47 research outputs found
Soliton oscillations in collisionally inhomogeneous attractive Bose-Einstein condensates
We investigate bright matter-wave solitons in the presence of a spatially
varying nonlinearity. It is demonstrated that a translation mode is excited due
to the spatial inhomogeneity and its frequency is derived analytically and also
studied numerically. Both cases of purely one-dimensional and ``cigar-shaped''
condensates are studied by means of different mean-field models, and the
oscillation frequencies of the pertinent solitons are found and compared with
the results obtained by the linear stability analysis.Numerical results are
shown to be in very good agreement with the corresponding analytical
predictions
Multimodal nested sampling: an efficient and robust alternative to MCMC methods for astronomical data analysis
In performing a Bayesian analysis of astronomical data, two difficult
problems often emerge. First, in estimating the parameters of some model for
the data, the resulting posterior distribution may be multimodal or exhibit
pronounced (curving) degeneracies, which can cause problems for traditional
MCMC sampling methods. Second, in selecting between a set of competing models,
calculation of the Bayesian evidence for each model is computationally
expensive. The nested sampling method introduced by Skilling (2004), has
greatly reduced the computational expense of calculating evidences and also
produces posterior inferences as a by-product. This method has been applied
successfully in cosmological applications by Mukherjee et al. (2006), but their
implementation was efficient only for unimodal distributions without pronounced
degeneracies. Shaw et al. (2007), recently introduced a clustered nested
sampling method which is significantly more efficient in sampling from
multimodal posteriors and also determines the expectation and variance of the
final evidence from a single run of the algorithm, hence providing a further
increase in efficiency. In this paper, we build on the work of Shaw et al. and
present three new methods for sampling and evidence evaluation from
distributions that may contain multiple modes and significant degeneracies; we
also present an even more efficient technique for estimating the uncertainty on
the evaluated evidence. These methods lead to a further substantial improvement
in sampling efficiency and robustness, and are applied to toy problems to
demonstrate the accuracy and economy of the evidence calculation and parameter
estimation. Finally, we discuss the use of these methods in performing Bayesian
object detection in astronomical datasets.Comment: 14 pages, 11 figures, submitted to MNRAS, some major additions to the
previous version in response to the referee's comment
Efficient Bayesian inference for multimodal problems in cosmology
Bayesian model selection provides the cosmologist with an exacting tool to
distinguish between competing models based purely on the data, via the Bayesian
evidence. Previous methods to calculate this quantity either lacked general
applicability or were computationally demanding. However, nested sampling
(Skilling 2004), which was recently applied successfully to cosmology by
Muhkerjee et al. 2006, overcomes both of these impediments. Their
implementation restricts the parameter space sampled, and thus improves the
efficiency, using a decreasing ellipsoidal bound in the n-dimensional parameter
space centred on the maximum likelihood point. However, if the likelihood
function contains any multi-modality, then the ellipse is prevented from
constraining the sampling region efficiently. In this paper we introduce a
method of clustered ellipsoidal nested sampling which can form multiple
ellipses around each individual peak in the likelihood.
In addition we have implemented a method for determining the expectation and
variance of the final evidence value without the need to use sampling error
from repetitions of the algorithm ; this further reduces the computational load
by at least an order of magnitude. We have applied our algorithm to a pair of
toy models and one cosmological example where we demonstrate that the number of
likelihood evaluations required is ~ 4% of that necessary for using previous
algorithms.
We have produced a fortran library containing our routines which can be
called from any sampling code, in addition for convenience we have incorporated
it into the popular CosmoMC code as CosmoClust. Both are available for download
at http://www.mrao.cam.ac.uk/software/cosmoclust .Comment: 7 pages, 8 figures, changed to match version accepted by MNRA
Cosmic Topology of Polyhedral Double-Action Manifolds
A special class of non-trivial topologies of the spherical space S^3 is
investigated with respect to their cosmic microwave background (CMB)
anisotropies. The observed correlations of the anisotropies on the CMB sky
possess on large separation angles surprising low amplitudes which might be
naturally be explained by models of the Universe having a multiconnected
spatial space. We analysed in CQG 29(2012)215005 the CMB properties of prism
double-action manifolds that are generated by a binary dihedral group D^*_p and
a cyclic group Z_n up to a group order of 180. Here we extend the CMB analysis
to polyhedral double-action manifolds which are generated by the three binary
polyhedral groups (T^*, O^*, I^*) and a cyclic group Z_n up to a group order of
1000. There are 20 such polyhedral double-action manifolds. Some of them turn
out to have even lower CMB correlations on large angles than the Poincare
dodecahedron
The current status of observational cosmology
Observational cosmology has indeed made very rapid progress in recent years.
The ability to quantify the universe has largely improved due to observational
constraints coming from structure formation. The transition to precision
cosmology has been spearheaded by measurements of the anisotropy in the cosmic
microwave background (CMB) over the past decade. Observations of the large
scale structure in the distribution of galaxies, high red-shift supernova, have
provided the required complementary information. We review the current status
of cosmological parameter estimates from joint analysis of CMB anisotropy and
large scale structure (LSS) data. We also sound a note of caution on
overstating the successes achieved thus far.Comment: 13 pages, 3 figures, Latex style files included, To appear in the
proceedings of ICGC-04. Minor rewording in the abstract and introductio
The spectral action and cosmic topology
The spectral action functional, considered as a model of gravity coupled to
matter, provides, in its non-perturbative form, a slow-roll potential for
inflation, whose form and corresponding slow-roll parameters can be sensitive
to the underlying cosmic topology. We explicitly compute the non-perturbative
spectral action for some of the main candidates for cosmic topologies, namely
the quaternionic space, the Poincare' dodecahedral space, and the flat tori. We
compute the corresponding slow-roll parameters and see we check that the
resulting inflation model behaves in the same way as for a simply-connected
spherical topology in the case of the quaternionic space and the Poincare'
homology sphere, while it behaves differently in the case of the flat tori. We
add an appendix with a discussion of the case of lens spaces.Comment: 55 pages, LaTe
Matter-Wave Solitons in the Presence of Collisional Inhomogeneities: Perturbation theory and the impact of derivative terms
We study the dynamics of bright and dark matter-wave solitons in the presence
of a spatially varying nonlinearity. When the spatial variation does not
involve zero crossings, a transformation is used to bring the problem to a
standard nonlinear Schrodinger form, but with two additional terms: an
effective potential one and a non-potential term. We illustrate how to apply
perturbation theory of dark and bright solitons to the transformed equations.
We develop the general case, but primarily focus on the non-standard special
case whereby the potential term vanishes, for an inverse square spatial
dependence of the nonlinearity. In both cases of repulsive and attractive
interactions, appropriate versions of the soliton perturbation theory are shown
to accurately describe the soliton dynamics.Comment: 12 pages, 5 fugure
Genome-wide association study of musical beat synchronization demonstrates high polygenicity
Moving in synchrony to the beat is a fundamental component of musicality. Here we conducted a genome-wide association study to identify common genetic variants associated with beat synchronization in 606,825 individuals. Beat synchronization exhibited a highly polygenic architecture, with 69 loci reaching genome-wide significance (Pâ<â5âĂâ10â8) and single-nucleotide-polymorphism-based heritability (on the liability scale) of 13%â16%. Heritability was enriched for genes expressed in brain tissues and for fetal and adult brain-specific gene regulatory elements, underscoring the role of central-nervous-system-expressed genes linked to the genetic basis of the trait. We performed validations of the self-report phenotype (through separate experiments) and of the genome-wide association study (polygenic scores for beat synchronization were associated with patients algorithmically classified as musicians in medical records of a separate biobank). Genetic correlations with breathing function, motor function, processing speed and chronotype suggest shared genetic architecture with beat synchronization and provide avenues for new phenotypic and genetic explorations
Collisionally inhomogeneous Bose-Einstein condensates in double-well potentials
In this work, we consider quasi-one-dimensional Bose-Einstein condensates
(BECs), with spatially varying collisional interactions, trapped in double well
potentials. In particular, we study a setup in which such a 'collisionally
inhomogeneous' BEC has the same (attractive-attractive or repulsive-repulsive)
or different (attractive-repulsive) type of interparticle interactions. Our
analysis is based on the continuation of the symmetric ground state and
anti-symmetric first excited state of the noninteracting (linear) limit into
their nonlinear counterparts. The collisional inhomogeneity produces a
saddle-node bifurcation scenario between two additional solution branches; as
the inhomogeneity becomes stronger, the turning point of the saddle-node tends
to infinity and eventually only the two original branches remain present, which
is completely different from the standard double-well phenomenology. Finally,
one of these branches changes its monotonicity as a function of the chemical
potential, a feature especially prominent, when the sign of the nonlinearity
changes between the two wells. Our theoretical predictions, are in excellent
agreement with the numerical results.Comment: 14 pages, 12 figures, Physica D, in pres
Suppressing CMB Quadrupole with a Bounce from Contracting Phase to Inflation
Recent released WMAP data show a low value of quadrupole in the CMB
temperature fluctuations, which confirms the early observations by COBE. In
this paper, a scenario, in which a contracting phase is followed by an
inflationary phase, is constructed. We calculate the perturbation spectrum and
show that this scenario can provide a reasonable explanation for lower CMB
anisotropies on large angular scales.Comment: 5 pages, 3 figure