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.     

Thermo-XRD analysis of the adsorption of Congo-red by montmorillonite saturated with different cations

The adsorption of the organic anionic dye Congo red (CR) by montmorillonite saturated with Na⁺, Cs⁺, Mg²⁺, Cu²⁺, Al³⁺ and Fe³⁺ was investigated by XRD of unwashed and washed samples after equilibration at 40% humidity and after heating at 360 and at 420°C. The clay was treated with different amounts of CR, most of which was adsorbed. Clay samples, untreated with CR, after heating showed collapsed interlayer space. Unwashed and washed samples, which contained CR, before heating were characterized by three peaks or shoulders, labeled A (at 0.96-0.99 nm, collapsed interlayers), B (at 1.24-1.36 nm) and C (at 2.10-2.50 nm). Peak B represents adsorbed monolayers of water and dye anions inside the interlayer spaces. Peak C represents interlayer spaces with different orientations of the adsorbed water and organic matter. Diffractograms of samples with small amounts of dye were similar to those without dye showing peak B whereas diffractograms of most samples with high amounts of dye showed an additional peak C. Heated unwashed and washed samples were also characterized by three peaks or shoulders, labeled A' (at 0.96 nm), B' (at 1.10-1.33 nm) and C' (at 1.61-2.10 nm), representing collapsed interlayers, and interlayers with charcoal composed of monolayers or multilayers of carbon. When the samples were heated from 360 to 420°C some of the charcoal monolayers underwent rearrangement to multilayers. In the case of Cu the charcoal decomposed and oxidized. The present results show that most of the adsorbed dye was located inside the interlayer space.This revised version was published online in November 2005 with corrections to the Cover Date.     

A review of computational modeling and deep brain stimulation: applications to Parkinson's disease

Biophysical computational models are complementary to experiments and theories, providing powerful tools for the study of neurological diseases. The focus of this review is the dynamic modeling and control strategies of Parkinson's disease (PD). In previous studies, the development of parkinsonian network dynamics modeling has made great progress. Modeling mainly focuses on the cortex-thalamus-basal ganglia (CTBG) circuit and its sub-circuits, which helps to explore the dynamic behavior of the parkinsonian network, such as synchronization. Deep brain stimulation (DBS) is an effective strategy for the treatment of PD. At present, many studies are based on the side effects of the DBS. However, the translation from modeling results to clinical disease mitigation therapy still faces huge challenges. Here, we introduce the progress of DBS improvement. Its specific purpose is to develop novel DBS treatment methods, optimize the treatment effect of DBS for each patient, and focus on the study in closed-loop DBS. Our goal is to review the inspiration and insights gained by combining the system theory with these computational models to analyze neurodynamics and optimize DBS treatment.     

Secondary adsorption of nitrobenzene and m-nitrophenol by hexadecyltrimethylammonium-montmorillonite thermo-XRD-analysis

In the present research we studied the effect of the solvent used, whether it was polar water or a non-polar organic solvent (n-hexane or n-hexadecane), on the basal-spacing and bulk structure of the sorbate-sorbent complexes obtained by the secondary adsorption of nitrobenzene and m-nitrophenol by two types of organo-montmorillonites. X-ray measured basal spacings before and after thermal treatments up to 360°C. The organo-clays were synthesized, with 41 and 90% replacement of the exchangeable Na⁺ by hexadecyltrimethylammonium (HDTMA), with mono-and bilayers of HDTMA cations in the interlayer space, labelled OC-41 and OC-90, respectively. After heating at 360°C both organo-clays showed spacing at 1.25–1.28 nm, due to the presence of interlayer-charcoal, indicating that in the preheated organo-clays the HDTMA was located in the interlayer. The thermo-XRD-analysis of Na-clay complexes showed that from organic solvents both sorbates were adsorbed on the external surface but from water they were intercalated. m-Nitrophenol complexes of both organo-clays obtained in aqueous suspensions contain water molecules. Spacings of nitrobenzene complexes of OC-41 and OC-90 and those of nitrophenol complexes of OC-41 showed that the adsorbed molecules were imbedded in cavities in the HDTMA layers. Adsorption of m-nitrophenol by OC-90 from water and n-hexane resulted in an increase of basal spacing (0.21 and 0.29 nm, respectively) suggesting the existence of a layer of nitrophenol molecules sandwiched between two parallel HDTMA layers.     

4H-SiC中基面位错发光特性研究

本文利用阴极荧光(CL)和选择性刻蚀的方法对4H-SiC同质外延材料中基面位错的发光特性进行了研究. 结果表明螺型基面位错(B_TSD)和混合型基面位错(B_MD)分别具有绿光和蓝绿光特性,其发光峰分别在530 nm附近和480 nm附近. 从测试结果中还发现B_MD 的发光位较B_TSD有所蓝移,分析认为B_TSD位错芯附近原子沿伯格斯 关键词： 4H-SiC 基面位错 发光特性 禁带宽度     

Large gaps between consecutive zeros of the Riemann zeta-function

Combining the amplifiers, we exhibit other choices of coefficients that improve the results on large gaps between the zeros of the Riemann zeta-function. Precisely, assuming the Generalized Riemann Hypothesis (GRH), we show that there exist infinitely many consecutive gaps greater than 3.033 times the average spacing.     

The empirical distribution function and strong laws for functions of order statistics of uniform spacings

Let N points be arbitrarily chosen on the circle with unit circumference, and order them clockwise. The uniform mth order spacings are then defined as the clockwise distances between any pair of points having m − 1 other points in between. A Glivenko-Cantelli theorem and nonlinear almost sure bounds for the empirical distribution function based on these uniform spacings are derived. The parameter m is allowed to increase with N to infinity. Applications to linear combinations of functions of mth order spacings are given.     

On exponential scores statistics for testing against positive aging

It has been shown in this paper that a test proposed by Barlow and Doksum (1972) based on the exponential scores statistic for testing exponentiality against increasing failure rate distributions is consistent for the much wider class of harmonic new better than used in expectation distributions.     

The Uniqueness of the Actions of Certain Branch Groups on Rooted Trees

It is proved that in many cases of interest the actions of groups on rooted trees can be recovered from the structure of the groups. The results apply to most of the groups introduced by the first author and to the Gupta–Sidki groups; they are proved in the wider context of branch groups satisfying two natural conditions.     

Crack growth on the basal plane in single crystal zinc: experiments and computations

Crack propagation on the basal planes in zinc was examined by means of in situ fracture testing of pre-cracked single crystals, with specific attention paid to the fracture mechanism. During quasistatic loading, crack propagation occurred in short bursts of dynamic crack extension followed by periods of arrests, the latter accompanied by plastic deformation and blunting of the crack-tip. In situ observations confirmed nucleation and propagation of microcracks on parallel basal planes and plastic deformation and failure of the linking ligaments. Pre-existing twins in the crack path serve as potent crack arrestors. The crystallographic orientation of the crack growth direction on the basal plane was found to influence both the fracture load as well as the deformation at the crack-tip, producing fracture surfaces of noticeably different appearances. Finite element analysis incorporating crystal plasticity was used to identify dominant slip systems and the stress distribution around the crack-tip in plane stress and plane strain. The computational results are helpful in rationalizing the experimental observations including the mechanism of crack propagation, the orientation dependence of crack-tip plasticity and the fracture surface morphology.