Hamiltonian Reduction of SL(2)SL(2)-theories at the Level of Correlators

Since the work of Bershadsky and Ooguri and Feigin and Frenkel it is well known that correlators of $SL(2)$ current algebra for admissible representations should reduce to correlators for conformal minimal models. A precise proposal for this relation has been given at the level of correlators: When $SL(2)$ primary fields are expressed as $\phi_j(z_n,x_n)$ with $x_n$ being a variable to keep track of the $SL(2)$ representation multiplet (possibly infinitely dimensional for admissible representations), then the minimal model correlator is supposed to be obtained simply by putting all $x_n=z_n$. Although strong support for this has been presented, to the best of our understanding a direct, simple proof seems to be missing so in this paper we present one based on the free field Wakimoto construction and our previous study of that in the present context. We further verify that the explicit $SL(2)$ correlators we have published in a recent preprint reduce in the above way, up to a constant which we also calculate. We further discuss the relation to more standard formulations of hamiltonian reduction.Comment: 13 pages, LaTe

Some aspects of the monthly atmospheric circulation affecting monthly precipitation over the Colorado River Basin

Includes bibliographical references.Research conducted between the Office of Naval Research and Colorado State University, under contract Nonr 1610(06)

Atmospheric water

Bibliography: page [16].Project A-0004-COLO, Grant agreement nos. 14-01-0001-553, 726, 900, 1074, 1625

Atmospheric water balance of the upper Colorado River basin

February, 1968.Includes bibliographical references.Sponsored by the U. S. Navy, Office of Naval Research NONR 1610(06)

Stochastic evolutions in superspace and superconformal field theory

Some stochastic evolutions of conformal maps can be described by SLE and may be linked to conformal field theory via stochastic differential equations and singular vectors in highest-weight modules of the Virasoro algebra. Here we discuss how this may be extended to superconformal maps of N=1 superspace with links to superconformal field theory and singular vectors of the N=1 superconformal algebra in the Neveu-Schwarz sector.Comment: 13 pages, LaTe

Modeling and visualizing uncertainty in gene expression clusters using Dirichlet process mixtures

Although the use of clustering methods has rapidly become one of the standard computational approaches in the literature of microarray gene expression data, little attention has been paid to uncertainty in the results obtained. Dirichlet process mixture (DPM) models provide a nonparametric Bayesian alternative to the bootstrap approach to modeling uncertainty in gene expression clustering. Most previously published applications of Bayesian model-based clustering methods have been to short time series data. In this paper, we present a case study of the application of nonparametric Bayesian clustering methods to the clustering of high-dimensional nontime series gene expression data using full Gaussian covariances. We use the probability that two genes belong to the same cluster in a DPM model as a measure of the similarity of these gene expression profiles. Conversely, this probability can be used to define a dissimilarity measure, which, for the purposes of visualization, can be input to one of the standard linkage algorithms used for hierarchical clustering. Biologically plausible results are obtained from the Rosetta compendium of expression profiles which extend previously published cluster analyses of this data

Affine su(3) and su(4) fusion multiplicities as polytope volumes

Affine su(3) and su(4) fusion multiplicities are characterised as discretised volumes of certain convex polytopes. The volumes are measured explicitly, resulting in multiple sum formulas. These are the first polytope-volume formulas for higher-rank fusion multiplicities. The associated threshold levels are also discussed. For any simple Lie algebra we derive an upper bound on the threshold levels using a refined version of the Gepner-Witten depth rule.Comment: 16 pages, LaTe

A comprehensive numerical study of aerosol-cloud-precipitation interactions in marine stratocumulus

Three-dimensional large-eddy simulations (LES) with detailed bin-resolved microphysics are performed to explore the diurnal variation of marine stratocumulus (MSc) clouds under clean and polluted conditions. The sensitivity of the aerosol-cloud-precipitation interactions to variation of sea surface temperature, free tropospheric humidity, large-scale divergence rate, and wind speed is assessed. The comprehensive set of simulations corroborates previous studies that (1) with moderate/heavy drizzle, an increase in aerosol leads to an increase in cloud thickness; and (2) with non/light drizzle, an increase in aerosol results in a thinner cloud, due to the pronounced effect on entrainment. It is shown that for higher SST, stronger large-scale divergence, drier free troposphere, or lower wind speed, the cloud thins and precipitation decreases. The sign and magnitude of the Twomey effect, droplet dispersion effect, cloud thickness effect, and cloud optical depth susceptibility to aerosol perturbations (i.e., change in cloud optical depth to change in aerosol number concentration) are evaluated by LES experiments and compared with analytical formulations. The Twomey effect emerges as dominant in total cloud optical depth susceptibility to aerosol perturbations. The dispersion effect, that of aerosol perturbations on the cloud droplet size spectrum, is positive (i.e., increase in aerosol leads to spectral narrowing) and accounts for 3% to 10% of the total cloud optical depth susceptibility at nighttime, with greater influence in heavier drizzling clouds. The cloud thickness effect is negative (i.e., increase in aerosol leads to thinner cloud) for non/light drizzling cloud and positive for a moderate/heavy drizzling clouds; the cloud thickness effect contributes 5% to 22% of the nighttime total cloud susceptibility. Overall, the total cloud optical depth susceptibility ranges from ~0.28 to 0.53 at night; an increase in aerosol concentration enhances cloud optical depth, especially with heavier precipitation and in a more pristine environment. During the daytime, the range of magnitude for each effect is more variable owing to cloud thinning and decoupling. The good agreement between LES experiments and analytical formulations suggests that the latter may be useful in evaluations of the total cloud susceptibility. The ratio of the magnitude of the cloud thickness effect to that of the Twomey effect depends on cloud base height and cloud thickness in unperturbed (clean) clouds

Free field realizations of 2D current algebras, screening currents and primary fields

In this paper we consider Wakimoto free field realizations of simple affine Lie algebras, a subject already much studied. We present three new sets of results, (i) Based on quantizing differential operator realizations of the corresponding Lie algebras we provide general universal very simple expressions for all currents, more compact than has been established so far. (ii) We supplement the treatment of screening currents of the first kind, known in the literature, by providing a direct proof of the properties for screening currents of the second kind. Finally (iii) we work out explicit free field realizations of primary fields with general non-integer weights. We use a formalism where the (generally infinite) multiplet is replaced by a generating function primary operator. These results taken together allow setting up integral representations for correlators of primary fields corresponding to non-integrable degenerate (in particular admissible) representations