14,899 research outputs found
Vortex pairing in two-dimensional Bose gases
Recent experiments on ultracold Bose gases in two dimensions have provided
evidence for the existence of the Berezinskii-Kosterlitz-Thouless (BKT) phase
via analysis of the interference between two independent systems. In this work
we study the two-dimensional quantum degenerate Bose gas at finite temperature
using the projected Gross-Pitaevskii equation classical field method. While
this describes the highly occupied modes of the gas below a momentum cutoff, we
have developed a method to incorporate the higher momentum states in our model.
We concentrate on finite-sized homogeneous systems in order to simplify the
analysis of the vortex pairing. We determine the dependence of the condensate
fraction on temperature and compare this to the calculated superfluid fraction.
By measuring the first order correlation function we determine the boundary of
the Bose-Einstein condensate and BKT phases, and find it is consistent with the
superfluid fraction decreasing to zero. We reveal the characteristic unbinding
of vortex pairs above the BKT transition via a coarse-graining procedure.
Finally, we model the procedure used in experiments to infer system
correlations [Hadzibabic et al., Nature 441, 1118 (2006)], and quantify its
level of agreement with directly calculated in situ correlation functions.Comment: published versio
Correlations of record events as a test for heavy-tailed distributions
A record is an entry in a time series that is larger or smaller than all
previous entries. If the time series consists of independent, identically
distributed random variables with a superimposed linear trend, record events
are positively (negatively) correlated when the tail of the distribution is
heavier (lighter) than exponential. Here we use these correlations to detect
heavy-tailed behavior in small sets of independent random variables. The method
consists of converting random subsets of the data into time series with a
tunable linear drift and computing the resulting record correlations.Comment: Revised version, to appear in Physical Review Letter
Effect of heuristics on serendipity in path-based storytelling with linked data
Path-based storytelling with Linked Data on the Web provides users the ability to discover concepts in an entertaining and educational way. Given a query context, many state-of-the-art pathfinding approaches aim at telling a story that coincides with the user's expectations by investigating paths over Linked Data on the Web. By taking into account serendipity in storytelling, we aim at improving and tailoring existing approaches towards better fitting user expectations so that users are able to discover interesting knowledge without feeling unsure or even lost in the story facts. To this end, we propose to optimize the link estimation between - and the selection of facts in a story by increasing the consistency and relevancy of links between facts through additional domain delineation and refinement steps. In order to address multiple aspects of serendipity, we propose and investigate combinations of weights and heuristics in paths forming the essential building blocks for each story. Our experimental findings with stories based on DBpedia indicate the improvements when applying the optimized algorithm
The Community Authorization Service: Status and Future
Virtual organizations (VOs) are communities of resource providers and users
distributed over multiple policy domains. These VOs often wish to define and
enforce consistent policies in addition to the policies of their underlying
domains. This is challenging, not only because of the problems in distributing
the policy to the domains, but also because of the fact that those domains may
each have different capabilities for enforcing the policy. The Community
Authorization Service (CAS) solves this problem by allowing resource providers
to delegate some policy authority to the VO while maintaining ultimate control
over their resources. In this paper we describe CAS and our past and current
implementations of CAS, and we discuss our plans for CAS-related research.Comment: Talk from the 2003 Computing in High Energy and Nuclear Physics
(CHEP03), La Jolla, Ca, USA, March 2003. 9 Pages, PD
Sampling properties of directed networks
For many real-world networks only a small "sampled" version of the original
network may be investigated; those results are then used to draw conclusions
about the actual system. Variants of breadth-first search (BFS) sampling, which
are based on epidemic processes, are widely used. Although it is well
established that BFS sampling fails, in most cases, to capture the
IN-component(s) of directed networks, a description of the effects of BFS
sampling on other topological properties are all but absent from the
literature. To systematically study the effects of sampling biases on directed
networks, we compare BFS sampling to random sampling on complete large-scale
directed networks. We present new results and a thorough analysis of the
topological properties of seven different complete directed networks (prior to
sampling), including three versions of Wikipedia, three different sources of
sampled World Wide Web data, and an Internet-based social network. We detail
the differences that sampling method and coverage can make to the structural
properties of sampled versions of these seven networks. Most notably, we find
that sampling method and coverage affect both the bow-tie structure, as well as
the number and structure of strongly connected components in sampled networks.
In addition, at low sampling coverage (i.e. less than 40%), the values of
average degree, variance of out-degree, degree auto-correlation, and link
reciprocity are overestimated by 30% or more in BFS-sampled networks, and only
attain values within 10% of the corresponding values in the complete networks
when sampling coverage is in excess of 65%. These results may cause us to
rethink what we know about the structure, function, and evolution of real-world
directed networks.Comment: 21 pages, 11 figure
Pre-freezing of multifractal exponents in Random Energy Models with logarithmically correlated potential
Boltzmann-Gibbs measures generated by logarithmically correlated random
potentials are multifractal. We investigate the abrupt change ("pre-freezing")
of multifractality exponents extracted from the averaged moments of the measure
- the so-called inverse participation ratios. The pre-freezing can be
identified with termination of the disorder-averaged multifractality spectrum.
Naive replica limit employed to study a one-dimensional variant of the model is
shown to break down at the pre-freezing point. Further insights are possible
when employing zero-dimensional and infinite-dimensional versions of the
problem. In particular, the latter version allows one to identify the pattern
of the replica symmetry breaking responsible for the pre-freezing phenomenon.Comment: This is published version, 11 pages, 1 figur
Record Statistics for Multiple Random Walks
We study the statistics of the number of records R_{n,N} for N identical and
independent symmetric discrete-time random walks of n steps in one dimension,
all starting at the origin at step 0. At each time step, each walker jumps by a
random length drawn independently from a symmetric and continuous distribution.
We consider two cases: (I) when the variance \sigma^2 of the jump distribution
is finite and (II) when \sigma^2 is divergent as in the case of L\'evy flights
with index 0 < \mu < 2. In both cases we find that the mean record number
grows universally as \sim \alpha_N \sqrt{n} for large n, but with a
very different behavior of the amplitude \alpha_N for N > 1 in the two cases.
We find that for large N, \alpha_N \approx 2 \sqrt{\log N} independently of
\sigma^2 in case I. In contrast, in case II, the amplitude approaches to an
N-independent constant for large N, \alpha_N \approx 4/\sqrt{\pi},
independently of 0<\mu<2. For finite \sigma^2 we argue, and this is confirmed
by our numerical simulations, that the full distribution of (R_{n,N}/\sqrt{n} -
2 \sqrt{\log N}) \sqrt{\log N} converges to a Gumbel law as n \to \infty and N
\to \infty. In case II, our numerical simulations indicate that the
distribution of R_{n,N}/\sqrt{n} converges, for n \to \infty and N \to \infty,
to a universal nontrivial distribution, independently of \mu. We discuss the
applications of our results to the study of the record statistics of 366 daily
stock prices from the Standard & Poors 500 index.Comment: 25 pages, 8 figure
New Approaches To Photometric Redshift Prediction Via Gaussian Process Regression In The Sloan Digital Sky Survey
Expanding upon the work of Way and Srivastava 2006 we demonstrate how the use
of training sets of comparable size continue to make Gaussian process
regression (GPR) a competitive approach to that of neural networks and other
least-squares fitting methods. This is possible via new large size matrix
inversion techniques developed for Gaussian processes (GPs) that do not require
that the kernel matrix be sparse. This development, combined with a
neural-network kernel function appears to give superior results for this
problem. Our best fit results for the Sloan Digital Sky Survey (SDSS) Main
Galaxy Sample using u,g,r,i,z filters gives an rms error of 0.0201 while our
results for the same filters in the luminous red galaxy sample yield 0.0220. We
also demonstrate that there appears to be a minimum number of training-set
galaxies needed to obtain the optimal fit when using our GPR rank-reduction
methods. We find that morphological information included with many photometric
surveys appears, for the most part, to make the photometric redshift evaluation
slightly worse rather than better. This would indicate that most morphological
information simply adds noise from the GP point of view in the data used
herein. In addition, we show that cross-match catalog results involving
combinations of the Two Micron All Sky Survey, SDSS, and Galaxy Evolution
Explorer have to be evaluated in the context of the resulting cross-match
magnitude and redshift distribution. Otherwise one may be misled into overly
optimistic conclusions.Comment: 32 pages, ApJ in Press, 2 new figures, 1 new table of comparison
methods, updated discussion, references and typos to reflect version in Pres
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