325 research outputs found
Analytic Continuation of Quantum Monte Carlo Data by Stochastic Analytical Inference
We present an algorithm for the analytic continuation of imaginary-time
quantum Monte Carlo data which is strictly based on principles of Bayesian
statistical inference. Within this framework we are able to obtain an explicit
expression for the calculation of a weighted average over possible energy
spectra, which can be evaluated by standard Monte Carlo simulations, yielding
as by-product also the distribution function as function of the regularization
parameter. Our algorithm thus avoids the usual ad-hoc assumptions introduced in
similar algortihms to fix the regularization parameter. We apply the algorithm
to imaginary-time quantum Monte Carlo data and compare the resulting energy
spectra with those from a standard maximum entropy calculation
Consistent Application of Maximum Entropy to Quantum-Monte-Carlo Data
Bayesian statistics in the frame of the maximum entropy concept has widely
been used for inferential problems, particularly, to infer dynamic properties
of strongly correlated fermion systems from Quantum-Monte-Carlo (QMC) imaginary
time data. In current applications, however, a consistent treatment of the
error-covariance of the QMC data is missing. Here we present a closed Bayesian
approach to account consistently for the QMC-data.Comment: 13 pages, RevTeX, 2 uuencoded PostScript figure
Maximum Entropy and Bayesian Data Analysis: Entropic Priors
The problem of assigning probability distributions which objectively reflect
the prior information available about experiments is one of the major stumbling
blocks in the use of Bayesian methods of data analysis. In this paper the
method of Maximum (relative) Entropy (ME) is used to translate the information
contained in the known form of the likelihood into a prior distribution for
Bayesian inference. The argument is inspired and guided by intuition gained
from the successful use of ME methods in statistical mechanics. For experiments
that cannot be repeated the resulting "entropic prior" is formally identical
with the Einstein fluctuation formula. For repeatable experiments, however, the
expected value of the entropy of the likelihood turns out to be relevant
information that must be included in the analysis. The important case of a
Gaussian likelihood is treated in detail.Comment: 23 pages, 2 figure
A Bayesian approach to the follow-up of candidate gravitational wave signals
Ground-based gravitational wave laser interferometers (LIGO, GEO-600, Virgo
and Tama-300) have now reached high sensitivity and duty cycle. We present a
Bayesian evidence-based approach to the search for gravitational waves, in
particular aimed at the followup of candidate events generated by the analysis
pipeline. We introduce and demonstrate an efficient method to compute the
evidence and odds ratio between different models, and illustrate this approach
using the specific case of the gravitational wave signal generated during the
inspiral phase of binary systems, modelled at the leading quadrupole Newtonian
order, in synthetic noise. We show that the method is effective in detecting
signals at the detection threshold and it is robust against (some types of)
instrumental artefacts. The computational efficiency of this method makes it
scalable to the analysis of all the triggers generated by the analysis
pipelines to search for coalescing binaries in surveys with ground-based
interferometers, and to a whole variety of signal waveforms, characterised by a
larger number of parameters.Comment: 9 page
Accurate discretization of advection-diffusion equations
We present an exact mathematical transformation which converts a wide class
of advection-diffusion equations into a form allowing simple and direct spatial
discretization in all dimensions, and thus the construction of accurate and
more efficient numerical algorithms. These discretized forms can also be viewed
as master equations which provides an alternative mesoscopic interpretation of
advection-diffusion processes in terms of diffusion with spatially varying
hopping rates
Maximum entropy and the problem of moments: A stable algorithm
We present a technique for entropy optimization to calculate a distribution
from its moments. The technique is based upon maximizing a discretized form of
the Shannon entropy functional by mapping the problem onto a dual space where
an optimal solution can be constructed iteratively. We demonstrate the
performance and stability of our algorithm with several tests on numerically
difficult functions. We then consider an electronic structure application, the
electronic density of states of amorphous silica and study the convergence of
Fermi level with increasing number of moments.Comment: 4 pages including 3 figure
Multi-Frequency Synthesis of VLBI Images Using a Generalized Maximum Entropy Method
A new multi-frequency synthesis algorithm for reconstructing images from
multi-frequency VLBI data is proposed. The algorithm is based on a generalized
maximum-entropy method, and makes it possible to derive an effective spectral
correction for images over a broad frequency bandwidth, while simultaneously
reconstructing the spectral-index distribution over the source. The results of
numerical simulations demonstrating the capabilities of the algorithm are
presented.Comment: 17 pages, 8 figure
Direct observation of non-local effects in a superconductor
We have used the technique of low energy muon spin rotation to measure the
local magnetic field profile B(z) beneath the surface of a lead film maintained
in the Meissner state (z depth from the surface, z <= 200 nm). The data
unambiguously show that B(z) clearly deviates from an exponential law and
represent the first direct, model independent proof for a non-local response in
a superconductor.Comment: 5 pages, 3 figure
Constraints On the Diffusive Shock Acceleration From the Nonthermal X-ray Thin Shells In SN1006 NE Rim
Characteristic scale lengths of nonthermal X-rays from the SN1006 NE rim,
which are observed by Chandra, are interpreted in the context of the diffusive
shock acceleration on the assumption that the observed spatial profile of
nonthermal X-rays corresponds to that of accelerated electrons with energies of
a few tens of TeV. To explain the observed scale lengths, we construct two
simple models with a test particle approximation, where the maximum energy of
accelerated electrons is determined by the age of SN1006 (age-limited model) or
the energy loss (energy loss-limited model), and constrain the magnetic field
configuration and the diffusion coefficients of accelerated electrons. When the
magnetic field is nearly parallel to the shock normal, the magnetic field
should be in the range of 20-85 micro Gauss and highly turbulent both in
upstream and downstream, which means that the mean free path of accelerated
electrons is on the order of their gyro-radius (Bohm limit). This situation can
be realized both in the age-limited and energy loss-limited model. On the other
hand, when the magnetic field is nearly perpendicular to the shock normal,
which can exist only in the age-limited case, the magnetic field is several
micro Gauss in the upstream and 14-20 micro Gauss in the downstream, and the
upstream magnetic field is less turbulent than the downstream.Comment: 9 pages, 4 figures, accepted for publication in A&
On the escape of cosmic rays from radio galaxy cocoons
(Abridged) A model for the escape of CR particles from radio galaxy cocoons
is presented here. It is assumed that the radio cocoon is poorly magnetically
connected to the environment. An extreme case of this kind is an insulating
boundary layer of magnetic fields, which can efficiently suppress particle
escape. More likely, magnetic field lines are less organised and allow the
transport of CR particles from the source interior to the surface region. For
such a scenario two transport regimes are analysed: diffusion of particles
along inter-phase magnetic flux tubes (leaving the cocoon) and cross field
transport of particles in flux tubes touching the cocoon surface. The cross
field diffusion is likely the dominate escape path, unless a significant
fraction of the surface is magnetically connected to the environment. Major
cluster merger should strongly enhance the particle escape by two complementary
mechanisms. i) The merger shock waves shred radio cocoons into filamentary
structures, allowing the CRs to easily reach the radio cocoon boundary due to
the changed morphology. ii) Also efficient particle losses can be expected for
radio cocoons not compressed in shock waves. There, for a short period after
the sudden injection of large scale turbulence, the (anomalous) cross field
diffusion can be enhanced by several orders of magnitude. This lasts until the
turbulent energy cascade has reached the microscopic scales, which determine
the value of the microscopic diffusion coefficients.Comment: A&A in press, 12 pages, 5 figures, minor language improvement
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