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PubMed2001

Using serial imaging data to model variabilities in organ position and shape during radiotherapy.

A model is proposed for incorporating the effects of organ motion into the calculation of dose in a statistical fashion based on serial imaging measurements of organ motion. These measurements can either come from a previously studied population of patients, or they can be specific to the particular patient undergoing therapy. The statistical distribution underlying the measurements of organ motion, including the changes in organ shape, is reconstructed non-parametrically without requiring any assumptions about its functional form. The model is thus capable of simulating organ motions that are not present in the original measurements, yet nonetheless come from the same underlying statistical distribution. The present model overcomes two particular limitations of many organ motion models: (a) the fact that they do not account for changes in organ shape, and (b) the fact that they make physically unrealistic assumptions about the functional form of the statistical distribution of organ motion, such as assuming that it is Gaussian. The present model can form the foundation of methods for the more accurate and clinically relevant calculation of the dose to the target volume and normal tissues.

Algorithms↗
PubMed2003

Power-law tail probabilities of drainage areas in river basins.

We examine the appearance of power-law behavior in rooted tree graphs in the context of river networks. It has long been observed that the tails of statistical distributions of upstream areas in river networks, measured above every link, obey a power-law relationship over a range of scales. We examine this behavior by considering a subset of all links, defined as those links which drain complete Strahler basins, where the Strahler order defines a discrete measure of scale, for self-similar networks with both deterministic and random topologies. We find an excellent power-law structure in the tail probabilities for complete Strahler basin areas, over many ranges of scale. We show analytically that the tail probabilities converge to a power law under the assumptions of (1) simple scaling of the distributions of complete Strahler basin areas and (2) application of Horton's law of stream numbers. The convergence to a power law does not occur for all underlying distributions, but for a large class of statistical distributions which have specific limiting properties. For example, underlying distributions which are exponential and gamma distributed, while not power-law scaling, produce power laws in the tail probabilities when rescaled and sampled according to Horton's law of stream numbers. The power-law exponent is given by the expression phi=ln(R(b))/ln(R(A)), where R(b) is the bifurcation ratio and R(A) is the Horton area ratio. It is commonly observed that R(b) approximately equal R(A) in many river basins, implying that the tail probability exponent for complete Strahler basins is close to 1.0.

Journal Article↗
PubMed2001

Regular and anomalous scaling of a randomly advected passive scalar.

Extending Kolmogorov's refined similarity hypothesis to study the inertial behavior <[T(x+r,t)-T(x,t)](2n)>~r(zeta(2n)) of a passive scalar T(x,t) advected by a rapidly changing incompressible velocity field, a random variable straight theta was introduced by Ching [Phys. Rev. Lett. 79, 3644 (1997)]. In this paper, the statistical distribution of the random variable X=straight theta/sqrt[ ] is investigated analytically for the scaling in two limits, n-independent scaling zeta(2n)=zeta(2) and regular scaling zeta(2n)=nzeta(2), and numerically for the scaling of the Kraichnan conjecture zeta(2n)=1 / 2[sqrt[4ndzeta(2)+(d-zeta(2))(2)]-(d-zeta(2))]. For n-independent scaling zeta(2n)=zeta(2), the statistical distribution of X tends to an exponential distribution when zeta(2)-->0 or d-->infinity and to a Gaussian distribution when zeta(2)-->2 and d=2. For regular scaling zeta(2n)=nzeta(2), the statistical distribution of X tends to a Gaussian distribution when zeta(2)-->0 or d-->infinity. In d=2, there seems to be a phase transition for the probability density function P(X) from a convex to a concave function when the value of zeta(2) is increased and the critical point is zeta(2)=4/3 where the random variable X has a uniform distribution in [-sqrt[3],sqrt[3]]. In d=3, P(X) is a convex function for all 0 2. For the scaling of the Kraichnan conjecture, P(X) has two peaks in d=2 for zeta(2)>1.33, but, in d=3, it has only one peak for all 0 2.

Journal Article↗
PubMed1982

Effects of visual angle on perspective reversal for ambiguous patterns.

Reversal rates of an ambiguous figure (the Necker cube) were studied for different pattern sizes covering a range of visual angles theta from approximately 1 to 62 deg. A large number of reversals was obtained for each observer and each pattern in order to examine the statistical distributions of reversal times. A pronounced flattening of the statistical distributions (represented throughout by a gamma distribution) and a growth of the mean duration of each percept, with increasing pattern size was found. A plateau in the range of theta between 5 and 20-30 deg was observed. For larger values of theta two kinds of observers have been identified: for 'fast' observers the inversion rate is little affected by theta, whilst for 'slow' observers, the mean reversal time increases strongly with theta. A tentative model, based on three different contributions to the duration of the alternation process, is proposed: a constant term, independent of theta, and two terms dependent on theta--a retinal term, and a cortical one. The last term is interpreted as due to the spreading of excitation with the characteristic of a filling-in process.

Adult↗
PubMed1988

Analysis of finite mixture of distributions: a statistical tool for biological classification problems.

A microcomputer program to analyze finite mixtures of normal, binomial, Poisson or exponential distributions by a maximum likelihood estimation procedure is described. The program is coded in Turbo Pascal. Some theoretical and practical aspects of the compound distributions are discussed, mainly mathematical characteristics, fitting procedures and tests of hypotheses. The statistical tool, which is a cluster analysis technique, is presented in a general context for applications in biology. In particular an ecological example is briefly described: the age class structure resolution of a white-tailed deer population. To improve the usefulness for classification purposes, the link with discriminant analysis is examined. For a successful analysis of finite mixture of distributions the need for a large sample size is emphasized.

Age Factors↗
PubMed2005

The Rician inverse Gaussian distribution: a new model for non-Rayleigh signal amplitude statistics.

In this paper, we introduce a new statistical distribution for modeling non-Rayleigh amplitude statistics, which we have called the Rician inverse Gaussian (RiIG) distribution. It is a mixture of the Rice distribution and the inverse Gaussian distribution. The probability density function (pdf) is given in closed form as a function of three parameters. This makes the pdf very flexible in the sense that it may be fitted to a variety of shapes, ranging from the Rayleigh-shaped pdf to a noncentral chi2-shaped pdf. The theoretical basis of the new model is quite thoroughly discussed, and we also give two iterative algorithms for estimating its parameters from data. Finally, we include some modeling examples, where we have tested the ability of the distribution to represent locale amplitude histograms of linear medical ultrasound data and single-look synthetic aperture radar data. We compare the goodness of fit of the RiIG model with that of the K model, and, in most cases, the new model turns out as a better statistical model for the data. We also include a series of log-likelihood tests to evaluate the predictive performance of the proposed model.

Algorithms↗
PubMed2002

Characterization of reperfused infarcted myocardium from high-frequency intracardiac ultrasound imaging using homodyned K distribution.

Myocardial changes caused by infarction/reperfusion (contraction band necrosis, hemorrhage, edema, etc.) may result in an increased scatterer density and a variation in scatterer arrangement. This paper, for the first time, models most of the scattering conditions resulting from the interaction of ultrasound and normal/reperfused infarcted myocardium using the homodyned K distribution. Furthermore, this method is used to characterize the change in scatterer density by calculating the effective scatterer number per resolution cell. The reliability and the effects of attenuation and scan conversion on effective scatterer number estimation are discussed. We used in vivo data acquired using high-frequency intracardiac ultrasound imaging (8.5 MHz) from the left and right ventricles of open-chest pigs in an acute infarction/reperfusion model. The results show that the homodyned K distribution describes the statistical distribution of backscattered signal from both normal and abnormal myocardium. A significant increase in scatterer density occurs in the infarcted region after reperfusion compared with the same region at baseline (normal myocardium prior to occlusion). The scatterer density of the normal region does not change significantly after reperfusion. We conclude that the homodyned K distribution may characterize normal and reperfused infarcted myocardium using high-frequency intracardiac ultrasound images.

Animals↗
PubMed2000

Impact of isospin breaking on the distribution of transition probabilities

In the present paper we investigate the effect of symmetry breaking in the statistical distributions of reduced transition amplitudes and reduced transition probabilities. These quantities are easier to access experimentally than the components of the eigenvectors and were measured by Adams et al. [Phys. Lett. B 422, 13 (1998)] for the electromagnetic transitions in 26Al. We focus on isospin symmetry breaking described by a matrix model where both the Hamiltonian and the electromagnetic operator break the symmetry. The results show that for partial isospin conservation, the statistical distribution of the reduced transition probability can considerably deviate from the Porter-Thomas distribution.

Journal Article↗
PubMedDate not supplied

Dimensions of homo- and heteropolymeric sections of DNA synthesized by reverse transcription from globin mRNA matrices.

The lengths of globin messenger RNAs, isolated from rabbit and pigeon reticulocytes, and single-stranded complementary DNAs, synthesized from mRNA in presence of RNA-directed DNA-polymerase and oligo(dt) have been investigated by polyacrylamide gel electrophoresis under denaturing conditions. The cDNA preparations contained a fraction which corresponded in length to the alpha and beta chains of the mRNA used as a matrix. The lengthwise distribution of poly(A) sequences, isolated from globin mRNAs, corresponded to a statistical distribution, with a maximum at 75-80 nucleotides and with a maximum length of approximately 150 nucleotides. The lengthwise distribution of poly(dt) sequences, isolated from cDNA, corresponded to the poly(A) sequence distribution. It was concluded that: 1) cDNA is heterogeneous with respect to the length of poly(dt) sequences located at the 5' end of the molecule; 2) there was no selective use as primer of only that oligo(dt) which was located within the complex formed with the 5' end of the mRNA poly(A) sequence; 3) the heterogeneity of poly(DT) corresponded qualitatively to two models of template-primer interaction: selective use as a true primer of the oligonucleotide located in the complex formed with the 3' end of mRNA, and a statistical distribution of primer along the poly(A) sequence; and 4) the heterogeneity of the homopolymeric section of the cDNA may affect the kinetics of hybridization with mRNA, which possibly explains the previously observed [1] anomalous dependence of the hybridization rate on time.

Animals↗
PubMed1993

Simple diagnostic statistical tests of models for DNA substitution.

The accuracy of models for DNA substitution used in phylogenetic analyses is becoming more important with the increasing availability and analysis of molecular sequence data. It is natural to look for ways of improving these models, and to do this in a planned manner it is useful to be able to identify features of sequences that may not be described adequately. In this paper, I describe three statistics which may give useful diagnostic information on departures from models' predictions. The statistical distributions of these statistics are discussed and simple significance tests are derived. These tests are based on the (estimated) phylogeny of the sequences and so have the advantage of using the information contained in this tree. Examples are given of the application of the new tests to Markov chain models describing the evolution of primate pseudogene sequences and small-subunit RNA sequences.

Animals↗
PubMed1977

Statistical comparison of power spectra: a computer program.

A general computer program, of interest to neurobiologists, for comparison of uncorrelated power spectra is presented. The program, ALPHAF, is written in Fortran V language and is easily compiled and executed in any computer with a Fortran software package. The purpose of the program is to read power spectral density (PSD) values into a computer from digital tape and then perform the following functions: (1) compute and report power; (2) compute and report averages of the computed power values over selected frequency bands and (3) compute and report statistical standardised normal distributions for a frequency spectrum of interest. The standardised normal distribution statistic is derived by using equation 7.20, page 250 of Random data: Analysis and measurement procedures (Bendat and Piersol, 1971).

Computers↗
PubMed2006

A deconvolution method for the separation of specific versus nonspecific interactions in noncovalent protein-ligand complexes analyzed by ESI-FT-ICR mass spectrometry.

A method to separate specific and nonspecific noncovalent interactions observed in ESI mass spectra between a protein and its ligands is presented. Assuming noncooperative binding, the specific ligand binding is modeled as a statistical distribution on identical binding sites. For the nonspecific fraction we assume a statistical distribution on a large number of "nonspecific" interacting sites. The model was successfully applied to the noncovalent interaction between the protein creatine kinase (CK) and its ligands adenosine diphosphate (ADP) and adenosine triphosphate (ATP) that both exhibit nonspecific binding in the mass spectrum. The two sequential dissociation constants obtained by applying our method are K(1,diss) = 11.8 +/- 1.5 microM and K(2,diss) = 48 +/- 6 microM for ADP. For ATP, the constants are K(1,diss) = 27 +/- 7 microM and K(2,diss) = 114 +/- 27 microM. All constants are in good correlation with reported literature values. The model should be valuable for systems with a large dissociation constant that require high ligand concentrations and thus have increased potential of forming nonspecific adducts.

Adenosine Diphosphate↗
PubMed1988

Postnatal development of the mouse temporal muscle and effects of a fine-grained diet on the muscle spindle.

The postnatal development of the mouse temporal muscle and effects of a fine-grained diet on muscle spindles were investigated. On d 25 after birth, 3 types of extrafusal muscle fibers could be distinguished on the basis of SDH activity, but not on the basis of their diameters. And in 50-d-old mice, 3 types of the muscle fibers had different diameters each other. In intrafusal muscle fibers, the postnatal changes of the SDH activity were similar to those of extrafusal muscle fibers, but the diameter distribution showed unimodal statistical distribution from 10th to 50th postnatal day. On the other hand, in control 180-d-old mice, 80 percent of muscle spindles in the temporal muscle had complete annulospiral endings, but the ratio of muscle spindles with complete annulospiral endings was decreased significantly in mice fed a fine-grained diet. The diet also decreased the diameter of the endings significantly. These results suggest that the main changes in the morphological and functional properties of the mouse temporal muscle occur in during and early after weaning period, and that normal mastication is needed to maintain the homeostatic condition of the mouse temporal muscle.

Animals↗
PubMed1996

Relevant parameters for describing the oxygenation status of solid tumors.

AIM: Several studies using different methods of pO2 measurement have shown that in many tumor entities tissue oxygenation is quite heterogeneous and thus cannot be sufficiently described by a single value. This study presents those distribution parameters which are mandatory to describe the complete oxygenation status of a solid tumor. METHODS: In determining the oxygenation status different aspects of relevancy have to be taken into account. First, several parameters are necessary to characterize the location, the spread, and the shape of the pO2 distribution from a statistical point of view (statistical parameters). In addition, parameters for the description of the biological relevance of the tumor oxygenation have to be considered (biological parameters). These parameters reflect the role of oxygenation for the metabolic microenvironment and the biological behavior of the tumor as well as the significance under therapeutic and diagnostic aspects. Finally, some parameters are necessary to assess the quality of pO2 measurement itself (quality parameters). RESULTS: By combining all pO2 readings from one tumor a statistical distribution is obtained, which is in many tumors asymmetrically shifted towards low pO2 values. In order to describe the location, spread, and shape of this distribution the following parameters should be stated: median, mean, 10% and 90% percentile, minimum, maximum and 10 to 90% interpercentile range. For data presentation these values can be combined in a box-whiskers plot. In order to reflect the importance of tumor oxygenation under diagnostic, therapeutic or cell-biological aspects the fraction of pO2 readings < or = 2.5 mm Hg, < or = 5 mm Hg, and < or = 10 mm Hg should be stated. Where negative pO2 readings occur in a study, the fraction of pO2 readings < 0 mm Hg as well as the most negative pO2 value should be presented in order to assess the quality of the pO2 measurement. CONCLUSIONS: For a comprehensive description of the oxygenation status of solid tumors the following distribution parameters should be stated: median, mean, 10% and 90% percentile, minimum, maximum, 10 to 90% interpercentile range, fraction of pO2 readings < 0 mm Hg, < or = 2.5 mm Hg, < or = 5 mm Hg, and < or = 10 mm Hg as well as the most negative pO2 reading.

Humans↗
PubMed1986

How should we estimate confidence intervals for a ratio, for example, between counts of colony-forming cells?

When calculating a ratio, of colony counts, for example, experimental hematologists often provide no indication of the uncertainty of the estimates, or the uncertainty is computed using a method with partially unknown properties. We have used empirical data on survival of colony-forming cells after exposure to hydroxyurea to select assumptions regarding the statistical properties of the survival ratios. Then, we have evaluated four alternative methods for constructing confidence intervals for such ratios. With simulations, the adequacy of the methods is shown to depend on the assumed statistical distributions of the data and on the number of observations in the numerator and denominator. Especially with few observations, some methods may produce misleading results. An easily calculable confidence interval, formally based on lognormal distributions, seems to be applicable to a fairly wide range of other plausible statistical distributions as well; it may be a reasonable choice in many situations. Whatever method is chosen, the confidence intervals for ratios are wide, and more data than is generally appreciated are needed for a precise determination of a ratio.

Animals↗
PubMed1984

Creation of the transformed Q statistic probability distribution to aid in the detection of abnormal computerized visual fields.

This paper describes the creation of a new Q statistic which can be calculated from the threshold data of a single computerized visual field. The Q statistic can then be used to decide, at a given significance level, whether the individual field is normal or abnormal. The Q statistic is constructed to be particularly sensitive to the situation in which only a small subset of the values in the field is depressed, making it particularly useful in the diagnosis of early glaucoma.

Adult↗