Multiple concentric annuli for characterizing spatially nonuniform backgrounds

A method is presented for estimating the background at a given location on a sky map by interpolating the estimated background from a set of concentric annuli which surround this location. If the background is nonuniform but smoothly varying, this method provides a more accurate (though less precise) estimate than can be obtained with a single annulus. Several applications of multi-annulus background estimation are discussed, including direct testing for point sources in the presence of a nonuniform background, the generation of "surrogate maps" for characterizing false alarm rates, and precise testing of the null hypothesis that the background is uniform.Comment: 35 pages, including 19 embedded postscript figures; LaTeX with AAS macros. Minor revisions, improved figures, as suggested by referee. To appear in Astrophysical Journa

A frequency measure robust to linear filtering

A definition of frequency (cycles per unit-time) based on an approximate reconstruction of the phase-space trajectory of an oscillator from a signal is introduced. It is shown to be invariant under linear filtering, and therefore inaccessible by spectral methods. The effect of filtering on frequency in cases where this definition does not perfectly apply is quantified.Comment: 10 pages, 2 figure

Bursts of extensive air showers: chaos vs. stochasticity

Bursts of the count rate of extensive air showers (EAS) lead to the appearance of clusters in time series that represent EAS arrival times. We apply methods of nonlinear time series analysis to twenty EAS cluster events found in the data set obtained with the EAS-1000 prototype array. In particular, we use the Grassberger-Procaccia algorithm to compute the correlation dimension of the time series in the vicinity of the clusters. We find that four cluster events produce signs of chaos in the corresponding time series. By applying a number of supplementary methods we assess that the nature of the observed behaviour of the correlation dimension is likely to be deterministic. We suggest a simple qualitative model that might explain an origin of clusters in general and "possibly chaotic" clusters in particular. Finally, we compare our conclusions with the results of similar investigations performed by the EAS-TOP and LAAS groups.Comment: An extended version of the paper to be submitted to Astroparticle Physics. Version 2: 22 pages, discussion extended, the main part shortened, accepted for publication. Version 1 is still valid (up to a number of typos

Majorana bound state localization and energy oscillations for magnetic impurity chains on conventional superconductors

We study a chain of magnetic impurities on a conventional superconductor with spin-orbit coupling, treating the superconducting order fully self-consistently. We find and quantify strong hybridization between the topological edge Majorana bound states (MBSs) and in-gap Yu-Shiba-Rusinov (YSR) states, which causes increasing energy oscillations as a function of magnetic impurity strength, even when the direct MBS overlap is negligible. By treating the MBS as a topological boundary state, dependent only on the effective mass gap, we arrive at a fully parameter-free functional form of the its localization which decreases with magnetic impurity strength, opposite to the behavior of the superconducting coherence length.Comment: 7 pages, 5 figure

Testing For Nonlinearity Using Redundancies: Quantitative and Qualitative Aspects

A method for testing nonlinearity in time series is described based on information-theoretic functionals -- redundancies, linear and nonlinear forms of which allow either qualitative, or, after incorporating the surrogate data technique, quantitative evaluation of dynamical properties of scrutinized data. An interplay of quantitative and qualitative testing on both the linear and nonlinear levels is analyzed and robustness of this combined approach against spurious nonlinearity detection is demonstrated. Evaluation of redundancies and redundancy-based statistics as functions of time lag and embedding dimension can further enhance insight into dynamics of a system under study.Comment: 32 pages + 1 table in separate postscript files, 12 figures in 12 encapsulated postscript files, all in uuencoded, compressed tar file. Also available by anon. ftp to santafe.edu, in directory pub/Users/mp/qq. To be published in Physica D., [email protected]

The Sugar Daddy's Game: How Wealthy Investors Change Competition in Professional Team Sports

Professional sports leagues have witnessed the appearance of so-called "sugar daddies" - people who invest enormous amounts of money into clubs and become their owners. This paper presents a contest model of a professional sports league that incorporates this phenomenon. We analyze how the appearance of a sugar daddy alters competitive balance and social welfare compared to a league with purely profit-maximizing club owners. We further show that the welfare effect of revenue sharing in a sugar daddy league is ambiguous and depends on the degree of redistribution and on whether the sugar daddy invests in a small or large club.Competitive balance, contest model, social welfare, sports leagues, sugar daddy