5,206 research outputs found
Rational Arithmetic Mathematica Functions to Evaluate the One-sided One-sample K-S Cumulative Sample Distribution
One of the most widely used goodness-of-fit tests is the Kolmogorov-Smirnov (KS) family of tests which have been implemented by many computer statistical software packages. To calculate a p value (evaluate the cumulative sampling distribution), these packages use various methods including recursion formulae, limiting distributions, and approximations of unknown accuracy developed over thirty years ago. Based on an extensive literature search for the one-sided one-sample K-S test, this paper identifies two direct formulae and five recursion formulae that can be used to calculate a p value and then develops two additional direct formulae and four iterative versions of the direct formulae for a total of thirteen formulae. To ensure accurate calculation by avoiding catastrophic cancelation and eliminating rounding error, each formula is implemented in rational arithmetic. Linear search is used to calculate the inverse of the cumulative sampling distribution (find the confidence interval bandwidth). Extensive tables of bandwidths are presented for sample sizes up to 2, 000. The results confirm the hypothesis that as the number of digits in the numerator and denominator integers of the rational number test statistic increases, the computation time also increases. In comparing the computational times of the thirteen formulae, the direct formulae are slightly faster than their iterative versions and much faster than all the recursion formulae. Computational times for the fastest formula are given for sample sizes up to fifty thousand.
Arbitrary Precision Mathematica Functions to Evaluate the One-Sided One Sample K-S Cumulative Sampling Distribution
Efficient rational arithmetic methods that can exactly evaluate the cumulative sampling distribution of the one-sided one sample Kolmogorov-Smirnov (K-S) test have been developed by Brown and Harvey (2007) for sample sizes n up to fifty thousand. This paper implements in arbitrary precision the same 13 formulae to evaluate the one-sided one sample K-S cumulative sampling distribution. Computational experience identifies the fastest implementation which is then used to calculate confidence interval bandwidths and p values for sample sizes up to ten million.
Rational Arithmetic Mathematica Functions to Evaluate the Two-Sided One Sample K-S Cumulative Sampling Distribution
One of the most widely used goodness-of-fit tests is the two-sided one sample Kolmogorov-Smirnov (K-S) test which has been implemented by many computer statistical software packages. To calculate a two-sided p value (evaluate the cumulative sampling distribution), these packages use various methods including recursion formulae, limiting distributions, and approximations of unknown accuracy developed over thirty years ago. Based on an extensive literature search for the two-sided one sample K-S test, this paper identifies an exact formula for sample sizes up to 31, six recursion formulae, and one matrix formula that can be used to calculate a p value. To ensure accurate calculation by avoiding catastrophic cancelation and eliminating rounding error, each of these formulae is implemented in rational arithmetic. For the six recursion formulae and the matrix formula, computational experience for sample sizes up to 500 shows that computational times are increasing functions of both the sample size and the number of digits in the numerator and denominator integers of the rational number test statistic. The computational times of the seven formulae vary immensely but the Durbin recursion formula is almost always the fastest. Linear search is used to calculate the inverse of the cumulative sampling distribution (find the confidence interval half-width) and tables of calculated half-widths are presented for sample sizes up to 500. Using calculated half-widths as input, computational times for the fastest formula, the Durbin recursion formula, are given for sample sizes up to two thousand.
What is the Temperature Dependence of the Casimir Effect?
There has been recent criticism of our approach to the Casimir force between
real metallic surfaces at finite temperature, saying it is in conflict with the
third law of thermodynamics and in contradiction with experiment. We show that
these claims are unwarranted, and that our approach has strong theoretical
support, while the experimental situation is still unclear.Comment: 6 pages, REVTeX, final revision includes two new references and
related discussio
On the Temperature Dependence of the Casimir Effect
The temperature dependence of the Casimir force between a real metallic plate
and a metallic sphere is analyzed on the basis of optical data concerning the
dispersion relation of metals such as gold and copper. Realistic permittivities
imply, together with basic thermodynamic considerations, that the transverse
electric zero mode does not contribute. This results in observable differences
with the conventional prediction, which does not take this physical requirement
into account. The results are shown to be consistent with the third law of
thermodynamics, as well as being consistent with current experiments. However,
the predicted temperature dependence should be detectable in future
experiments. The inadequacies of approaches based on {\it ad hoc} assumptions,
such as the plasma dispersion relation and the use of surface impedance without
transverse momentum dependence, are discussed.Comment: 14 pages, 3 eps figures, revtex4. New version includes clarifications
and new reference. Accepted for publication in Phys. Rev.
PT-Symmetric Quantum Electrodynamics and Unitarity
More than 15 years ago, a new approach to quantum mechanics was suggested, in
which Hermiticity of the Hamiltonian was to be replaced by invariance under a
discrete symmetry, the product of parity and time-reversal symmetry,
. It was shown that if is unbroken, energies were,
in fact, positive, and unitarity was satisifed. Since quantum mechanics is
quantum field theory in 1 dimension, time, it was natural to extend this idea
to higher-dimensional field theory, and in fact an apparently viable version of
-invariant quantum electrodynamics was proposed. However, it has
proved difficult to establish that the unitarity of the scattering matrix, for
example, the K\"all\'en spectral representation for the photon propagator, can
be maintained in this theory. This has led to questions of whether, in fact,
even quantum mechanical systems are consistent with probability conservation
when Green's functions are examined, since the latter have to possess physical
requirements of analyticity. The status of QED will be reviewed
in this report, as well as the general issue of unitarity.Comment: 13 pages, 2 figures. Revised version includes new evidence for the
violation of unitarit
Identity of the van der Waals Force and the Casimir Effect and the Irrelevance of these Phenomena to Sonoluminescence
We show that the Casimir, or zero-point, energy of a dilute dielectric ball,
or of a spherical bubble in a dielectric medium, coincides with the sum of the
van der Waals energies between the molecules that make up the medium. That
energy, which is finite and repulsive when self-energy and surface effects are
removed, may be unambiguously calculated by either dimensional continuation or
by zeta function regularization. This physical interpretation of the Casimir
energy seems unambiguous evidence that the bulk self-energy cannot be relevant
to sonoluminescence.Comment: 7 pages, no figures, REVTe
Feasibility of an onboard wake vortex avoidance system
It was determined that an onboard vortex wake detection system using existing, proven instrumentation is technically feasible. This system might be incorporated into existing onboard systems such as a wind shear detection system, and might provide the pilot with the location of a vortex wake, as well as an evasive maneuver so that the landing separations may be reduced. It is suggested that this system might be introduced into our nation's commuter aircraft fleet and major air carrier fleet and permit a reduction of current landing separation standards, thereby reducing takeoff and departure delays
Casimir Force on a Micrometer Sphere in a Dip: Proposal of an Experiment
The attractive Casimir force acting on a micrometer-sphere suspended in a
spherical dip, close to the wall, is discussed. This setup is in principle
directly accessible to experiment. The sphere and the substrate are assumed to
be made of the same perfectly conducting material.Comment: 11 pages, 1 figure; to appear in J. Phys. A: Math. Ge
Sonoluminescence as a QED vacuum effect: Probing Schwinger's proposal
Several years ago Schwinger proposed a physical mechanism for
sonoluminescence in terms of photon production due to changes in the properties
of the quantum-electrodynamic (QED) vacuum arising from a collapsing dielectric
bubble. This mechanism can be re-phrased in terms of the Casimir effect and has
recently been the subject of considerable controversy. The present paper probes
Schwinger's suggestion in detail: Using the sudden approximation we calculate
Bogolubov coefficients relating the QED vacuum in the presence of the expanded
bubble to that in the presence of the collapsed bubble. In this way we derive
an estimate for the spectrum and total energy emitted. We verify that in the
sudden approximation there is an efficient production of photons, and further
that the main contribution to this dynamic Casimir effect comes from a volume
term, as per Schwinger's original calculation. However, we also demonstrate
that the timescales required to implement Schwinger's original suggestion are
not physically relevant to sonoluminescence. Although Schwinger was correct in
his assertion that changes in the zero-point energy lead to photon production,
nevertheless his original model is not appropriate for sonoluminescence. In
other works (see quant-ph/9805023, quant-ph/9904013, quant-ph/9904018,
quant-ph/9905034) we have developed a variant of Schwinger's model that is
compatible with the physically required timescales.Comment: 18 pages, ReV_TeX 3.2, 9 figures. Major revisions: This document is
now limited to providing a probe of Schwinger's original suggestion for
sonoluminescence. For details on our own variant of Schwinger's ideas see
quant-ph/9805023, quant-ph/9904013, quant-ph/9904018, quant-ph/990503
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