analyze the dynamics of snowdrift games (characterized by a metastable coexistence state) on scale-free networks. Using an effective diffusion theory in the weak selection limit, we demonstrate how the scale-free structure affects the system's metastable state and leads to anomalous fixation. In particular, we analytically and numerically show that the probability and mean time of fixation are characterized by stretched exponential behaviors with exponents depending on the network's degree distribution.Comment: 5 pages, 4 figures, to appear in Physical Review Letter

Characterization of complex networks: A survey of measurements

Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics of processes executed on the network. The analysis, discrimination, and synthesis of complex networks therefore rely on the use of measurements capable of expressing the most relevant topological features. This article presents a survey of such measurements. It includes general considerations about complex network characterization, a brief review of the principal models, and the presentation of the main existing measurements. Important related issues covered in this work comprise the representation of the evolution of complex networks in terms of trajectories in several measurement spaces, the analysis of the correlations between some of the most traditional measurements, perturbation analysis, as well as the use of multivariate statistics for feature selection and network classification. Depending on the network and the analysis task one has in mind, a specific set of features may be chosen. It is hoped that the present survey will help the proper application and interpretation of measurements.Comment: A working manuscript with 78 pages, 32 figures. Suggestions of measurements for inclusion are welcomed by the author

Modelling of Vaccination Strategies for Epidemics using Evolutionary Computation

Personal contact networks that represent social interactions can be used to identify who can infect whom during the spread of an epidemic. The structure of a personal contact network has great impact upon both epidemic duration and the total number of infected individuals. A vaccine, with varying degrees of success, can reduce both the length and spread of an epidemic, but in the case of a limited supply of vaccine a vaccination strategy must be chosen, and this has a significant effect on epidemic behaviour.In this study we consider four different vaccination strategies and compare their effects upon epidemic duration and spread. These are random vaccination, high degree vaccination, ring vaccination, and the base case of no vaccination. All vaccinations are applied as the epidemic progresses, as opposed to in advance. The strategies are initially applied to static personal contact networks that are known ahead of time. They are then applied to personal contact networks that are evolved as the vaccination strategy is applied. When any form of vaccination is applied, all strategies reduce both duration and spread of the epidemic. When applied to a static network, random vaccination performs poorly in terms of reducing epidemic duration in comparison to strategies that take into account connectivity of the network. However, it performs surprisingly well when applied on the evolved networks, possibly because the evolutionary algorithm is unable to take advantage of a fixed strategy