On a Classical, Geometric Origin of Magnetic Moments, Spin-Angular Momentum and the Dirac Gyromagnetic Ratio

By treating the real Maxwell Field and real linearized Einstein equations as being imbedded in complex Minkowski space, one can interpret magnetic moments and spin-angular momentum as arising from a charge and mass monopole source moving along a complex world line in the complex Minkowski space. In the circumstances where the complex center of mass world-line coincides with the complex center of charge world-line, the gyromagnetic ratio is that of the Dirac electron.Comment: 17 page

Electromagnetic Dipole Radiation Fields, Shear-Free Congruences and Complex Center of Charge World Lines

We show that for asymptotically vanishing Maxwell fields in Minkowski space with non-vanishing total charge, one can find a unique geometric structure, a null direction field, at null infinity. From this structure a unique complex analytic world-line in complex Minkowski space that can be found and then identified as the complex center of charge. By ''sitting'' - in an imaginary sense, on this world-line both the (intrinsic) electric and magnetic dipole moments vanish. The (intrinsic) magnetic dipole moment is (in some sense) obtained from the `distance' the complex the world line is from the real space (times the charge). This point of view unifies the asymptotic treatment of the dipole moments For electromagnetic fields with vanishing magnetic dipole moments the world line is real and defines the real (ordinary center of charge). We illustrate these ideas with the Lienard-Wiechert Maxwell field. In the conclusion we discuss its generalization to general relativity where the complex center of charge world-line has its analogue in a complex center of mass allowing a definition of the spin and orbital angular momentum - the analogues of the magnetic and electric dipole moments.Comment: 17 page

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

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

Optimization in Gradient Networks

Gradient networks can be used to model the dominant structure of complex networks. Previous works have focused on random gradient networks. Here we study gradient networks that minimize jamming on substrate networks with scale-free and Erd\H{o}s-R\'enyi structure. We introduce structural correlations and strongly reduce congestion occurring on the network by using a Monte Carlo optimization scheme. This optimization alters the degree distribution and other structural properties of the resulting gradient networks. These results are expected to be relevant for transport and other dynamical processes in real network systems.Comment: 5 pages, 4 figure

The Universal Cut Function and Type II Metrics

In analogy with classical electromagnetic theory, where one determines the total charge and both electric and magnetic multipole moments of a source from certain surface integrals of the asymptotic (or far) fields, it has been known for many years - from the work of Hermann Bondi - that energy and momentum of gravitational sources could be determined by similar integrals of the asymptotic Weyl tensor. Recently we observed that there were certain overlooked structures, {defined at future null infinity,} that allowed one to determine (or define) further properties of both electromagnetic and gravitating sources. These structures, families of {complex} `slices' or `cuts' of Penrose's null infinity, are referred to as Universal Cut Functions, (UCF). In particular, one can define from these structures a (complex) center of mass (and center of charge) and its equations of motion - with rather surprising consequences. It appears as if these asymptotic structures contain in their imaginary part, a well defined total spin-angular momentum of the source. We apply these ideas to the type II algebraically special metrics, both twisting and twist-free.Comment: 32 page

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