scholarly journals VSS: Variance-stabilized signals for sequencing-based genomic signals

2020 ◽  
Author(s):  
Faezeh Bayat ◽  
Maxwell Libbrecht
Keyword(s):  
Negative Binomial ◽  
Empirical Relationship ◽  
Data Sets ◽  
Data Set ◽  
Variance Stabilization ◽  
Mean And Variance ◽  
The Mean ◽  
Genomic Signals ◽  
Mean Variance ◽  
Inverse Hyperbolic Sine

AbstractMotivationA sequencing-based genomic assay such as ChIP-seq outputs a real-valued signal for each position in the genome that measures the strength of activity at that position. Most genomic signals lack the property of variance stabilization. That is, a difference between 100 and 200 reads usually has a very different statistical importance from a difference between 1,100 and 1,200 reads. A statistical model such as a negative binomial distribution can account for this pattern, but learning these models is computationally challenging. Therefore, many applications—including imputation and segmentation and genome annotation (SAGA)—instead use Gaussian models and use a transformation such as log or inverse hyperbolic sine (asinh) to stabilize variance.ResultsWe show here that existing transformations do not fully stabilize variance in genomic data sets. To solve this issue, we propose VSS, a method that produces variance-stabilized signals for sequencingbased genomic signals. VSS learns the empirical relationship between the mean and variance of a given signal data set and produces transformed signals that normalize for this dependence. We show that VSS successfully stabilizes variance and that doing so improves downstream applications such as SAGA. VSS will eliminate the need for downstream methods to implement complex mean-variance relationship models, and will enable genomic signals to be easily understood by [email protected]://github.com/faezeh-bayat/Variance-stabilized-units-for-sequencing-based-genomic-signals.

scholarly journals Never-buyers of consumer non-durables

1984 ◽  
Vol 15 (3) ◽  
pp. 155-161
Author(s):  
C. Firer
Keyword(s):  
Graduate School ◽  
Negative Binomial ◽  
Toilet Soap ◽  
Traditional Theory ◽  
Data Sets ◽  
Data Set ◽  
Frequency Distributions ◽  
Unpublished Work ◽  
Time Period ◽  
Zero Cell

In this article the concept of never-buyers of consumer non-durables is discussed. The traditional Negative Binomial Distribution approach of Ehrenberg to the question is presented. Previously unpublished work carried out at the Graduate School of Business Administration, University of the Witwatersrand, is reviewed and hypotheses are put forward that the observed large zero cell in the purchase frequency distributions may be caused by the existence of a group of never-buyers of the product, or by the superimposition of at least two distinct buying populations, previously identified as brand-loyal and multibrand/brand-switching households. The results of the research aimed at testing the first hypothesis are presented here. Two carefully monitored data sets were modelled using zero-augmented Negative Binomial and Sichel distributions. The data were previously shown to exhibit the necessary mean households purchase/consumption stationarity. Individual brands in one data set (purchases of toilet soap) were shown to follow the predictions of the traditional theory - the proportion of non-buyers decreasing with time. In the second data set (consumption of packaged soup) the proportion of non-consumers of the brands fell towards zero as the length of the time period studied was increased, but at a rate faster than that predicted by the theory. The hypothesis of the existence of never-buyers/users of individual brands in these two product classes was therefore rejected.

Expected consequences of the segregation of a major gene in a sheep population in relation to observations on the ovulation rate of a flock of Cambridge sheep

1990 ◽  
Vol 51 (2) ◽  
pp. 277-282 ◽  
Author(s):  
J. B. Owen ◽  
C. J. Whitaker ◽  
R. F. E. Axford ◽  
I. Ap Dewi
Keyword(s):  
Gene Frequency ◽  
Major Gene ◽  
Ovulation Rate ◽  
Phenotypic Effect ◽  
Data Set ◽  
Sheep Population ◽  
Mean Values ◽  
Population Mean ◽  
Mean And Variance ◽  
The Mean

ABSTRACTA simple model was derived relating the phenotypic effect (g) of a major gene to observed values of the population mean and variance for a trait, at specified values of the major gene frequency and at specified basal values of the population mean and variance (in the absence of the major gene). This model was applied to a total of 549 observed values of ovulation rate in ewes of the Cambridge breed at Bangor under a range of assumptions. The mean values of ovulation rate were 2·44 for 243 ewes of 1 year of age and 37·54 for 306 ewes of 2 and 3 years of age with a coefficient of variation for both age sets of 0·50.The results indicate a minimum value for g, in this data set, of 1·07 for 1 year old and 1·72 for 2 and 3 year old ewes. The results are also consistent with a frequency value in the region of 0·3 to 0·4, with the absence of dominance and with a reasonable concordance with Hardy-Weinburg equilibrium. The results also indicate that the value of g varies according to the background phenotype since it is lower for younger as compared with older ewes.

A Graphic Approach to Summarizing Forestry Data

1987 ◽  
Vol 63 (5) ◽  
pp. 347-350 ◽  
Author(s):  
Stephen J. Titus
Keyword(s):  
Forest Inventory ◽  
Data Distribution ◽  
Data Sets ◽  
Summary Statistics ◽  
Tree Diameter ◽  
Volume Function ◽  
Mean And Variance ◽  
The Mean ◽  
Diameter Distributions

Boxplots are a useful enhancement to the traditional summary statistics such as the mean and variance. Based on the median and other percentiles of the data distribution, they provide more information in a graphic format which is convenient for interpreting the nature of one or several data sets Use of boxplots is illustrated with three common types of forestry data: 1) tree diameter distributions, 2) tree volume function residuals, and 3) forest inventory summaries.

Crystal and Molecular Structure of Thiocarbonyl-ethoxo(tetraphenylporphyrinato)ruthenium(II), [Ru(TPP)(CS)(HOC2H5)]. A Case of Centrosymmetric–Noncentrosymmetric Ambiguity

1997 ◽  
Vol 53 (5) ◽  
pp. 767-772 ◽  
Author(s):  
T. J. Bartczak ◽  
K. Rachlewicz ◽  
L. Latos-Grażynski
Keyword(s):  
Crystal And Molecular Structure ◽  
Bond Angle ◽  
Data Sets ◽  
Alpha Radiation ◽  
Data Set ◽  
Fourier Methods ◽  
Space Group ◽  
Space Groups ◽  
The Mean ◽  
Difference Fourier

[Ru(TPP)(CS)(EtOH)] crystallizes in the triclinic system. Crystal data: C47H34N4ORuS, M r = 803.91, a = 10.607 (3), b = 11.308 (5), c = 17.699 (2) Å, \alpha = 77.53 (2), \beta = 73.17 (1), \gamma = 69.85 (3)°, V = 1891.6 (10) Å3, P\overline 1 (C^{1}_{i}, no. 2), Z = 2, F(000) = 824, D x = 1.410, D m = 1.39 Mg m−3 (by flotation in aqueous KI), \mu(Mo K\alpha) = 0.512 mm−1, R = 0.094, wR = 0.098, S = 2.28 for 4610 independent reflections with F o > 5\sigma(F o ). A second data set was collected using Cu K\alpha radiation. The structure was refined by standard least-squares and difference-Fourier methods in space groups P1 and P\overline 1 using both the Mo K\alpha and Cu K\alpha data sets. Both data sets favor space group P\overline 1, the Mo data giving a slightly better result than the Cu data. The two independent Ru atoms lie on the inversion centers ½,0,0 and ½,½,½ of space group P\overline 1. Consequently, the two independent molecules have crystallographically imposed \overline 1 symmetry, the CS and EtOH axial groups are disordered and the RuN4 portions of the molecules are planar. The deviations from planarity of the porphyrinato core are very small. The Ru—C—S groups are essentially linear with an average Ru—C—S bond angle of 174 (1)°. The mean Ru—C(CS) and Ru—O (Et) bond lengths are 1.92 (4) and 2.15 (3) Å, respectively.

Variance heterogeneity, transformations, and models of species abundance: a cautionary tale

2004 ◽  
Vol 61 (7) ◽  
pp. 1294-1302 ◽  
Author(s):  
Brian H McArdle ◽  
Marti J Anderson
Keyword(s):  
Type I Error ◽  
Species Abundance ◽  
Ecological Systems ◽  
Type I ◽  
Data Set ◽  
Bootstrap Tests ◽  
Inflated Type ◽  
The Mean ◽  
Nonparametric Alternatives ◽  
Mean Variance

Ecological systems have intrinsic heterogeneity. Counts of abundances of species often show heterogeneity of variances among observational groups or populations. This is most often dealt with by using a transformation of the data followed by a traditional statistical analysis that requires homogeneity. Such an approach is extremely useful when the mean–variance relationship is consistent across the data set. In some situations, however, the mean–variance relationship does not stay constant, e.g., the degree of spatial aggregation of organisms can change in space and time. In these cases, transforming the data to "fix" the problem of heterogeneity can result in apparently grossly inflated type I error. The use of a transformation alters the model under test and also has an important effect on the spatial scale of the hypothesis. The use of nonparametric alternatives, such as permutation or bootstrap tests, does not solve this problem. Explicit models of these kinds of distributional changes, where they occur, are necessary.

scholarly journals Effects of environmental factors on multiple ovulation of zebu donors

2006 ◽  
Vol 58 (4) ◽  
pp. 567-574 ◽  
Author(s):  
M.G.C.D. Peixoto ◽  
J.A.G. Bergmann ◽  
C.G. Fonseca ◽  
V.M. Penna ◽  
C.S. Pereira
Keyword(s):  
Environmental Factors ◽  
Least Squares ◽  
Inbreeding Coefficient ◽  
Corpora Lutea ◽  
Data Sets ◽  
Data Set ◽  
The Third ◽  
Multiple Ovulation ◽  
The Mean ◽  
Best Responses

Data on 1,294 superovulations of Brahman, Gyr, Guzerat and Nellore females were used to evaluate the effects of: breed; herd; year of birth; inbreeding coefficient and age at superovulation of the donor; month, season and year of superovulation; hormone source and dose; and the number of previous treatments on the superovulation results. Four data sets were considered to study the influence of donors’ elimination effect after each consecutive superovulation. Each one contained only records of the first, or of the two firsts, or three firsts or all superovulations. The average number of palpated corpora lutea per superovulation varied from 8.6 to 12.6. The total number of recovered structures and viable embryos ranged from 4.1 to 7.3 and from 7.3 to 13.8, respectively. Least squares means of the number of viable embryos at first superovulation were 7.8 ± 6.6 (Brahman), 3.7 ± 4.5 (Gyr), 6.1 ± 5.9 (Guzerat) and 5.2 ± 5.9 (Nellore). The numbers of viable embryos of the second and the third superovulations were not different from those of the first superovulation. The mean intervals between first and second superovulations were 91.8 days for Brahman, 101.8 days for Gyr, 93.1 days for Guzerat and 111.3 days for Nellore donors. Intervals between the second and the third superovulations were 134.3, 110.3, 116.4 and 108.5 days for Brahman, Gyr, Guzerat and Nellore donors, respectively. Effects of herd nested within breed and dose nested within hormone affected all traits. For some data sets, the effects of month and order of superovulation on three traits were importants. The maximum number of viable embryos was observed for 7-8 year-old donors. The best responses for corpora lutea and recovered structures were observed for 4-5 year-old donors. Inbreeding coefficient was positively associated to the number of recovered structures when data set on all superovulations was considered.

scholarly journals Aerosol-cirrus interactions: A number based phenomenon at all?

2003 ◽  
Vol 3 (4) ◽  
pp. 3625-3657
Author(s):  
M. Seifert ◽  
J. Ström ◽  
R. Krejci ◽  
A. Minikin ◽  
A. Petzold ◽  
...  
Keyword(s):  
Aerosol Particles ◽  
Cloud Formation ◽  
Data Sets ◽  
Number Density ◽  
Cloud Droplets ◽  
Data Set ◽  
Local Maxima ◽  
The Mean ◽  
Positive Correlations ◽  
Aerosol Cloud Interactions

Abstract. In situ measurements of the partitioning of aerosol particles within cirrus clouds were used to investigate aerosol-cloud interactions in ice clouds. The number density of interstitial aerosol particles (non-activated particles in between the cirrus crystals) was compared to the number density of cirrus crystal residuals. The data was obtained during the two INCA (Interhemispheric Differences in Cirrus Properties form Anthropogenic Emissions) campaigns, performed in the Southern Hemisphere (SH) and Northern Hemisphere (NH) midlatitudes. Different aerosol-cirrus interactions can be linked to the different stages of the cirrus lifecycle. Cloud formation is linked to positive correlations between the number density of interstitial aerosol (Nint) and crystal residuals (Ncvi), whereas the correlations are smaller or even negative in a dissolving cloud. Unlike warm clouds, where the number density of cloud droplets is positively related to the aerosol number density, we observed a rather complex relationship when expressing Ncvi as a function of Nint for forming clouds. The data sets are similar in that they both show local maxima in the Nint range 100 to 200 cm−3, where the SH-maximum is shifted towards the higher value. For lower number densities Nint and Ncvi are positively related. The slopes emerging from the data suggest that a tenfold increase in the aerosol number density corresponds to a 3 to 4 times increase in the crystal number density. As Nint increases beyond the ca. 100 to 200 cm−3, the mean crystal number density decreases at about the same rate for both data sets. For much higher aerosol number densities, only present in the NH data set, the mean Ncvi remains low. The situation for dissolving clouds presents two alternative interactions between aerosols and cirrus. Either evaporating clouds are associated with a source of aerosol particles, or air pollution (high aerosol number density) retards evaporation rates.

scholarly journals The Mean and Variance of the Mean‐Variance Decision Rule

1990 ◽  
Vol 72 (4) ◽  
pp. 966-974 ◽  
Author(s):  
James A. Chalfant ◽  
Robert N. Collender ◽  
Shankar Subramanian
Keyword(s):  
Decision Rule ◽  
Mean And Variance ◽  
The Mean ◽  
Mean Variance

Analysis of anomaly correlations

Geophysics ◽  
1997 ◽  
Vol 62 (1) ◽  
pp. 342-351 ◽  
Author(s):  
Ralph R. B. von Frese ◽  
Michael B. Jones ◽  
Jeong Woo Kim ◽  
Jeong‐Hee Kim
Keyword(s):  
Graphical Representation ◽  
The Other ◽  
Digital Data ◽  
Data Sets ◽  
Correlation Filters ◽  
Geophysical Interpretation ◽  
Frequency Domains ◽  
Mean And Variance ◽  
The Mean ◽  
Normalization Factors

Recognizing correlations between data sets is the basis for rationalizing geophysical interpretation and theory. Procedures are presented that constitute an effective process for identifying correlative features between two or more digital data sets. The procedures include the development of normalization factors from the mean and variance properties of the data sets. Using these factors, the data sets may be transformed so that they have common amplitude ranges, means, and variances, thereby allowing a common graphical representation of the data sets that facilitates the visualization of feature correlations. Anomaly features that show direct, inverse, or no correlations between data sets may be separated by the application of correlation filters in the frequency domains of the data sets. The correlation filter passes or rejects wavenumbers between coregistered data sets based on the correlation coefficient between common wavenumbers as given by the cosine of their phase difference. Standardizing and summing the filtered outputs where directly correlative features have been enhanced yields local favorability indices that optimize the perception of these features. Differencing the standardized outputs where inversely correlative features have been enhanced, on the other hand, provides favorability indices that improve the perception of the inverse correlations. This study includes a generic example, as well as magnetic and gravity anomaly profile examples that illustrate the usefulness of these procedures for extracting correlative features between digital data sets.

scholarly journals An Effective Technique on Clustering in Perspective of Huge Data Set

2020 ◽  
Vol 8 (6) ◽  
pp. 4485-4491
Keyword(s):  
Data Sets ◽  
Statistical Machine Learning ◽  
Science And Engineering ◽  
Effective Technique ◽  
Data Set ◽  
Cluster Technique ◽  
Data Object ◽  
Cluster Set ◽  
Huge Data ◽  
The Mean

Analysis of data plays a crucial job considering the different phenomenon. It explores the prior knowledge, consisting of development across the extensively different communities. Cluster technique is the collecting of data object placed into groups. Therefore objects are the same nature or similar place within a cluster different nature (i.e. dissimilar) put in other cluster. Differences and likeness are refereed on the attribute values say that the objects involved in measuring distance. We have reviewed a few clustering techniques for data sets in data mining of various field of computer science and engineering, statistical, machine learning and a novel attracting field of demanding efforts. Several closely related concepts of neural network, fuzzy and genetic algorithm are also discussed. In this research paper to also discussed the facebook data set to mining the attributes from the cluster set to changing the mean square error 0-10 -6 and also discuss measuring the performance.

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