454 research outputs found
Foundations of Inference
We present a simple and clear foundation for finite inference that unites and significantly extends the approaches of Kolmogorov and Cox. Our approach is based on quantifying lattices of logical statements in a way that satisfies general lattice symmetries. With other applications such as measure theory in mind, our derivations assume minimal symmetries, relying on neither negation nor continuity nor differentiability. Each relevant symmetry corresponds to an axiom of quantification, and these axioms are used to derive a unique set of quantifying rules that form the familiar probability calculus. We also derive a unique quantification of divergence, entropy and information
Model selection in cosmology
Model selection aims to determine which theoretical models are most plausible given some data, without necessarily considering preferred values of model parameters. A common model selection question is to ask when new data require introduction of an additional parameter, describing a newly discovered physical effect. We review model selection statistics, then focus on the Bayesian evidence, which implements Bayesian analysis at the level of models rather than parameters. We describe our CosmoNest code, the first computationally efficient implementation of Bayesian model selection in a cosmological context. We apply it to recent WMAP satellite data, examining the need for a perturbation spectral index differing from the scaleinvariant (Harrison–Zel'dovich) case
Quantum critical dynamics of a S = 1/2 antiferromagnetic Heisenberg chain studied by 13C-NMR spectroscopy
We present a 13C-NMR study of the magnetic field driven transition to
complete polarization of the S=1/2 antiferromagnetic Heisenberg chain system
copper pyrazine dinitrate Cu(C_4H_4N_2)(NO_3)_2 (CuPzN). The static local
magnetization as well as the low-frequency spin dynamics, probed via the
nuclear spin-lattice relaxation rate 1/T_1, were explored from the low to the
high field limit and at temperatures from the quantum regime (k_B T << J) up to
the classical regime (k_B T >> J). The experimental data show very good
agreement with quantum Monte Carlo calculations over the complete range of
parameters investigated. Close to the critical field, as derived from static
experiments, a pronounced maximum in 1/T_1 is found which we interpret as the
finite-temperature manifestation of a diverging density of zero-energy magnetic
excitations at the field-driven quantum critical point.Comment: 5 pages, 4 figure
Nested sampling for materials: the case of hard spheres
The recently introduced nested sampling algorithm allows the direct and
efficient calculation of the partition function of atomistic systems. We
demonstrate its applicability to condensed phase systems with periodic boundary
conditions by studying the three dimensional hard sphere model. Having obtained
the partition function, we show how easy it is to calculate the compressibility
and the free energy as functions of the packing fraction and local order,
verifying that the transition to crystallinity has a very small barrier, and
that the entropic contribution of jammed states to the free energy is
negligible for packing fractions above the phase transition. We quantify the
previously proposed schematic phase diagram and estimate the extent of the
region of jammed states. We find that within our samples, the maximally random
jammed configuration is surprisingly disordered
Feedback Heating by Cosmic Rays in Clusters of Galaxies
Recent observations show that the cooling flows in the central regions of
galaxy clusters are highly suppressed. Observed AGN-induced cavities/bubbles
are a leading candidate for suppressing cooling, usually via some form of
mechanical heating. At the same time, observed X-ray cavities and synchrotron
emission point toward a significant non-thermal particle population. Previous
studies have focused on the dynamical effects of cosmic-ray pressure support,
but none have built successful models in which cosmic-ray heating is
significant. Here we investigate a new model of AGN heating, in which the
intracluster medium is efficiently heated by cosmic-rays, which are injected
into the ICM through diffusion or the shredding of the bubbles by
Rayleigh-Taylor or Kelvin-Helmholtz instabilities. We include thermal
conduction as well. Using numerical simulations, we show that the cooling
catastrophe is efficiently suppressed. The cluster quickly relaxes to a
quasi-equilibrium state with a highly reduced accretion rate and temperature
and density profiles which match observations. Unlike the conduction-only case,
no fine-tuning of the Spitzer conduction suppression factor f is needed. The
cosmic ray pressure, P_c/P_g <~ 0.1 and dP_c/dr <~ 0.1 \rho g, is well within
observational bounds. Cosmic ray heating is a very attractive alternative to
mechanical heating, and may become particularly compelling if GLAST detects the
gamma-ray signature of cosmic-rays in clusters.Comment: Revised version accepted for publication in MNRAS. Significantly
expanded discussion and new simulations exploring parameter space/model
robustness; conclusions unchange
Application of Bayesian model averaging to measurements of the primordial power spectrum
Cosmological parameter uncertainties are often stated assuming a particular
model, neglecting the model uncertainty, even when Bayesian model selection is
unable to identify a conclusive best model. Bayesian model averaging is a
method for assessing parameter uncertainties in situations where there is also
uncertainty in the underlying model. We apply model averaging to the estimation
of the parameters associated with the primordial power spectra of curvature and
tensor perturbations. We use CosmoNest and MultiNest to compute the model
Evidences and posteriors, using cosmic microwave data from WMAP, ACBAR,
BOOMERanG and CBI, plus large-scale structure data from the SDSS DR7. We find
that the model-averaged 95% credible interval for the spectral index using all
of the data is 0.940 < n_s < 1.000, where n_s is specified at a pivot scale
0.015 Mpc^{-1}. For the tensors model averaging can tighten the credible upper
limit, depending on prior assumptions.Comment: 7 pages with 7 figures include
A method for spatial deconvolution of spectra
A method for spatial deconvolution of spectra is presented. It follows the
same fundamental principles as the ``MCS image deconvolution algorithm''
(Magain, Courbin, Sohy, 1998) and uses information contained in the spectrum of
a reference Point Spread Function (PSF) to spatially deconvolve spectra of very
blended sources. An improved resolution rather than an infinite one is aimed
at, overcoming the well known problem of ``deconvolution artefacts''. As in the
MCS algorithm, the data are decomposed into a sum of analytical point sources
and a numerically deconvolved background, so that the spectrum of extended
sources in the immediate vicinity of bright point sources may be accurately
extracted and sharpened. The algorithm has been tested on simulated data
including seeing variation as a function of wavelength and atmospheric
refraction. It is shown that the spectra of severely blended point sources can
be resolved while fully preserving the spectrophotometric properties of the
data. Extended objects ``hidden'' by bright point sources (up to 4-5 magnitudes
brighter) can be accurately recovered as well, provided the data have a
sufficiently high total signal-to-noise ratio (200-300 per spectral resolution
element). Such spectra are relatively easy to obtain, even down to faint
magnitudes, within a few hours of integration time with 10m class telescopes.Comment: 18 pages, 6 postscript figures, in press in Ap
Extending emission line Doppler tomography ; mapping modulated line flux
Emission line Doppler tomography is a powerful tool that resolves the
accretion flow in binaries on micro-arcsecond scales using time-resolved
spectroscopy. I present an extension to Doppler tomography that relaxes one of
its fundamental axioms and permits the mapping of time-dependent emission
sources. Significant variability on the orbital period is a common
characteristic of the emission sources that are observed in the accretion flows
of cataclysmic variables and X-ray binaries. Modulation Doppler tomography maps
sources varying harmonically as a function of the orbital period through the
simultaneous reconstruction of three Doppler tomograms. One image describes the
average flux distribution like in standard tomography, while the two additional
images describe the variable component in terms of its sine and cosine
amplitudes. I describe the implementation of such an extension in the form of
the maximum entropy based fitting code MODMAP. Test reconstructions of
synthetic data illustrate that the technique is robust and well constrained.
Artifact free reconstructions of complex emission distributions can be achieved
under a wide range of signal to noise levels. An application of the technique
is illustrated by mapping the orbital modulations of the asymmetric accretion
disc emission in the dwarf nova IP Pegasi.Comment: 8 pages, 4 figures; accepted for publication in MNRA
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