Higher criticism, or second-level significance testing, is a multiple-comparisons concept mentioned in passing by Tukey. It concerns a situation where there are many independent tests of significance and one is interested in rejecting the joint null hypothesis. Tukey suggested comparing the fraction of observed significances at a given \alpha-level to the expected fraction under the joint null. In fact, he suggested standardizing the difference of the two quantities and forming a z-score; the resulting z-score tests the significance of the body of significance tests. We consider a generalization, where we maximize this z-score over a range of significance levels 0<\alpha\leq\alpha_0. We are able to show that the resulting higher criticism statistic is effective at resolving a very subtle testing problem: testing whether n normal means are all zero versus the alternative that a small fraction is nonzero. The subtlety of this ``sparse normal means'' testing problem can be seen from work of Ingster and Jin, who studied such problems in great detail. In their studies, they identified an interesting range of cases where the small fraction of nonzero means is so small that the alternative hypothesis exhibits little noticeable effect on the distribution of the p-values either for the bulk of the tests or for the few most highly significant tests. In this range, when the amplitude of nonzero means is calibrated with the fraction of nonzero means, the likelihood ratio test for a precisely specified alternative would still succeed in separating the two hypotheses.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Statistics (http://www.imstat.org/aos/) at http://dx.doi.org/10.1214/00905360400000026

The gene transient receptor potential-melastatin-like 7 (Trpm7) encodes a protein that functions as an ion channel and a kinase. TRPM7 has been proposed to be required for cellular Mg 2+ homeostasis in vertebrates. Deletion of mouse Trpm7 revealed that it is essential for embryonic development. Tissue-specific deletion of Trpm7 in the T cell lineage disrupted thymopoiesis, which led to a developmental block of thymocytes at the double-negative stage and a progressive depletion of thymic medullary cells. However, deletion of Trpm7 in T cells did not affect acute uptake of Mg 2+ or the maintenance of total cellular Mg 2+ . Trpm7-deficient thymocytes exhibited dysregulated synthesis of many growth factors that are necessary for the differentiation and maintenance of thymic epithelial cells. The thymic medullary cells lost signal transducer and activator of transcription 3 activity, which accounts for their depletion when Trpm7 is disrupted in thymocytes.The transient receptor potential (TRP) superfamily comprises cation-permeant ion channels that have diverse functions (1-3). TRPM7 (1,2) and TRPM6 (4,5) proteins also contain a Cterminal kinase domain (6). TRPM7 is expressed in all examined cell types (3) and mediates the outwardly rectifying Mg 2+ -inhibitable current (MIC) (7). TRPM6 and TRPM7 exhibit nearly identical current-voltage (I-V) relations, conducting only a few pA of inward current at physiological pH levels (1,2,8,9).A chicken DT-40 B cell line targeted for Trpm7 gene disruption was reported to require high concentrations of extracellular Mg 2+ (10 mM) for survival (10). Given the permeability of TRPM7 to Mg 2+ , the results have been interpreted to indicate that TRPM7 was critical for cellular Mg 2+ homeostasis in vertebrates. A role for TRPM7 in vertebrate development was suggested by a Danio rerio Trpm7 mutant that exhibited abnormal skeletogenesis and melanophore development, but whether this developmental defect is related to Mg 2+ homeostasis remains unclear (11).We generated multiple mouse lines with a targeted deletion of the Trpm7 gene ( fig. S1A) (12). Mouse lines with disruption of Trpm7 in all tissues (global deletion), generated using †To whom correspondence should be addressed.

Consider a network where the nodes split into K different communities. The community labels for the nodes are unknown and it is of major interest to estimate them (i.e., community detection). Degree Corrected Block Model (DCBM) is a popular network model. How to detect communities with the DCBM is an interesting problem, where the main challenge lies in the degree heterogeneity.We propose a new approach to community detection which we call the Spectral Clustering On Ratios-of-Eigenvectors (SCORE). Compared to classical spectral methods, the main innovation is to use the entry-wise ratios between the first leading eigenvector and each of the other leading eigenvectors for clustering. Let A be the adjacency matrix of the network. We first obtain the K leading eigenvectors of A, say,η1, . . . ,ηK , and letR be the n × (K − 1) matrix such thatWe then useR for clustering by applying the k-means method.The central surprise is, the effect of degree heterogeneity is largely ancillary, and can be effectively removed by taking entry-wise ratiosThe method is successfully applied to the web blogs data and the karate club data, with error rates of 58/1222 and 1/34, respectively. These results are more satisfactory than those by the classical spectral methods. Additionally, compared to modularity methods, SCORE is easier to implement, computationally faster, and also has smaller error rates.We develop a theoretic framework where we show that under mild conditions, the SCORE stably yields consistent community detection. In the core of the analysis is the recent development on Random Matrix Theory (RMT), where the matrix-form Bernstein inequality is especially helpful.

Summary A plethora of growth factors regulate keratinocyte proliferation and differentiation that control hair morphogenesis and skin barrier formation. Wavy hair phenotypes in mice result from naturally occurring loss-of-function mutations in the genes for TGF-α and EGFR. Conversely, excessive activities of TGF-α/EGFR result in hairless phenotypes and skin cancers. Unexpectedly, we found that mice lacking the TRPV3 gene also exhibit wavy hair coat and curly whiskers. Here we show that keratinocyte TRPV3, a member of the Transient Receptor Potential (TRP) family of Ca2+-permeant channels, forms a signaling complex with TGF-α/EGFR. Activation of EGFR leads to increased TRPV3 channel activity, which in turn stimulates TGF-α release. TRPV3 is also required for the formation of the skin barrier by regulating the activities of transglutaminases, a family of Ca2+-dependent cross-linking enzymes essential for keratinocyte cornification. Our results show that a TRP channel plays a role in regulating growth factor signaling by direct complex formation.

Direct imaging or counting of RNA molecules has been difficult owing to its relatively low electron density for EM and insufficient resolution in AFM. Bacteriophage phi29 DNA-packaging motor is geared by a packaging RNA (pRNA) ring. Currently, whether the ring is a pentagon or hexagon is under fervent debate. We report here the assembly of a highly sensitive imaging system for direct counting of the copy number of pRNA within this 20-nm motor. Single fluorophore imaging clearly identified the quantized photobleaching steps from pRNA labeled with a single fluorophore and concluded its stoichiometry within the motor. Almost all of the motors contained six copies of pRNA before and during DNA translocation, identified by dual-color detection of the stalled intermediates of motors containing Cy3-pRNA and Cy5-DNA. The stalled motors were restarted to observe the motion of DNA packaging in real time. Heat-denaturation analysis confirmed that the stoichiometry of pRNA is the common multiple of 2 and 3. EM imaging of procapsid/pRNA complexes clearly revealed six ferritin particles that were conjugated to each pRNA ring.

SUMMARY In a recent paper [4], Efron pointed out that an important issue in large-scale multiple hypothesis testing is that the null distribution may be unknown and need to be estimated. Consider a Gaussian mixture model, where the null distribution is known to be normal but both null parameters-the mean and the variance-are unknown. We address the problem with a method based on Fourier transformation. The Fourier approach was first studied by Jin and Cai [9], which focuses on the scenario where any non-null effect has either the same or a larger variance than that of the null effects. In this paper, we review the main ideas in [9], and propose a generalized Fourier approach to tackle the problem under another scenario: any non-null effect has a larger mean than that of the null effects, but no constraint is imposed on the variance. This approach and that in [9] complement with each other: each approach is successful in a wide class of situations where the other fails. Also, we extend the Fourier approach to estimate the proportion of non-null effects. The proposed procedures perform well both in theory and on simulated data.

The context of Donoho and Jin's [18] work was that where the noise is white, although a small number of investigations have been made of the case of correlated noise (Hall, Pittelkow and Ghosh [29], Hall and Jin [30], Delaigle and Hall [17]). However, that research has focused on the ability of standard HC, applied in the form that is appropriate for independent data, to accommodate the nonindependent case. In this paper we address the problem of how to modify HC by developing innovated higher criticism (iHC) and showing how to optimize performance for correlated noise.Curiously, it turns out that when using the iHC method tuned to give optimal performance, the case of independence is the most difficult of all, statistically speaking. To appreciate why this result is reasonable, note that if the noise is correlated then it does not vary so much from one location to a nearby location, and so is a little easier to identify. In an extreme case, if the noise is perfectly correlated at different locations then it is constant, and in this instance it can be easily removed.On the other hand, standard HC does not perform well in the case of correlated noise, because it utilizes only the marginal information in the data without much attention to the correlation structure. Innovated HC is designed to exploit the advantages offered by correlation and gives good performance across a wide range of settings.The concept of the "detection boundary" was introduced by Donoho and Jin [18] in the context of white noise. In this paper, we extend it to the correlated case. In brief, the detection boundary describes the relationship between signal sparsity and signal strength that characterizes the boundary between cases where the signal can be detected and cases where it cannot. In the setting of dependent data, this watershed depends on the correlation structure of the noise as well as on the sparsity and strength of the signal. When correlation decays at a polynomial rate we are able to characterize the detection boundary quite precisely. In particular, we show how to construct concise lower/upper bounds to the detection boundary, based on the diagonal components of the inverse of the correlation matrix, Σ n . A special case is where Σ n is Toeplitz; there the upper and the lower bounds to the detection boundary are asymptotically the same. In the Toeplitz case, the iHC is optimal for signal detection but standard HC is not.There is a particularly extensive literature on multiple hypothesis testing under conditions of dependence. It includes contributions to the control of family-wise error rate and false discovery rate, and work of Abramovich et al. [1], Benjamini and Hochberg [2], Benjamini and Yekutieli [3], Brown and Russel [7], Cai and Sun [9], Clarke and Hall [12], Cohen, Sackrowitz and Xu [13], Donoho and Jin [19], Dunnett and Tamhane [22], Efron [23], Finner and Roters [24], Genovese and Wasserman [25], Jin and Cai [40], Olejnik et al. [46], Rom [47], Sarkar and Chang [48] and Wu [54]. Work of Kuelbs and Vidyashankar [41] i...

The non-Gaussian cold spot detected in wavelet space in the WMAP 1 yr data is detected again in the co-added WMAP 3 yr data at the same position (b ¼ À57 , l ¼ 209 ) and size in the sky (%10 ). The present analysis is based on several statistical methods: kurtosis, maximum absolute temperature, number of pixels below a given threshold, volume, and higher criticism. All these methods detect deviations from Gaussianity in the 3 yr data set at a slightly higher confidence level than in the WMAP 1 yr data. These small differences are mainly due to the new foreground reduction technique and not to the reduction of the noise level, which is negligible at the scale of the spot. In order to avoid a posteriori analyses, we recalculate for the WMAP 3 yr data the significance of the deviation in the kurtosis. The skewness and kurtosis tests were the first tests performed with wavelets for the WMAP data. We obtain that the probability of finding an at least as high deviation in Gaussian simulations is 1:85%. The frequency dependence of the spot is shown to be extremely flat. Galactic foreground emissions are not likely to be responsible for the detected deviation from Gaussianity.