Multiple Window and Cluster Size Scan Procedures

Researchers apply scan statistics to test for unusually large clusters of events within a time window of specified length w, or alternatively an unusually small window w that contains a specified number of events. In some cases, the researcher is interested in testing for a range of specified window lengths, or a set of several specified number of events k (cluster sizes). In this paper, we derive accurate approximations for the joint distributions of scan statistics for a range of values of w, or of k, that can be used to set an experiment-wide level of significance that takes into account the multiple comparisons involved. We use these methods to compare different ways of choosing the window sizes for the different cluster sizes. One special case is a multiple comparison procedure based on a generalized likelihood ratio test (GLRT) for a range of window sizes. We compare the power of the GLRT with another method for allocating the window sizes. We find that the GLRT is sensitive for very small window sizes at the expense of moderate and larger window sizes. We illustrate these results on two examples, one involving clustering of translocation breakpoints in DNA, and the other involving disease clusters.     

Complex Geometry of the Universal Teichmuller Space

We prove that all invariant distances on the universal Teichmuller space agree and are determined by the Grunsky coefficients of the naturally related conformal maps. This fact yields various important consequences; in particular, we obtain solutions of certain well-known geometric problems in complex analysis and related fields.     

左截断右删失下核密度估计的L1距离的界

本文在左截断右删失数据下获得了概论密度的核估计的L1距离的一个上界．     

Microcalorimetry as a possible tool for phylogenetic studies of Tetrahymena

Using isothermal microcalorimetry, the growth power-time curves of three strains of Tetrahymena were determined at 28°C. Their Euclidean distances and cluster analysis diagram were obtained by using two thermokinetic parameters (r and Q_log), which showed that T. thermophila BF₁ and T. thermophila BF₅ had a closer relationship. Compared with the single molecular biomarker (ITS1) method, microcalorimetry wasmaybe a simpler, more sensitive andmore economic technique in the phylogenetic studies of Tetrahymena species.     

A constructive proof by elementary transformations of Roth's removal theorems in the theory of matrix equations

W. E. Roth gave necessary and sufficient conditions for the existence of solution(s) of certain types of linear matrix equations. Proofs were based on invariant factors and were long and complicated. Other shorter but non-constructive proofs have since been provided by later authors. We present here very brief constructive proofs based on the simplest of mathematical techniques, namely row- and column-reduction of a matrix.     

Trehalose-protected lipid membranes for determining membrane protein structure and insertion

Trehalose preserves lipid bilayers during dehydration and rehydration by replacing water to form hydrogen bonds between its own OH groups and lipid headgroups. We compare the lipid conformation and dynamics between trehalose-protected lyophilized membranes and hydrated membranes, to assess the suitability of the trehalose-containing membrane as a matrix for membrane protein structure determination. (31)P spectra indicate that the lipid headgroup of trehalose-protected dry POPC membrane (TRE-POPC) have an effective phase transition temperature that is approximately 50K higher than that of the hydrated POPC membrane. In contrast, the acyl chains have similar transition temperatures in the two membranes. Intramolecular lipid (13)C'-(31)P distances are the same in TRE-POPC and crystalline POPC, indicating that the lipid headgroup and glycerol backbone conformation is unaffected by trehalose incorporation. Intermolecular (13)C-(31)P distances between a membrane peptide and the lipid headgroups are 10% longer in the hydrated membrane at 226 K than in the trehalose-protected dry membrane at 253 K. This is attributed to residual motions in the hydrated membrane, manifested by the reduced (31)P chemical shift anisotropy, even at the low temperature of 226 K. Thus, trehalose lyoprotection facilitates the study of membrane protein structure by allowing experiments to be conducted at higher temperatures than possible with the hydrated membranes.     

关于微分方程解的一致非常稳定性与一致距离有界性

讨论了一般非自治方程解的一致非常稳定性与一致距离有界性.