3,589 research outputs found

    Stochastic Heisenberg limit: Optimal estimation of a fluctuating phase

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    The ultimate limits to estimating a fluctuating phase imposed on an optical beam can be found using the recently derived continuous quantum Cramer-Rao bound. For Gaussian stationary statistics, and a phase spectrum scaling asymptotically as 1/omega^p with p>1, the minimum mean-square error in any (single-time) phase estimate scales as N^{-2(p-1)/(p+1)}, where N is the photon flux. This gives the usual Heisenberg limit for a constant phase (as the limit p--> infinity) and provides a stochastic Heisenberg limit for fluctuating phases. For p=2 (Brownian motion), this limit can be attained by phase tracking.Comment: 5+4 pages, to appear in Physical Review Letter

    The quantum Bell-Ziv-Zakai bounds and Heisenberg limits for waveform estimation

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    We propose quantum versions of the Bell-Ziv-Zakai lower bounds on the error in multiparameter estimation. As an application we consider measurement of a time-varying optical phase signal with stationary Gaussian prior statistics and a power law spectrum 1/ωp\sim 1/|\omega|^p, with p>1p>1. With no other assumptions, we show that the mean-square error has a lower bound scaling as 1/N2(p1)/(p+1)1/{\cal N}^{2(p-1)/(p+1)}, where N{\cal N} is the time-averaged mean photon flux. Moreover, we show that this accuracy is achievable by sampling and interpolation, for any p>1p>1. This bound is thus a rigorous generalization of the Heisenberg limit, for measurement of a single unknown optical phase, to a stochastically varying optical phase.Comment: 18 pages, 6 figures, comments welcom

    Optimal Heisenberg-style bounds for the average performance of arbitrary phase estimates

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    The ultimate bound to the accuracy of phase estimates is often assumed to be given by the Heisenberg limit. Recent work seemed to indicate that this bound can be violated, yielding measurements with much higher accuracy than was previously expected. The Heisenberg limit can be restored as a rigorous bound to the accuracy provided one considers the accuracy averaged over the possible values of the unknown phase, as we have recently shown [Phys. Rev. A 85, 041802(R) (2012)]. Here we present an expanded proof of this result together with a number of additional results, including the proof of a previously conjectured stronger bound in the asymptotic limit. Other measures of the accuracy are examined, as well as other restrictions on the generator of the phase shifts. We provide expanded numerical results for the minimum error and asymptotic expansions. The significance of the results claiming violation of the Heisenberg limit is assessed, followed by a detailed discussion of the limitations of the Cramer-Rao bound.Comment: 22 pages, 4 figure

    An SVD-based comparison of nine whole eukaryotic genomes supports a coelomate rather than ecdysozoan lineage

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    BACKGROUND: Eukaryotic whole genome sequences are accumulating at an impressive rate. Effective methods for comparing multiple whole eukaryotic genomes on a large scale are needed. Most attempted solutions involve the production of large scale alignments, and many of these require a high stringency pre-screen for putative orthologs in order to reduce the effective size of the dataset and provide a reasonably high but unknown fraction of correctly aligned homologous sites for comparison. As an alternative, highly efficient methods that do not require the pre-alignment of operationally defined orthologs are also being explored. RESULTS: A non-alignment method based on the Singular Value Decomposition (SVD) was used to compare the predicted protein complement of nine whole eukaryotic genomes ranging from yeast to man. This analysis resulted in the simultaneous identification and definition of a large number of well conserved motifs and gene families, and produced a species tree supporting one of two conflicting hypotheses of metazoan relationships. CONCLUSIONS: Our SVD-based analysis of the entire protein complement of nine whole eukaryotic genomes suggests that highly conserved motifs and gene families can be identified and effectively compared in a single coherent definition space for the easy extraction of gene and species trees. While this occurs without the explicit definition of orthologs or homologous sites, the analysis can provide a basis for these definitions

    Discovering gene functional relationships using FAUN (Feature Annotation Using Nonnegative matrix factorization)

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    Background Searching the enormous amount of information available in biomedical literature to extract novel functional relationships among genes remains a challenge in the field of bioinformatics. While numerous (software) tools have been developed to extract and identify gene relationships from biological databases, few effectively deal with extracting new (or implied) gene relationships, a process which is useful in interpretation of discovery-oriented genome-wide experiments. Results In this study, we develop a Web-based bioinformatics software environment called FAUN or Feature Annotation Using Nonnegative matrix factorization (NMF) to facilitate both the discovery and classification of functional relationships among genes. Both the computational complexity and parameterization of NMF for processing gene sets are discussed. FAUN is tested on three manually constructed gene document collections. Its utility and performance as a knowledge discovery tool is demonstrated using a set of genes associated with Autism. Conclusions FAUN not only assists researchers to use biomedical literature efficiently, but also provides utilities for knowledge discovery. This Web-based software environment may be useful for the validation and analysis of functional associations in gene subsets identified by high-throughput experiments

    Lesson Plan Designs

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    [First paragraph] The principal must observe teachers to improve and evaluate effectiveness. Since instructional planning is one of the keys to good instruction, one component of improving teacher effectiveness is the lesson plan. This article provides two formats for lesson planning: a narrative approach and a skeleton approach. Although the ideas in this article may be used whenever written plans are required, not all written plans require elaborate detail

    Gene Tree Labeling Using Nonnegative Matrix Factorization on Biomedical Literature

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    Identifying functional groups of genes is a challenging problem for biological applications. Text mining approaches can be used to build hierarchical clusters or trees from the information in the biological literature. In particular, the nonnegative matrix factorization (NMF) is examined as one approach to label hierarchical trees. A generic labeling algorithm as well as an evaluation technique is proposed, and the effects of different NMF parameters with regard to convergence and labeling accuracy are discussed. The primary goals of this study are to provide a qualitative assessment of the NMF and its various parameters and initialization, to provide an automated way to classify biomedical data, and to provide a method for evaluating labeled data assuming a static input tree. As a byproduct, a method for generating gold standard trees is proposed

    Major features and forcing of high‐latitude northern hemisphere atmospheric circulation using a 110,000‐year‐long glaciochemical series

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    The Greenland Ice Sheet Project 2 glaciochemical series (sodium, potassium, ammonium, calcium, magnesium, sulfate, nitrate, and chloride) provides a unique view of the chemistry of the atmosphere and the history of atmospheric circulation over both the high latitudes and mid‐low latitudes of the northern hemisphere. Interpretation of this record reveals a diverse array of environmental signatures that include the documentation of anthropogenically derived pollutants, volcanic and biomass burning events, storminess over marine surfaces, continental aridity and biogenic source strength plus information related to the controls on both high‐ and low‐frequency climate events of the last 110,000 years. Climate forcings investigated include changes in insolation of the order of the major orbital cycles that control the long‐term behavior of atmospheric circulation patterns through changes in ice volume (sea level), events such as the Heinrich events (massive discharges of icebergs first identified in the marine record) that are found to operate on a 6100‐year cycle due largely to the lagged response of ice sheets to changes in insolation and consequent glacier dynamics, and rapid climate change events (massive reorganizations of atmospheric circulation) that are demonstrated to operate on 1450‐year cycles. Changes in insolation and associated positive feedbacks related to ice sheets may assist in explaining favorable time periods and controls on the amplitude of massive rapid climate change events. Explanation for the exact timing and global synchroneity of these events is, however, more complicated. Preliminary evidence points to possible solar variability‐climate associations for these events and perhaps others that are embedded in our ice‐core‐derived atmospheric circulation records

    United States Patent: COMPOSITION AND METHOD FOR INHIBITING PATHOGENS AND SPOILAGE ORGANISMS IN FOOD

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    The method of the invention uses live cells of non-fermenting and/or non-growing lactic acid bacteria to deliver bacteriocin into edible food substances to inhibit the growth of food spoilage and/or food-borne pathogenic organisms. The method of the invention may be used to inhibit growth of these organisms in raw food substances and finished food products after processing. The lactic acid bacteria within the food mixture are capable of producing bacteriocin in the desired microbial- inhibiting amounts under conditions of non-growth and non-fermentatio
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