15,737 research outputs found
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 and per cubic centimeter (random and systematic
errors) respectively. We use X-ray data to place an upper limit of 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
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