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Letter to the Editor
The paper by Alfons, Croux and Gelper (2013), Sparse least trimmed squares
regression for analyzing high-dimensional large data sets, considered a
combination of least trimmed squares (LTS) and lasso penalty for robust and
sparse high-dimensional regression. In a recent paper [She and Owen (2011)], a
method for outlier detection based on a sparsity penalty on the mean shift
parameter was proposed (designated by "SO" in the following). This work is
mentioned in Alfons et al. as being an "entirely different approach." Certainly
the problem studied by Alfons et al. is novel and interesting.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS640 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
The centripetal force law and the equation of motion for a particle on a curved hypersurface
It is pointed out that the current form of extrinsic equation of motion for a
particle constrained to remain on a hypersurface is in fact a half-finished
version for it is established without regard to the fact that the particle can
never depart from the geodesics on the surface. Once the fact be taken into
consideration, the equation takes that same form as that for centripetal force
law, provided that the symbols are re-interpreted so that the law is applicable
for higher dimensions. The controversial issue of constructing operator forms
of these equations is addressed, and our studies show the quantization of
constrained system based on the extrinsic equation of motion is favorable.Comment: 5 pages, major revisio
Heisenberg equation for a nonrelativistic particle on a hypersurface: from the centripetal force to a curvature induced force
In classical mechanics, a nonrelativistic particle constrained on an
curved hypersurface embedded in flat space experiences the centripetal
force only. In quantum mechanics, the situation is totally different for the
presence of the geometric potential. We demonstrate that the motion of the
quantum particle is "driven" by not only the the centripetal force, but also a
curvature induced force proportional to the Laplacian of the mean curvature,
which is fundamental in the interface physics, causing curvature driven
interface evolution.Comment: 4 page
Soft vibrational mode associated with incommensurate orbital order in multiferroic CaMnO
We report inelastic light scattering measurements of lattice dynamics related
to the incommensurate orbital order in . Below the
ordering temperature , we observe extra
phonon peaks as a result of Brillouin-zone folding, as well as a soft
vibrational mode with a power-law -dependent energy, . This temperature dependence demonstrates the
second-order nature of the transition at , and it indicates that
the soft mode can be regarded as the amplitude excitation of the composite
order parameter. Our result strongly suggests that the lattice degrees of
freedom are actively involved in the orbital-ordering mechanism.Comment: 7 pages, 8 figure
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