Scale-free networks with tunable degree distribution exponents

We propose and study a model of scale-free growing networks that gives a degree distribution dominated by a power-law behavior with a model-dependent, hence tunable, exponent. The model represents a hybrid of the growing networks based on popularity-driven and fitness-driven preferential attachments. As the network grows, a newly added node establishes $m$ new links to existing nodes with a probability $p$ based on popularity of the existing nodes and a probability $1-p$ based on fitness of the existing nodes. An explicit form of the degree distribution $P(p,k)$ is derived within a mean field approach. For reasonably large $k$, $P(p,k) \sim k^{-\gamma(p)}{\cal F}(k,p)$, where the function ${\cal F}$ is dominated by the behavior of $1/\ln(k/m)$ for small values of $p$ and becomes $k$-independent as $p \to 1$, and $\gamma(p)$ is a model-dependent exponent. The degree distribution and the exponent $\gamma(p)$ are found to be in good agreement with results obtained by extensive numerical simulations.Comment: 12 pages, 2 figures, submitted to PR

Building an alternative economic network? Consumer cooperation in Scotland from the 1870s to the 1960s

Peer reviewedPostprin

Instability of scale-free networks under node-breaking avalanches

The instability introduced in a large scale-free network by the triggering of node-breaking avalanches is analyzed using the fiber-bundle model as conceptual framework. We found, by measuring the size of the giant component, the avalanche size distribution and other quantities, the existence of an abrupt transition. This test of strength for complex networks like Internet is more stringent than others recently considered like the random removal of nodes, analyzed within the framework of percolation theory. Finally, we discuss the possible implications of our results and their relevance in forecasting cascading failures in scale-free networks.Comment: 4 pages, 4 figures, final version to be published in Europhys. Let

Deep-ocean Bottom Pressure and Temperature Sensors Report: Methods and Data

This report documents ocean bottom pressure data collected from September 1983 to May 1985 in eleven deployments of pressure sensors under the Gulf Stream northeast of Cape Hatteras in depths of 3300 to 3900 m, as part of the Gulf Stream Dynamics Experiment. In past experiments, pressure sensors suitable for ocean depths have typically exhibited systematic drifts in calibration that seriously contaminate any observed periodicities longer than a few days. We used Digiquartz sensors (manufactured by Paroscientific, Inc.), because these sensors offered potentially much lower drift than other commercially available sensors. In these sensors, either a bellows or a Bourdon tube applies stress to an osciilating quartz-crystal beam, causing its oscillation frequency to vary. Several factors influence the amount of drift: bellows vs. Bourdon-tube construction, the applied pressure, the duration of deployment, and, for some sensors, high-pressure preconditioning in the lab. For the sensors deployed in the Gulf Stream, the total drift during deployments lasting from 3 to 12 months ranged from undetectable (≦0.01 dbar) to 0.20 to 0.50 dbar. About half of the total drift typically occurred within the first 6 days of deployment. We estimate the residual error in the final pressure records, after the dedrifting calculations, to be typically 0.02 dbar r.m.s. (or 0.06 dbar r.m.s.) if the first 6 days of the record are excluded (or included, respectively). This low drift-error opens many possibilities for studies that require knowledge of the low-frequency dynamic pressure signal in the deep ocean. Part I on Methods contains a short review of bottom pressure measurement in the deep ocean, a description of the sensors that we used, a discussion of their performance and drift relative to type of construction and prior pressurization history ( preconditioning ), and estimates of the accuracy of the dedrifted pressure records. In Part II of this report, the full data processing is described, including calibaration parameters, corrections for the influence of temperature variations on the pressure sensor, and parameterization to remove sendor drift errors by least-squares regression onto an exponentially decaying time-dependence. Time series are plotted which illustrate several steps in the processing: the edited half-hourly pressure records, the detided pressures with drift-model curves superimposed, and the low-pass filtered, dedrifted pressure records (i.e., after subtracting the estimated drift curve)

Spreading and shortest paths in systems with sparse long-range connections

Spreading according to simple rules (e.g. of fire or diseases), and shortest-path distances are studied on d-dimensional systems with a small density p per site of long-range connections (``Small-World'' lattices). The volume V(t) covered by the spreading quantity on an infinite system is exactly calculated in all dimensions. We find that V(t) grows initially as t^d/d for t>t^*$, generalizing a previous result in one dimension. Using the properties of V(t), the average shortest-path distance \ell(r) can be calculated as a function of Euclidean distance r. It is found that \ell(r) = r for r<r_c=(2p \Gamma_d (d-1)!)^{-1/d} log(2p \Gamma_d L^d), and \ell(r) = r_c for r>r_c. The characteristic length r_c, which governs the behavior of shortest-path lengths, diverges with system size for all p>0. Therefore the mean separation s \sim p^{-1/d} between shortcut-ends is not a relevant internal length-scale for shortest-path lengths. We notice however that the globally averaged shortest-path length, divided by L, is a function of L/s only.Comment: 4 pages, 1 eps fig. Uses psfi

Experimental Heat Transfer Supporting Simulated Water Well Performance on Mars

Favorable indications of massive quantities of water on Mars have initiated studies of potential changes to human Mars missions. Using a technique known as a Rodriguez Well to melt the ice, store the resulting water in a subsurface ice cavity until needed, and then pump water to the surface for use is one potential means to effect these changes. A computer simulation of the Rodriguez Well in a terrestrial environment is one of the engineering tools being used to characterize the performance of this type of well on Mars. An experiment at the NASA Johnson Space Center is gathering data for convective heat transfer and evaporation rates at Mars surface conditions so that this computer simulation can be properly modified to predict performance on Mars. While quantitative results await processing, tests have indicated that a pool of water can be maintained at 1C to 2 C while at Mars surface temperatures and pressures

STEPS - an approach for human mobility modeling

In this paper we introduce Spatio-TEmporal Parametric Stepping (STEPS) - a simple parametric mobility model which can cover a large spectrum of human mobility patterns. STEPS makes abstraction of spatio-temporal preferences in human mobility by using a power law to rule the nodes movement. Nodes in STEPS have preferential attachment to favorite locations where they spend most of their time. Via simulations, we show that STEPS is able, not only to express the peer to peer properties such as inter-ontact/contact time and to reflect accurately realistic routing performance, but also to express the structural properties of the underlying interaction graph such as small-world phenomenon. Moreover, STEPS is easy to implement, exible to configure and also theoretically tractable

Phase transition in the modified fiber bundle model

We extend the standard fiber bundle model (FBM) with the local load sharing in such a way that the conservation of the total load is relaxed when an isolated fiber is broken. In this modified FBM in one dimension (1D), it is revealed that the model exhibits a well-defined phase transition at a finite nonzero value of the load, which is in contrast to the standard 1D FBM. The modified FBM defined in the Watts-Strogatz network is also investigated, and found is the existences of two distinct transitions: one discontinuous and the other continuous. The effects of the long-range shortcuts are also discussed.Comment: 7 pages, to appear in Europhys. Let

Phase transition of a one-dimensional Ising model with distance-dependent connections

The critical behavior of Ising model on a one-dimensional network, which has long-range connections at distances $l>1$ with the probability $\Theta(l)\sim l^{-m}$, is studied by using Monte Carlo simulations. Through studying the Ising model on networks with different $m$ values, this paper discusses the impact of the global correlation, which decays with the increase of $m$, on the phase transition of the Ising model. Adding the analysis of the finite-size scaling of the order parameter $[]$, it is observed that in the whole range of $0<m<2$, a finite-temperature transition exists, and the critical exponents show consistence with mean-field values, which indicates a mean-field nature of the phase transition.Comment: 5 pages,8 figure

Mean-field solution of the small-world network model

The small-world network model is a simple model of the structure of social networks, which simultaneously possesses characteristics of both regular lattices and random graphs. The model consists of a one-dimensional lattice with a low density of shortcuts added between randomly selected pairs of points. These shortcuts greatly reduce the typical path length between any two points on the lattice. We present a mean-field solution for the average path length and for the distribution of path lengths in the model. This solution is exact in the limit of large system size and either large or small number of shortcuts.Comment: 14 pages, 2 postscript figure