A Method to Find Community Structures Based on Information Centrality

Community structures are an important feature of many social, biological and technological networks. Here we study a variation on the method for detecting such communities proposed by Girvan and Newman and based on the idea of using centrality measures to define the community boundaries (M. Girvan and M. E. J. Newman, Community structure in social and biological networks Proc. Natl. Acad. Sci. USA 99, 7821-7826 (2002)). We develop an algorithm of hierarchical clustering that consists in finding and removing iteratively the edge with the highest information centrality. We test the algorithm on computer generated and real-world networks whose community structure is already known or has been studied by means of other methods. We show that our algorithm, although it runs to completion in a time O(n^4), is very effective especially when the communities are very mixed and hardly detectable by the other methods.Comment: 13 pages, 13 figures. Final version accepted for publication in Physical Review

The Universe is not a Computer

When we want to predict the future, we compute it from what we know about the present. Specifically, we take a mathematical representation of observed reality, plug it into some dynamical equations, and then map the time-evolved result back to real-world predictions. But while this computational process can tell us what we want to know, we have taken this procedure too literally, implicitly assuming that the universe must compute itself in the same manner. Physical theories that do not follow this computational framework are deemed illogical, right from the start. But this anthropocentric assumption has steered our physical models into an impossible corner, primarily because of quantum phenomena. Meanwhile, we have not been exploring other models in which the universe is not so limited. In fact, some of these alternate models already have a well-established importance, but are thought to be mathematical tricks without physical significance. This essay argues that only by dropping our assumption that the universe is a computer can we fully develop such models, explain quantum phenomena, and understand the workings of our universe. (This essay was awarded third prize in the 2012 FQXi essay contest; a new afterword compares and contrasts this essay with Robert Spekkens' first prize entry.)Comment: 10 pages with new afterword; matches published versio

The Ithaca Interpretation of Quantum Mechanics

I list several strong requirements for what I would consider a sensible interpretation of quantum mechanics and I discuss two simple theorems. One, as far as I know, is new; the other was only noted a few years ago. Both have important implications for such a sensible interpretation. My talk will not clear everything up; indeed, you may conclude that it has not cleared anything up. But I hope it will provide a different perspective from which to view some old and vexing puzzles (or, if you believe nothing needs to be cleared up, some ancient verities.)Comment: 21 pages, plain TEX. Notes for a lecture given at the Golden Jubilee Workshop on Foundations of Quantum Theory, Tata Institute, Bombay, September 9-12, 199

The Transit Light Curve Project. VI. Three Transits of the Exoplanet TrES-2

Of the nearby transiting exoplanets that are amenable to detailed study, TrES-2 is both the most massive and has the largest impact parameter. We present z-band photometry of three transits of TrES-2. We improve upon the estimates of the planetary, stellar, and orbital parameters, in conjunction with the spectroscopic analysis of the host star by Sozzetti and co-workers. We find the planetary radius to be 1.222 +/- 0.038 R_Jup and the stellar radius to be 1.003 +/- 0.027 R_Sun. The quoted uncertainties include the systematic error due to the uncertainty in the stellar mass (0.980 +/- 0.062 M_Sun). The timings of the transits have an accuracy of 25s and are consistent with a uniform period, thus providing a baseline for future observations with the NASA Kepler satellite, whose field of view will include TrES-2.Comment: 15 pages, including 2 figures, accepted Ap

The Transit Light Curve Project. VIII. Six Occultations of the Exoplanet TrES-3

We present photometry of the exoplanet host star TrES-3 spanning six occultations (secondary eclipses) of its giant planet. No flux decrements were detected, leading to 99%-confidence upper limits on the planet-to-star flux ratio of 0.00024, 0.0005, and 0.00086 in the i, z, and R bands respectively. The corresponding upper limits on the planet's geometric albedo are 0.30, 0.62, and 1.07. The upper limit in the i band rules out the presence of highly reflective clouds, and is only a factor of 2-3 above the predicted level of thermal radiation from the planet.Comment: To appear in AJ [14 pages

The Transit Light Curve Project. IX. Evidence for a Smaller Radius of the Exoplanet XO-3b

We present photometry of 13 transits of XO-3b, a massive transiting planet on an eccentric orbit. Previous data led to two inconsistent estimates of the planetary radius. Our data strongly favor the smaller radius, with increased precision: R_p = 1.217 +/- 0.073 R_Jup. A conflict remains between the mean stellar density determined from the light curve, and the stellar surface gravity determined from the shapes of spectral lines. We argue the light curve should take precedence, and revise the system parameters accordingly. The planetary radius is about 1 sigma larger than the theoretical radius for a hydrogen-helium planet of the given mass and insolation. To help in planning future observations, we provide refined transit and occultation ephemerides.Comment: To appear in ApJ [22 pages