Quadrant marked mesh patterns in 123-avoiding permutations

Given a permutation $\sigma = \sigma_1 \ldots \sigma_n$ in the symmetric group $\mathcal{S}_{n}$, we say that $\sigma_i$ matches the quadrant marked mesh pattern $\mathrm{MMP}(a,b,c,d)$ in $\sigma$ if there are at least $a$ points to the right of $\sigma_i$ in $\sigma$ which are greater than $\sigma_i$, at least $b$ points to the left of $\sigma_i$ in $\sigma$ which are greater than $\sigma_i$, at least $c$ points to the left of $\sigma_i$ in $\sigma$ which are smaller than $\sigma_i$, and at least $d$ points to the right of $\sigma_i$ in $\sigma$ which are smaller than $\sigma_i$. Kitaev, Remmel, and Tiefenbruck systematically studied the distribution of the number of matches of $\mathrm{MMP}(a,b,c,d)$ 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 $\mathrm{MMP}(a,b,c,d)$ matches in 231-avoiding, 213-avoiding, and 312-avoiding permutations. In this paper, we study the distribution of the number of matches of $\mathrm{MMP}(a,b,c,d)$ 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 $\alpha_s A^{1/3}/Q^2$-type of leading nuclear size enhanced power corrections significantly slow down the growth of gluon density at small-$x$. 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