595,089 research outputs found

    An adaptive significance threshold criterion for massive multiple hypotheses testing

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    This research deals with massive multiple hypothesis testing. First regarding multiple tests as an estimation problem under a proper population model, an error measurement called Erroneous Rejection Ratio (ERR) is introduced and related to the False Discovery Rate (FDR). ERR is an error measurement similar in spirit to FDR, and it greatly simplifies the analytical study of error properties of multiple test procedures. Next an improved estimator of the proportion of true null hypotheses and a data adaptive significance threshold criterion are developed. Some asymptotic error properties of the significant threshold criterion is established in terms of ERR under distributional assumptions widely satisfied in recent applications. A simulation study provides clear evidence that the proposed estimator of the proportion of true null hypotheses outperforms the existing estimators of this important parameter in massive multiple tests. Both analytical and simulation studies indicate that the proposed significance threshold criterion can provide a reasonable balance between the amounts of false positive and false negative errors, thereby complementing and extending the various FDR control procedures. S-plus/R code is available from the author upon request.Comment: Published at http://dx.doi.org/10.1214/074921706000000392 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

    Advance in dynamical spontaneous symmetry breaking

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    Recently, a condition is derived for a nontrivial solution of the Schwinger-Dyson equation to be accompanied by a Goldstone bound state in a special quantum electrodynamics model. This result is extended and a new form of the Goldstone theorem is obtained in a general quantum field theory framework.Comment: 3 pages, LaTeX, no figure

    Anomalous Dimension in the Solution of the Barenblatt's Equation

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    A new method is presented to obtain the anomalous dimension in the solution of the Barenblatt's equation. The result is the same as that in the renormalization group (RG) approach. It gives us insight on the perturbative solution of the Barenblatt's equation in the RG approach. Based on this discussion, an improvement is made to take into account, in more complete way, the nonlinear effect, which is included in the Heaviside function in higher orders. This improved result is better than that in RG approach.Comment: 17 pages, LaTex, no figur

    Penguin-induced Radiative Baryonic B Decays Revisited

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    Weak radiative baryonic B decays BˉB1Bˉ2γ\bar B\to B_1\bar B_2\gamma mediated by the electromagnetic penguin process bsγb\to s\gamma are re-examined within the framework of the pole model. The meson pole contribution that has been neglected before is taken into account in this work. It is found that the intermediate KK^* contribution dominates in the Σpˉγ\Sigma\bar p\gamma mode and is comparable to the baryon pole effect in Λpˉγ\Lambda\bar p\gamma and ΞΛˉγ\Xi\bar\Lambda\gamma modes. The branching ratios for BΛpˉγB^-\to\Lambda\bar p\gamma and BΞ0ΣˉγB^-\to\Xi^0\bar\Sigma^-\gamma are of order 2.6×1062.6\times 10^{-6} and 6×1076\times 10^{-7}, respectively. The threshold enhancement effect in the dibaryon mass spectrum is responsible by the meson pole diagram. We also study the angular distribution of the baryon in the dibaryon rest frame. The baryon pole diagrams imply that the antibaryon tends to emerge in the direction of the photon in the baryon-pair rest frame. The predicted angular asymmetry agrees with experiment for BΛpˉγB^-\to\Lambda\bar p\gamma. Measurements of the correlation of the photon with the baryon allow us to discriminate between different models for describing the radiative baryonic B decays. For decays BΞΣˉγB\to\Xi\bar\Sigma\gamma, a large correlation of the photon to the Σˉ\bar\Sigma and a broad bump in the dibaryon mass spectrum are predicted.Comment: 10 pages, 4 figure

    Kostant homology formulas for oscillator modules of Lie superalgebras

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    We provide a systematic approach to obtain formulas for characters and Kostant u{\mathfrak u}-homology groups of the oscillator modules of the finite dimensional general linear and ortho-symplectic superalgebras, via Howe dualities for infinite dimensional Lie algebras. Specializing these Lie superalgebras to Lie algebras, we recover, in a new way, formulas for Kostant homology groups of unitarizable highest weight representations of Hermitian symmetric pairs. In addition, two new reductive dual pairs related to the above-mentioned u{\mathfrak u}-homology computation are worked out

    Collapsing strange quark matter in Vaidya geometry

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    Exact solutions of the gravitational field equations for a mixture of a null charged strange quark fluid and radiation are obtained in a Vaidya space-time. The conditions for the formation of a naked singularity are analyzed by considering the behavior of radial geodesics originating from the central singularity.Comment: 6 pages, no figure