26,825 research outputs found
Quadrant marked mesh patterns in 123-avoiding permutations
Given a permutation in the symmetric
group , we say that matches the quadrant marked
mesh pattern in if there are at least
points to the right of in which are greater than
, at least points to the left of in which are
greater than , at least points to the left of in
which are smaller than , and at least points to the
right of in which are smaller than . Kitaev,
Remmel, and Tiefenbruck systematically studied the distribution of the number
of matches of in 132-avoiding permutations. The
operation of reverse and complement on permutations allow one to translate
their results to find the distribution of the number of
matches in 231-avoiding, 213-avoiding, and 312-avoiding permutations. In this
paper, we study the distribution of the number of matches of
in 123-avoiding permutations. We provide explicit
recurrence relations to enumerate our objects which can be used to give closed
forms for the generating functions associated with such distributions. In many
cases, we provide combinatorial explanations of the coefficients that appear in
our generating functions
Nuclear Modification to Parton Distribution Functions and Parton Saturation
We introduce a generalized definition of parton distribution functions (PDFs)
for a more consistent all-order treatment of power corrections. We present a
new set of modified DGLAP evolution equations for nuclear PDFs, and show that
the resummed -type of leading nuclear size enhanced power
corrections significantly slow down the growth of gluon density at small-.
We discuss the relation between the calculated power corrections and the
saturation phenomena.Comment: 4 pages, to appear in the proceedings of QM200
Cylindrical Superlens by a Coordinate Transformation
Cylinder-shaped perfect lens deduced from the coordinate transformation
method is proposed. The previously reported perfect slab lens is noticed to be
a limiting form of the cylindrical lens when the inner radius approaches
infinity with respect to the lens thickness. Connaturality between a
cylindrical lens and a slab lens is affirmed by comparing their eigenfield
transfer functions. We numerically confirm the subwavelength focusing
capability of such a cylindrical lens with consideration of material
imperfection. Compared to a slab lens, a cylindrical lens has several
advantages, including finiteness in cross-section, and ability in lensing with
magnification or demagnification. Immediate applications of such a cylindrical
lens can be in high-resolution imaging and lithography technologies. In
addition, its invisibility property suggests that it may be valuable for
non-invasive electromagnetic probing.Comment: Minor changes to conform with the published versio
Dilatation of Lateral Ventricles with Brain Volumes in Infants with 3D Transfontanelle US
Ultrasound (US) can be used to assess brain development in newborns, as MRI
is challenging due to immobilization issues, and may require sedation.
Dilatation of the lateral ventricles in the brain is a risk factor for poorer
neurodevelopment outcomes in infants. Hence, 3D US has the ability to assess
the volume of the lateral ventricles similar to clinically standard MRI, but
manual segmentation is time consuming. The objective of this study is to
develop an approach quantifying the ratio of lateral ventricular dilatation
with respect to total brain volume using 3D US, which can assess the severity
of macrocephaly. Automatic segmentation of the lateral ventricles is achieved
with a multi-atlas deformable registration approach using locally linear
correlation metrics for US-MRI fusion, followed by a refinement step using
deformable mesh models. Total brain volume is estimated using a 3D ellipsoid
modeling approach. Validation was performed on a cohort of 12 infants, ranging
from 2 to 8.5 months old, where 3D US and MRI were used to compare brain
volumes and segmented lateral ventricles. Automatically extracted volumes from
3D US show a high correlation and no statistically significant difference when
compared to ground truth measurements. Differences in volume ratios was 6.0 +/-
4.8% compared to MRI, while lateral ventricular segmentation yielded a mean
Dice coefficient of 70.8 +/- 3.6% and a mean absolute distance (MAD) of 0.88
+/- 0.2mm, demonstrating the clinical benefit of this tool in paediatric
ultrasound
Open charm tomography of cold nuclear matter
We study the relative contribution of partonic sub-processes to D meson
production and D meson-triggered inclusive di-hadrons to lowest order in
perturbative QCD. While gluon fusion dominates the creation of large angle
DD-bar pairs, charm on light parton scattering determines the yield of single
inclusive D mesons. The distinctly different non-perturbative fragmentation of
c quarks into D mesons versus the fragmentation of quarks and gluons into light
hadrons results in a strong transverse momentum dependence of anticharm content
of the away-side charm-triggered jet. In p+A reactions, we calculate and resum
the coherent nuclear-enhanced power corrections from the final state partonic
scattering in the medium. We find that single and double inclusive open charm
production can be suppressed as much as the yield of neutral pions from
dynamical high-twist shadowing. Effects of energy loss in p+A collisions are
also investigated phenomenologically and may lead to significantly weaker
transverse momentum dependence of the nuclear attenuation.Comment: 24 pages, 21 figure
Scattering of Glue by Glue on the Light-cone Worldsheet I: Helicity Non-conserving Amplitudes
We give the light-cone gauge calculation of the one-loop on-shell scattering
amplitudes for gluon-gluon scattering which violate helicity conservation. We
regulate infrared divergences by discretizing the p^+ integrations, omitting
the terms with p^+=0. Collinear divergences are absent diagram by diagram for
the helicity non-conserving amplitudes. We also employ a novel ultraviolet
regulator that is natural for the light-cone worldsheet description of planar
Feynman diagrams. We show that these regulators give the known answers for the
helicity non-conserving one-loop amplitudes, which don't suffer from the usual
infrared vagaries of massless particle scattering. For the maximal helicity
violating process we elucidate the physics of the remarkable fact that the loop
momentum integrand for the on-shell Green function associated with this
process, with a suitable momentum routing of the different contributing
topologies, is identically zero. We enumerate the counterterms that must be
included to give Lorentz covariant results to this order, and we show that they
can be described locally in the light-cone worldsheet formulation of the sum of
planar diagrams.Comment: 30 pages, 17 figure
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