The Saito-Kurokawa lifting and Darmon points

Let E_{/_\Q} be an elliptic curve of conductor $Np$ with $p\nmid N$ and let $f$ be its associated newform of weight 2. Denote by $f_\infty$ the $p$-adic Hida family passing though $f$, and by $F_\infty$ its $\Lambda$-adic Saito-Kurokawa lift. The $p$-adic family $F_\infty$ of Siegel modular forms admits a formal Fourier expansion, from which we can define a family of normalized Fourier coefficients $\{\widetilde A_T(k)\}_T$ indexed by positive definite symmetric half-integral matrices $T$ of size $2\times 2$. We relate explicitly certain global points on $E$ (coming from the theory of Stark-Heegner points) with the values of these Fourier coefficients and of their $p$-adic derivatives, evaluated at weight $k=2$.Comment: 14 pages. Title change

Minimally-destructive detection of magnetically-trapped atoms using frequency-synthesised light

We present a technique for atomic density measurements by the off-resonant phase-shift induced on a two-frequency, coherently-synthesised light beam. We have used this scheme to measure the column density of a magnetically trapped atom cloud and to monitor oscillations of the cloud in real time by making over a hundred non-destructive local density measurments. For measurements using pulses of 10,000-100,000 photons lasting ~10 microsecond, the precision is limited by statistics of the photons and the photodiode avalanche. We explore the relationship between measurement precision and the unwanted loss of atoms from the trap and introduce a figure of merit that characterises it. This method can be used to probe the density of a BEC with minimal disturbance of its phase.Comment: Submitted to New Journal of Physic

Modular differential equations for characters of RCFT

We discuss methods, based on the theory of vector-valued modular forms, to determine all modular differential equations satisfied by the conformal characters of RCFT; these modular equations are related to the null vector relations of the operator algebra. Besides describing effective algorithmic procedures, we illustrate our methods on an explicit example.Comment: 13 page

Neighbor Detection Induces Organ-Specific Transcriptomes, Revealing Patterns Underlying Hypocotyl-Specific Growth.

In response to neighbor proximity, plants increase the growth of specific organs (e.g., hypocotyls) to enhance access to sunlight. Shade enhances the activity of Phytochrome Interacting Factors (PIFs) by releasing these bHLH transcription factors from phytochrome B-mediated inhibition. PIFs promote elongation by inducing auxin production in cotyledons. In order to elucidate spatiotemporal aspects of the neighbor proximity response, we separately analyzed gene expression patterns in the major light-sensing organ (cotyledons) and in rapidly elongating hypocotyls of Arabidopsis thaliana PIFs initiate transcriptional reprogramming in both organs within 15 min, comprising regulated expression of several early auxin response genes. This suggests that hypocotyl growth is elicited by both local and distal auxin signals. We show that cotyledon-derived auxin is both necessary and sufficient to initiate hypocotyl growth, but we also provide evidence for the functional importance of the local PIF-induced response. With time, the transcriptional response diverges increasingly between organs. We identify genes whose differential expression may underlie organ-specific elongation. Finally, we uncover a growth promotion gene expression signature shared between different developmentally regulated growth processes and responses to the environment in different organs

Experiments on a videotape atom chip: fragmentation and transport studies

This paper reports on experiments with ultra-cold rubidium atoms confined in microscopic magnetic traps created using a piece of periodically-magnetized videotape mounted on an atom chip. The roughness of the confining potential is studied with atomic clouds at temperatures of a few microKelvin and at distances between 30 and 80 microns from the videotape-chip surface. The inhomogeneities in the magnetic field created by the magnetized videotape close to the central region of the chip are characterized in this way. In addition, we demonstrate a novel transport mechanism whereby we convey cold atoms confined in arrays of videotape magnetic micro-traps over distances as large as ~ 1 cm parallel to the chip surface. This conveying mechanism enables us to survey the surface of the chip and observe potential-roughness effects across different regions.Comment: 29 pages, 22 figures

An integrated atom-photon junction

Photonic chips that integrate guides, switches, gratings and other components, process vast amounts of information rapidly on a single device. A new branch of this technology becomes possible if the light is coupled to cold atoms in a junction of small enough cross section, so that small numbers of photons interact appreciably with the atoms. Cold atoms are among the most sensitive of metrological tools and their quantum nature also provides a basis for new information processing methods. Here we demonstrate a photonic chip which provides multiple microscopic junctions between atoms and photons. We use the absorption of light at a junction to reveal the presence of one atom on average. Conversely, we use the atoms to probe the intensity and polarisation of the light. Our device paves the way for a new type of chip with interconnected circuits of atoms and photons.Comment: 5 pages, 4 figure. Submitted to Nature Photonic

A single atom detector integrated on an atom chip: fabrication, characterization and application

We describe a robust and reliable fluorescence detector for single atoms that is fully integrated into an atom chip. The detector allows spectrally and spatially selective detection of atoms, reaching a single atom detection efficiency of 66%. It consists of a tapered lensed single-mode fiber for precise delivery of excitation light and a multi-mode fiber to collect the fluorescence. The fibers are mounted in lithographically defined holding structures on the atom chip. Neutral 87Rb atoms propagating freely in a magnetic guide are detected and the noise of their fluorescence emission is analyzed. The variance of the photon distribution allows to determine the number of detected photons / atom and from there the atom detection efficiency. The second order intensity correlation function of the fluorescence shows near-perfect photon anti-bunching and signs of damped Rabi-oscillations. With simple improvements one can boost the detection efficiency to > 95%.Comment: 24 pages, 11 figure

Averages of Fourier coefficients of Siegel modular forms and representation of binary quadratic forms by quadratic forms in four variables

Let $-d$ be a a negative discriminant and let $T$ vary over a set of representatives of the integral equivalence classes of integral binary quadratic forms of discriminant $-d$. We prove an asymptotic formula for $d \to \infty$ for the average over $T$ of the number of representations of $T$ by an integral positive definite quaternary quadratic form and obtain results on averages of Fourier coefficients of linear combinations of Siegel theta series. We also find an asymptotic bound from below on the number of binary forms of fixed discriminant $-d$ which are represented by a given quaternary form. In particular, we can show that for growing $d$ a positive proportion of the binary quadratic forms of discriminant $-d$ is represented by the given quaternary quadratic form.Comment: v5: Some typos correcte

The long-term treatment of restless legs syndrome/Willis–Ekbom disease: evidence-based guidelines and clinical consensus best practice guidance: a report from the International Restless Legs Syndrome Study Group

AbstractA Task Force was established by the International Restless Legs Syndrome Study Group (IRLSSG) to develop evidence-based and consensus-based recommendations for the long-term pharmacologic treatment of restless legs syndrome/Willis–Ekbom disease (RLS/WED). The Task Force reviewed the results of all studies of RLS/WED treatments with durations of 6months or longer presented at meetings over the past 2years, posted on Web sites of pharmaceutical companies, or published in peer-reviewed journals, asking the questions, “What is the efficacy of this treatment in patients with RLS/WED?” and “What is the safety of this treatment in patients with RLS/WED?”The Task Force developed guidelines based on their review of 61 papers meeting inclusion criteria, and using a modified evidence-grading scheme. Pregabalin has been established as effective for up to 1year in treating RLS/WED (Level A evidence). Pramipexole, ropinirole, and rotigotine have been established as effective for up to 6months in treating RLS/WED (Level A). The following drugs have been established as probably effective (Level B) in treating RLS/WED for durations ranging from 1 to 5years: gabapentin enacarbil, pramipexole, and ropinirole (1year); levodopa (2years); and rotigotine (5years). Because of associated safety concerns, pergolide and cabergoline should not be used in the treatment of RLS/WED unless the benefits clearly outweigh the risks. Other pharmacologic therapies have insufficient evidence to support their long-term use in treating RLS/WED.The IRLSSG Task Force also developed consensus-based strategies for the prevention and treatment of complications (such as augmentation, loss of efficacy, excessive daytime sleepiness, and impulse control disorders) that may develop with the long-term pharmacologic treatment of RLS/WED. The use of either a dopamine-receptor agonist or α2δ calcium-channel ligand is recommended as the first-line treatment of RLS/WED for most patients, with the choice of agent dependent on the patient’s severity of RLS/WED symptoms, cognitive status, history, and comorbid conditions