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PubMed2001

A New Population Balance Model for Crystal Size Distributions: Reversible, Size-Dependent Growth and Dissolution.

A new approach to crystal growth and dissolution, based on a population balance equation (PBE) similar to models of reversible chain polymerization, describes reversible solute addition to crystal surfaces. The PBE, in combination with a mass balance for solute, can be solved for mass moments of the crystal size distribution (CSD). The first three moments provide the number, average mass, and CSD variance, which allow representation of the CSD by two-parameter, normalized statistical distributions, such as lognormal or gamma distributions. With realistic initial conditions, operating parameters, and rate coefficients, the new theory describes crystal growth, dissolution, and recrystallization (Ostwald ripening) processes. Size-dependent interfacial energy affects solubility and nucleation and determines the driving force for growth or dissolution. Because the model is reversible, the CSD evolves appropriately to equilibrium. The moment equations are readily solved and show properties consistent with observed crystal growth behavior. Copyright 2001 Academic Press.

Journal Article↗
PubMed1982

Comparative pharmacokinetics of benzodiazepines in dog and man.

The pharmacokinetic parameters disposition half-life, metabolic clearance, volume of distribution, intrinsic clearance of unbound drug, and (distributive tissue volume/unbound fraction in tissue) were compared for 12 benzodiazepines in dog and man. With the exception of volume of distribution, statistically significant correlations were obtained when parameters were plotted on a double logarithmic grid. In general, benzodiazepines were metabolized more rapidly and exhibited greater tissue distribution in dog than in man. The variability in parameters was such, however, as to make extrapolations from one species to another subject to considerable error.

Animals↗
PubMed1999

Analytical propagation of errors in dynamic SPECT: estimators, degrading factors, bias and noise.

Dynamic SPECT is a relatively new technique that may potentially benefit many imaging applications. Though similar to dynamic PET, the accuracy and precision of dynamic SPECT parameter estimates are degraded by factors that differ from those encountered in PET. In this work we formulate a methodology for analytically studying the propagation of errors from dynamic projection data to kinetic parameter estimates. This methodology is used to study the relationships between reconstruction estimators, image degrading factors, bias and statistical noise for the application of dynamic cardiac imaging with 99mTc-teboroxime. Dynamic data were simulated for a torso phantom, and the effects of attenuation, detector response and scatter were successively included to produce several data sets. The data were reconstructed to obtain both weighted and unweighted least squares solutions, and the kinetic rate parameters for a two-compartment model were estimated. The expected values and standard deviations describing the statistical distribution of parameters that would be estimated from noisy data were calculated analytically. The results of this analysis present several interesting implications for dynamic SPECT. Statistically weighted estimators performed only marginally better than unweighted ones, implying that more computationally efficient unweighted estimators may be appropriate. This also suggests that it may be beneficial to focus future research efforts upon regularization methods with beneficial bias-variance trade-offs. Other aspects of the study describe the fundamental limits of the bias variance trade-off regarding physical degrading factors and their compensation. The results characterize the effects of attenuation, detector response and scatter, and they are intended to guide future research into dynamic SPECT reconstruction and compensation methods.

Algorithms↗
PubMed2005

A procedure to define natural groundwater conditions of groundwater bodies in Germany.

Commissioned by Germany's Working Group of the Federal States on Water Problems (LAWA) the authors developed a procedure to define natural groundwater conditions from groundwater monitoring data. The distribution pattern of a specific groundwater parameter observed by a number of groundwater monitoring stations within a petrographically comparable groundwater typology is reproduced by two statistical distribution functions, representing the "natural" and "influenced" components. The range of natural groundwater concentrations is characterized by confidence intervals of the distribution function of the natural component. The applicability of the approach was established for four hydrochemically different groundwater typologies occurring throughout Germany. Based on groundwater monitoring data from 7920 groundwater monitoring stations, 15 different hydrochemical parameters were evaluated for each groundwater typology. For all investigated parameters the range of natural groundwater concentrations has been identified. According to the requirements of the EC Water Framework Directive (article 17) (WFD) this study is a basis for the German position to propose criteria for assessing a reference state for a "good groundwater chemical status".

Environmental Monitoring↗
PubMed1987

[Effect of new imaging procedures on conventional roentgen diagnostic methods].

The diagnostic radiology workload of a general hospital served as basis to assess the statistical distribution of various diagnostic radiology methods and the inroads made by new imaging methods on the conventional ones: CT, DAS, sonography and endoscopy. In particular, the statistical breakdown shows how these methods have been applied in examining the gastrointestinal tract, the kidneys, the gallbladder and biliary tract, and how they have influenced the frequency rate of special examination methods such as angiography and myelography. Statistic assessment of the results obtained during the past ten years shows an increasing predominance of less invasive examination methods and increasing use of endoscopic methods for examining the gastrointestinal tract, the sum total of examinations remaining approximately the same throughout.

Angiography↗
PubMed2004

Effects of the Gaussian energy dispersion on the statistics of polarons and bipolarons in conducting polymers.

We discuss the interpretation of usually broad oxidation peaks observed in electronically conducting polymers, in terms of the statistical distributions functions of polarons and bipolarons. The analysis is based on examining the chemical capacitance, that relates the change of concentration to a modification of the chemical potential of a given species, for different statistical models. We first review the standard models for single energy species that provide a nernstian dependence, and the limitations of these models are discussed. A new model that assumes a Gaussian distribution of energies related to molecular geometry fluctuations is suggested, and this model shows excellent agreement with the results of electrochemical oxidation of polypyrrole in quasiequilibrium conditions. From a fit of the data, it is found that the density of conjugated chain segments in polypyrrole, Ns approximately 10(21) cm(-3), shows a Gaussian distribution of half width sigma approximately 170 meV, tentatively attributed to bipolaron formation energies.

Journal Article↗
PubMed2002

Common mental disorder symptom counts in populations: are there distinct case groups above epidemiological cut-offs?

BACKGROUND: At the lower end of IQ distributions in general populations, there is a clear excess of cases, representing the distinct pathology of severe learning disability. This study aimed to establish whether such a subpopulation exists in distributions of common mental disorder and depression symptom scores, above epidemiological 'case' cut-offs. METHOD: Data from 9556 non-psychotic respondents to the 1993 OPCS (Office of Population Censuses and Surveys) National Household Psychiatric Morbidity Survey were analysed. The distribution of total neurotic symptom and depression scores from the revised Clinical Interview Schedule were examined. Automated least squares methods were used to fit the best single statistical distribution to the data. RESULTS: A single exponential curve provided the best fit for the whole population, but floor effects produced deviations at symptom counts of 0-3. After truncation, exponential distributions fitted excellently. Proportions of the population above conventional cut-offs of > or = 12 symptoms differed by < 12% from expected for a range of low and high prevalence groups. The single exponential model also fitted the depression score. CONCLUSIONS: Symptom counts for the common mental disorders fall within single population distributions, with little apparent numerical excess in the case range. High and low prevalences of these disorders appear to be population characteristics, with shifts in exponential means predicting proportions above case cut-offs.

Adolescent↗
PubMed2005

Properties of crowding indices and statistical tools to analyze parasite crowding data.

Crowding, i.e., the size of the infrapopulation inhabiting an individual host, is a major component of parasites' environment, which often influences both morphological and life-history characters (the so-called density-dependent characters) in different parasite taxa. Although crowding equals intensity in case of a single parasite individual, mean intensity of the host population does not define mean crowding of the parasite population. Crowding indices are notoriously hard to handle statistically because of the inherently large number of nonindependent values in data. In this study, we aim to investigate the apparently paradox features of crowding indices and to make some proposals and also to introduce statistical methods to calculate confidence intervals and 1-sample and 2-sample tests for mean crowding. All methods described in this study are supported by the freely distributed statistical software Quantitative Parasitology.

Animals↗
PubMed2004

Dependence of threshold behavior upon surface distribution of polymer chains in a twisted nematic liquid crystal.

On the basis of a general Rapini and Papoular equation and a unified surface anchoring energy theory, dependence of the threshold behavior of the liquid crystal director upon the statistical distribution of polyimide chains is theoretically investigated for a twisted nematic liquid crystal cell. We assumed that the anisotropy distribution of polyimide chains induced by the rubbing can be dominated by a Gaussian distribution around the rubbing direction. Our results show that the threshold behavior of a twisted nematic liquid crystal is affected strongly by the surface distribution of polymer chains.

Journal Article↗
PubMed1999

Critical analysis of methods for assessment of predicted no-effect concentration.

Current risk assessment procedures for chemical substances are based on hazard quotients and require determination of a predicted no-effect concentration (PNEC). These concentrations are usually computed by applying an assessment factor to the lowest available toxicity value. However, other approaches have also been proposed based on statistical distribution of ecotoxicity data. This paper compares the various approaches in terms of precision and robustness. When only a few data are available, an assessment factor approach can be used. However, whenever possible (i.e. for a large set of chronic data), a statistical approach like that developed by T. Aldenberg and W. Slob (1991, Confidence Limits for Hazardous Concentrations Based on Logistically Distributed NOEC Toxicity Data, RIVM Report 71902002) with a 50% confidence level is the most precise and provides a stable value with increasing confidence when the number of tests increases.

Animals↗
PubMed2006

LATER predicts saccade latency distributions in reading.

When saccades are evoked by suddenly presented visual stimuli, the stochastic distribution of their reaction times is typically recinormal, in conformity with the LATER model of decision-making, sometimes with an additional sub-population of early responses. In the real world, saccades are more often spontaneous responses to static features of the visual world; nevertheless, the time between the end of one saccade and the start of the next may be regarded as a reaction time to the new image that is presented to the retina. The distribution of these times is qualitatively similar to that of evoked saccades, but typically with a longer median and more of the early responses. Here, we analyse the statistical distributions of fixation times from a large database of spontaneous saccades made while reading and show that the distributions are altered in characteristic ways by particular features of the current fixation: likely familiarity of the currently fixated word, and its proximity to the preceding fixation. These alterations are of the kind predicted by LATER: familiarity appears to influence the mean rate at which the decision signal approaches completion, whereas proximity to the previous fixation, presumably because it provides partial prior information about the upcoming word, appears to increase prior probability. We conclude that spontaneous saccades may be successfully described by the same decision-making model that can be used for evoked ones.

Humans↗
PubMed1988

Applications of statistical analysis in diagnostic histopathology and cytopathology.

Corresponding to the rapid increase in the amount of data available for use in clinical diagnoses, there is an increased need for procedures that can provide the diagnostician with meaningful statistical summaries of data and with statements concerning the statistical significance associated with a diagnostic evaluation. It has been demonstrated that multivariate statistical assessment of clinical material can provide consistent, reliable and highly sensitive diagnostic clues, even in instances in which trained personnel are unable to see any change. Several examples of applications of statistical analyses in diagnostic cytology and histopathology are given in this paper. The examples were chosen to be illustrative of the different types of problems for which statistical analyses have been found useful. These problems differ with respect to the extent of the statistical methods thus far developed and the difficulty involved in developing further analyses. For many problems, appropriate statistical analyses are readily available; other problems require definition of custom-made test statistics and, in some cases, also definition of new statistical distributions. The problems discussed here are only a small sample of the existing problems, but they provide at least an indication of the scope of the role that statistics plays in cytopathologic and histopathologic diagnosis.

Cytological Techniques↗
PubMed2004

Large phenotype jumps in biomolecular evolution.

By defining the phenotype of a biopolymer by its active three-dimensional shape, and its genotype by its primary sequence, we propose a model that predicts and characterizes the statistical distribution of a population of biopolymers with a specific phenotype that originated from a given genotypic sequence by a single mutational event. Depending on the ratio g(0) that characterizes the spread of potential energies of the mutated population with respect to temperature, three different statistical regimes have been identified. We suggest that biopolymers found in nature are in a critical regime with g(0) approximately 1-6, corresponding to a broad, but not too broad, phenotypic distribution resembling a truncated Lévy flight. Thus the biopolymer phenotype can be considerably modified in just a few mutations. The proposed model is in good agreement with the experimental distribution of activities determined for a population of single mutants of a group-I ribozyme.

Biopolymers↗
PubMed1986

Normative and reliability data for the Children's Depression Inventory.

The present study was undertaken to examine some of the psychometric properties of the Children's Depression Inventory (CDI), a self-report inventory devised by Kovacs and Beck (1977) to measure depression in children and adolescents. Normative and reliability data were obtained from three independent samples taken from eight public schools in central Pennsylvania. Age- and gender-related differences in reported characteristics of depression were also investigated. The subjects were 594 males and 658 females whose ages ranged from 8 to 16 years and whose combined mean age was 11.67 years (SD = 1.91). The CDI was group-administered to all 1,252 subjects; 155 fifth-grade subjects (77 males and 78 females) were retested after 3 weeks, and 107 seventh- and eight-grade subjects (45 males and 62 females) were retested after 1 year. The distribution statistics for the combined samples yielded an overall CDI mean of 9.09, a standard deviation of 7.04, and a cutoff score of 19 for the upper 10% of the distribution. Reliability assessed through coefficient alpha, item-total score product-moment correlations, and test-retest coefficients proved acceptable. Gender differences were obtained for several item-total score correlations and for test-retest reliability of CDI scores.

Adolescent↗
PubMed2001

Non-gaussianity versus nonlinearity of cosmological perturbations.

Following the discovery of the cosmic microwave background, the hot big-bang model has become the standard cosmological model. In this theory, small primordial fluctuations are subsequently amplified by gravity to form the large-scale structure seen today. Different theories for unified models of particle physics, lead to different predictions for the statistical properties of the primordial fluctuations, that can be divided in two classes: gaussian and non-gaussian. Convincing evidence against or for gaussian initial conditions would rule out many scenarios and point us toward a physical theory for the origin of structures. The statistical distribution of cosmological perturbations, as we observe them, can deviate from the gaussian distribution in several different ways. Even if perturbations start off gaussian, nonlinear gravitational evolution can introduce non-gaussian features. Additionally, our knowledge of the Universe comes principally from the study of luminous material such as galaxies, but galaxies might not be faithful tracers of the underlying mass distribution. The relationship between fluctuations in the mass and in the galaxies distribution (bias), is often assumed to be local, but could well be nonlinear. Moreover, galaxy catalogues use the redshift as third spatial coordinate: the resulting redshift-space map of the galaxy distribution is nonlinearly distorted by peculiar velocities. Nonlinear gravitational evolution, biasing, and redshift-space distortion introduce non-gaussianity, even in an initially gaussian fluctuation field. I investigate the statistical tools that allow us, in principle, to disentangle the above different effects, and the observational datasets we require to do so in practice.

Journal Article↗
PubMed2005

Stereoscopic correspondence for ambiguous targets is affected by elevation and fixation distance.

Binocular correspondence must be determined if disparity is to be used to provide information about three-dimensional shape. The current study investigated whether knowledge of the statistical distribution of disparities in the natural environment is employed in this process. A simple model, which produces distributions of distances similar to those found in the natural environment, was used to predict the distribution of disparities in natural images. This model predicts that crossed disparities will be more likely as (i) stimulus elevation decreases below fixation and (ii) fixation distance increases. To determine whether these factors influence binocular correspondence for human observers, ambiguous stereograms were presented to observers, as stimulus elevation and fixation distance were manipulated. Clear biases were observed in the depth perceived in these stereograms, which were more likely to be seen as closer than fixation (i) for stimuli presented below fixation and (ii) as fixation distance increased. These results suggest that binocular correspondence is determined in a manner consistent with the distributions of disparities expected in natural scenes.

Depth Perception↗
PubMed1995

Dimensional distribution of human erythrocytes obtained from electropermeabilization experiments.

Electropermeabilization of erythrocyte membrane was performed using square electric field pulses of 50 microseconds and 1 ms pulse length. The electrohemolysis efficiency has a sigmoid dependence on the electric field strength given mainly by the statistical distribution of erythrocytes radius. The normalized dimensional distribution function for a human erythrocyte population was determined from electropermeabilization data.

Cell Membrane Permeability↗
PubMed1979

Areawide fluctuations in hospital daily census.

The importance of variations in hospital census for planning bed requirements has long been recognized. Traditional models assume Poisson or normal distribution patterns accurately describe such variations in specific hospital units, entire facilities, and groups of hospitals serving the same area. A study of 20 groups of hospitals in five states indicates that these traditional statistical distributions are only occasionally accurate. Different services display different census variation patterns. The standard deviation of the daily census distribution becomes increasingly higher than the square root of the mean estimate as the size of the mean increases. Implications of this finding for regional planning and coordination of hospitals are discussed.

Bed Occupancy↗