4,283 research outputs found
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]
Constrained-Realization Monte-Carlo Method for Hypothesis Testing
We compare two theoretically distinct approaches to generating artificial (or
``surrogate'') data for testing hypotheses about a given data set. The first
and more straightforward approach is to fit a single ``best'' model to the
original data, and then to generate surrogate data sets that are ``typical
realizations'' of that model. The second approach concentrates not on the model
but directly on the original data; it attempts to constrain the surrogate data
sets so that they exactly agree with the original data for a specified set of
sample statistics. Examples of these two approaches are provided for two simple
cases: a test for deviations from a gaussian distribution, and a test for
serial dependence in a time series. Additionally, we consider tests for
nonlinearity in time series based on a Fourier transform (FT) method and on
more conventional autoregressive moving-average (ARMA) fits to the data. The
comparative performance of hypothesis testing schemes based on these two
approaches is found to depend on whether or not the discriminating statistic is
pivotal. A statistic is ``pivotal'' if its distribution is the same for all
processes consistent with the null hypothesis. The typical-realization method
requires that the discriminating statistic satisfy this property. The
constrained-realization approach, on the other hand, does not share this
requirement, and can provide an accurate and powerful test without having to
sacrifice flexibility in the choice of discriminating statistic.Comment: 19 pages, single spaced, all in one postscript file, figs included.
Uncompressed .ps file is 425kB (sorry, it's over the 300kB recommendation).
Also available on the WWW at http://nis-www.lanl.gov/~jt/Papers/ To appear in
Physica
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