Symbolic Powers of Monomial Ideals

We investigate symbolic and regular powers of monomial ideals. For a square-free monomial ideal $I$ in $k[x_0, \ldots, x_n]$ we show $I^{t(m+e-1)-e+r)}$ is a subset of $M^{(t-1)(e-1)+r-1}(I^{(m)})^t$ for all positive integers $m$, $t$ and $r$, where $e$ is the big-height of $I$ and $M = (x_0, \ldots, x_n)$. This captures two conjectures ($r=1$ and $r=e$): one of Harbourne-Huneke and one of Bocci-Cooper-Harbourne. We also introduce the symbolic polyhedron of a monomial ideal and use this to explore symbolic powers of non-square-free monomial ideals.Comment: 15 pages. Fixed typ

Resumming the large-N approximation for time evolving quantum systems

In this paper we discuss two methods of resumming the leading and next to leading order in 1/N diagrams for the quartic O(N) model. These two approaches have the property that they preserve both boundedness and positivity for expectation values of operators in our numerical simulations. These approximations can be understood either in terms of a truncation to the infinitely coupled Schwinger-Dyson hierarchy of equations, or by choosing a particular two-particle irreducible vacuum energy graph in the effective action of the Cornwall-Jackiw-Tomboulis formalism. We confine our discussion to the case of quantum mechanics where the Lagrangian is $L(x,\dot{x}) = (1/2) \sum_{i=1}^{N} \dot{x}_i^2 - (g/8N) [ \sum_{i=1}^{N} x_i^2 - r_0^2 ]^{2}$. The key to these approximations is to treat both the $x$ propagator and the $x^2$ propagator on similar footing which leads to a theory whose graphs have the same topology as QED with the $x^2$ propagator playing the role of the photon. The bare vertex approximation is obtained by replacing the exact vertex function by the bare one in the exact Schwinger-Dyson equations for the one and two point functions. The second approximation, which we call the dynamic Debye screening approximation, makes the further approximation of replacing the exact $x^2$ propagator by its value at leading order in the 1/N expansion. These two approximations are compared with exact numerical simulations for the quantum roll problem. The bare vertex approximation captures the physics at large and modest $N$ better than the dynamic Debye screening approximation.Comment: 30 pages, 12 figures. The color version of a few figures are separately liste

Chaos in Time Dependent Variational Approximations to Quantum Dynamics

Dynamical chaos has recently been shown to exist in the Gaussian approximation in quantum mechanics and in the self-consistent mean field approach to studying the dynamics of quantum fields. In this study, we first show that any variational approximation to the dynamics of a quantum system based on the Dirac action principle leads to a classical Hamiltonian dynamics for the variational parameters. Since this Hamiltonian is generically nonlinear and nonintegrable, the dynamics thus generated can be chaotic, in distinction to the exact quantum evolution. We then restrict attention to a system of two biquadratically coupled quantum oscillators and study two variational schemes, the leading order large N (four canonical variables) and Hartree (six canonical variables) approximations. The chaos seen in the approximate dynamics is an artifact of the approximations: this is demonstrated by the fact that its onset occurs on the same characteristic time scale as the breakdown of the approximations when compared to numerical solutions of the time-dependent Schrodinger equation.Comment: 10 pages (12 figures), RevTeX (plus macro), uses epsf, minor typos correcte

Improved fidelity of triggered entangled photons from single quantum dots

We demonstrate the on-demand emission of polarisation-entangled photon pairs from the biexciton cascade of a single InAs quantum dot embedded in a GaAs/AlAs planar microcavity. Improvements in the sample design blue shifts the wetting layer to reduce the contribution of background light in the measurements. Results presented show that >70% of the detected photon pairs are entangled. The high fidelity of the (|HxxHx>+|VxxVx>)/2^0.5 state that we determine is sufficient to satisfy numerous tests for entanglement. The improved quality of entanglement represents a significant step towards the realisation of a practical quantum dot source compatible with applications in quantum information.Comment: 9 pages. Paper is available free of charge at http://www.iop.org/EJ/abstract/1367-2630/8/2/029/, see also 'A semiconductor source of triggered entangled photon pairs', R. M. Stevenson et al., Nature 439, 179 (2006

Home Ranges of Rat Snakes (Colubridae: Elaphe) in Different Habitats

Based on our findings, we suggest that rat snakes represent not only a major predator of kites, but also of other canopy and mid-story nesting species in the southeastern United States. For example, rat snakes are the most dominant snake nest predator of bird nests throughout the Southeast (DeGregorio et al. 2014) and are skilled tree climbers that often occupy arboreal habitats (Jackson 1976, Keller and Heske 2000, Sperry et al. 2009), particularly in bottomland forests (Mullin et al. 2000, Carfagno and Weatherhead 2009). Thus, the role of rat snakes as predators of nests above the understory is likely underappreciated because of the paucity of information on causes of failure among mid-story and canopy nest

Photoreceptor Inner Segment Morphology in Best Vitelliform Macular Dystrophy

PURPOSE To characterize outer retina structure in best vitelliform macular dystrophy (BVMD) and to determine the effect of macular lesions on overlying and adjacent photoreceptors. METHODS Five individuals with BVMD were followed prospectively with spectral domain optical coherence tomography and confocal and nonconfocal split-detector adaptive optics scanning light ophthalmoscopy (AOSLO). The AOSLO cone photoreceptor mosaic images were obtained within and around retinal lesions. Cone density was measured inside and outside lesions. In 2 subjects, densities were compared with published measurements acquired ∼2.5 years before. One subject was imaged 3 times over a 5-month period. RESULTS The AOSLO imaging demonstrated that photoreceptor morphology within BVMD retinal lesions was highly variable depending on the disease stage, with photoreceptor structure present even in advanced disease. The AOSLO imaging was repeatable even in severe disease over short-time and long-time intervals. Photoreceptor density was normal in retinal areas immediately adjacent to lesions and stable over ∼2.5 years. Mobile disk-like structures possibly representing subretinal macrophages were also observed. CONCLUSION Combined confocal and nonconfocal split-detector AOSLO imaging reveals substantial variability within clinical lesions in all stages of BVMD. Longitudinal cellular photoreceptor imaging could prove a powerful tool for understanding disease progression and monitoring emerging therapeutic treatment response in inherited degenerations such as BVMD

Medium-Energy Gamma-Ray Astrophysics with the 3-DTI Gamma-Ray Telescope

Gamma-ray observations in the medium energy range (0.50-50.0 MeV) are central to unfolding many outstanding questions in astrophysics. The challenges of medium-energy gamma-ray observations, however, are the low photon statistics and large backgrounds. We review these questions, address the telescope technology requirements, and describe our development of the 3-Dimensional Track Imaging (3-DTI) Compton telescope and its performance for a new mediumenergy gamma-ray mission. The 3-DTI is a large-volume time projection chamber (TPC) with a 2-dimensional gas micro-well detector (MWD) readout

Genetic diversity of the dengue vector Aedes aegypti in Australia and implications for future surveillance and mainland incursion monitoring

In February 2004, the discovery of an incursion of the dengue vector Aedes aegypti into the town of Tennant Creek in the Northern Territory caused concern for the Northern Territory health authorities who proceeded to implement a Commonwealth-funded eradication program. To determine the origin of the incursion, we performed a genetic analysis on Ae. aegypti from several Queensland and overseas localities. A comparison of DNA sequences from the mitochondrial cytochrome oxidase 1 gene indicated that the incursion was probably from Cairns or Camooweal. This genetic marker was also useful in identifying a separate Townsville haplotype population and another population on Thursday Island in the Torres Strait that is genetically distant to the mainland populations. The possible use of this marker as a surveillance tool for identifying the origins of local and overseas incursions is discussed