On a Matrix Representation Lemma Useful in Determining Maximal Invariance Groups

AbstractBanken (1986, J. Multivariate Anal.19, 156–161) proposed a useful method for determining the group of all affine transformations leaving a multivariate normal testing problem invariant. His main result concerning the derivation of the maximal invariance group is heavily based on a matrix representation lemma which can be considered interesting in its own right. Unfortunately, the proof of this lemma is erroneous and there seems to be no trivial way to correct it. The aim of this note is to show the validity of the assertion

Classes of Multiple Decision Functions Strongly Controlling FWER and FDR

This paper provides two general classes of multiple decision functions where each member of the first class strongly controls the family-wise error rate (FWER), while each member of the second class strongly controls the false discovery rate (FDR). These classes offer the possibility that an optimal multiple decision function with respect to a pre-specified criterion, such as the missed discovery rate (MDR), could be found within these classes. Such multiple decision functions can be utilized in multiple testing, specifically, but not limited to, the analysis of high-dimensional microarray data sets.Comment: 19 page

Evidence of Runaway Gas Cooling in the Absence of Supermassive Black Hole Feedback at the Epoch of Cluster Formation

Cosmological simulations, as well as mounting evidence from observations, have shown that supermassive black holes play a fundamental role in regulating the formation of stars throughout cosmic time. This has been clearly demonstrated in the case of galaxy clusters in which powerful feedback from the central black hole is preventing the hot intracluster gas from cooling catastrophically, thus reducing the expected star formation rates by orders of magnitude. These conclusions, however, have been almost entirely based on nearby clusters. Based on new Chandra X-ray observations, we present the first observational evidence for massive, runaway cooling occurring in the absence of supermassive black hole feedback in the high-redshift galaxy cluster SpARCS104922.6 + 564032.5 (z = 1.709). The hot intracluster gas appears to be fueling a massive burst of star formation (≈900 M⊙ yr⁻¹) that is offset by dozens of kpc from the central galaxy. The burst is co-spatial with the coolest intracluster gas but not associated with any galaxy in the cluster. In less than 100 million years, such runaway cooling can form the same amount of stars as in the Milky Way. Therefore, intracluster stars are not only produced by tidal stripping and the disruption of cluster galaxies, but can also be produced by runaway cooling of hot intracluster gas at early times. Overall, these observations show the dramatic impact when supermassive black hole feedback fails to operate in clusters. They indicate that in the highest overdensities, such as clusters and protoclusters, runaway cooling may be a new and important mechanism for fueling massive bursts of star formation in the early universe

Dictyostelium discoideum as a Model to Study Inositol Polyphosphates and Inorganic Polyphosphate

The yeast Saccharomyces cerevisiae has given us much information on the metabolism and function of inositol polyphosphates and inorganic polyphosphate. To expand our knowledge of the metabolic as well as functional connections between inositol polyphosphates and inorganic polyphosphate, we have refined and developed techniques to extract and analyze these molecules in a second eukaryotic experimental model, the amoeba Dictyostelium discoideum. This amoeba, possessing a well-defined developmental program, is ideal to study physiological changes in the levels of inositol polyphosphates and inorganic polyphosphate, since levels of both molecules increase at late stages of development. We detail here the methods used to extract inositol polyphosphates using perchloric acid and inorganic polyphosphate using acidic phenol. We also present the postextraction procedures to visualize and quantify these molecules by polyacrylamide gel electrophoresis and by malachite green assay

A P-value model for theoretical power analysis and its applications in multiple testing procedures

Background: Power analysis is a critical aspect of the design of experiments to detect an effect of a given size. When multiple hypotheses are tested simultaneously, multiplicity adjustments to p-values should be taken into account in power analysis. There are a limited number of studies on power analysis in multiple testing procedures. For some methods, the theoretical analysis is difficult and extensive numerical simulations are often needed, while other methods oversimplify the information under the alternative hypothesis. To this end, this paper aims to develop a new statistical model for power analysis in multiple testing procedures. Methods: We propose a step-function-based p-value model under the alternative hypothesis, which is simple enough to perform power analysis without simulations, but not too simple to lose the information from the alternative hypothesis. The first step is to transform distributions of different test statistics (e.g., t, chi-square or F) to distributions of corresponding p-values. We then use a step function to approximate each of the p-value’s distributions by matching the mean and variance. Lastly, the step-function-based p-value model can be used for theoretical power analysis. Results: The proposed model is applied to problems in multiple testing procedures. We first show how the most powerful critical constants can be chosen using the step-function-based p-value model. Our model is then applied to the field of multiple testing procedures to explain the assumption of monotonicity of the critical constants. Lastly, we apply our model to a behavioral weight loss and maintenance study to select the optimal critical constants. Conclusions: The proposed model is easy to implement and preserves the information from the alternative hypothesis

Abell 746: A highly disturbed cluster undergoing multiple mergers

We present deep \textit{XMM-Newton}, Karl Jansky Very Large Array, and upgraded Giant Metrewave Radio Telescope observations of Abell 746, a cluster that hosts a plethora of diffuse emission sources that provide evidence for the acceleration of relativistic particles. Our new \textit{XMM-Newton} images reveal a complex morphology of the thermal gas with several substructures. We observe an asymmetric temperature distribution across the cluster: the southern regions exhibit higher temperatures, reaching $\sim$9\,keV, while the northern regions have lower temperatures ($\rm \leq4\,keV$), likely due to a complex merger. We find evidence of four surface brightness edges, of which three are merger-driven shock fronts. Combining our new data with the published LOw-Frequency ARray observations has unveiled the nature of diffuse sources in this system. The bright northwest relic shows thin filaments and high degree of polarization with aligned magnetic field vectors. We detect a density jump, aligned with the fainter relic to the north. To the south, we detect high-temperature regions, consistent with shock-heated regions and density jump coincident with the northern tip of the southern radio structure. Its integrated spectrum shows a high-frequency steepening. Lastly, we find that the cluster hosts large-scale radio halo emission. The comparison of the thermal and nonthermal emission reveals an anticorrelation between the bright radio and X-ray features at the center. Our findings suggest that Abell 746 is a complex system that involves multiple mergers.Comment: 21 pages, 13 figures, submitted to Ap

Agonist-stimulated high-affinity GTPase in Dictyostelium membranes

AbstractGTP hydrolysis in Dictyostelium discoideum membranes is caused by a low (Km> 1 mM) and a high affinity (Km 6.5 μM) GTPase. cAMP enhances GTP hydrolysis apparently by increasing the affinity of the high affinity GTPase (stimulated Km 4.5 μM); the low affinity GTPase was not affected by cAMP. Stimulation of GTP hydrolysis by cAMP was maximal at early time points and declined thereafter. A half-maximal stimulation of GTPase occurred at 3 μM cAMP and the specificity of cAMP derivatives for stimulation of GTPase activity showed a close correlation with the specificity for binding to the cell surface cAMP receptor. Treatment of D. discoideum cells with pertussis toxin decreased the cAMP-induced stimulation of GTPase from 42 ± 6% in control cells to 17 ± 9% in pertussis toxin-treated cells. These results suggest that the interaction of cAMP with its surface receptor leads to stimulation of high affinity GTPase in D. discoideum membranes. At least one of those enzymes may represent a guanine nucleotide-binding protein sensitive to pertussis toxin