Linear recurrences and asymptotic behavior of exponential sums of symmetric boolean functions

In this paper we give an improvement of the degree of the homogeneous linear recurrence with integer coefficients that exponential sums of symmetric Boolean functions satisfy. This improvement is tight. We also compute the asymptotic behavior of symmetric Boolean functions and provide a formula that allows us to determine if a symmetric boolean function is asymptotically not balanced. In particular, when the degree of the symmetric function is a power of two, then the exponential sum is much smaller than $2^n$.Comment: 18 pages, 3 figure

Strategies for prompt searches for GRB afterglows: the discovery of the GRB 001011 optical/near-infrared counterpart using colour-colour selection

We report the discovery of the optical and near-infrared counterparts to GRB 001011. The GRB 001011 error box determined by Beppo-SAX was simultaneously imaged in the near-infrared by the 3.58-m New Technology Telescope and in the optical by the 1.54-m Danish Telescope ~8 hr after the gamma-ray event. Here we implement the colour-colour discrimination technique proposed by Rhoads (2001) and extend it using near-IR data as well. We present the results provided by an automatic colour-colour discrimination pipe-line developed to discern the different populations of objects present in the GRB 001011 error box. Our software revealed three candidates based on single-epoch images. Second-epoch observations carried out ~3.2 days after the burst revealed that the most likely candidate had faded, thus identifying it with the counterpart to the GRB. In deep R-band images obtained 7 months after the burst a faint (R=25.38+/-0.25) elongated object, presumably the host galaxy of GRB 001011, was detected at the position of the afterglow. The GRB 001011 afterglow is the first discovered with the assistance of colour-colour diagram techniques. We discuss the advantages of using this method and its application to error boxes determined by future missions.Comment: Accepted for publication in Astronomy and Astrophysics, 13 pages, 16 figure

Genes for de novo biosynthesis of omega-3 polyunsaturated fatty acids are widespread in animals

Marine ecosystems are responsible for virtually all production of omega-3 (ω3) long-chain polyunsaturated fatty acids (PUFA), which are essential nutrients for vertebrates. Current consensus is that marine microbes account for this production, given their possession of key enzymes including methyl-end (or "ωx") desaturases. ωx desaturases have also been described in a small number of invertebrate animals, but their precise distribution has not been systematically explored. This study identifies 121 ωx desaturase sequences from 80 species within the Cnidaria, Rotifera, Mollusca, Annelida, and Arthropoda. Horizontal gene transfer has contributed to this hitherto unknown widespread distribution. Functional characterization of animal ωx desaturases provides evidence that multiple invertebrates have the ability to produce ω3 PUFA de novo and further biosynthesize ω3 long-chain PUFA. This finding represents a fundamental revision in our understanding of ω3 long-chain PUFA production in global food webs, by revealing that numerous widespread and abundant invertebrates have the endogenous capacity to make significant contributions beyond that coming from marine microbes. Copyright © 2018 The Authors, some rights reserved.Acknowledgments: We thank A. Magurran and J. Napier for comments on the manuscript and R. Ruivo for drawings in Figs. 1 and 3. Funding: This work received funding from the MASTS pooling initiative (The Marine Alliance for Science and Technology for Scotland) funded by the Scottish Funding Council (grant reference HR09011), and their support is gratefully acknowledged. Access to the Institute of Aquaculture laboratories was funded by the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement no. 262336 (AQUAEXCEL), Transnational Access Project Number 0095/06/03/13

Measurements of branching fraction ratios and CP-asymmetries in suppressed B^- -> D(-> K^+ pi^-)K^- and B^- -> D(-> K^+ pi^-)pi^- decays

We report the first reconstruction in hadron collisions of the suppressed decays B^- -> D(-> K^+ pi^-)K^- and B^- -> D(-> K^+ pi^-)pi^-, sensitive to the CKM phase gamma, using data from 7 fb^-1 of integrated luminosity collected by the CDF II detector at the Tevatron collider. We reconstruct a signal for the B^- -> D(-> K^+ pi^-)K^- suppressed mode with a significance of 3.2 standard deviations, and measure the ratios of the suppressed to favored branching fractions R(K) = [22.0 \pm 8.6(stat)\pm 2.6(syst)]\times 10^-3, R^+(K) = [42.6\pm 13.7(stat)\pm 2.8(syst)]\times 10^-3, R^-(K)= [3.8\pm 10.3(stat)\pm 2.7(syst]\times 10^-3, as well as the direct CP-violating asymmetry A(K) = -0.82\pm 0.44(stat)\pm 0.09(syst) of this mode. Corresponding quantities for B^- -> D(-> K^+ pi^-)pi^- decay are also reported.Comment: 8 pages, 1 figure, accepted by Phys.Rev.D Rapid Communications for Publicatio

Search for the standard model Higgs boson in the H to ZZ to 2l 2nu channel in pp collisions at sqrt(s) = 7 TeV

A search for the standard model Higgs boson in the H to ZZ to 2l 2nu decay channel, where l = e or mu, in pp collisions at a center-of-mass energy of 7 TeV is presented. The data were collected at the LHC, with the CMS detector, and correspond to an integrated luminosity of 4.6 inverse femtobarns. No significant excess is observed above the background expectation, and upper limits are set on the Higgs boson production cross section. The presence of the standard model Higgs boson with a mass in the 270-440 GeV range is excluded at 95% confidence level.Comment: Submitted to JHE

Constraints on the χ_(c1) versus χ_(c2) polarizations in proton-proton collisions at √s = 8 TeV

The polarizations of promptly produced χ_(c1) and χ_(c2) mesons are studied using data collected by the CMS experiment at the LHC, in proton-proton collisions at √s=8  TeV. The χ_c states are reconstructed via their radiative decays χ_c → J/ψγ, with the photons being measured through conversions to e⁺e⁻, which allows the two states to be well resolved. The polarizations are measured in the helicity frame, through the analysis of the χ_(c2) to χ_(c1) yield ratio as a function of the polar or azimuthal angle of the positive muon emitted in the J/ψ → μ⁺μ⁻ decay, in three bins of J/ψ transverse momentum. While no differences are seen between the two states in terms of azimuthal decay angle distributions, they are observed to have significantly different polar anisotropies. The measurement favors a scenario where at least one of the two states is strongly polarized along the helicity quantization axis, in agreement with nonrelativistic quantum chromodynamics predictions. This is the first measurement of significantly polarized quarkonia produced at high transverse momentum