Component sizes in networks with arbitrary degree distributions

We give an exact solution for the complete distribution of component sizes in random networks with arbitrary degree distributions. The solution tells us the probability that a randomly chosen node belongs to a component of size s, for any s. We apply our results to networks with the three most commonly studied degree distributions -- Poisson, exponential, and power-law -- as well as to the calculation of cluster sizes for bond percolation on networks, which correspond to the sizes of outbreaks of SIR epidemic processes on the same networks. For the particular case of the power-law degree distribution, we show that the component size distribution itself follows a power law everywhere below the phase transition at which a giant component forms, but takes an exponential form when a giant component is present.Comment: 5 pages, 1 figur

Introduction

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An analysis of the fixation probability of a mutant on special classes of non-directed graphs

There is a growing interest in the study of evolutionary dynamics on populations with some non-homogeneous structure. In this paper we follow the model of Lieberman et al. (Lieberman et al. 2005 Nature 433, 312–316) of evolutionary dynamics on a graph. We investigate the case of non-directed equally weighted graphs and find solutions for the fixation probability of a single mutant in two classes of simple graphs. We further demonstrate that finding similar solutions on graphs outside these classes is far more complex. Finally, we investigate our chosen classes numerically and discuss a number of features of the graphs; for example, we find the fixation probabilities for different initial starting positions and observe that average fixation probabilities are always increased for advantageous mutants as compared with those of unstructured populations

Identity and Search in Social Networks

Social networks have the surprising property of being "searchable": Ordinary people are capable of directing messages through their network of acquaintances to reach a specific but distant target person in only a few steps. We present a model that offers an explanation of social network searchability in terms of recognizable personal identities: sets of characteristics measured along a number of social dimensions. Our model defines a class of searchable networks and a method for searching them that may be applicable to many network search problems, including the location of data files in peer-to-peer networks, pages on the World Wide Web, and information in distributed databases.Comment: 4 page, 3 figures, revte

Conservative versus nonconservative differencing: Transonic streamline shape effects

Streamline patterns calculated from transonic flow solutions which were generated using a nonconservative finite difference scheme showed a net streamtube area increase far downstream of the disturbance indicating that the global mass balance was destroyed. Similar calculations using a conservative finite difference scheme did not show this defect. Comparative calculations were made at several free-stream Mach numbers for nonlifting flow over a 10% parabolic arc airfoil. In a transonic internal flow, this nonconservation of mass may be of greater concern than in an unconfined external flow

Cascade control and defense in complex networks

Complex networks with heterogeneous distribution of loads may undergo a global cascade of overload failures when highly loaded nodes or edges are removed due to attacks or failures. Since a small attack or failure has the potential to trigger a global cascade, a fundamental question regards the possible strategies of defense to prevent the cascade from propagating through the entire network. Here we introduce and investigate a costless strategy of defense based on a selective further removal of nodes and edges, right after the initial attack or failure. This intentional removal of network elements is shown to drastically reduce the size of the cascade.Comment: 4 pages, 2 figures, Revte

Real eigenvalue analysis in NASTRAN by the tridiagonal reduction (FEER) method

Implementation of the tridiagonal reduction method for real eigenvalue extraction in structural vibration and buckling problems is described. The basic concepts underlying the method are summarized and special features, such as the computation of error bounds and default modes of operation are discussed. In addition, the new user information and error messages and optional diagnostic output relating to the tridiagonal reduction method are presented. Some numerical results and initial experiences relating to usage in the NASTRAN environment are provided, including comparisons with other existing NASTRAN eigenvalue methods

Design of a 12-GHz multicarrier earth-terminal for satellite-CATV interconnection

The design and development of the front-end for a multi-carrier system that allows multiplex signal transmission from satellite-borne transponders is described. Detailed systems analyses provided down-converter specifications. The 12 GHz carrier down-converter uses waveguide, coaxial, and microstrip transmission line elements in its implementation. Mixing is accomplished in a single-ended coaxial mixer employing a field-replacable cartridge style diode