Power-law distributions from additive preferential redistributions

We introduce a non-growth model that generates the power-law distribution with the Zipf exponent. There are N elements, each of which is characterized by a quantity, and at each time step these quantities are redistributed through binary random interactions with a simple additive preferential rule, while the sum of quantities is conserved. The situation described by this model is similar to those of closed $N$-particle systems when conservative two-body collisions are only allowed. We obtain stationary distributions of these quantities both analytically and numerically while varying parameters of the model, and find that the model exhibits the scaling behavior for some parameter ranges. Unlike well-known growth models, this alternative mechanism generates the power-law distribution when the growth is not expected and the dynamics of the system is based on interactions between elements. This model can be applied to some examples such as personal wealths, city sizes, and the generation of scale-free networks when only rewiring is allowed.Comment: 12 pages, 4 figures; Changed some expressions and notations; Added more explanations and changed the order of presentation in Sec.III while results are the sam

Properties of weighted complex networks

We study two kinds of weighted networks, weighted small-world (WSW) and weighted scale-free (WSF). The weight $w_{ij}$ of a link between nodes $i$ and $j$ in the network is defined as the product of endpoint node degrees; that is $w_{ij}=(k_{i}k_{j})^{\theta}$. In contrast to adding weights to links during networks being constructed, we only consider weights depending on the `` popularity\rq\rq of the nodes represented by their connectivity. It was found that the both weighted networks have broad distributions on characterization the link weight, vertex strength, and average shortest path length. Furthermore, as a survey of the model, the epidemic spreading process in both weighted networks was studied based on the standard \emph{susceptible-infected} (SI) model. The spreading velocity reaches a peak very quickly after the infection outbreaks and an exponential decay was found in the long time propagation.Comment: 14 pages, 5 figure

Quantum Portfolios

Quantum computation holds promise for the solution of many intractable problems. However, since many quantum algorithms are stochastic in nature they can only find the solution of hard problems probabilistically. Thus the efficiency of the algorithms has to be characterized both by the expected time to completion {\it and} the associated variance. In order to minimize both the running time and its uncertainty, we show that portfolios of quantum algorithms analogous to those of finance can outperform single algorithms when applied to the NP-complete problems such as 3-SAT.Comment: revision includes additional data and corrects minor typo

Quantitative description and modeling of real networks

In this letter we present data analysis and modeling of two particular cases of study in the field of growing networks. We analyze WWW data set and authorship collaboration networks in order to check the presence of correlation in the data. The results are reproduced with a pretty good agreement through a suitable modification of the standard AB model of network growth. In particular, intrinsic relevance of sites plays a role in determining the future degree of the vertex.Comment: 4 pages, 3 figure

Drift- or Fluctuation-Induced Ordering and Self-Organization in Driven Many-Particle Systems

According to empirical observations, some pattern formation phenomena in driven many-particle systems are more pronounced in the presence of a certain noise level. We investigate this phenomenon of fluctuation-driven ordering with a cellular automaton model of interactive motion in space and find an optimal noise strength, while order breaks down at high(er) fluctuation levels. Additionally, we discuss the phenomenon of noise- and drift-induced self-organization in systems that would show disorder in the absence of fluctuations. In the future, related studies may have applications to the control of many-particle systems such as the efficient separation of particles. The rather general formulation of our model in the spirit of game theory may allow to shed some light on several different kinds of noise-induced ordering phenomena observed in physical, chemical, biological, and socio-economic systems (e.g., attractive and repulsive agglomeration, or segregation).Comment: For related work see http://www.helbing.or

Heterogeneity shapes groups growth in social online communities

Many complex systems are characterized by broad distributions capturing, for example, the size of firms, the population of cities or the degree distribution of complex networks. Typically this feature is explained by means of a preferential growth mechanism. Although heterogeneity is expected to play a role in the evolution it is usually not considered in the modeling probably due to a lack of empirical evidence on how it is distributed. We characterize the intrinsic heterogeneity of groups in an online community and then show that together with a simple linear growth and an inhomogeneous birth rate it explains the broad distribution of group members.Comment: 5 pages, 3 figure panel

Kink Solution in a Fluid Model of Traffic Flows

Traffic jam in a fluid model of traffic flows proposed by Kerner and Konh\"auser (B. S. Kerner and P. Konh\"auser, Phys. Rev. E 52 (1995), 5574.) is analyzed. An analytic scaling solution is presented near the critical point of the hetero-clinic bifurcation. The validity of the solution has been confirmed from the comparison with the simulation of the model.Comment: RevTeX v3.1, 6 pages, and 2 figure

Evolution of reference networks with aging

We study the growth of a reference network with aging of sites defined in the following way. Each new site of the network is connected to some old site with probability proportional (i) to the connectivity of the old site as in the Barab\'{a}si-Albert's model and (ii) to $\tau^{-\alpha}$, where $\tau$ is the age of the old site. We consider $\alpha$ of any sign although reasonable values are $0 \leq \alpha \leq \infty$. We find both from simulation and analytically that the network shows scaling behavior only in the region $\alpha < 1$. When $\alpha$ increases from $-\infty$ to 0, the exponent $\gamma$ of the distribution of connectivities ($P(k) \propto k^{-\gamma}$ for large $k$) grows from 2 to the value for the network without aging, i.e. to 3 for the Barab\'{a}si-Albert's model. The following increase of $\alpha$ to 1 makes $\gamma$ to grow to $\infty$. For $\alpha>1$ the distribution $P(k)$ is exponentional, and the network has a chain structure.Comment: 4 pages revtex (twocolumn, psfig), 5 figure

The Fractal Properties of Internet

In this paper we show that the Internet web, from a user's perspective, manifests robust scaling properties of the type $P(n)\propto n^{-\tau}$ where n is the size of the basin connected to a given point, $P$ represents the density of probability of finding n points downhill and $\tau=1.9 \pm 0.1$ s a characteristic universal exponent. This scale-free structure is a result of the spontaneous growth of the web, but is not necessarily the optimal one for efficient transport. We introduce an appropriate figure of merit and suggest that a planning of few big links, acting as information highways, may noticeably increase the efficiency of the net without affecting its robustness.Comment: 6 pages,2 figures, epl style, to be published on Europhysics Letter

Circadian patterns of Wikipedia editorial activity: A demographic analysis

Wikipedia (WP) as a collaborative, dynamical system of humans is an appropriate subject of social studies. Each single action of the members of this society, i.e. editors, is well recorded and accessible. Using the cumulative data of 34 Wikipedias in different languages, we try to characterize and find the universalities and differences in temporal activity patterns of editors. Based on this data, we estimate the geographical distribution of editors for each WP in the globe. Furthermore we also clarify the differences among different groups of WPs, which originate in the variance of cultural and social features of the communities of editors