Flag Hilbert schemes, colored projectors and Khovanov-Rozansky homology

We construct a categorification of the maximal commutative subalgebra of the type A Hecke algebra. Specifically, we propose a monoidal functor from the (symmetric) monoidal category of coherent sheaves on the flag Hilbert scheme to the (non-symmetric) monoidal category of Soergel bimodules. The adjoint of this functor allows one to match the Hochschild homology of any braid with the Euler characteristic of a sheaf on the flag Hilbert scheme. The categorified Jones-Wenzl projectors studied by Abel, Elias and Hogancamp are idempotents in the category of Soergel bimodules, and they correspond to the renormalized Koszul complexes of the torus fixed points on the flag Hilbert scheme. As a consequence, we conjecture that the endomorphism algebras of the categorified projectors correspond to the dg algebras of functions on affine charts of the flag Hilbert schemes. We define a family of differentials dN on these dg algebras and conjecture that their homology matches that of the glN projectors, generalizing earlier conjectures of the first and third authors with Oblomkov and Shende

In field N transfer, build-up, and leaching in ryegrass-clover mixtures

Two field experiments investigating dynamics in grass-clover mixtures were conducted, using 15N- and 14C-labelling to trace carbon (C) and nitrogen (N) from grass (Lolium perenne L.) and clover (Trifolium repens L. and Trifolium pratense L.). The leaching of dissolved inorganic nitrogen (DIN), as measured in pore water sampled by suction cups, increased during the autumn and winter, whereas the leaching of dissolved organic nitrogen (DON) was fairly constant during this period. Leaching of 15N from the sward indicated that ryegrass was the direct source of less than 1-2 percent of the total N leaching measured, whereas N dynamics pointed to clover as an important contributor to N leaching. Sampling of roots indicates that the dynamics in smaller roots were responsible for N and C build-up in the sward, and that N became available for transfer among species and leaching from the root zone. The bi-directional transfer of N between ryegrass and clover could however not be explained only by root turnover. Other processes like direct uptake of organic N compounds, may have contributed

Bent-Double Radio Sources as Probes of Intergalactic Gas

As the most common environment in the universe, groups of galaxies are likely to contain a significant fraction of the missing baryons in the form of intergalactic gas. The density of this gas is an important factor in whether ram pressure stripping and strangulation affect the evolution of galaxies in these systems. We present a method for measuring the density of intergalactic gas using bent-double radio sources that is independent of temperature, making it complementary to current absorption line measurements. We use this method to probe intergalactic gas in two different environments: inside a small group of galaxies as well as outside of a larger group at a 2 Mpc radius and measure total gas densities of $4 \pm 1_{-2}^{+6} \times 10^{-3}$ and $9 \pm 3_{-5}^{+10} \times 10^{-4}$ per cubic centimeter (random and systematic errors) respectively. We use X-ray data to place an upper limit of $2 \times 10^6$ K on the temperature of the intragroup gas in the small group.Comment: 6 pages, 1 figure, accepted for publication in Ap

Single wall carbon nanotube double quantum dot

We report on two top-gate defined, coupled quantum dots in a semiconducting single wall carbon nanotube, constituting a tunable double quantum dot system. The single wall carbon nanotubes are contacted by titanium electrodes, and gated by three narrow top-gate electrodes as well as a back-gate. We show that a bias spectroscopy plot on just one of the two quantum dots can be used to extract the addition energy of both quantum dots. Furthermore, honeycomb charge stability diagrams are analyzed by an electrostatic capacitor model that includes cross capacitances, and we extract the coupling energy of the double quantum dot.Comment: Published in Applied Physics Letters 4 December 2006. http://link.aip.org/link/?APL/89/23211

Efficient Bayesian hierarchical functional data analysis with basis function approximations using Gaussian-Wishart processes

Functional data are defined as realizations of random functions (mostly smooth functions) varying over a continuum, which are usually collected with measurement errors on discretized grids. In order to accurately smooth noisy functional observations and deal with the issue of high-dimensional observation grids, we propose a novel Bayesian method based on the Bayesian hierarchical model with a Gaussian-Wishart process prior and basis function representations. We first derive an induced model for the basis-function coefficients of the functional data, and then use this model to conduct posterior inference through Markov chain Monte Carlo. Compared to the standard Bayesian inference that suffers serious computational burden and unstableness for analyzing high-dimensional functional data, our method greatly improves the computational scalability and stability, while inheriting the advantage of simultaneously smoothing raw observations and estimating the mean-covariance functions in a nonparametric way. In addition, our method can naturally handle functional data observed on random or uncommon grids. Simulation and real studies demonstrate that our method produces similar results as the standard Bayesian inference with low-dimensional common grids, while efficiently smoothing and estimating functional data with random and high-dimensional observation grids where the standard Bayesian inference fails. In conclusion, our method can efficiently smooth and estimate high-dimensional functional data, providing one way to resolve the curse of dimensionality for Bayesian functional data analysis with Gaussian-Wishart processes.Comment: Under revie

Meteorological application of Apollo photography Final report

Development of meteorological information and parameters based on cloud photographs taken during Apollo 9 fligh