Error estimation in the histogram Monte Carlo method

We examine the sources of error in the histogram reweighting method for Monte Carlo data analysis. We demonstrate that, in addition to the standard statistical error which has been studied elsewhere, there are two other sources of error, one arising through correlations in the reweighted samples, and one arising from the finite range of energies sampled by a simulation of finite length. We demonstrate that while the former correction is usually negligible by comparison with statistical fluctuations, the latter may not be, and give criteria for judging the range of validity of histogram extrapolations based on the size of this latter correction.Comment: 7 pages including 3 postscript figures, typeset in LaTeX using the RevTeX macro packag

Interacting epidemics and coinfection on contact networks

The spread of certain diseases can be promoted, in some cases substantially, by prior infection with another disease. One example is that of HIV, whose immunosuppressant effects significantly increase the chances of infection with other pathogens. Such coinfection processes, when combined with nontrivial structure in the contact networks over which diseases spread, can lead to complex patterns of epidemiological behavior. Here we consider a mathematical model of two diseases spreading through a single population, where infection with one disease is dependent on prior infection with the other. We solve exactly for the sizes of the outbreaks of both diseases in the limit of large population size, along with the complete phase diagram of the system. Among other things, we use our model to demonstrate how diseases can be controlled not only by reducing the rate of their spread, but also by reducing the spread of other infections upon which they depend.Comment: 9 pages, 3 figure

A study of defect structures with the field ion microscope Semiannual report, Sep. 1, 1966 - Feb. 28, 1967

Defect structures in ion emission images of metals and stress distributions under imaging conditions studied with field ion microscop

CR Structures and Asymptotically Flat Space-Times

We discuss the unique existence, arising by analogy to that in algebraically special space-times, of a CR structure realized on null infinity for any asymptotically flat Einstein or Einstein-Maxwell space-time.Comment: 6 page

MgB2 tunnel junctions with native or thermal oxide barriers

MgB2 tunnel junctions (MgB2/barrier/MgB2) were fabricated using a native oxide grown on the bottom MgB2 film as the tunnel barrier. Such barriers therefore survive the deposition of the second electrode at 300oC, even over junction areas of ~1 mm2. Studies of such junctions, and those of the type MgB2/native or thermal oxide/metal (Pb, Au, or Ag) show that tunnel barriers grown on MgB2 exhibit a wide range of barrier heights and widths.Comment: 9 pages, 3 figure

Statistics of Certain Models of Evolution

In a recent paper, Newman surveys the literature on power law spectra in evolution, self-organised criticality and presents a model of his own to arrive at a conclusion that self-organised criticality is not necessary for evolution. Not only did he miss a key model (Ecolab) that has a clear self-organised critical mechanism, but also Newman's model exhibits the same mechanism that gives rise to power law behaviour as does Ecolab. Newman's model is, in fact, a ``mean field'' approximation of a self-organised critical system. In this paper, I have also implemented Newman's model using the Ecolab software, removing the restriction that the number of species remains constant. It turns out that the requirement of constant species number is non-trivial, leading to a global coupling between species that is similar in effect to the species interactions seen in Ecolab. In fact, the model must self-organise to a state where the long time average of speciations balances that of the extinctions, otherwise the system either collapses or explodes. In view of this, Newman's model does not provide the hoped-for counter example to the presence of self-organised criticality in evolution, but does provide a simple, almost analytic model that can used to understand more intricate models such as Ecolab.Comment: accepted in Phys Rev E.; RevTeX; See http://parallel.hpc.unsw.edu.au/rks/ecolab.html for more informatio

Characterizing the structure of small-world networks

We give exact relations which are valid for small-world networks (SWN's) with a general `degree distribution', i.e the distribution of nearest-neighbor connections. For the original SWN model, we illustrate how these exact relations can be used to obtain approximations for the corresponding basic probability distribution. In the limit of large system sizes and small disorder, we use numerical studies to obtain a functional fit for this distribution. Finally, we obtain the scaling properties for the mean-square displacement of a random walker, which are determined by the scaling behavior of the underlying SWN

Clustering and preferential attachment in growing networks

We study empirically the time evolution of scientific collaboration networks in physics and biology. In these networks, two scientists are considered connected if they have coauthored one or more papers together. We show that the probability of scientists collaborating increases with the number of other collaborators they have in common, and that the probability of a particular scientist acquiring new collaborators increases with the number of his or her past collaborators. These results provide experimental evidence in favor of previously conjectured mechanisms for clustering and power-law degree distributions in networks.Comment: 13 pages, 2 figure