Numerical instability of the Akhmediev breather and a finite-gap model of it

In this paper we study the numerical instabilities of the NLS Akhmediev breather, the simplest space periodic, one-mode perturbation of the unstable background, limiting our considerations to the simplest case of one unstable mode. In agreement with recent theoretical findings of the authors, in the situation in which the round-off errors are negligible with respect to the perturbations due to the discrete scheme used in the numerical experiments, the split-step Fourier method (SSFM), the numerical output is well-described by a suitable genus 2 finite-gap solution of NLS. This solution can be written in terms of different elementary functions in different time regions and, ultimately, it shows an exact recurrence of rogue waves described, at each appearance, by the Akhmediev breather. We discover a remarkable empirical formula connecting the recurrence time with the number of time steps used in the SSFM and, via our recent theoretical findings, we establish that the SSFM opens up a vertical unstable gap whose length can be computed with high accuracy, and is proportional to the inverse of the square of the number of time steps used in the SSFM. This neat picture essentially changes when the round-off error is sufficiently large. Indeed experiments in standard double precision show serious instabilities in both the periods and phases of the recurrence. In contrast with it, as predicted by the theory, replacing the exact Akhmediev Cauchy datum by its first harmonic approximation, we only slightly modify the numerical output. Let us also remark, that the first rogue wave appearance is completely stable in all experiments and is in perfect agreement with the Akhmediev formula and with the theoretical prediction in terms of the Cauchy data.Comment: 27 pages, 8 figures, Formula (30) at page 11 was corrected, arXiv admin note: text overlap with arXiv:1707.0565

Ratio of the Isolated Photon Cross Sections at \sqrt{s} = 630 and 1800 GeV

The inclusive cross section for production of isolated photons has been measured in \pbarp collisions at $\sqrt{s} = 630$ GeV with the \D0 detector at the Fermilab Tevatron Collider. The photons span a transverse energy ($E_T$) range from 7-49 GeV and have pseudorapidity $|\eta| < 2.5$. This measurement is combined with to previous \D0 result at $\sqrt{s} = 1800$ GeV to form a ratio of the cross sections. Comparison of next-to-leading order QCD with the measured cross section at 630 GeV and ratio of cross sections show satisfactory agreement in most of the $E_T$ range.Comment: 7 pages. Published in Phys. Rev. Lett. 87, 251805, (2001

Performance of long modules of silicon mcrostrip detectors

This note describes the performance of modules assembled with up to 12 silicon microstrip detectors. These modules were built for the instrumented Silicon Target (STAR) that has been installed in the NOMAD spectrometer. Laboratory and test beam results are compared with model predictions. For a module of nine detectors, test beam results indicate a signal-to-noise ratio of 19, a hit finding efficiency of 99.8% and a spatial resolution of 6.0 μm. Laboratory measurements indicate that modules of twelve detectors exhibit a signal-to-noise ratio of the order of 16

Performance of the CMS Cathode Strip Chambers with Cosmic Rays

The Cathode Strip Chambers (CSCs) constitute the primary muon tracking device in the CMS endcaps. Their performance has been evaluated using data taken during a cosmic ray run in fall 2008. Measured noise levels are low, with the number of noisy channels well below 1%. Coordinate resolution was measured for all types of chambers, and fall in the range 47 microns to 243 microns. The efficiencies for local charged track triggers, for hit and for segments reconstruction were measured, and are above 99%. The timing resolution per layer is approximately 5 ns

Wave instabilities in the presence of non vanishing background in nonlinear Schrodinger systems

We investigate wave collapse ruled by the generalized nonlinear Schroedinger (NLS) equation in 1+1 dimensions, for localized excitations with non-zero background, establishing through virial identities a new criterion for blow-up. When collapse is arrested, a semiclassical approach allows us to show that the system can favor the formation of dispersive shock waves. The general findings are illustrated with a model of interest to both classical and quantum physics (cubic-quintic NLS equation), demonstrating a radically novel scenario of instability, where solitons identify a marginal condition between blow-up and occurrence of shock waves, triggered by arbitrarily small mass perturbations of different sign

Bias correction and Bayesian analysis of aggregate counts in SAGE libraries

<p>Abstract</p> <p>Background</p> <p>Tag-based techniques, such as SAGE, are commonly used to sample the mRNA pool of an organism's transcriptome. Incomplete digestion during the tag formation process may allow for multiple tags to be generated from a given mRNA transcript. The probability of forming a tag varies with its relative location. As a result, the observed tag counts represent a biased sample of the actual transcript pool. In SAGE this bias can be avoided by ignoring all but the 3' most tag but will discard a large fraction of the observed data. Taking this bias into account should allow more of the available data to be used leading to increased statistical power.</p> <p>Results</p> <p>Three new hierarchical models, which directly embed a model for the variation in tag formation probability, are proposed and their associated Bayesian inference algorithms are developed. These models may be applied to libraries at both the tag and aggregate level. Simulation experiments and analysis of real data are used to contrast the accuracy of the various methods. The consequences of tag formation bias are discussed in the context of testing differential expression. A description is given as to how these algorithms can be applied in that context.</p> <p>Conclusions</p> <p>Several Bayesian inference algorithms that account for tag formation effects are compared with the DPB algorithm providing clear evidence of superior performance. The accuracy of inferences when using a particular non-informative prior is found to depend on the expression level of a given gene. The multivariate nature of the approach easily allows both univariate and joint tests of differential expression. Calculations demonstrate the potential for false positive and negative findings due to variation in tag formation probabilities across samples when testing for differential expression.</p

Observation of Kuznetsov-Ma soliton dynamics in optical fibre

The nonlinear Schrödinger equation (NLSE) is a central model of nonlinear science, applying to hydrodynamics, plasma physics, molecular biology and optics. The NLSE admits only few elementary analytic solutions, but one in particular describing a localized soliton on a finite background is of intense current interest in the context of understanding the physics of extreme waves. However, although the first solution of this type was the Kuznetzov-Ma (KM) soliton derived in 1977, there have in fact been no quantitative experiments confirming its validity. We report here novel experiments in optical fibre that confirm the KM soliton theory, completing an important series of experiments that have now observed a complete family of soliton on background solutions to the NLSE. Our results also show that KM dynamics appear more universally than for the specific conditions originally considered, and can be interpreted as an analytic description of Fermi-Pasta-Ulam recurrence in NLSE propagation

Modeling SAGE tag formation and its effects on data interpretation within a Bayesian framework

<p>Abstract</p> <p>Background</p> <p>Serial Analysis of Gene Expression (SAGE) is a high-throughput method for inferring mRNA expression levels from the experimentally generated sequence based tags. Standard analyses of SAGE data, however, ignore the fact that the probability of generating an observable tag varies across genes and between experiments. As a consequence, these analyses result in biased estimators and posterior probability intervals for gene expression levels in the transcriptome.</p> <p>Results</p> <p>Using the yeast <it>Saccharomyces cerevisiae </it>as an example, we introduce a new Bayesian method of data analysis which is based on a model of SAGE tag formation. Our approach incorporates the variation in the probability of tag formation into the interpretation of SAGE data and allows us to derive exact joint and approximate marginal posterior distributions for the mRNA frequency of genes detectable using SAGE. Our analysis of these distributions indicates that the frequency of a gene in the tag pool is influenced by its mRNA frequency, the cleavage efficiency of the anchoring enzyme (AE), and the number of informative and uninformative AE cleavage sites within its mRNA.</p> <p>Conclusion</p> <p>With a mechanistic, model based approach for SAGE data analysis, we find that inter-genic variation in SAGE tag formation is large. However, this variation can be estimated and, importantly, accounted for using the methods we develop here. As a result, SAGE based estimates of mRNA frequencies can be adjusted to remove the bias introduced by the SAGE tag formation process.</p

Search for a new gauge boson in pi(0) decays

A search was made for a new light gauge boson X which might be produced in pi(0) -->, gamma + X decay from neutral pions generated by 450 GeV protons in the CERN SPS neutrino target. The X's would penetrate the downstream shielding and be observed in the NOMAD detector via the Primakoff effect, in the process of X --> pi(0) conversion in the external Coulomb field of a nucleus. With 1.45 x 10(18) protons on target, 20 candidate events with energy between 8 and 140 GeV were found from the analysis of neutrino data. This number is in agreement with the expectation of 18.1 +/- 2.8 background events from standard neutrino processes. A new 90% C.L. upper limit on the branching ratio Br(pi(0) --> Y + X)< (3.3 to 1.9)X 10(-5) for X masses ranging from 0 to 120 MeV/c(2) is obtained

Search for New Physics Using Quaero: A General Interface to - D0 Event Data

We describe Quaero, a method that i) enables the automatic optimization of searches for physics beyond the standard model, and ii) provides a mechanism for making high energy collider data generally available. We apply Quaero to searches for standard model WW, ZZ, and ttbar production, and to searches for these objects produced through a new heavy resonance. Through this interface, we make three data sets collected by the D0 experiment at sqrt(s)=1.8 TeV publicly available