Effective equidistribution and the Sato-Tate law for families of elliptic curves

Extending recent work of others, we provide effective bounds on the family of all elliptic curves and one-parameter families of elliptic curves modulo p (for p prime tending to infinity) obeying the Sato-Tate Law. We present two methods of proof. Both use the framework of Murty-Sinha; the first involves only knowledge of the moments of the Fourier coefficients of the L-functions and combinatorics, and saves a logarithm, while the second requires a Sato-Tate law. Our purpose is to illustrate how the caliber of the result depends on the error terms of the inputs and what combinatorics must be done.Comment: Version 1.1, 24 pages: corrected the interpretation of Birch's moment calculations, added to the literature review of previous results

Genomic analysis of heat-shock factor targets in Drosophila.

We have used a chromatin immunoprecipitation-microarray (ChIP-array) approach to investigate the in vivo targets of heat-shock factor (Hsf) in Drosophila embryos. We show that this method identifies Hsf target sites with high fidelity and resolution. Using cDNA arrays in a genomic search for Hsf targets, we identified 141 genes with highly significant ChIP enrichment. This study firmly establishes the potential of ChIP-array for whole-genome transcription factor target mapping in vivo using intact whole organisms.RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are

Astrophysical implications of hypothetical stable TeV-scale black holes

We analyze macroscopic effects of TeV-scale black holes, such as could possibly be produced at the LHC, in what is regarded as an extremely hypothetical scenario in which they are stable and, if trapped inside Earth, begin to accrete matter. We examine a wide variety of TeV-scale gravity scenarios, basing the resulting accretion models on first-principles, basic, and well-tested physical laws. These scenarios fall into two classes, depending on whether accretion could have any macroscopic effect on the Earth at times shorter than the Sun's natural lifetime. We argue that cases with such effect at shorter times than the solar lifetime are ruled out, since in these scenarios black holes produced by cosmic rays impinging on much denser white dwarfs and neutron stars would then catalyze their decay on timescales incompatible with their known lifetimes. We also comment on relevant lifetimes for astronomical objects that capture primordial black holes. In short, this study finds no basis for concerns that TeV-scale black holes from the LHC could pose a risk to Earth on time scales shorter than the Earth's natural lifetime. Indeed, conservative arguments based on detailed calculations and the best-available scientific knowledge, including solid astronomical data, conclude, from multiple perspectives, that there is no risk of any significance whatsoever from such black holes.Comment: Version2: Minor corrections/fixed typos; updated reference

Towards an 'average' version of the Birch and Swinnerton-Dyer Conjecture

The Birch and Swinnerton-Dyer conjecture states that the rank of the Mordell-Weil group of an elliptic curve E equals the order of vanishing at the central point of the associated L-function L(s,E). Previous investigations have focused on bounding how far we must go above the central point to be assured of finding a zero, bounding the rank of a fixed curve or on bounding the average rank in a family. Mestre showed the first zero occurs by O(1/loglog(N_E)), where N_E is the conductor of E, though we expect the correct scale to study the zeros near the central point is the significantly smaller 1/log(N_E). We significantly improve on Mestre's result by averaging over a one-parameter family of elliptic curves, obtaining non-trivial upper and lower bounds for the average number of normalized zeros in intervals on the order of 1/log(N_E) (which is the expected scale). Our results may be interpreted as providing further evidence in support of the Birch and Swinnerton-Dyer conjecture, as well as the Katz-Sarnak density conjecture from random matrix theory (as the number of zeros predicted by random matrix theory lies between our upper and lower bounds). These methods may be applied to additional families of L-functions.Comment: 20 pages, 2 figures, revised first draft (fixed some typos

Genomic mapping of Suppressor of Hairy-wing binding sites in Drosophila.

BACKGROUND: Insulator elements are proposed to play a key role in the organization of the regulatory architecture of the genome. In Drosophila, one of the best studied is the gypsy retrotransposon insulator, which is bound by the Suppressor of Hairy-wing (Su [Hw]) transcriptional regulator. Immunolocalization studies suggest that there are several hundred Su(Hw) sites in the genome, but few of these endogenous Su(Hw) binding sites have been identified. RESULTS: We used chromatin immunopurification with genomic microarray analysis to identify in vivo Su(Hw) binding sites across the 3 megabase Adh region. We find 60 sites, and these enabled the construction of a robust new Su(Hw) binding site consensus. In contrast to the gypsy insulator, which contains tightly clustered Su(Hw) binding sites, endogenous sites generally occur as isolated sites. These endogenous sites have three key features. In contrast to most analyses of DNA-binding protein specificity, we find that strong matches to the binding consensus are good predictors of binding site occupancy. Examination of occupancy in different tissues and developmental stages reveals that most Su(Hw) sites, if not all, are constitutively occupied, and these isolated Su(Hw) sites are generally highly conserved. Analysis of transcript levels in su(Hw) mutants indicate widespread and general changes in gene expression. Importantly, the vast majority of genes with altered expression are not associated with clustering of Su(Hw) binding sites, emphasizing the functional relevance of isolated sites. CONCLUSION: Taken together, our in vivo binding and gene expression data support a role for the Su(Hw) protein in maintaining a constant genomic architecture

The representation of the West-African Monsoon vertical cloud structure in the Met Office Unified Model: an evaluation with CloudSat

Weather and climate model simulations of the West African Monsoon (WAM) have generally poor representation of the rainfall distribution and monsoon circulation because key processes, such as clouds and convection, are poorly characterized. The vertical distribution of cloud and precipitation during the WAM are evaluated in Met Office Unified Model simulations against CloudSat observations. Simulations were run at 40-km and 12-km horizontal grid length using a convection parameterization scheme and at 12-km, 4-km, and 1.5-km grid length with the convection scheme effectively switched off, to study the impact of model resolution and convection parameterization scheme on the organisation of tropical convection. Radar reflectivity is forward-modelled from the model cloud fields using the CloudSat simulator to present a like-with-like comparison with the CloudSat radar observations. The representation of cloud and precipitation at 12-km horizontal grid length improves dramatically when the convection parameterization is switched off, primarily because of a reduction in daytime (moist) convection. Further improvement is obtained when reducing model grid length to 4 km or 1.5 km, especially in the representation of thin anvil and mid-level cloud, but three issues remain in all model configurations. Firstly, all simulations underestimate the fraction of anvils with cloud top height above 12 km, which can be attributed to too low ice water contents in the model compared to satellite retrievals. Secondly, the model consistently detrains mid-level cloud too close to the freezing level, compared to higher altitudes in CloudSat observations. Finally, there is too much low-level cloud cover in all simulations and this bias was not improved when adjusting the rainfall parameters in the microphysics scheme. To improve model simulations of the WAM, more detailed and in-situ observations of the dynamics and microphysics targeting these non-precipitating cloud types are required

Evaluation of multi-season convection permitting atmosphere - mixed layer ocean simulations of the Maritime Continent

A multi-season convection permitting regional climate simulation of the Maritime Continent using the Met Office Unified Model with 2.2-km grid spacing is presented and evaluated. The simulations pioneer the use of atmosphere-ocean coupling with the multi-column K profile parametrisation (KPP) mixed layer ocean model in atmospheric convection permitting climate simulations. Comparisons are made against a convection parametrised simulation in which it is nested, and which in turn derives boundary conditions from ERA5 reanalysis. This paper describes the configuration, performance of the mean state and variability of the two simulations compared against observational datasets. The models both have minor sea surface temperature (SST) and wet precipitation biases. The diurnal cycle, representation of equatorial waves and relationship between SST and precipitation are all improved in the convection permitting model compared to the convection parametrised model. The MJO is present in both models with a faster than observed propagation speed. However, it is unclear whether fidelity of the MJO simulation is inherent to the model or whether it predominantly arises from the forcing at the boundaries