The extended empirical process test for non-Gaussianity in the CMB, with an application to non-Gaussian inflationary models

In (Hansen et al. 2002) we presented a new approach for measuring non-Gaussianity of the Cosmic Microwave Background (CMB) anisotropy pattern, based on the multivariate empirical distribution function of the spherical harmonics a_lm of a CMB map. The present paper builds upon the same ideas and proposes several improvements and extensions. More precisely, we exploit the additional information on the random phases of the a_lm to provide further tests based on the empirical distribution function. Also we take advantage of the effect of rotations in improving the power of our procedures. The suggested tests are implemented on physically motivated models of non-Gaussian fields; Monte-Carlo simulations suggest that this approach may be very promising in the analysis of non-Gaussianity generated by non-standard models of inflation. We address also some experimentally meaningful situations, such as the presence of instrumental noise and a galactic cut in the map.Comment: 15 pages, 6 figures, submitted to Phys. Rev.

Long Cycles in a Perturbed Mean Field Model of a Boson Gas

In this paper we give a precise mathematical formulation of the relation between Bose condensation and long cycles and prove its validity for the perturbed mean field model of a Bose gas. We decompose the total density $\rho=\rho_{{\rm short}}+\rho_{{\rm long}}$ into the number density of particles belonging to cycles of finite length ($\rho_{{\rm short}}$) and to infinitely long cycles ($\rho_{{\rm long}}$) in the thermodynamic limit. For this model we prove that when there is Bose condensation, $\rho_{{\rm long}}$ is different from zero and identical to the condensate density. This is achieved through an application of the theory of large deviations. We discuss the possible equivalence of $\rho_{{\rm long}}\neq 0$ with off-diagonal long range order and winding paths that occur in the path integral representation of the Bose gas.Comment: 10 page

The resummation of inter-jet energy flow for gaps-between-jets processes at HERA

We calculate resummed perturbative predictions for gaps-between-jets processes and compare to HERA data. Our calculation of this non-global observable needs to include the effects of primary gluon emission (global logarithms) and secondary gluon emission (non-global logarithms) to be correct at the leading logarithm (LL) level. We include primary emission by calculating anomalous dimension matrices for the geometry of the specific event definitions and estimate the effect of non-global logarithms in the large $N_c$ limit. The resulting predictions for energy flow observables are consistent with experimental data.Comment: 31 pages, 4 figures, 2 table

Diffractive Dijet Production

We explore the diffractive interaction of a proton with an anti-proton which results in centrally produced dijets. This process has been recently studied at the Tevatron. We make predictions within an Ingelman-Schlein approach and compare them to the recent data presented by the CDF collaboration. Earlier calculations resulted in theoretical cross-sections which are much larger than those observed by CDF. We find that, after consideration of hadronisation effects and the parton shower, and using parton density functions extracted from diffractive deep inelastic scattering at HERA, it is possible to explain the CDF data. We need to assume a gap survival probability of around 10% and this is in good agreement with the value predicted by theory. We also find that the non-diffractive contribution to the process is probably significant in the kinematical region probed by the Tevatron.Comment: 12 pages, 6 figures, 3 table

The quantitative soil pit method for measuring belowground carbon and nitrogen stocks

Many important questions in ecosystem science require estimates of stocks of soil C and nutrients. Quantitative soil pits provide direct measurements of total soil mass and elemental content in depth-based samples representative of large volumes, bypassing potential errors associated with independently measuring soil bulk density, rock volume, and elemental concentrations. The method also allows relatively unbiased sampling of other belowground C and nutrient stocks, including roots, coarse organic fragments, and rocks. We present a comprehensive methodology for sampling these pools with quantitative pits and assess their accuracy, precision, effort, and sampling intensity as compared to other methods. At 14 forested sites in New Hampshire, nonsoil belowground pools (which other methods may omit, double-count, or undercount) accounted for upward of 25% of total belowground C and N stocks: coarse material accounted for 4 and 1% of C and N in the O horizon; roots were 11 and 4% of C and N in the O horizon and 10 and 3% of C and N in the B horizon; and soil adhering to rocks represented 5% of total B-horizon C and N. The top 50 cm of the C horizon contained the equivalent of 17% of B-horizon carbon and N. Sampling procedures should be carefully designed to avoid treating these important pools inconsistently. Quantitative soil pits have fewer sources of systematic error than coring methods; the main disadvantage is that because they are time-consuming and create a larger zone of disturbance, fewer observations can be made than with cores

On the Tensor/Scalar Ratio in Inflation with UV Cutoff

Anisotropy of the cosmic microwave background radiation (CMB) originates from both tensor and scalar perturbations. To study the characteristics of each of these two kinds of perturbations, one has to determine the contribution of each to the anisotropy of CMB. For example, the ratio of the power spectra of tensor/scalar perturbations can be used to tighten bounds on the scalar spectral index. We investigate here the implications for the tensor/scalar ratio of the recent discovery (noted in astro-ph/0410139) that the introduction of a minimal length cutoff in the structure of spacetime does not leave boundary terms invariant. Such a cutoff introduces an ambiguity in the choice of action for tensor and scalar perturbations, which in turn can affect this ratio. We numerically solve for both tensor and scalar mode equations in a near-de-sitter background and explicitly find the cutoff dependence of the tensor/scalar ratio during inflation.Comment: 19 pages, 14 figures, to appear in Nucl. Phys. B; v4: typos corrected, matched with the published versio

Carbon clusters near the crossover to fullerene stability

The thermodynamic stability of structural isomers of $\mathrm{C}_{24}$, $\mathrm{C}_{26}$, $\mathrm{C}_{28}$ and $\mathrm{C}_{32}$, including fullerenes, is studied using density functional and quantum Monte Carlo methods. The energetic ordering of the different isomers depends sensitively on the treatment of electron correlation. Fixed-node diffusion quantum Monte Carlo calculations predict that a $\mathrm{C}_{24}$ isomer is the smallest stable graphitic fragment and that the smallest stable fullerenes are the $\mathrm{C}_{26}$ and $\mathrm{C}_{28}$ clusters with $\mathrm{C}_{2v}$ and $\mathrm{T}_{d}$ symmetry, respectively. These results support proposals that a $\mathrm{C}_{28}$ solid could be synthesized by cluster deposition.Comment: 4 pages, includes 4 figures. For additional graphics, online paper and related information see http://www.tcm.phy.cam.ac.uk/~prck

Functional conservation of a forebrain enhancer from the elephant shark (Callorhinchus milii) in zebrafish and mice

Background: The phylogenetic position of the elephant shark (Callorhinchus milii ) is particularly relevant to study the evolution of genes and gene regulation in vertebrates. Here we examine the evolution of Dlx homeobox gene regulation during vertebrate embryonic development with a particular focus on the forebrain. We first identified the elephant shark sequence orthologous to the URE2 cis -regulatory element of the mouse Dlx1/Dlx2 locus (herein named CmURE2). We then conducted a comparative study of the sequence and enhancer activity of CmURE2 with that of orthologous regulatory sequences from zebrafish and mouse. Results: The CmURE2 sequence shows a high percentage of identity with its mouse and zebrafish counterparts but is overall more similar to mouse URE2 (MmURE2) than to zebrafish URE2 (DrURE2). In transgenic zebrafish and mouse embryos, CmURE2 displayed enhancer activity in the forebrain that overlapped with that of DrURE2 and MmURE2. However, we detected notable differences in the activity of the three sequences in the diencephalon. Outside of the forebrain, CmURE2 shows enhancer activity in areas such as the pharyngeal arches and dorsal root ganglia where its' counterparts are also active. Conclusions: Our transgenic assays show that part of the URE2 enhancer activity is conserved throughout jawed vertebrates but also that new characteristics have evolved in the different groups. Our study demonstrates that the elephant shark is a useful outgroup to study the evolution of regulatory mechanisms in vertebrates and to address how changes in the sequence of cis -regulatory elements translate into changes in their regulatory activity

Expanded Vandermonde powers and sum rules for the two-dimensional one-component plasma

The two-dimensional one-component plasma (2dOCP) is a system of $N$ mobile particles of the same charge $q$ on a surface with a neutralising background. The Boltzmann factor of the 2dOCP at temperature $T$ can be expressed as a Vandermonde determinant to the power $\Gamma=q^{2}/(k_B T)$. Recent advances in the theory of symmetric and anti-symmetric Jack polymonials provide an efficient way to expand this power of the Vandermonde in their monomial basis, allowing the computation of several thermodynamic and structural properties of the 2dOCP for $N$ values up to 14 and $\Gamma$ equal to 4, 6 and 8. In this work, we explore two applications of this formalism to study the moments of the pair correlation function of the 2dOCP on a sphere, and the distribution of radial linear statistics of the 2dOCP in the plane

Ac Stark Effects and Harmonic Generation in Periodic Potentials

The ac Stark effect can shift initially nonresonant minibands in semiconductor superlattices into multiphoton resonances. This effect can result in strongly enhanced generation of a particular desired harmonic of the driving laser frequency, at isolated values of the amplitude.Comment: RevTeX, 10 pages (4 figures available on request), Preprint UCSBTH-93-2