4,638 research outputs found
Use of the geometric mean as a statistic for the scale of the coupled Gaussian distributions
The geometric mean is shown to be an appropriate statistic for the scale of a
heavy-tailed coupled Gaussian distribution or equivalently the Student's t
distribution. The coupled Gaussian is a member of a family of distributions
parameterized by the nonlinear statistical coupling which is the reciprocal of
the degree of freedom and is proportional to fluctuations in the inverse scale
of the Gaussian. Existing estimators of the scale of the coupled Gaussian have
relied on estimates of the full distribution, and they suffer from problems
related to outliers in heavy-tailed distributions. In this paper, the scale of
a coupled Gaussian is proven to be equal to the product of the generalized mean
and the square root of the coupling. From our numerical computations of the
scales of coupled Gaussians using the generalized mean of random samples, it is
indicated that only samples from a Cauchy distribution (with coupling parameter
one) form an unbiased estimate with diminishing variance for large samples.
Nevertheless, we also prove that the scale is a function of the geometric mean,
the coupling term and a harmonic number. Numerical experiments show that this
estimator is unbiased with diminishing variance for large samples for a broad
range of coupling values.Comment: 17 pages, 5 figure
Management of High Blood Pressure in Those without Overt Cardiovascular Disease Utilising Absolute Risk Scores
Increasing blood pressure has a continuum of adverse risk for cardiovascular events. Traditionally this single measure was used to determine who to treat and how vigorously. However, estimating absolute risk rather than measurement of a single risk factor such as blood pressure is a superior method to identify who is most at risk of having an adverse cardiovascular event such as stroke or myocardial infarction, and therefore who would most likely benefit from therapeutic intervention. Cardiovascular disease (CVD) risk calculators must be used to estimate absolute risk in those without overt CVD as physician estimation is unreliable. Incorporation into usual practice and limitations of the strategy are discussed
Thermodynamics and the Global Optimization of Lennard-Jones clusters
Theoretical design of global optimization algorithms can profitably utilize
recent statistical mechanical treatments of potential energy surfaces (PES's).
Here we analyze the basin-hopping algorithm to explain its success in locating
the global minima of Lennard-Jones (LJ) clusters, even those such as \LJ{38}
for which the PES has a multiple-funnel topography, where trapping in local
minima with different morphologies is expected. We find that a key factor in
overcoming trapping is the transformation applied to the PES which broadens the
thermodynamic transitions. The global minimum then has a significant
probability of occupation at temperatures where the free energy barriers
between funnels are surmountable.Comment: 13 pages, 13 figures, revte
The double-funnel energy landscape of the 38-atom Lennard-Jones cluster
The 38-atom Lennard-Jones cluster has a paradigmatic double-funnel energy
landscape. One funnel ends in the global minimum, a face-centred-cubic (fcc)
truncated octahedron. At the bottom of the other funnel is the second lowest
energy minimum which is an incomplete Mackay icosahedron. We characterize the
energy landscape in two ways. Firstly, from a large sample of minima and
transition states we construct a disconnectivity tree showing which minima are
connected below certain energy thresholds. Secondly we compute the free energy
as a function of a bond-order parameter. The free energy profile has two
minima, one which corresponds to the fcc funnel and the other which at low
temperature corresponds to the icosahedral funnel and at higher temperatures to
the liquid-like state. These two approaches show that the greater width of the
icosahedral funnel, and the greater structural similarity between the
icosahedral structures and those associated with the liquid-like state, are the
cause of the smaller free energy barrier for entering the icosahedral funnel
from the liquid-like state and therefore of the cluster's preferential entry
into this funnel on relaxation down the energy landscape. Furthermore, the
large free energy barrier between the fcc and icosahedral funnels, which is
energetic in origin, causes the cluster to be trapped in one of the funnels at
low temperature. These results explain in detail the link between the
double-funnel energy landscape and the difficulty of global optimization for
this cluster.Comment: 12 pages, 11 figures, revte
A Duty Everlasting: The Perils of Applying Traditional Doctrines of Spoliation to Electronic Discovery
Amendments to the Federal Rules of Civil Procedure regarding electronic discovery are expected to take effect on December 1, 2006. These amendments are designed to alleviate the burden, expense and uncertainty that has resulted from the application of traditional discovery principles in the electronic age. These principles worked well in an era where discovery was primarily limited to the production of paper documentation, but have proved unworkable when applied to the discovery of electronic data, particularly in the “corporate world,” where even the most routine business discussions are captured in electronic format.
Interacting Topological Defects on Frozen Topographies
We propose and analyze an effective free energy describing the physics of disclination defects in particle arrays constrained to move on an arbitrary two-dimensional surface. At finite temperature the physics of interacting disclinations is mapped to a Laplacian Sine-Gordon Hamiltonian suitable for numerical simulations. We then specialize to the case of a spherical crystal at zero temperature. The ground state is analyzed as a function of the ratio of the defect core energy to the Young\u27s modulus. We argue that the core energy contribution becomes less and less important in the limit R \u3e\u3e a, where R is the radius of the sphere and a is the particle spacing. For large core energies there are twelve disclinations forming an icosahedron. For intermediate core energies unusual finite-length grain boundaries are preferred. The complicated regime of small core energies, appropriate to the limit R/a goes to infinity, is also addressed. Finally we discuss the application of our results to the classic Thomson problem of finding the ground state of electrons distributed on a two-sphere
Cubic autocatalysis in a reaction-diffusion annulus: semi-analytical solutions
Semi-analytical solutions for cubic autocatalytic reactions are considered in a circularly symmetric reaction-diffusion annulus. The Galerkin method is used to approximate the spatial structure of the reactant and autocatalyst concentrations. Ordinary differential equations are then obtained as an approximation to the governing partial differential equations and analyzed to obtain semi-analytical results for this novel geometry. Singularity theory is used to determine the regions of parameter space in which the different types of steady-state diagram occur. The region of parameter space, in which Hopf bifurcations can occur, is found using a degenerate Hopf bifurcation analysis. A novel feature of this geometry is the effect, of varying the width of the annulus, on the static and dynamic multiplicity. The results show that for a thicker annulus, Hopf bifurcations and multiple steady-state solutions occur in a larger portion of parameter space. The usefulness and accuracy of the semi-analytical results are confirmed by comparison with numerical solutions of the governing partial differential equations
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