The S-Distribution A Tool for Approximation and Classification of Univariate,Unimodal Probability Distributions

In many statistical applications a data set needs to be evaluated but there is no solid information about which probability distribution might be most appropriate. Typical solutions to this problems are: to make assumptions that facilitate mathematical treatment; to use a family of distribution functions that contains all relevant distributions as special cases; or, to employ nonparametric methods. All three solutions have disadvantages since assumptions are usually difficult to justify, families of distributions contain too many parameters to be of practical use, and nonparametric methods make it difficult to characterize data in a succinct quantitative form. The S-distribution introduced here is a compromise between the conflicting goals of simplicity in analysis and generality in scope. It is characterized by four parameters, one of which reflects its location, the second one its spread, and the remaining two its shape; transformation to a standard form reduces the number of free parameters to two. Cumulatives and densities are computed numerically in fractions of seconds, key features like quantiles and moments are easily obtained, and results can be presented in terms of parameter values. The S-distribution rather accurately models different distribution functions, including central and noncentral distributions, and thus competes in flexibility with some distribution families. As an approximation, the S-distribution provides a graphical method for demonstrating relationships between distributions, such as the relationships between central F, χ² and χ^?2 or central and noncentral t, χ^-1, and normal.     

Scalability Properties of the S-Distribution

Previous work has shown that the S-distribution is a valuable tool for data analysis and for the classification of continuous and discrete distribution functions. The distribution has four parameters: one determines its location, one is related to the variance, and two control its shape. The distributional structure allows symmetry as well as skewness to the right or the left. This offers great flexibility and, among other analyses, facilitates the simultaneous investigation of random variables whose distributions differ in shape. The present paper demonstrates that mean, variance, and quantiles of any S-distribution can be computed with simple algebraic operations from corresponding properties of a standard S-distribution, sSd , which is characterized by only the two shape parameters. This scalability is comparable with the use of z-scores when dealing with normal distributions.     

Some Applications of the Family of Discrete Exponential Distributions in Biology and Toxicology

In this paper the relationship between the number of males and females in a community, between the number of boys and girls in a family, between the number of animals trapped and untrapped in an animal experiment, between the number of infected and uninfected in an epidemiological study, between the number of mutagens and non-mutagens in a given sample of toxicological experiments, and others, is studied. The general expression for the correlation coefficient, ?, is obtained when N, the community size N, has a discrete exponential family distribution recently studied by Janardan (1980). This is then specialized to some well known discrete distributions.     

Discrete Distributions of Adenosine Receptors in Mammalian Retina

Binding sites for both the adenosine A1 receptor agonists [3H]phenylisopropyladenosine and [3H]cyclohexyladenosine and the mixed A1-A2 agonist N-[3H]ethylcarboxamidoadenosine [( 3H]NECA) were localized in rabbit and mouse retinas using autoradiographic techniques. These two classes of agonists bound to very different regions of mammalian retinas. A1 agonist binding was localized to the inner retina, particularly over the inner plexiform layer. The binding of [3H]NECA was observed primarily over the retinal pigmented epithelium and the outer and inner segments of photoreceptors. [3H]NECA labeling was not affected either by including a low concentration of unlabeled A1 agonist or by pretreating tissue with N-ethylmaleimide to inhibit ligand binding at A1 sites. While virtually all of the [3H]NECA binding was displaced by an excess of unlabeled NECA, displacement with antagonist or a large excess of cyclohexyladenosine revealed that approximately 30% of the [3H]NECA binding was at non-A1,A2 sites. The majority of the binding in the outer retina thus labeled A2 receptor sites. The unique localizations of the two classes of adenosine receptors suggest different functions in visual processing.     

浙江海兽及其分布

根据文献记载和历年来采集到的标本,提出了浙江省17种海兽的名录和分布。其中1种为浙江省新纪录,1种为大陆沿海新纪录。并且简述了其主要形态特征。     

A Suprasystem of Probability Distributions

A set of differential equations is described whose solutions represent a general system of probability distribution functions. Previously reported systems of such distribution functions are special cases of this general system. The differential equations can be used to represent distribution functions and generate their related statistics in cases for which no simple formula for the distribution is known. The generality of this suprasystem of distribution functions and its potential utility are discussed.     

Life-and-Death Decisions in a Neonatal Intensive Care Unit in Denmark: The Discrete Authority of Origin Stories

In what ways are care and compassion implicated in efforts to establish lives worth living? Drawing on fieldwork in a Danish Neonatal Intensive Care Unit (NICU), in this article we investigate the role of family biographies in conducting life-and-death decisions around premature infants. Guided by a larger literature on citizenship, we view decisions in the NICU as political acts of assigning citizenship. We ask what bodies and biographies can generate and evoke care and compassion among NICU staff and forge entries or exits from the Danish Welfare State. We demonstrate that infants’ origin stories are appointed legitimate forms of suffering in contemporary Danish society and are thus granted an unnoticed form of authority in life-and-death decisions. In this way, we conclude that what comes to constitute a life worth living in the twenty-first-century Danish Welfare State is in fact the worth of the family.     

General Mathematical Frame for Open or Closed Biomembranes (Part I): Equilibrium Theory and Geometrically Constraint Equation

This paper aims at constructing a general mathematical frame for the equilibrium theory of open or closed biomembranes. Based on the generalized potential functional, the equilibrium differential equation for open biomembrane (with free edge) or closed one (without boundary) is derived. The boundary conditions for open biomembranes are obtained. Besides, the geometrically constraint equation for the existence, formation and disintegration of open or closed biomembranes is revealed. The physical and biological meanings of the equilibrium differential equation and the geometrically constraint equation are discussed. Numerical simulation results for axisymmetric open biomembranes show the effectiveness and convenience of the present theory.     

A Deterministic Approximation to the Number of Mutants in Growing Clones

The use of an approximation to the median of the Poisson distribution to represent each occurrence of mutations in a growing clone permits the prediction of the number of mutants per clone without the limitations imposed by more heuristic expressions. Its application to the evaluation of mutation rates yields results comparable to those obtained by fluctuation analysis.     

Genome-wide and molecular evolution analysis of the subtilase gene family in Vitis vinifera

Background

Vitis vinifera (grape) is one of the most economically significant fruit crops in the world. The availability of the recently released grape genome sequence offers an opportunity to identify and analyze some important gene families in this species. Subtilases are a group of subtilisin-like serine proteases that are involved in many biological processes in plants. However, no comprehensive study incorporating phylogeny, chromosomal location and gene duplication, gene organization, functional divergence, selective pressure and expression profiling has been reported so far for the grape.

Results

In the present study, a comprehensive analysis of the subtilase gene family in V. vinifera was performed. Eighty subtilase genes were identified. Phylogenetic analyses indicated that these subtilase genes comprised eight groups. The gene organization is considerably conserved among the groups. Distribution of the subtilase genes is non-random across the chromosomes. A high proportion of these genes are preferentially clustered, indicating that tandem duplications may have contributed significantly to the expansion of the subtilase gene family. Analyses of divergence and adaptive evolution show that while purifying selection may have been the main force driving the evolution of grape subtilases, some of the critical sites responsible for the divergence may have been under positive selection. Further analyses of real-time PCR data suggested that many subtilase genes might be important in the stress response and functional development of plants.

Conclusions

Tandem duplications as well as purifying and positive selections have contributed to the functional divergence of subtilase genes in V. vinifera. The data may contribute to a better understanding of the grape subtilase gene family.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2164-15-1116) contains supplementary material, which is available to authorized users.     

Use of the Score Statistic for Testing Goodness-of-Fit of Some Generalised Distributions

The use of the score statistic to test whether a generalised distribution gives an improved fit over a non-generalised distribution is recommended. The score statistic for a generalised exponential family is derived. Several specific examples are given.     

Approximation of continuous growth of Cephalotaxus harringtonia plant cell cultures using fed-batch operation

In Cephalotaxus harringtonia plant cell cultures, periods of batch growth that are limited by hexose uptake are too short to make an accurate estimate of the Monod saturation constant. Continuous cultures are infeasible on a laboratory scale, and semicontinuous cultures require too frequent sampling. Fed-batch operation, consisting of intermittent removal from a culture that is fed continuously, was investigated as a possible solution to these problems. For a constant feed rate, computer simulations showed that a steady state can be achieved which is useful for studying growth at different specific growth rates. In terms of the dilution rate it was confirmed that the operation is essentially equivalent to continuous culture when the samples represent a small fraction of the total culture volume. Experiments with glucose or fructose as the carbon source were carried out in shake flasks fed by a multichannel syringe pump. Results indicate that Monod kinetics based on medium glucose levels cannot adequately describe growth under these conditions. Monod's expression for specific growth rate using internal glucose concentration gives an improved correlation.     

沙丘鹤在中国的分布状况

沙丘鹤（Grus canadensis）在中国的分布状况传统上被认为是迷鸟。2013年3月29日在辽宁省沈阳市法库县獾子洞湿地进行水鸟调查时,发现一只大型涉禽,经野外观察和查阅文献后确认为沙丘鹤,是辽宁省鸟类新纪录。目前我国已有沙丘鹤分布记录的地区还包括上海、江苏、江西、山东、北京、河北、吉林和黑龙江。结合文献及近年来沙丘鹤在我国稳定的越冬记录,我们认为该种在中国的分布状况应为罕见冬候鸟。     

气候变化对5种植物分布的潜在影响

利用CART(分类和回归树Classification and regression tree)模型,采用A2和B2气候情景,模拟分析了气候变化对观光木(Tsoongiodendron odorum)、鹅掌楸(Liriodendron chinense)、独叶草(Kingdonia uniflora)、草苁蓉(Boschniakia rossica)和刺五加(Acanthopanax senticosus)分布范围及空间格局的影响。结果表明:与目前适宜分布范围相比,气候发生变化后,观光木的分布范围变化不大,其它植物则缩小;观光木的新适宜与总适宜分布范围扩大,而其它植物缩小;草丛蓉和刺五加的目前适宜、新适宜及总适宜分布范围缩小幅度较大,鹅掌楸和独叶草次之;观光木和鹅掌楸向目前适宜分布区北部区域扩展,独叶草向西南区域扩展,草丛蓉和刺五加的适宜范围在2081～2100年会散失。气候变化下,这些植物的适宜分布范围随年降水量和年均气温的变化不一致,观光木的目前适宜、独叶草的新适宜及总适宜分布范围与年降水量和年均气温,以及草苁蓉的分布范围与降水量的相关性不显著(P0.05)。这些植物的空间分布格局将随气候变化而发生变化。     

The Bacillus subtilis Chemoreceptor McpC Senses Multiple Ligands Using Two Discrete Mechanisms

Bacillus subtilis can perform chemotaxis toward all 20 l-amino acids normally found in proteins. Loss of a single chemoreceptor, McpC, was previously found to reduce chemotaxis to 19 of these amino acids. In this study, we investigated the amino acid-sensing mechanism of McpC. We show that McpC alone can support chemotaxis to 17 of these amino acids to varying degrees. Eleven amino acids were found to directly bind the amino-terminal sensing domain of McpC in vitro. Sequence analysis indicates that the McpC sensing domain exhibits a dual Per-Arnt-Sim (PAS) domain structure. Using this structure as a guide, we were able to isolate mutants that suggest that four amino acids (arginine, glutamine, lysine, and methionine) are sensed by an indirect mechanism. We identified four candidate binding lipoproteins associated with amino acid transporters that may function in indirect sensing: ArtP, GlnH, MetQ, and YckB. ArtP was found to bind arginine and lysine; GlnH, glutamine; MetQ, methionine; and YckB, tryptophan. In addition, we found that ArtP, MetQ, and YckB bind the sensing domain of McpC, suggesting that the three participate in the indirect sensing of arginine, lysine, methionine, and possibly tryptophan as well. Taken together, these results further our understanding of amino acid chemotaxis in B. subtilis and gain insight into how a single chemoreceptor is able to sense many amino acids.     

A Comment on Maximum Likelihood Estimation for Finite Mixtures of Distributions

Iterative numerical methods are necessary to find the maximum likelihood estimates for finite mixture distributions. This paper shows that it will often be possible to analytically reduce the number of equations that must ultimately be solved numerically. Such a reduction in dimensionality has not generally been used, or sought after, for mixture distributions. Yet such results are easily derived when each mixture component is assumed to be from the same parametric model within the exponential family.