Analogs of Schur functions for rank two Weyl groups obtained from grid-like posets

In prior work, the authors, along with M. McClard, R. A. Proctor, and N. J. Wildberger, studied certain distributive lattice models for the "Weyl bialternants" (aka "Weyl characters") associated with the rank two root systems/Weyl groups. These distributive lattices were uniformly described as lattices of order ideals taken from certain grid-like posets, although the arguments connecting the lattices to Weyl bialternants were case-by-case depending on the type of the rank two root system. Using this connection with Weyl bialternants, these lattices were shown to be rank symmetric and rank unimodal, and their rank generating functions were shown to have beautiful quotient-of-products expressions. Here, these results are re-derived from scratch using completely uniform and elementary combinatorial reasoning in conjunction with some new combinatorial methodology developed elsewhere by the second listed author.Comment: 15 page

Steady-state evolution of debris disks around A stars

In this paper a simple analytical model for the steady-state evolution of debris disks due to collisions is confronted with Spitzer observations of main sequence A stars. All stars are assumed to have planetesimal belts with a distribution of initial masses and radii. In the model disk mass is constant until the largest planetesimals reach collisional equilibrium whereupon the mass falls off oc 1/t. We find that the detection statistics and trends seen at both 24 and 70um can be fitted well by the model. While there is no need to invoke stochastic evolution or delayed stirring to explain the statistics, a moderate rate of stochastic events is not ruled out. Potentially anomalous systems are identified by a high dust luminosity compared with the maximum permissible in the model (HD3003, HD38678, HD115892, HD172555). Their planetesimals may have unusual properties (high strength or low eccentricity) or this dust could be transient. While transient phenomena are also favored for a few systems in the literature, the overall success of our model, which assumes planetesimals in all belts have the same strength, eccentricity and maximum size, suggests a large degree of uniformity in the outcome of planet formation. The distribution of planetesimal belt radii, once corrected for detection bias, follows N(r) oc r^{-0.8+-0.3} for 3-120AU. Since the inner edge is often attributed to an unseen planet, this provides a unique constraint on the planetary systems of A stars. It is also shown that P-R drag may sculpt the inner edges of A star disks close to the Spitzer detection threshold (HD2262, HD19356, HD106591, HD115892). This model can be readily applied to the interpretation of future surveys, and predictions are made for the upcoming SCUBA-2 survey, including that >17% of A stars should be detectable at 850um.Comment: Accepted by Ap

The importance of epithelial uptake systems in lung toxicity.

The discovery that the herbicide paraquat was selectively accumulated by the lung, both in vivo and in vitro, in comparison with other tissues, provided an explanation for its selective toxicity to the lung. This uptake process is energy dependent and obeys saturation kinetics. A characterization of the process led to the identification of endogenous chemicals that are the natural substrates for the system. Among these are a series of diamines and polyamines, as well as the diaminodisulfide cystamine. It appears that paraquat, because of specific structural similarities to these endogenous polyamines, is mistakenly accumulated by the lung. This uptake process is specifically located in the alveolar Type II cell, the Clara cell, and probably the alveolar Type I cell. With the development of knowledge of the structural requirements of chemicals to be accumulated by this system, it is possible to predict which chemicals will be accumulated by the lung or design molecules that are targeted to the alveolar epithelial and Clara cells. In the wider perspective, this polyamine uptake system has been found on a number of cancerous cells or tissues. With the knowledge of the uptake system in the lung, it should be possible to design drugs that will be specifically concentrated in cells that possess this system

Quantum vortices and trajectories in particle diffraction

We investigate the phenomenon of the diffraction of charged particles by thin material targets using the method of the de Broglie-Bohm quantum trajectories. The particle wave function can be modeled as a sum of two terms $\psi=\psi_{ingoing}+\psi_{outgoing}$. A thin separator exists between the domains of prevalence of the ingoing and outgoing wavefunction terms. The structure of the quantum-mechanical currents in the neighborhood of the separator implies the formation of an array of \emph{quantum vortices}. The flow structure around each vortex displays a characteristic pattern called `nodal point - X point complex'. The X point gives rise to stable and unstable manifolds. We find the scaling laws characterizing a nodal point-X point complex by a local perturbation theory around the nodal point. We then analyze the dynamical role of vortices in the emergence of the diffraction pattern. In particular, we demonstrate the abrupt deflections, along the direction of the unstable manifold, of the quantum trajectories approaching an X-point along its stable manifold. Theoretical results are compared to numerical simulations of quantum trajectories. We finally calculate the {\it times of flight} of particles following quantum trajectories from the source to detectors placed at various scattering angles $\theta$, and thereby propose an experimental test of the de Broglie - Bohm formalism.Comment: 17 pages, 7 figures, accepted by IJB

Improved statistical methods for estimating infestation rates in quarantine research when hosts are naturally infested

Trading partners often require phytosanitary or quarantine treatments for fresh horticultural produce to ensure no economically important pest species are moved with the imported product. When developing such treatments, it is essential that the level of treatment efficacy can be determined. This is often based on the mortality of the total number of target pests exposed to treatment, but in naturally infested products this number is not always known. In such cases, the infestation rate and subsequently an estimate of the number of pests are obtained directly from a set of untreated control samples of the host product. The International Plant Protection Convention (IPPC) Secretariat has provided 2 formulas for these situations that place an interval around the point estimate obtained from the control samples to obtain an estimate of the infestation rate. However, these formulas do not allow a confidence level to be assigned to the estimate, and there are concerns with the assumptions regarding the distribution and the measure of variability used in the formulas. In this article, we propose 2 alternative formulas. We propose that the lower one-sided confidence limit should be applied to all infestation datasets that are approximately normally distributed. As infestation data are sometimes skewed, it is proposed the lower one-sided modified Cox confidence limit is applied to data approximately log-normal distributed. These well-recognized formulas are compared to the formulas recommended by the IPPC and applied to 3 datasets involving natural infestation

Forming the first planetary systems: debris around Galactic thick disc stars

The thick disc contains stars formed within the first Gyr of Galactic history, and little is known about their planetary systems. The Spitzer MIPS instrument was used to search 11 of the closest of these old low-metal stars for circumstellar debris, as a signpost that bodies at least as large as planetesimals were formed. A total of 22 thick disc stars has now been observed, after including archival data, but dust is not found in any of the systems. The data rule out a high incidence of debris among star systems from early in the Galaxy's formation. However, some stars of this very old population do host giant planets, at possibly more than the general incidence among low-metal Sun-like stars. As the Solar System contains gas giants but little cometary dust, the thick disc could host analogue systems that formed many Gyr before the Sun.Comment: accepted by MNRAS Letters; 5 pages, 4 figure