Some Approximations of the Borel-Tanner or the Generalized Poisson Distribution

This paper considers some approximations for the Borel-Tanner (Generalized Poisson) sums by using (i) Gram-Charlier Poisson expansion, (ii) Mixture of two Poisson distributions, (iii) Variance stabilizing technique, and (iv) negative binomial distribution. It has been found that the approximation obtained by using the negative binomial distribution seems to be more efficient than the other approximation.     

Confidence Intervals for the Mean of a Poisson Distribution: A Review

The paper provides a comprehensive review of methodology for setting confidence intervals for the parameter of a Poisson distribution. The results are illustrated by a numerical example.     

一类重随机Poisson过程的等待时间的分布密度公式及其在害虫预测预报中的应用

对具有强度过程λｔ（Ｘ）＝Ｘ＾αＶ（ｔ）（α∈Ｒ＋）的重随机Ｐｏｉｓｓｏｎ过程「Ｎｔ：ｔ≥ｔ０」,推导出其等待时间Ｗｎ的分布密度函数ｆＷｎ（ｔ）的表达式;讨论了进一步推广所得结果的途径;利用所得结果解决了一个预测害虫最适防治时刻的问题。     

耐受性定律的一个数学注记

在许多著作中关于耐受性定律的叙述大同小异。为了视限制因子原理和Liebig 最小因子定律为耐受性定律的特殊情况(某些侧面),我们采用[1]对耐受性定律的叙述:一种环境因子对每一种生物都有一个范     

A moment-based method for estimating the proportion of true null hypotheses and its application to microarray gene expression data

Due to advances in experimental technologies, it is feasible to collect measurements for a large number of variables. When these variables are simultaneously screened by a statistical test, it is necessary to consider the adjustment for multiple hypothesis testing. The false discovery rate has been proposed and widely used to address this issue. A related problem is the estimation of the proportion of true null hypotheses. The long-standing difficulty to this problem is the identifiability of the nonparametric model. In this study, we propose a moment-based method coupled with sample splitting for estimating this proportion. If the p values from the alternative hypothesis are homogeneously distributed, then the proposed method will solve the identifiability and give its optimal performances. When the p values from the alternative hypothesis are heterogeneously distributed, we propose to approximate this mixture distribution so that the identifiability can be achieved. Theoretical aspects of the approximation error are discussed. The proposed estimation method is completely nonparametric and simple with an explicit formula. Simulation studies show the favorable performances of the proposed method when it is compared to the other existing methods. Two microarray gene expression data sets are considered for applications.     

A Comparison of Models to Infer the Distribution of Fitness Effects of New Mutations

Knowing the distribution of fitness effects (DFE) of new mutations is important for several topics in evolutionary genetics. Existing computational methods with which to infer the DFE based on DNA polymorphism data have frequently assumed that the DFE can be approximated by a unimodal distribution, such as a lognormal or a gamma distribution. However, if the true DFE departs substantially from the assumed distribution (e.g., if the DFE is multimodal), this could lead to misleading inferences about its properties. We conducted simulations to test the performance of parametric and nonparametric discretized distribution models to infer the properties of the DFE for cases in which the true DFE is unimodal, bimodal, or multimodal. We found that lognormal and gamma distribution models can perform poorly in recovering the properties of the distribution if the true DFE is bimodal or multimodal, whereas discretized distribution models perform better. If there is a sufficient amount of data, the discretized models can detect a multimodal DFE and can accurately infer the mean effect and the average fixation probability of a new deleterious mutation. We fitted several models for the DFE of amino acid-changing mutations using whole-genome polymorphism data from Drosophila melanogaster and the house mouse subspecies Mus musculus castaneus. A lognormal DFE best explains the data for D. melanogaster, whereas we find evidence for a bimodal DFE in M. m. castaneus.     

On the Theory for RYANS Universal Multiple Comparison Procedure with Treatment of Ties in the Ranks of Samples

The proposal of RYAN (1960) for multiple comparison procedures has not become well known despite of its universal applicability. Only his idea of adjusted levels has been used in a modified manner, cf. EINOT and GABRIEL (1975), WELSCH (1977), RAMSEY (1978). This article re-introduces the procedure and demonstrates its broad applicability also as a nonparametric method. Above all an exact mathematical foundation is aspired. The case of ties in the ranks of samples has been taken into consideration.     

A Performance Comparison of Coscheduling Strategies for Workstation Clusters

Workstation clusters are emerging as a general-purpose computing platform for the execution of workloads comprising parallel and sequential applications. The scalability and flexibility typical of implicit coscheduling strategies makes them a very promising solution to the scheduling needs of workstation clusters. In this paper we present a simulation study that compares, for a variety of workloads (that include both parallel and sequential applications) and operating system schedulers, 12 implicit coscheduling strategies in terms of the performance they are able to deliver to applications. By using a detailed simulator, we evaluate the performance of different coscheduling alternatives for a variety of simulation scenarios, and we identify the set of strategies that deliver the best performance to all the applications composing typical cluster workloads. Moreover, we show that for schedulers providing immediate preemption, the best strategies are also the simplest ones to implement.     

Comparison of Resubstitution,Data Splitting,the Bootstrap,and the Jackknife as Methods for Estimating Validity Indices of New Marker Tests: A Monte Carlo Study

Estimating the diagnostic efficiency of marker tests on the basis of the training set is an intricate problem of discriminant analysis for which no analytical solution exists. The paper outline the problem, describes various popular estimation procedures and presents the results of computer simulations comparing the estimators with respect to both bias and variance.     

A comparison of planned unbalanced designs for estimating heritability in perennial tree crops

Summary One hundred families of average size 10 are allocated in single-tree plots to 20 blocks in several planned unbalanced designs. Based on the variance of the estimate of heritability from the Minimum Variance Quadratic Unbiased Estimates and 100% survival, the three partially balanced designs are equally efficient. A design with variable family size is more efficient for heritabilities (h²) generally less than 0.25; an equal family size design is more efficient for h² generally greater than 0.25. A design with a large number of small families is more efficient at high h² than that with a small number of large families; a design with fewer families of larger size is more efficient at low h². Two-tree plot designs are never more efficient than single-tree plot designs and are also shown to be sensitive to the magnitude of the variance components that generate a given h², whereas the single-tree plot designs are not.Paper No. 9853 of the Journal series of the North Carolina Agricultural Research Service, Raleigh, NC, USA     

A Statistical Method for Comparison of Two Structures and Its Biological Applications

Some experimental methods applied to biological investigations allow to find a number q of homogeneous discrete components that determine a structure of the object in the study and the to establish the presence of some components from these q in compositions of other n objects. Such data form a nXq incidence matrix. In this paper a statistical approach is suggested for revealing the associated components in two different structures of the object. The procedure is based on joint consideration of two sampling incidence matrices. An application of this method is demonstrated by analysis of relationships between antigens and proteins of one strain of cyanobacteria. The method may be useful in different scientific areas, e.g. psychology, when direct experimental comparison of components from two structures is difficult.     

A Comparison Between Several Goodness of Fit Tests for Cox's Model

A comparison is made between two approaches to testing goodness of fit of Cox's regression model for survival data. The first approach is based on the inclusion of time dependent covariates, whereas the second one is based on the autocovariance of successive contributions to the derivative of the loglikelihood. It appears that the second test is most appropriate for testing in situations where the structure of the departure from proportional hazards is not known a priori. An approximate expression for the relative efficiency of the two test procedures is presented.     

埋伏倒置阻生上颌中切牙不同正畸牵引方式的比较

目的：比较前方牵引器及下颌支抗颌间牵引两种正畸牵引方式矫治上中切牙埋伏倒置阻生的疗效。方法：选择10例患者10颗埋伏倒置阻生上领中切牙,在三维CT片上的位置、三维方向和埋伏阻生的程度均相似,随机分为两组,分别行前方牵引器牵引和颌间牵引,对两组的牵引时间和成功率进行比较,分别采用t检验和x2检验进行统计学处理。结果：前方牵引组牵引时间长于颌间牵引组,有显著差异（P〈0．05）,前方牵引组成功率为100％,颌间牵引组为60％,差异有显著性（P〈0．01）。结论：埋伏倒置阻生的上中切牙外科开窗术后,通过前方牵引器牵引的时间显著长于下颌支抗颌间牵引,但成功率显著高于颌间牵引。     

Temperature Sensitivity of Photosynthesis in Lolium perenne Swards: A Comparison of Two Methods for Deriving Photosynthetic Parameters from in vivo Measurements

The seasonal variation in photosynthetic rate of grass swards is partly the result of changes in the environment and partly the result of changes in the photosynthetic capacity of the sward itself. We evaluated two types of photosynthesis equations regarding their capacity to analyse seasonal and short-term temperature effects on photosynthesis of ryegrass (Lolium perenne L.). Intact cores of a field-grown ryegrass sward were taken to the laboratory 10 d after cutting for measurement of photosynthesis under controlled conditions. This was done during two four-week periods, in summer and autumn. Net photosynthetic rate (P _N) of the sward was lower in autumn than in summer. Both a simple negatively exponential photosynthesis irradiance-response curve and the Farquhar equations for photosynthesis were applied to the in vivo canopy measurements. Application of the irradiance-response curve showed that irradiance-saturated gross photosynthetic rate increased linearly with increasing temperature and was higher in summer than in autumn. The initial radiation use efficiency did not differ between the seasons but decreased with the temperature rise. This explains the observation that total canopy photosynthetic rate decreased after short-term temperature increases in both seasons. The parameters in Farquhar equations that represent the temperature sensitivity of the maximum electron transport rate and of the Michaelis-Menten constants for CO₂ and O₂ fixation could not be quantified satisfactorily. Parameterisation of the Farquhar equations was hampered by a lack of robust information on many biochemical parameters, and the use of simple empirical response-functions may be preferable in the case of in vivo canopy measurements on grass swards.     

A Bayesian MCMC Approach to Assess the Complete Distribution of Fitness Effects of New Mutations: Uncovering the Potential for Adaptive Walks in Challenging Environments

The role of adaptation in the evolutionary process has been contentious for decades. At the heart of the century-old debate between neutralists and selectionists lies the distribution of fitness effects (DFE)—that is, the selective effect of all mutations. Attempts to describe the DFE have been varied, occupying theoreticians and experimentalists alike. New high-throughput techniques stand to make important contributions to empirical efforts to characterize the DFE, but the usefulness of such approaches depends on the availability of robust statistical methods for their interpretation. We here present and discuss a Bayesian MCMC approach to estimate fitness from deep sequencing data and use it to assess the DFE for the same 560 point mutations in a coding region of Hsp90 in Saccharomyces cerevisiae across six different environmental conditions. Using these estimates, we compare the differences in the DFEs resulting from mutations covering one-, two-, and three-nucleotide steps from the wild type—showing that multiple-step mutations harbor more potential for adaptation in challenging environments, but also tend to be more deleterious in the standard environment. All observations are discussed in the light of expectations arising from Fisher’s geometric model.     

A thiol labelling competition experiment as a probe for sidechain packing in the kinetic folding intermediate of N-PGK

Protein folding is directed by the sequence of sidechains along the polypeptide backbone, but despite this the developement of sidechain interactions during folding is not well understood. Here, the thiol-active reagent, dithio-nitrobenzoic acid (DTNB), is used to probe the exposure of the cysteine sidechain thiols in the kinetic folding intermediates of the N-terminal domain of phosphoglycerate kinase (N-PGK) and a number of conservative (I-, L-, or V-to-C) single cysteine variants. Rapid dilution of chemically denatured protein into folding conditions in the presence of DTNB allowed the degree of sidechain protection in any rapidly formed intermediate to be determined through the analysis of the kinetics of labelling. The protection factors derived for the intermediate(s) were generally small (<25), indicating only partial burial of the sidechains. The distribution of protection parallels the previously reported backbone amide protection for the folding intermediate of N-PGK. These observations are consistent with the hypothesis that such intermediates resemble molten globule states; i.e. with native-like backbone hydrogen bonding and overall tertiary structure, but with the sidechains that make up the hydrophobic protein core dynamic and intermittently solvent exposed. The success of the competition technique in characterizing this kinetic intermediate invites application to other model systems.