The fundamental gap of simplices

The fundamental gap conjecture was recently proven by Andrews and Clutterbuck: for any convex domain in $\R^n$ normalized to have unit diameter, the difference between the first two Dirichlet eigenvalues of the Laplacian is bounded below by that of the interval. In this work, we focus on the moduli spaces of simplices in all dimensions, and later specialize to the moduli space of Euclidean triangles. Our first theorem is a compactness result for the gap function on the moduli space of simplices in any dimension. Our second main result verifies a recent conjecture of Antunes-Freitas: for any Euclidean triangle normalized to have unit diameter, the fundamental gap is uniquely minimized by the equilateral triangle.Comment: Final version, Journal ref adde

Salerno's model of DNA reanalysed: could solitons have biological significance?

We investigate the sequence-dependent behaviour of localised excitations in a toy, nonlinear model of DNA base-pair opening originally proposed by Salerno. Specifically we ask whether ``breather'' solitons could play a role in the facilitated location of promoters by RNA polymerase. In an effective potential formalism, we find excellent correlation between potential minima and {\em Escherichia coli} promoter recognition sites in the T7 bacteriophage genome. Evidence for a similar relationship between phage promoters and downstream coding regions is found and alternative reasons for links between AT richness and transcriptionally-significant sites are discussed. Consideration of the soliton energy of translocation provides a novel dynamical picture of sliding: steep potential gradients correspond to deterministic motion, while ``flat'' regions, corresponding to homogeneous AT or GC content, are governed by random, thermal motion. Finally we demonstrate an interesting equivalence between planar, breather solitons and the helical motion of a sliding protein ``particle'' about a bent DNA axis.Comment: Latex file 20 pages, 5 figures. Manuscript of paper to appear in J. Biol. Phys., accepted 02/09/0

Subduction controls of Hf and Nd isotopes in lavas of the Aleutian island arc

The Hf and Nd isotopic compositions of 71 Quaternary lavas collected from locations along the full length of the Aleutian island arc are used to constrain the sources of Aleutian magmas and to provide insight into the geochemical behavior of Nd and Hf and related elements in the Aleutian subduction-magmatic system. Isotopic compositions of Aleutian lavas fall approximately at the center of, and form a trend parallel to, the terrestrial Hf-Nd isotopic array with {var_epsilon}{sub Hf} of +12.0 to +15.5 and {var_epsilon}{sub Nd} of +6.5 to +10.5. Basalts, andesites, and dacites within volcanic centers or in nearby volcanoes generally all have similar isotopic compositions, indicating that there is little measurable effect of crustal or other lithospheric assimilation within the volcanic plumbing systems of Aleutian volcanoes. Hafnium isotopic compositions have a clear pattern of along-arc increase that is continuous from the eastern-most locations near Cold Bay to Piip Seamount in the western-most part of the arc. This pattern is interpreted to reflect a westward decrease in the subducted sediment component present in Aleutian lavas, reflecting progressively lower rates of subduction westward as well as decreasing availability of trench sediment. Binary bulk mixing models (sediment + peridotite) demonstrate that 1-2% of the Hf in Aleutian lavas is derived from subducted sediment, indicating that Hf is mobilized out of the subducted sediment with an efficiency that is similar to that of Sr, Pb and Nd. Low published solubility for Hf and Nd in aqueous subduction fluids lead us to conclude that these elements are mobilized out of the subducted component and transferred to the mantle wedge as bulk sediment or as a silicate melt. Neodymium isotopes also generally increase from east to west, but the pattern is absent in the eastern third of the arc, where the sediment flux is high and increases from east to west, due to the presence of abundant terrigenous sediment in the trench east of the Amlia Fracture Zone, which is being subducting beneath the arc at Seguam Island. Mixing trends between mantle wedge and sediment end members become flatter in Hf-Nd isotope space at locations further west along the arc, indicating that the sediment end member in the west has either higher Nd/Hf or is more radiogenic in Hf compared to Nd. This pattern is interpreted to reflect an increase in pelagic clay relative to the terrigenous subducted sedimentary component westward along the arc. Results of this study imply that Hf does not behave as a conservative element in the Aleutian subduction system, as has been proposed for some other arcs

Water use and grain yield response of rainfed soybean to tillage-mulch practices in southeastern Nigeria

Despite the agronomic, economic and food values of soybean (Glycine max L. Merrill), there is still dearth of information on the tillage need and the implications of surface mulch for the crop in the eastern part of the forest-savanna transition zone of Nigeria. This study was therefore carried out on a sandy loam Ultisol at Nsukka with a sub-humid climate, during 2006 and 2007 cropping seasons. Our objective was to devise an appropriate tillage method for the crop from evaluated effects of no-till (NT), conventional tillage (CT) and mulch on selected key agronomic indices. Each of the NT and the CT was either unmulched (U) or mulched (M) in a split-plot, giving four treatments/tillage methods (NTU, NTM, CTU and CTM) randomized in four blocks. Rainfall was more favorable in the first than in the second season. The mean seasonal soil water storage (range, 99-109 mm) within 0.5-m soil layer differed among the treatments (NTU < CTU < NTM = CTM). However, for the first and second seasons, both water use (582-616 and 667-709 mm respectively) and grain yield (0.71-0.81 and 1.22-1.91 Mg ha-1 respectively) were not different. Mulch lowered the crop water use but had no influence on grain yield. Water use efficiency was enhanced with mulch only in the second season. Although either of the two mulch treatments (NTM/CTM) would be suitable for growing soybean especially in years of unfavorably distributed rainfall, NTM is a more rational choice than CTM. Rainfall adequacy at the critical reproductive stage of the crop showed to be a more important yield factor than the tested tillage methods

Bilarge Neutrino Mixing and \mu - \tau Permutation Symmetry for Two-loop Radiative Mechanism

The presence of approximate electron number conservation and \mu-\tau permutation symmetry of S_2 is shown to naturally provide bilarge neutrino mixing. First, the bimaximal neutrino mixing together with U_{e3}=0 is guaranteed to appear owing to S_2 and, then, the bilarge neutrino mixing together with |U_{e3}|<<1 arises as a result of tiny violation of S_2. The observed mass hierarchy of \Delta m^2_{\odot}<<\Delta m^2_{atm} is subject to another tiny violation of the electron number conservation. This scenario is realized in a specific model based on SU(3)_L x U(1)_N with two-loop radiative mechanism for neutrino masses. The radiative effects from heavy leptons contained in lepton triplets generate the bimaximal structure and those from charged leptons, which break S_2, generate the bilarge structure together with |U_{e3}|<<1. To suppress dangerous flavor-changing neutral current interactions due to Higgs exchanges especially for quarks, this S_2 symmetry is extended to a discrete Z_8 symmetry, which also ensures the absence of one-loop radiative mechanism.Comment: 18 pages, 7 figures, to appear in Phys. Rev.

STRIDER (Sildenafil TheRapy in dismal prognosis early onset fetal growth restriction): An international consortium of randomised placebo-controlled trials

Background: Severe, early-onset fetal growth restriction due to placental insufficiency is associated with a high risk of perinatal mortality and morbidity with long-lasting sequelae. Placental insufficiency is the result of abnormal formation and function of the placenta with inadequate remodelling of the maternal spiral arteries. There is currently no effective therapy available. Some evidence suggests sildenafil citrate may improve uteroplacental blood flow, fetal growth, and meaningful infant outcomes. The objective of the Sildenafil TheRapy In Dismal prognosis Early onset fetal growth Restriction (STRIDER) collaboration is to evaluate the effectiveness of sildenafil versus placebo in achieving healthy perinatal survival through the conduct of randomised clinical trials and systematic review including individual patient data meta-analysis.  Methods: Five national/bi-national multicentre randomised placebo-controlled trials have been launched. Women with a singleton pregnancy between 18 and 30 weeks with severe fetal growth restriction of likely placental origin, and where the likelihood of perinatal death/severe morbidity is estimated to be significant are included. Participants will receive either sildenafil 25 mg or matching placebo tablets orally three times daily from recruitment to 32 weeks gestation.  Discussion: The STRIDER trials were conceived and designed through international collaboration. Although the individual trials have different primary outcomes for reasons of sample size and feasibility, all trials will collect a standard set of outcomes including survival without severe neonatal morbidity at time of hospital discharge. This is a summary of all the STRIDER trial protocols and provides an example of a prospectively planned international clinical research collaboration. All five individual trials will contribute to a pre-planned systematic review of the topic including individual patient data meta-analysis

All-sky search for long-duration gravitational wave transients with initial LIGO

We present the results of a search for long-duration gravitational wave transients in two sets of data collected by the LIGO Hanford and LIGO Livingston detectors between November 5, 2005 and September 30, 2007, and July 7, 2009 and October 20, 2010, with a total observational time of 283.0 days and 132.9 days, respectively. The search targets gravitational wave transients of duration 10-500 s in a frequency band of 40-1000 Hz, with minimal assumptions about the signal waveform, polarization, source direction, or time of occurrence. All candidate triggers were consistent with the expected background; as a result we set 90% confidence upper limits on the rate of long-duration gravitational wave transients for different types of gravitational wave signals. For signals from black hole accretion disk instabilities, we set upper limits on the source rate density between 3.4×10-5 and 9.4×10-4 Mpc-3 yr-1 at 90% confidence. These are the first results from an all-sky search for unmodeled long-duration transient gravitational waves. © 2016 American Physical Society