439 research outputs found
Apparent horizons in simplicial Brill wave initial data
We construct initial data for a particular class of Brill wave metrics using
Regge calculus, and compare the results to a corresponding continuum solution,
finding excellent agreement. We then search for trapped surfaces in both sets
of initial data, and provide an independent verification of the existence of an
apparent horizon once a critical gravitational wave amplitude is passed. Our
estimate of this critical value, using both the Regge and continuum solutions,
supports other recent findings.Comment: 7 pages, 6 EPS figures, LaTeX 2e. Submitted to Class. Quant. Gra
Connected component identification and cluster update on GPU
Cluster identification tasks occur in a multitude of contexts in physics and
engineering such as, for instance, cluster algorithms for simulating spin
models, percolation simulations, segmentation problems in image processing, or
network analysis. While it has been shown that graphics processing units (GPUs)
can result in speedups of two to three orders of magnitude as compared to
serial codes on CPUs for the case of local and thus naturally parallelized
problems such as single-spin flip update simulations of spin models, the
situation is considerably more complicated for the non-local problem of cluster
or connected component identification. I discuss the suitability of different
approaches of parallelization of cluster labeling and cluster update algorithms
for calculations on GPU and compare to the performance of serial
implementations.Comment: 15 pages, 14 figures, one table, submitted to PR
Rotating star initial data for a constrained scheme in numerical relativity
A new numerical code for computing stationary axisymmetric rapidly rotating
stars in general relativity is presented. The formulation is based on a fully
constrained-evolution scheme for 3+1 numerical relativity using the Dirac gauge
and maximal slicing. We use both the polytropic and MIT bag model equations of
state to demonstrate that the code can construct rapidly rotating neutron star
and strange star models. We compare numerical models obtained by our code and a
well-established code, which uses a different gauge condition, and show that
the two codes agree to high accuracy.Comment: Minor changes and one figure added. Version accepted for publication
in Class. Quant. Gra
The constraints as evolution equations for numerical relativity
The Einstein equations have proven surprisingly difficult to solve
numerically. A standard diagnostic of the problems which plague the field is
the failure of computational schemes to satisfy the constraints, which are
known to be mathematically conserved by the evolution equations. We describe a
new approach to rewriting the constraints as first-order evolution equations,
thereby guaranteeing that they are satisfied to a chosen accuracy by any
discretization scheme. This introduces a set of four subsidiary constraints
which are far simpler than the standard constraint equations, and which should
be more easily conserved in computational applications. We explore the manner
in which the momentum constraints are already incorporated in several existing
formulations of the Einstein equations, and demonstrate the ease with which our
new constraint-conserving approach can be incorporated into these schemes.Comment: 10 pages, updated to match published versio
Reliable estimation of prediction uncertainty for physico-chemical property models
The predictions of parameteric property models and their uncertainties are
sensitive to systematic errors such as inconsistent reference data, parametric
model assumptions, or inadequate computational methods. Here, we discuss the
calibration of property models in the light of bootstrapping, a sampling method
akin to Bayesian inference that can be employed for identifying systematic
errors and for reliable estimation of the prediction uncertainty. We apply
bootstrapping to assess a linear property model linking the 57Fe Moessbauer
isomer shift to the contact electron density at the iron nucleus for a diverse
set of 44 molecular iron compounds. The contact electron density is calculated
with twelve density functionals across Jacob's ladder (PWLDA, BP86, BLYP, PW91,
PBE, M06-L, TPSS, B3LYP, B3PW91, PBE0, M06, TPSSh). We provide systematic-error
diagnostics and reliable, locally resolved uncertainties for isomer-shift
predictions. Pure and hybrid density functionals yield average prediction
uncertainties of 0.06-0.08 mm/s and 0.04-0.05 mm/s, respectively, the latter
being close to the average experimental uncertainty of 0.02 mm/s. Furthermore,
we show that both model parameters and prediction uncertainty depend
significantly on the composition and number of reference data points.
Accordingly, we suggest that rankings of density functionals based on
performance measures (e.g., the coefficient of correlation, r2, or the
root-mean-square error, RMSE) should not be inferred from a single data set.
This study presents the first statistically rigorous calibration analysis for
theoretical Moessbauer spectroscopy, which is of general applicability for
physico-chemical property models and not restricted to isomer-shift
predictions. We provide the statistically meaningful reference data set MIS39
and a new calibration of the isomer shift based on the PBE0 functional.Comment: 49 pages, 9 figures, 7 table
A fully (3+1)-D Regge calculus model of the Kasner cosmology
We describe the first discrete-time 4-dimensional numerical application of
Regge calculus. The spacetime is represented as a complex of 4-dimensional
simplices, and the geometry interior to each 4-simplex is flat Minkowski
spacetime. This simplicial spacetime is constructed so as to be foliated with a
one parameter family of spacelike hypersurfaces built of tetrahedra. We
implement a novel two-surface initial-data prescription for Regge calculus, and
provide the first fully 4-dimensional application of an implicit decoupled
evolution scheme (the ``Sorkin evolution scheme''). We benchmark this code on
the Kasner cosmology --- a cosmology which embodies generic features of the
collapse of many cosmological models. We (1) reproduce the continuum solution
with a fractional error in the 3-volume of 10^{-5} after 10000 evolution steps,
(2) demonstrate stable evolution, (3) preserve the standard deviation of
spatial homogeneity to less than 10^{-10} and (4) explicitly display the
existence of diffeomorphism freedom in Regge calculus. We also present the
second-order convergence properties of the solution to the continuum.Comment: 22 pages, 5 eps figures, LaTeX. Updated and expanded versio
Measuring degree-degree association in networks
The Pearson correlation coefficient is commonly used for quantifying the
global level of degree-degree association in complex networks. Here, we use a
probabilistic representation of the underlying network structure for assessing
the applicability of different association measures to heavy-tailed degree
distributions. Theoretical arguments together with our numerical study indicate
that Pearson's coefficient often depends on the size of networks with equal
association structure, impeding a systematic comparison of real-world networks.
In contrast, Kendall-Gibbons' is a considerably more robust measure
of the degree-degree association
Components of multifractality in the Central England Temperature anomaly series
We study the multifractal nature of the Central England Temperature (CET)
anomaly, a time series that spans more than 200 years. The series is analyzed
as a complete data set and considering a sliding window of 11 years. In both
cases, we quantify the broadness of the multifractal spectrum as well as its
components defined by the deviations from the Gaussian distribution and the
influence of the dependence between measurements. The results show that the
chief contribution to the multifractal structure comes from the dynamical
dependencies, mainly the weak ones, followed by a residual contribution of the
deviations from Gaussianity. However, using the sliding window, we verify that
the spikes in the non-Gaussian contribution occur at very close dates
associated with climate changes determined in previous works by component
analysis methods. Moreover, the strong non-Gaussian contribution found in the
multifractal measures from the 1960s onwards is in agreement with global
results very recently proposed in the literature.Comment: 21 pages, 10 figure
Whole Genome Sequencing for Public Health Surveillance of Shiga Toxin-Producing Escherichia coli Other than Serogroup O157
Shiga toxin-producing Escherichia coli (STEC) are considered to be a significant threat to public health due to the severity of gastrointestinal symptoms associated with human infection. In England STEC O157 is the most commonly detected STEC serogroup, however, the implementation of PCR at local hospital laboartories has resulted in an increase in the detection of STEC other than serogroup O157 (non-O157 STEC). The aim of this study was to evaluate the use of whole genome sequencing (WGS) for routine public health surveillance of non-O157 STEC by comparing this approach to phenotypic serotyping and PCR for subtyping the stx-encoding genes. Of the 102 isolates where phenotypic and genotypic serotyping could be compared, 98 gave fully concordant results. The most common non-O157 STEC serogroups detected were O146 (22) and O26 (18). All but one of the 38 isolates that could not be phenotypically serotyped (designated O unidentifiable or O rough) were serotyped using the WGS data. Of the 73 isolates where a flagella type was available by traditional phenotypic typing, all results matched the H-type derived from the WGS data. Of the 140 sequenced non-O157 isolates, 52 (37.1%) harboured stx1 only, 42 (30.0%) had stx2 only, 46 (32.9%) carried stx1 and stx2. Of these, stx subtyping PCR results were available for 131 isolates and 121 of these had concordant results with the stx subtype derived from the WGS data. Non-specific primer binding during PCR amplification, due to the similarity of the stx2 subtype gene sequences was the most likely cause. The results of this study showed WGS provided a reliable and robust one-step process for characterisation of STEC. Deriving the full serotype from WGS data in real time has enabled us to report a higher level of strain discrimination while stx subtyping provides data on the pathogenic potential of each isolate, enabling us to predict clinical outcome of each case and to monitor the emergence of hyper-virulent strains
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