A study of the understanding and use of social agencies by physicians in a given community

Thesis (M.S.)--Boston Universit

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

The Real Meaning of Complex Minkowski-Space World-Lines

In connection with the study of shear-free null geodesics in Minkowski space, we investigate the real geometric effects in real Minkowski space that are induced by and associated with complex world-lines in complex Minkowski space. It was already known, in a formal manner, that complex analytic curves in complex Minkowski space induce shear-free null geodesic congruences. Here we look at the direct geometric connections of the complex line and the real structures. Among other items, we show, in particular, how a complex world-line projects into the real Minkowski space in the form of a real shear-free null geodesic congruence.Comment: 16 page

Complex Systems: A Survey

A complex system is a system composed of many interacting parts, often called agents, which displays collective behavior that does not follow trivially from the behaviors of the individual parts. Examples include condensed matter systems, ecosystems, stock markets and economies, biological evolution, and indeed the whole of human society. Substantial progress has been made in the quantitative understanding of complex systems, particularly since the 1980s, using a combination of basic theory, much of it derived from physics, and computer simulation. The subject is a broad one, drawing on techniques and ideas from a wide range of areas. Here I give a survey of the main themes and methods of complex systems science and an annotated bibliography of resources, ranging from classic papers to recent books and reviews.Comment: 10 page

Twisting Null Geodesic Congruences, Scri, H-Space and Spin-Angular Momentum

The purpose of this work is to return, with a new observation and rather unconventional point of view, to the study of asymptotically flat solutions of Einstein equations. The essential observation is that from a given asymptotically flat space-time with a given Bondi shear, one can find (by integrating a partial differential equation) a class of asymptotically shear-free (but, in general, twistiing) null geodesic congruences. The class is uniquely given up to the arbitrary choice of a complex analytic world-line in a four-parameter complex space. Surprisingly this parameter space turns out to be the H-space that is associated with the real physical space-time under consideration. The main development in this work is the demonstration of how this complex world-line can be made both unique and also given a physical meaning. More specifically by forcing or requiring a certain term in the asymptotic Weyl tensor to vanish, the world-line is uniquely determined and becomes (by several arguments) identified as the `complex center-of-mass'. Roughly, its imaginary part becomes identified with the intrinsic spin-angular momentum while the real part yields the orbital angular momentum.Comment: 26 pages, authors were relisted alphabeticall

Community detection and graph partitioning

Many methods have been proposed for community detection in networks. Some of the most promising are methods based on statistical inference, which rest on solid mathematical foundations and return excellent results in practice. In this paper we show that two of the most widely used inference methods can be mapped directly onto versions of the standard minimum-cut graph partitioning problem, which allows us to apply any of the many well-understood partitioning algorithms to the solution of community detection problems. We illustrate the approach by adapting the Laplacian spectral partitioning method to perform community inference, testing the resulting algorithm on a range of examples, including computer-generated and real-world networks. Both the quality of the results and the running time rival the best previous methods.Comment: 5 pages, 2 figure

Prediction of highly cited papers

In an article written five years ago [arXiv:0809.0522], we described a method for predicting which scientific papers will be highly cited in the future, even if they are currently not highly cited. Applying the method to real citation data we made predictions about papers we believed would end up being well cited. Here we revisit those predictions, five years on, to see how well we did. Among the over 2000 papers in our original data set, we examine the fifty that, by the measures of our previous study, were predicted to do best and we find that they have indeed received substantially more citations in the intervening years than other papers, even after controlling for the number of prior citations. On average these top fifty papers have received 23 times as many citations in the last five years as the average paper in the data set as a whole, and 15 times as many as the average paper in a randomly drawn control group that started out with the same number of citations. Applying our prediction technique to current data, we also make new predictions of papers that we believe will be well cited in the next few years.Comment: 6 pages, 3 figures, 2 table