A study of the statistical distribution of the volumes of celluar nuclei and and its relation to the statistical distribution of their projection areas.
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Cell Nucleus↗
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Results for “Statistical Distributions”
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[On the problem of the separation of statistical distributions deviating from normal into 2 normal distributions. I. Symmetric distributions].
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Humans↗
Problem of resolution of statistical distributions deviating from normal into two normal distributions. I. Asymmetrical distributions.
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Humans↗
Constrained systems and statistical distribution
Theoretical advances in the statistical description of non-Hamiltonian systems [Tuckerman, Mundy, and Martyna, Europhys. Lett. 45, 149 (1999)] have recently led us to rethink the definition of the phase-space probability by using the proper invariant measure. Starting from this point of view, we will derive the statistical distribution of constrained systems, considered as non-Hamiltonian, in Cartesian coordinates, in a way independent from the standard Lagrangian treatment. Furthermore, we will analyze the statistical distribution of the Nose-Hoover isothermal (canonical or NVT) dynamics, considering with care the conservation laws hidden in the evolution equations. Consequently, we will correct the equations of motion in order to obtain the proper statistical ensemble. The isobaric-isothermal (constant pressure or NpT) form of the Nose-Hoover dynamics is then considered as a nontrivial extension of the described procedure and, similarly to the NVT case, we will correct the equations of motion with respect to previous versions. The case of a constrained system coupled to a thermostat and a piston is easily handled by means of the same formalism, whereas the Lagrangian treatment becomes involved.
Journal Article↗
The statistical distribution of colony counts in the spleen colony assay.
The statistical distribution of colony counts in the spleen colony assay was determined in C57BL/6 and C3H mice under varying conditions of the assay procedure. Assay mice were given syngeneic bone marrow cells from normal or irradiated donors. The mice were injected intravenously with marrow cells either immediately or 3 days after irradiation. Eight days after engraftment, spleen colonies were counted and the statistical distribution of colony counts was determined using a mean to variance ratio criterion. Analysis of the data indicated that the statistical distribution of colony counts was different in the two strains of mice. In addition, delaying time of injection of mice with bone marrow cells or injecting bone marrow cells form irradiated donors also changed the statistical distribution. The significance of this work lies in the fact that modification of the usual assay procedure can alter the statistical distribution of colony counts, thus changing the statistical accuracy of the assay. Modification in the assay procedure, such that an increase occurs in the variance of the distribution of colony counts, must be compensated for by increasing the number of spleens counted in order to maintain a constant level of statistical accuracy in experiments.
Animals↗
The depth of the lingual fossa in permanent maxillary incisors of East Greenland Eskimos. I. Statistical distribution and fluctuating dental asymmetry.
Maxillary incisor lingual fossa depth was measured in East Greenland Eskimos. It was shown that the statistical distribution for the trait may vary from population to population, from tooth type to tooth type and between the sexes. Examination of statistical distribution should be a part of studies giving detailed statistical analysis of trait. The statistical distribution is probably compatible with a hypothesis of polygenic inheritance. The correlations across the midline were higher for I1 than for I2, and I1 to I2 correlations were lower than across midline correlations for both I1 and I2. It was shown that the degree of fluctuating asymmetry may vary from one dental trait to another. For lingual fossa depth no population variation in fluctuating asymmetry could be demonstrated, in spite of obvious differences in environmental conditions for the populations compared. No sex differences in fluctuating asymmetry were found.
Female↗
Survival equations for red blood cells with statistical distributions in life spans.
The survival equations for labelled RBCs taking into account a hypothetical Gaussian (or binomial) statistical distribution for the life spans, with and without random destruction, have been derived in this paper. The numerical integration of these equations emphasises some particularities which will result from the existence of broad life span distributions. The differences between the results obtained with hypothetical populations of RBCs having statistical distributions for the life spans and hypothetical populations of RBCs with life spans equal to the distributions mean value for every cell are also discussed.
Erythrocyte Aging↗
Statistical distributions of optimal global alignment scores of random protein sequences.
BACKGROUND: The inference of homology from statistically significant sequence similarity is a central issue in sequence alignments. So far the statistical distribution function underlying the optimal global alignments has not been completely determined. RESULTS: In this study, random and real but unrelated sequences prepared in six different ways were selected as reference datasets to obtain their respective statistical distributions of global alignment scores. All alignments were carried out with the Needleman-Wunsch algorithm and optimal scores were fitted to the Gumbel, normal and gamma distributions respectively. The three-parameter gamma distribution performs the best as the theoretical distribution function of global alignment scores, as it agrees perfectly well with the distribution of alignment scores. The normal distribution also agrees well with the score distribution frequencies when the shape parameter of the gamma distribution is sufficiently large, for this is the scenario when the normal distribution can be viewed as an approximation of the gamma distribution. CONCLUSION: We have shown that the optimal global alignment scores of random protein sequences fit the three-parameter gamma distribution function. This would be useful for the inference of homology between sequences whose relationship is unknown, through the evaluation of gamma distribution significance between sequences.
Algorithms↗
A family of statistical distributions for modelling occupational radiation doses in low dose occupations.
New statistical distributions have been defined to describe occupational exposures to ionising radiation. These distributions are particularly useful in modelling occupations where most doses are low. The maximum likelihood method was used for parameter estimation and has been adapted to allow doses that are recorded as zero to be included in the calculations. The method can then be applied to estimate true doses from the complete set of recorded dose values when the a priori dose distribution and the dose measurement distributions have been derived previously. This application is important in epidemiological cohort studies where it can improve the accuracy of excess relative risk estimates.
Humans↗
Fundamentals and systematics of the non-statistical distributions of isotopes in natural compounds.
The intermolecular and intramolecular non-statistical distribution of the isotopes of the bio-elements in natural compounds must obviously be controlled by logical principles. However, a critical review of the available isotope patterns of natural compounds indicates that a previously discussed general thermodynamic order and its mechanistic foundation cannot satisfactorily explain all experimental data. In the present contribution it is shown that a partial thermodynamic order can eventually be attained for defined positions and compounds under steady-state conditions of metabolism. However, as biological systems are generally open and irreversible, many other in vivo isotope discriminations are dominated by kinetic isotope effects, even in context with reversible reactions. On the other hand, kinetic isotope effects can only become effective in vivo in combination with metabolic branching and the implied isotope shifts of the products are balanced by their relative yields. In vivo, the influences of thermodynamic and kinetic isotope effects are modulated by interferences of the actual metabolic conditions, such as the nature and kind of precursors, alternative metabolic pathways, metabolite pools and fluxes, and by reaction mechanisms. This is demonstrated by giving examples for the isotopes of hydrogen, carbon, nitrogen, oxygen and sulfur, while simultaneously the particularities of the individual elements are elaborated. The resulting general theory of the origin of non-statistical isotope distributions in biological systems permits the interpretation and prediction of isotope patterns and provides the scientific basis for the elucidation of biosyntheses and origin assignments of natural compounds.
Biological Factors↗
Statistical distributions of ambient air pollutants in Shanghai, China.
OBJECTIVE: To determine the best statistical distribution of concentration data of major air pollutants in Shanghai. METHODS: Four types of theoretic distributions (lognormal, gamma, Pearson V and extreme value) were chosen to fit daily average concentration data of PM10, SO2 and NO2 from June 1, 2000 to May 31, 2003 in Shanghai by using the maximum likelihood method. The fit results were evaluated by Chi-square test. RESULTS: The best-fit distributions for PM10, SO2 and NO2 concentrations in Shanghai were lognormal, Pearson V, and extreme value distributions, respectively. CONCLUSION: The results can be further applied to local air pollution prediction and control, e.g., the probabilities exceeding the air quality standard and emission source reduction of air pollutant concentration to meet the standard.
Air Pollutants↗
[On the problem of dissociation of statistical distributions deviating from normal values into 2 normal distributions. II. Asymmetric distributions].
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Humans↗
Statistics in medical research--IV. Sampling distribution, statistical testing of hypothesis and student's t-test.
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Data Interpretation, Statistical↗
Quantitating the statistical distribution of deuterium incorporation to extend the utility of H/D exchange MS data.
Measuring the statistical distribution of deuterium incorporated into enzymatically derived peptide fragments provides a valuable dimension to hydrogen/deuterium exchange mass spectrometry data. In this paper, we will discuss our improvement to the linear least-squares method for determining this distribution, through the addition of "zeroes" to the end of the deuterated isotopic envelope, to partially compensate for data truncation due to finite instrumental signal-to-noise ratios. The value of the distribution is demonstrated in a simple experimental example, where the linearity between average deuteration and percent D2O used to label test peptides hides a more complex relationship between the site-labeling probability and the total number of sites. This method offers the opportunity to resolve cases where a single peptide experiences distinct, independent biochemical states with each bearing a unique average deuteration; this can occur when a protein is modified to substoichiometric levels. From the experimentally determined distribution of a heterogeneously deuterated peptide, it was possible to extract the average deuteration of each component of the mixture.
Deuterium↗
Statistical distribution of foveal transverse chromatic aberration, pupil centration, and angle psi in a population of young adult eyes.
Subjective transverse chromatic aberration (sTCA) manifest at the fovea was determined for a population of 85 young adults (19-38 years old) by means of a two-dimensional, two-color, vernier alignment technique. The statistical distribution of sTCA was well fitted by a bivariate Gaussian function with mean values that were not significantly different from zero in either the horizontal or the vertical direction. We conclude from this result that a hypothetical, average eye representing the population mean of human eyes with medium-sized pupils is free of foveal sTCA. However, the absolute magnitude of sTCA for any given individual was often significantly greater than zero and ranged from 0.05 to 2.67 arcmin for the red and the blue lights of a computer monitor (mean wavelengths, 605 and 497 nm, respectively). The statistical distribution of the absolute magnitude of sTCA was well described by a Rayleigh probability distribution with a mean of 0.8 arcmin. A simple device useful for population screening in a clinical setting was also tested and gave concordant results. Assuming that sTCA at the fovea is due to decentering of the pupil with respect to the visual axis, we infer from these results that the pupil is, on average, well centered in human eyes. The average magnitude of pupil decentration in individual eyes is less than 0.5 mm, which corresponds to psi = 3 deg for the angle between the achromatic and the visual axes of the eye.
Accommodation, Ocular↗
[Statistical distribution of dipeptides in protein structures and dynamic characteristics of some protein fragments].
Statistical distributions of the occurrence of dipeptide fragments in proteins were studied. Various algorithms of ordering of files of frequency distribution were used. A correlation of occurrence of pairs of amino acid residues in various classes of proteins was established. The problem of the dynamic compatibility of amino acid residues in protein structures is discussed. The dynamic properties of frequently and seldom occurring dimers of amino acids are compared.
Amino Acid Sequence↗
Statistical distribution of hydrophobic residues along the length of protein chains. Implications for protein folding and evolution.
We consider in this paper the statistical distribution of hydrophobic residues along the length of protein chains. For this purpose we used a binary hydrophobicity scale which assigns hydrophobic residues a value of one and non-hydrophobes a value of zero. The resulting binary sequences are tested for randomness using the standard run test. For the majority of the 5,247 proteins examined, the distribution of hydrophobic residues along a sequence cannot be distinguished from that expected for a random distribution. This suggests that (a) functional proteins may have originated from random sequences, (b) the folding of proteins into compact structures may be much more permissive with less sequence specificity than previously thought, and (c) the clusters of hydrophobic residues along chains which are revealed by hydrophobicity plots are a natural consequence of a random distribution and can be conveniently described by binomial statistics.
Amino Acids↗
A statistical distribution with an unbounded hazard function and its application to a theory from demography.
We introduce a statistical distribution with hazard function mu(t) proportional to (psi-t)beta-1 for 0 less than or equal to t less than psi and shape parameter beta satisfying 0 less than beta less than 1. This hazard function is suggested by a theory of aging in demography. We discuss properties of this distribution and maximum likelihood estimates of its parameters. Mixture distributions are considered to account for pooling across dissimilar populations. This model is compared with the Gompertz and generalized Pareto distributions and used to estimate a finite limit on human lifespan based on the survival of a group of female centenarians.
Aged↗