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PubMed1997

Statistical comparison of DLT versus ILSSC in the calibration of a photogrammetric stereo-system.

This paper compares the DLT and ILSSC approaches in the geometrical calibration of a photogrammetric stereo-system in terms of accuracy and speed. To come up with an unbiased quantitative evaluation of the accuracy of the algorithms, the concept of reliable estimate has been introduced: the statistical distribution of the accuracy is assessed over different calibration experiments performed with the same data but with different noise distribution and different test sets. Results show that in the simulations where the only error on the two-dimensional points was Gaussian, zero mean, and on real data which were corrected for distortions through polynomial or linear interpolation, the accuracy of the two methods was quite similar. DLT showed more accurate than ILSSC on simulated data with residual distortion errors and on real data which were not corrected for distortions. As far as speed is concerned, a fast triangulation algorithm is associated with ILSSC while the simultaneous solution of two pairs of DLT equations is associated to DLT. The first algorithm is much faster, requiring 113 flops per point versus 259 of DLT; the fast triangulation with DLT parameters does not achieve the same accuracy on the reconstructed three-dimensional position. Taken all together the results suggest that ILSSC can be theoretically considered the best approach to three-dimensional reconstruction, provided that distortions are corrected in advance. The statistical evaluation of the accuracy allows a fair judgement of the performances of the algorithms to be obtained, unbiased by particular distributions of measurement errors and test points.

Algorithms↗
PubMed2005

Osmotic pressure of aqueous chondroitin sulfate solution: a molecular modeling investigation.

The osmotic pressure of chondroitin sulfate (CS) solution in contact with an aqueous 1:1 salt reservoir of fixed ionic strength is studied using a recently developed coarse-grained molecular model. The effects of sulfation type (4- vs. 6-sulfation), sulfation pattern (statistical distribution of sulfate groups along a chain), ionic strength, CS intrinsic stiffness, and steric interactions on CS osmotic pressure are investigated. At physiological ionic strength (0.15 M NaCl), the sulfation type and pattern, as measured by a standard statistical description of copolymerization, are found to have a negligible influence on CS osmotic pressure, which depends principally on the mean volumetric fixed charge density. The intrinsic backbone stiffness characteristic of polysaccharides such as CS, however, is demonstrated to contribute significantly to its osmotic pressure behavior, which is similar to that of a solution of charged rods for the 20-disaccharide chains considered. Steric excluded volume is found to play a negligible role in determining CS osmotic pressure at physiological ionic strength due to the dominance of repulsive intermolecular electrostatic interactions that maintain chains maximally spaced in that regime, whereas at high ionic-strength steric interactions become dominant due to electrostatic screening. Osmotic pressure predictions are compared to experimental data and to well-established theoretical models including the Donnan theory and the Poisson-Boltzmann cylindrical cell model.

Chondroitin Sulfates↗
PubMed2001

A note on the distribution of the number of vaccinated infected under non-random mixing conditions.

A common situation in vaccine efficacy (VE) estimation is dealing with non-randomly mixing populations, which may subject vaccinated and unvaccinated individuals to a different infection pressure. These conditions may lead to a bias in VE estimates. The derivation of the statistical distribution of the number of vaccinated and infected out of a sample of n infections in a VE trial is essential to develop estimates and their properties. For randomly mixing populations, it has been shown recently that this follows a hypergeometric distribution for 'all/nothing' vaccines, whereas it is a non-central hypergeometric distribution for 'leaky' ones. Here it is shown that these distributions still hold under non-random mixing conditions, provided that mixing preferences and contact rates are independent of vaccination status. These conditions are met when vaccine and placebo are randomized.

Humans↗
PubMed1994

Stratification of summary statistic tests according to missing data patterns.

Summary statistics, such as slope or area under the time-response curve, reduce the dimensionality of repeated measures data and can thereby simplify the comparison of groups in longitudinal studies. Since summary statistic distributions vary according to the amount, timing, and type of any missingness that occurs, one must choose between analysing the data unconditionally or conditionally on the missingness patterns. This paper uses simulations to compare such unstratified and stratified summary statistic analyses with respect to their size and power under models that allow for both non-informative and informative missingness mechanisms. Of particular interest is the robustness of these methods to violations of the assumptions that one must make if they are to have proper test size. It is found that stratification of the analysis tends to result in an increase of power, and improves the robustness to violations of missing data assumptions.

Computer Simulation↗
PubMed2000

Is the genotype-phenotype map modular? A statistical approach using mouse quantitative trait loci data.

Various theories about the evolution of complex characters make predictions about the statistical distribution of genetic effects on phenotypic characters, also called the genotype-phenotype map. With the advent of QTL technology, data about these distributions are becoming available. In this article, we propose simple tests for the prediction that functionally integrated characters have a modular genotype-phenotype map. The test is applied to QTL data on the mouse mandible. The results provide statistical support for the notion that the ascending ramus region of the mandible is modularized. A data set comprising the effects of QTL on a more extensive portion of the phenotype is required to determine if the alveolar region of the mandible is also modularized.

Alleles↗
PubMed1994

[Computer technology of the genogeographic study of the gene pool. I. Statistical information from the genogeographic map].

General statistical information that can be derived from an electronic map and listed in its legend is reviewed. Certain map information (extrema, mean and variance of mapped values, the number of initial and mapped values, their statistical distributions) can be used in analysis not only of gene pool, but also of phene pool maps. Another portion of map information, on total gene diversity, heterozygosity, and interpopulation differentiation, is important for consequent detailed analysis of a gene pool. Statistical information that is derived from a genogeographic map aids understanding of the content of a map and is used in comparative quantitative analysis of different regions and various mapped parameters. The possibilities for interpretation of statistical information of genogeographic maps are shown using the human gene pool as an example. Maps of frequencies of ABO-O and Rh-d blood group genes in three hierarchically subordinate gene pools of native inhabitants of Belarus, the Black Sea-Baltic region, and northeast Eurasia are presented for this purpose.

Computer Simulation↗
PubMed2000

Studying avalanches in the ground state of the two-dimensional random-field ising model driven by an external field

We study the exact ground state of the two-dimensional random-field Ising model as a function of both the external applied field B and the standard deviation sigma of the Gaussian random-field distribution. The equilibrium evolution of the magnetization consists in a sequence of discrete jumps. These are very similar to the avalanche behavior found in the out-of-equilibrium version of the same model with local relaxation dynamics. We compare the statistical distributions of magnetization jumps and find that both exhibit power-law behavior for the same value of sigma. The corresponding exponents are compared.

Journal Article↗
PubMed1976

Particle size-shape distributions: the general spheroid problem. I. Mathematical model.

The development of stereological methods for the study of dilute phases of particles, voids or organelles embedded in a matrix, from measurements made on plane or linear intercepts through the aggregate, has deserved a great deal of effort. With almost no exception, the problem of describing the particulate phase is reduced to that of identifying the statistical distribution--histogram in practice--of a relevant size parameter, with the previous assumption that the particles are modelled by geometrical objects of a constant shape (e.g. spheres). Therefore, particles exhibiting a random variation about a given type of shape as well as a random variation in size, escape previous analyses. Such is the case of unequiaxed particles modelled by triaxial ellipsoids of variable size and eccentricity parameters. It has been conjectured (Moran, 1972) that this problem is indetermined in its generally (i.e. the elliptical sections do not furnish a sufficient information which permits a complete description of the ellipsoids). A proof of this conjecture is given in the Appendix. When the ellipsoids are biaxial (spheroids) and of the same type (prolate or oblate), the problem is identifiable. Previous attempts to solve it assume statistical independence between size and shape. A complete, theoretical solution of the spheroids problem--with the independence condition relaxed--is presented. A number of exact relationships--some of them of a striking simplicity--linking particle properties (e.g. mean-mean caliper length, mean axial ratio, correlation coefficient between principal diameters, etc.) on the one hand, with the major and minor dimensions of the ellipses of section on the other, emerge, and natural, consistent estimators of the mentioned properties are made easily accessible for practical computation. Finally, the scope and limitations of the mathematical model are discussed.

Mathematics↗
PubMed1995

Surveillance monitoring of soils for radioactivity: Lawrence Livermore National Laboratory 1976 to 1992.

Environmental monitoring of soils at the U.S. Department of Energy's Lawrence Livermore National Laboratory in California has been conducted for more than 20 years. The purposes of the program are to determine the effects, if any, of LLNL's operations on the surrounding areas near its two separate sites and to determine if there are any long-term trends. Data from 1976 to 1992 were analyzed to determine their appropriate statistical distribution, and differences among locations and changes with time were evaluated. The data generally followed lognormal distributions, and results for 239 + 240Pu and 137Cs data were consistent with previously reported values for world-wide fallout. Although all values for 239 + 240Pu were small, 239 + 240Pu data for locations downwind from the Livermore site were found to be statistically significantly higher than for upwind locations. Results for 238U at Site 300 locations near where 238U is used were significantly higher than background locations. Results for 137Cs and 40K were not significantly different between sites, whereas results for 232Th were significantly higher for Site 300 than for the Livermore site. Doses for all radionuclides were below acceptable levels, and doses for most radionuclides were negligible. Evaluation of trends with time yielded small or statistically insignificant changes for all radionuclides.

Cesium Radioisotopes↗
PubMed2001

Software based digital signal processing and spectrum deconvolution in X-ray spectroscopy.

Approaches for software based digital signal processing and numerical deconvolution of measured signals which overcome limitations of state-of-the-art systems are described. The basic technical equipment for digital signal processing consists of an energy resolving detector with a preamplifier followed by a fast sampling analogue-to-digital converter (ADC). The main idea is the numerical decomposition of the measured signal into contributions caused by single photon absorption using standard pulses. The latter can be obtained by measurements under definite conditions. The maximum pulse rate is then limited only by the ratio of sampling time to the time between two pulses which should be attributed to single events. Thus pulse overlaps do not require pulse rejection. At sampling rates of 10(8) samples per second theoretically a comparable photon rate can be detected at throughputs of 100%. Beyond that it is outlined that in a comparable manner a numerical deconvolution of measured energy spectra (statistic distribution functions of single events) into combinations of standard spectra, which can likewise be determined by measurement, offers outstanding possibilities, too. On the one hand the energy resolution attainable for individual events for a given detector can be improved drastically by the statistical treatment of spectra. On the other hand an energy resolving work principle becomes possible for certain detectors, which do not permit this conventionally due to their poor signal to noise ratio.

Journal Article↗
PubMed2002

Beyond bixels: generalizing the optimization parameters for intensity modulated radiation therapy.

Intensity modulated radiation therapy (IMRT) treatment planning systems optimize fluence distributions by subdividing the fluence distribution into rectangular bixels. The algorithms typically optimize the fluence intensity directly, often leading to fluence distributions with sharp discontinuities. These discontinuities may yield difficulties in delivery of the fluence distribution, leading to inaccurate dose delivery. We have developed a method for decoupling the bixel intensities from the optimization parameters; either by introducing optimization control points from which the bixel intensities are interpolated or by parametrizing the fluence distribution using basis functions. In either case, the number of optimization search parameters is reduced from the direct bixel optimization method. To illustrate the concept, the technique is applied to two-dimensional idealized head and neck treatment plans. The interpolation algorithms investigated were nearest-neighbor, linear and cubic spline, and radial basis functions serve as the basis function test. The interpolation and basis function optimization techniques were compared against the direct bixel calculation. The number of optimization parameters were significantly reduced relative to the bixel optimization, and this was evident in the reduction of computation time of as much as 58% from the full bixel optimization. The dose distributions obtained using the reduced optimization parameter sets were very similar to the full bixel optimization when examined by dose distributions, statistics, and dose-volume histograms. To evaluate the sensitivity of the fluence calculations to spatial misalignment caused either by delivery errors or patient motion, the doses were recomputed with a 1 mm shift in each beam and compared to the unshifted distributions. Except for the nearest-neighbor algorithm, the reduced optimization parameter dose distributions were generally less sensitive to spatial shifts than the bixel optimization. These results indicate that significant reductions in optimization parameter sets can be accomplished with a negligible reduction in dose distribution quality. The decreased parameters can result in a reduced optimization time, or can be used to allow an improved and consequently more computation-intensive dose calculation for more accurate dose calculations during the optimization process. The basis functions may be generalized to model the accelerator motion for direct computation of the accelerator motion sequence, removing the need for developing an independent leaf sequence step.

Algorithms↗
PubMedDate not supplied

Dosimetry of solid tumors.

Dosimetry data arising from a decade of radioimmunotherapy are summarized along with techniques utilized to arrive at the reported dose estimates. Generality of the MIRD methodology allows it to serve as a vehicle for the calculation of solid tumor dosimetry although several limitations exist. Nonstandard geometries of solid tumors will ultimately necessitate determination of absorbed fractions for the individual tumors. Several approaches currently under investigation are described. For reasons of practicality, solid tumor dosimetry estimates continue to use the assumption of homogeneous activity distribution in a source organ, accounting for either all radiation or only nonpenetrating radiation. As computation tools become available for incorporating inhomogeneous cellular level data, the currently used "average dose" as an index of tumor sterilization will likely be replaced with a statistical distribution based on the number of viable cells in the tumor volume. Estimates of a tumor control dose would be based upon a linear extension of dose coupled with a threshold dose for cell sterilization.

Humans↗
PubMed1990

A comparison of multivariable mathematical methods for predicting survival--I. Introduction, rationale, and general strategy.

This paper and the two following papers (Parts I-III) report an investigation of performance variability for four multivariable methods: discriminant function analysis, and linear, logistic, and Cox regression. Each method was examined for its performance in using the same independent variables to develop predictive models for survival of a large cohort of patients with lung cancer. The cogent biologic attributes of the patients had previously been divided into five ordinal stages having a strong prognostic gradient. With stratified random sampling, we prepared seven "generating" sets of data in which the five biologic stages were arranged in proportional, uniform, symmetrical unimodal, decreasing exponential, increasing exponential, U-shaped, or bi-modal distributions. Each of the multivariable methods was applied to each of the seven generating distributions, and the results were tested in a separate "challenge" set, which had not been included in any of the generating sets. The research was intended not merely to compare the performance of the multivariable methods, but also to see how their performance would be affected by different statistical distributions of the same cogent biologic attributes. The results, which are presented in the second and third papers, were compared for selection of independent variables and coefficients, and for accuracy in fitting the generating sets and the challenge set.

Cohort Studies↗
PubMed2006

Assessing spatial, temporal, and analytical variation of groundwater chemistry in a large nuclear complex, USA.

Statistical analyses were applied at the Hanford Site, USA, to assess groundwater contamination problems that included (1) determining local backgrounds to ascertain whether a facility is affecting the groundwater quality and (2) determining a 'pre-Hanford' groundwater background to allow formulation of background-based cleanup standards. The primary purpose of this paper is to extend the random effects models for (1) assessing the spatial, temporal, and analytical variability of groundwater background measurements; (2) demonstrating that the usual variance estimate s2, which ignores the variance components, is a biased estimator; (3) providing formulas for calculating the amount of bias; and (4) recommending monitoring strategies to reduce the uncertainty in estimating the average background concentrations. A case study is provided. Results indicate that (1) without considering spatial and temporal variability, there is a high probability of false positives, resulting in unnecessary remediation and/or monitoring expenses; (2) the most effective way to reduce the uncertainty in estimating the average background, and enhance the power of the statistical tests in general, is to increase the number of background wells; and (3) background for a specific constituent should be considered as a statistical distribution, not as a single value or threshold. The methods and the related analysis of variance tables discussed in this paper can be used as diagnostic tools in documenting the extent of inherent spatial and/or temporal variation and to help select an appropriate statistical method for testing purposes.

Analysis of Variance↗
PubMed2003

Electronic changes due to thermal disorder of hydrogen bonds in liquids: pyridine in an aqueous environment.

Combined Metropolis Monte Carlo computer simulation and first-principles quantum mechanical calculations of pyridine in water are performed to analyze the role of thermal disorder in the electronic properties of hydrogen bonds in an aqueous environment. The simulation uses the NVT ensemble and includes one pyridine and 400 water molecules. Using a very efficient geometric-energetic criterion, the hydrogen bonds between pyridine and water C5H5N---H2O are identified and separated for subsequent quantum mechanical calculations of the electronic and spectroscopic properties. Statistically uncorrelated configurations composed of one pyridine and one water molecule are used to represent the configuration space of the hydrogen bonds in the liquid. The quantum mechanical calculations on these structures are performed at the correlated second-order perturbation theory level and all results are corrected for basis-set superposition error. The results are compared with the equivalent electronic properties of the hydrogen bond in the minimum-energy configuration. Charge transfer, dipole moment, and dipole polarizabilities are calculated for the thermally disordered and minimum-energy structures. In addition, using the mean and anisotropic polarizabilities, the Rayleigh depolarizations are obtained. All properties obtained for the thermally disordered structures are represented by a statistical distribution and a convergence of the average values is obtained. The results indicate that the charge transfer, dipole moment, and average depolarization ratios are systematically decreased in the liquid compared to the optimized cluster. This study quantifies, using ab initio quantum mechanics and statistical analysis, the important aspect of the thermal disorder of the hydrogen bond in a liquid system.

Journal Article↗
PubMed2003

DNA probability profiles: examples from the Treponema pallidum genome.

In this paper we apply an algorithm developed by Poland (Biopolymers 13 (1974) 1859) to treat the statistical mechanics of the thermal unwinding of DNA to the genome of Treponema pallidum, the syphilis spirochete. We calculate probability profiles (giving the probability that each unit in the molecule is in the helix-state) and other statistical distributions for genes and sequences of genes, the longest containing 100 genes and 107,139 base pairs (approximately 10% of the genome).

Algorithms↗
PubMed2005

Vibrational and rotational distributions of the CH(A2Delta) product of the C(2)H + O(3P) reaction studied by fourier transform visible (FTVIS) emission spectroscopy.

The C(2)H + O((3)P) --> CH(A) + CO reaction is investigated using Fourier transform visible emission spectroscopy. The O((3)P) and C(2)H radicals are produced by simultaneous 193 nm photolysis of SO(2) and C(2)H(2) precursors, respectively. The nascent vibrational and rotational distributions of the CH(A) product are obtained under time-resolved, but quasi-steady-state, conditions facilitated by the short lifetime of the CH(A) emission. The vibrational temperature of the CH(A) product is found to be appreciably hotter (2800 +/- 100 K) than the rotational distributions in the v' = 0 (1400 +/- 100 K) and v' = 1 (1250 +/- 250 K) levels. The results suggest that the reaction may proceed through an electronically excited HCCO() intermediate; moreover, the vibrational excitation compared to rotational excitation is higher than expected based on a statistical distribution of energy and may be the result of geometrical changes in the transition state. The CH(A) emission is also observed in a C(2)H(2)/O/H reaction mixture using a microwave discharge apparatus to form O atoms, with subsequent H atom production. The nascent rotational and vibrational distributions of the CH(A) determined by the microwave discharge apparatus are very similar to the CH(A) distributions obtained in the photodissociation experiment. The results support the idea that the C(2)H + O((3)P) reaction may play a role in low-pressure C(2)H(2)/O/H flames, as previously concluded.

Journal Article↗
PubMed2004

The role of increasing temperature variability in European summer heatwaves.

Instrumental observations and reconstructions of global and hemispheric temperature evolution reveal a pronounced warming during the past approximately 150 years. One expression of this warming is the observed increase in the occurrence of heatwaves. Conceptually this increase is understood as a shift of the statistical distribution towards warmer temperatures, while changes in the width of the distribution are often considered small. Here we show that this framework fails to explain the record-breaking central European summer temperatures in 2003, although it is consistent with observations from previous years. We find that an event like that of summer 2003 is statistically extremely unlikely, even when the observed warming is taken into account. We propose that a regime with an increased variability of temperatures (in addition to increases in mean temperature) may be able to account for summer 2003. To test this proposal, we simulate possible future European climate with a regional climate model in a scenario with increased atmospheric greenhouse-gas concentrations, and find that temperature variability increases by up to 100%, with maximum changes in central and eastern Europe.

Journal Article↗