2,232 research outputs found
Foreground contamination of the WMAP CMB maps from the perspective of the matched circle test
WMAP has provided CMB maps of the full sky. The raw data is subject to
foreground contamination, in particular near to the Galactic plane. Foreground
cleaned maps have been derived, e.g., the internal linear combination (ILC) map
of Bennett et al. and the reduced foreground TOH map of Tegmark et al. Using S
statistics we examine whether residual foreground contamination is left over in
the foreground cleaned maps. In particular, we specify which parts of the
foreground cleaned maps are sufficiently accurate for the circle-in-the-sky
signature. We generalise the S statistic, called D statistic, such that the
circle test can deal with CMB maps in which the contaminated regions of the sky
are excluded with masks
Maass cusp forms for large eigenvalues
We investigate the numerical computation of Maass cusp forms for the modular
group corresponding to large eigenvalues. We present Fourier coefficients of
two cusp forms whose eigenvalues exceed r=40000. These eigenvalues are the
largest that have so far been found in the case of the modular group. They are
larger than the 130millionth eigenvalue.Comment: 24 pages, 7 figures, 3 table
Large sets of consecutive Maass forms and fluctuations in the Weyl remainder
We explore an algorithm which systematically finds all discrete eigenvalues
of an analytic eigenvalue problem. The algorithm is more simple and elementary
as could be expected before. It consists of Hejhal's identity, linearisation,
and Turing bounds. Using the algorithm, we compute more than one hundredsixty
thousand consecutive eigenvalues of the Laplacian on the modular surface, and
investigate the asymptotic and statistic properties of the fluctuations in the
Weyl remainder. We summarize the findings in two conjectures. One is on the
maximum size of the Weyl remainder, and the other is on the distribution of a
suitably scaled version of the Weyl remainder.Comment: A version with higher resolution figures can be downloaded from
http://www.maths.bris.ac.uk/~mahlt/research/T2012a.pd
Spectral resolution in hyperbolic orbifolds, quantum chaos, and cosmology
We present a few subjects from physics that have one in common: the spectral
resolution of the Laplacian.Comment: 24 pages. Contribution to the TSL Expository Lecture Series V
"Computational Physical Sciences 2006", Universiti Putra Malaysi
A characteristic of Bennett's acceptance ratio method
A powerful and well-established tool for free-energy estimation is
Bennett's acceptance ratio method. Central properties of this estimator,
which employs samples of work values of a forward and its time reversed
process, are known: for given sets of measured work values, it results in the
best estimate of the free-energy difference in the large sample limit. Here we
state and prove a further characteristic of the acceptance ratio method: the
convexity of its mean square error. As a two-sided estimator, it depends on the
ratio of the numbers of forward and reverse work values used. Convexity of its
mean square error immediately implies that there exists an unique optimal ratio
for which the error becomes minimal. Further, it yields insight into the
relation of the acceptance ratio method and estimators based on the Jarzynski
equation. As an application, we study the performance of a dynamic strategy of
sampling forward and reverse work values
Rapid computation of -functions attached to Maass forms
Let be a degree- -function associated to a Maass cusp form. We
explore an algorithm that evaluates values of on the critical line in
time . We use this algorithm to rigorously compute an
abundance of consecutive zeros and investigate their distribution
Measuring the convergence of Monte Carlo free energy calculations
The nonequilibrium work fluctuation theorem provides the way for calculations
of (equilibrium) free energy based on work measurements of nonequilibrium,
finite-time processes and their reversed counterparts by applying Bennett's
acceptance ratio method. A nice property of this method is that each free
energy estimate readily yields an estimate of the asymptotic mean square error.
Assuming convergence, it is easy to specify the uncertainty of the results.
However, sample sizes have often to be balanced with respect to experimental or
computational limitations and the question arises whether available samples of
work values are sufficiently large in order to ensure convergence. Here, we
propose a convergence measure for the two-sided free energy estimator and
characterize some of its properties, explain how it works, and test its
statistical behavior. In total, we derive a convergence criterion for Bennett's
acceptance ratio method.Comment: 14 pages, 17 figure
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