4,480 research outputs found
Shape Theory via QR decomposition
This work sets the non isotropic noncentral elliptical shape distributions
via QR decomposition in the context of zonal polynomials, avoiding the
invariant polynomials and the open problems for their computation. The new
shape distributions are easily computable and then the inference procedure can
be studied under exact densities instead under the published approximations and
asymptotic densities under isotropic models. An application in Biology is
studied under the classical gaussian approach and a two non gaussian models.Comment: 13 page
On power corrections to the event shape distributions in QCD
We study power corrections to the differential thrust, heavy jet mass and
C-parameter distributions in the two-jet kinematical region in e^+e^-
annihilation. We argue that away from the end-point region, e>>
\Lambda_{QCD}/Q, the leading 1/Q-power corrections are parameterized by a
single nonperturbative scale while for e \Lambda_{QCD}/Q one encounters a novel
regime in which power corrections of the form 1/(Qe)^n have to be taken into
account for arbitrary n. These nonperturbative corrections can be resummed and
factor out into a universal nonperturbative distribution, the shape function,
and the differential event shape distributions are given by convolution of the
shape function with perturbative cross-sections. Choosing a simple ansatz for
the shape function we demonstrate a good agreement of the obtained QCD
predictions for the distributions and their lowest moments with the existing
data over a wide energy interval.Comment: 18 pages, LaTeX style, 4 figure
Shape theory via polar decomposition
This work proposes a new model in the context of statistical theory of shape,
based on the polar decomposition. The non isotropic noncentral elliptical shape
distributions via polar decomposition is derived in the context of zonal
polynomials, avoiding the invariant polynomials and the open problems for their
computation. The new polar shape distributions are easily computable and then
the inference procedure can be studied under exact densities. As an example of
the technique, a classical application in Biology is studied under three
models, the usual Gaussian and two non normal Kotz models; the best model is
selected by a modified BIC criterion, then a test for equality in polar shapes
is performed.Comment: 14 page
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