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PubMed2004

The shape of neural dependence.

The product-moment correlation coefficient is often viewed as a natural measure of dependence. However, this equivalence applies only in the context of elliptical distributions, most commonly the multivariate gaussian, where linear correlation indeed sufficiently describes the underlying dependence structure. Should the true probability distributions deviate from those with elliptical contours, linear correlation may convey misleading information on the actual underlying dependencies. It is often the case that probability distributions other than the gaussian distribution are necessary to properly capture the stochastic nature of single neurons, which as a consequence greatly complicates the construction of a flexible model of covariance. We show how arbitrary probability densities can be coupled to allow greater flexibility in the construction of multivariate neural population models.

Action Potentials↗
PubMed1998

Fast temporal encoding and decoding with spiking neurons.

We propose a simple theoretical structure of interacting integrate-and-fire neurons that can handle fast information processing and may account for the fact that only a few neuronal spikes suffice to transmit information in the brain. Using integrate-and-fire neurons that are subjected to individual noise and to a common external input, we calculate their first passage time (FPT), or interspike interval. We suggest using a population average for evaluating the FPT that represents the desired information. Instantaneous lateral excitation among these neurons helps the analysis. By employing a second layer of neurons with variable connections to the first layer, we represent the strength of the input by the number of output neurons that fire, thus decoding the temporal information. Such a model can easily lead to a logarithmic relation as in Weber's law. The latter follows naturally from information maximization if the input strength is statistically distributed according to an approximate inverse law.

Action Potentials↗
PubMed1987

Theory and methods of local tissue-pO2 monitoring in experimental angiology.

The platinum-multiwire-surface electrode after Kessler and Lübbers gives the opportunity of direct measuring of the local tissue-pO2-pressure; this 8-wire electrode with a Pt-wire-diameter of 15 microns operates on the polarographic principle. Each Pt-wire has a hemispheric collecting area of about 30 microns. Pressure ischemia by compression of capillaries is prevented by proportioning the weight (2.1 g) of the electrode. Data output is done by continuous pO2 measuring; pO2 histograms. During the continuous pO2 measurement the electrode stays on the tissue measuring point thus enabling the direct record of quickly proceeding reactions. The pO2-histogram exhibits the statistical distribution of the local partial oxygen pressures in a studied organ, a quasi sample inquiry is performed in the tissue, based on minimum 100 single values that are obtained by repeated manual repositioning of the electrode. By this, values are obtained on the level and distribution of local pO2 in the tissue so that condition and function of the microcirculation can be objectively assessed. Immediate alterations in the local tissue pO2 suggest regulatory adjustment after hemodynamic changes. Technical problems connected with pO2 measurement in clinical use (sterilization, data acquisition and presentation) are described. The presented technique gives the chance to exactly assess the effects of vasoactive drugs on the microcirculation and to quantify the results of operations, for example after bypass-surgery.

Blood Vessels↗
PubMed2001

Analysis of ordinal dental data: evaluation of conflicting recommendations.

Although recommendations for the appropriate analysis of non-normal and ordinal-scaled data have appeared in the dental research literature for many years, there is no consensus. When one is conducting statistical tests for differences between groups, the central concern is whether it is safe to use parametric tests (e.g., analysis of variance), or if only non-parametric ranking tests should be considered. Relevant statistical and scientific issues associated with non-normality and measurement scale are reviewed, and three conclusions are reached regarding the analysis of dental data: (1) Parametric tests are sufficiently robust relative to typical violations of normality; (2) presumed statistical prohibitions against the application of parametric methods to ordinal data do not actually exist; and (3) 'ordinal' dental indices have sufficient quantitative meaning to be considered quasi-interval. For these reasons, parametric tests should not be avoided; they will be valid and usually more powerful and more easily applied to complex designs than non-parametric alternatives.

Analysis of Variance↗
PubMedDate not supplied

Gains in accuracy from replicated readings of diagnostic images: prediction and assessment in terms of ROC analysis.

From the perspective of signal detection theory, human variation in image reading degrades diagnostic accuracy by broadening the statistical distributions of perceived evidence upon which decisions were based. A new multivariate "random-effects" model formulates the total variation in a diagnostic decision variable as a sum of three uncorrelated components that represent differences among cases, readers, and repeated readings by a given reader. This model provides a basis for quantitative predictions concerning the amount by which diagnostic accuracy, as specified by ROC analysis, can be enhanced by the replication of image readings. Although these predictions apply exactly only to the hypothetical situation in which normally distributed decision variables from equivalent readers are averaged, computer-simulation studies and an analysis of mammographic image-reading data from five radiologists show that similar gains in accuracy can be achieved by averaging discrete confidence ratings.

Decision Support Techniques↗
PubMedDate not supplied

Relative entropy as a measure of diagnostic information.

Relative entropy is a concept within information theory that provides a measure of the distance between two probability distributions. The author proposes that the amount of information gained by performing a diagnostic test can be quantified by calculating the relative entropy between the posttest and pretest probability distributions. This statistic, in essence, quantifies the degree to which the results of a diagnostic test are likely to reduce our surprise upon ultimately learning a patient's diagnosis. A previously proposed measure of diagnostic information that is also based on information theory (pretest entropy minus posttest entropy) has been criticized as failing, in some cases, to agree with our intuitive concept of diagnostic information. The proposed formula passes the tests used to challenge this previous measure.

Clinical Medicine↗
PubMed1995

Efficiency pattern analysis for medical rehabilitation.

Efficiency pattern analysis (EPA) is a technique proposed for use in medical rehabilitation that links patient functional gain to resource use, as approximated by length of stay (LOS), after adjusting for initial severity. The Functional Independence Measure version of the Function Relation Groups (FIM-FRGs) is used to adjust for patient severity and to define the efficiency groups. The efficiency groups are based on LOS and functional gain cut point values in the statistical distribution that are above, below, or within the national interquartile range for each of 53 FRGs. Data from 32,494 patients discharged in 1990 from 123 rehabilitation facilities were used. EPA is a simple way to monitor change in functional gain in response to transformations in health care practices and resource availability. The technique could also provide individual facilities with a means to evaluate treatment efficiencies across time and to compare patterns of LOS and functional gain to national norms.

Activities of Daily Living↗
PubMed1991

The relationship and reproducibility of angle ANB and the Wits appraisal.

An analysis is presented of the errors and variations in the Wits analysis and the angle ANB, using computer simulation. The method is applicable to any index where the identification errors have been established for the points and planes used in its derivation. A standard deviation may be determined for the index produced and the statistical distribution of values for any number of observations.

Cephalometry↗
PubMed2004

Use of Bayes rule and MIB-1 proliferation index to discriminate Spitz nevus from malignant melanoma.

Differentiating Spitz nevus from malignant melanoma is difficult and controversial. Despite helpful lists of differential diagnostic features, uncertainty about the diagnosis often provokes some to stain the tumor for MIB-1 antibody to Ki-67 and measure the proliferation index (PI) of the tumor. Of the many reports about MIB-1 PI in Spitz nevi and melanoma, none have consolidated the information to provide guidelines for the predictive probability that a lesion is a Spitz nevus, given that the MIB-1 PI falls into a certain interval. The present study used previously published data and exponential and gamma probability density functions to model statistical distributions of PI, respectively, in Spitz nevi and melanomas and Bayes rule to estimate the predictive probability that a lesion is a Spitz nevus, given an observed PI. Results indicate that PIs more than 10% favor a melanoma diagnosis and PIs less than 2%, Spitz nevus. PI values between 2% and 10% yield various predictive values for Spitz nevus, depending on the a priori probability that the lesion is a Spitz nevus. The algorithm tabulates guidelines for the predictive probabilities of Spitz nevus given an observed PI.

Bayes Theorem↗
PubMed2002

Discriminatory ability of quantitative ultrasound parameters and bone mineral density in a population-based sample of postmenopausal women with vertebral fractures: results of the Basel Osteoporosis Study.

The discriminatory potential to classify subjects with or without vertebral fractures was tested cross-sectionally with different methods for the measurement of bone status in a population-based sample of postmenopausal women. Quantitative ultrasound (QUS) measurement at the calcaneus (Lunar Achilles, Hologic Sahara), the proximal phalanges (Igea Bone Profiler), and measurement of bone mineral density (BMD) with dual-energy X-ray absorptiometry (DXA; Lunar Expert) at several anatomic sites was performed in 500 postmenopausal women (aged 65-75 years) randomly selected from the population. In addition, 50 young female subjects (20-40 years old) had QUS measurements and served as controls to express QUS results as T-score values. Radiographs of the lumbar and thoracic spine were performed in the elderly women. Two independent radiologists reviewed the X-rays for the presence of vertebral fractures. Of 486 eligible study participants, no fracture was seen in 396 participants. Single vertebral fractures were observed in 71 subjects; 19 individuals presented multiple fractures. The overall prevalence of vertebral fractures was 18.5%. Participants without vertebral fractures were compared with subjects with vertebral fractures. Normal statistical distributions were found for all bone measurement results. Risk of vertebral fracture in subjects with no and multiple vertebral fracture was estimated using age adjusted odds ratios (ORs) for QUS and dual-energy X-ray absorptiometry (DXA) values. Each SD decrease in bone measurement increased the risk of multiple vertebral fracture by 3.0 (95% CI, 1.6-5.6) for the Achilles stiffness, by 3.8 (95% CI, 1.8-8.2) for the Sahara QUI, 2.1 (95% CI, 1.3-3.4) for the Bone Profiler amplitude-dependent speed of sound (AD-SOS), and 2.1 (95% CI, 1.2-3.9) and 2.4 (95% CI, 1.3-4.3) for DXA lumbar spine and for DXA total hip, respectively. Results of a discriminant analysis showed sensitivities between 84% and 58% and specificities between 72% and 58% for the respective DXA and QUS parameters. Optimum fracture thresholds for QUS measurements derived from this analysis were calculated also. Optimum T-score threshold values for QUS measurements tended to be higher than those for DXA measurements. However, the performance of QUS measurements is at least comparable with DXA measurements in identifying subjects with multiple vertebral fractures randomly selected from the population.

Aged↗
PubMed2003

Conditional data processing for single-shot spectral analysis by use of laser-induced breakdown spectroscopy.

Schemes of conditional data processing are evaluated based on either the peak-to-base ratio or the signal-to-noise ratio as a metric for analyte detection in single-shot laser-induced breakdown spectra. The analyte signal investigated is the 288.1-nm Si I emission line provided by an aerosol stream of monodisperse 2.5-microm-sized silica microspheres. Both the Si emission line and a spectral region corresponding to continuum emission are used to evaluate the statistical distribution of spectral noise. The probability of false hits is determined by evaluating various conditional processing thresholds. As the detection threshold increases, the rate of detected silica particle hits decreases along with the expected fraction of false-particle hits (i.e., spectral noise). For all threshold values the signal-to-noise ratio is found to provide a more robust metric for single-shot analyte detection compared with the peak-to-base ratio.

Journal Article↗
PubMed2005

Analysis of shipboard aerosol optical thickness measurements from multiple sunphotometers aboard the R/V Ronald H. Brown during the Aerosol Characterization Experiment--Asia.

Marine sunphotometer measurements collected aboard the R/V Ronald H. Brown during the Aerosol Characterization Experiment-Asia (ACE-Asia) are used to evaluate the ability of complementary instrumentation to obtain the best possible estimates of aerosol optical thickness and Angstrom exponent from ships at sea. A wide range of aerosol conditions, including clean maritime conditions and highly polluted coastal environments, were encountered during the ACE-Asia cruise. The results of this study suggest that shipboard hand-held sunphotometers and fast-rotating shadow-band radiometers (FRSRs) yield similar measurements and uncertainties if proper measurement protocols are used and if the instruments are properly calibrated. The automated FRSR has significantly better temporal resolution (2 min) than the hand-held sunphotometers when standard measurement protocols are used, so it more faithfully represents the variability of the local aerosol structure in polluted regions. Conversely, results suggest that the hand-held sunphotometers may perform better in clean, maritime air masses for unknown reasons. Results also show that the statistical distribution of the Angstrom exponent measurements is different when the distributions from hand-held sunphotometers are compared with those from the FRSR and that the differences may arise from a combination of factors.

Journal Article↗
PubMed2004

Model of noise-grating selectivity in volume holographic recording materials by use of Monte Carlo simulations.

A model describing the angular selectivity of noise gratings in volume holographic recording materials is presented. The noise grating is treated as an ensemble of superimposed, statistically distributed planar gratings. Rigorous coupled-wave analysis is used to treat reconstruction with various polarization states. The model accounts for material properties such as thickness change, absorption, and the angular distribution of scattered light within the recording medium. Results show good agreement with noise gratings that are experimentally formed in a thick cationic ring-opening photopolymer material.

Journal Article↗
PubMed2003

Anomalous diffraction of light with geometrical path statistics of rays and a Gaussian ray approximation.

The anomalous-diffraction theory (ADT) of extinction of light by soft particles is shown to be determined by a statistical distribution of the geometrical paths of individual rays inside the particles. Light extinction depends on the mean and the mean-squared geometrical paths of the rays. Analytical formulas for optical efficiencies from a Gaussian distribution of the geometrical paths of rays are derived. This Gaussian ray approximation reduces to the exact ADT in the intermediate case of light scattering for an arbitrary soft particle and describes well the extinction of light from a system of randomly oriented and (or) polydisperse particles. The implications for probing of the sizes and shapes of particles by light extinction are discussed.

Journal Article↗
PubMed2006

Preparation and measurement of tunable high-power sub-Poissonian light using twin beams.

Widely frequency tunable bright sub-Poissonian field preparation has been experimentally achieved with quantum-correlated twin beams in the continuously variable regime. The noise of the sub-Poissonian field is reduced to more than 2 dB below the shot-noise level throughout the entire wavelength-tunable range of 7.4 nm. A maximum noise reduction of 45% (2.6 dB) is observed. The statistical distribution of a sub-Poissonian field is also obtained.

Journal Article↗
PubMed1998

Basics of flow cytometry.

In summary, a beginner requires fundamental knowledge about flow cytometric instrumentation in order to effectively use this technology. It is important to remember that flow cytometers are very complex instruments that are composed of four closely related systems. The fluidic system transports particles from a suspension through the cytometer for interrogation by an illumination system. The resulting light scattering and fluorescence is collected, filtered, and converted into electrical signals by the optical and electronics system. The data storage and computer control system saves acquired data and is also the user interface for controlling most instrument functions. These four systems provide a very unique and powerful analytical tool for researchers and clinicians. This is because they analyze the properties of individual particles, and thousands of particles can be analyzed in a matter of seconds. Thus, data for a flow cytometric sample are a collection of many measurements instead of a single bulk measurement. Basic knowledge of instrumentation is a tremendous aid to designing experiments that can be successfully analyzed using flow cytometry. For example, it is important to know the emission wavelength of the laser in the instrument that will be used for analysis. This wavelength is critical knowledge for selecting probes. It is also important to understand that a different range of wavelengths is detected for each fluorescent channel. This will aid selection of probes that are compatible with the flow cytometer. Understanding the complication that emission spectra overlap contributes to detection can be used to guide fluorochrome selections for multicolor analysis. All of these experiment design considerations that rely on knowledge of how flow cytometers work are a very practical and effective means of avoiding wasted time, energy, and costly reagents. Data analysis is a paramount issue in flow cytometry. Analysis includes interpreting as well as presenting data that has been stored in list-mode files. Data analysis is very graphically oriented. There are a number of types of graphic representation that are available to visually aid data analysis. Two standard types of displays are used. These data plots are one-parameter histograms and bivariate plots. A user must be familiar with these two fundamental types of display in order to effectively analyze data. Histograms are the most simple modes of data representation. Histograms allow visualization of a single acquired parameter. Mean fluorescence and distributional statistics can be obtained based on markers that the user can graphically set on the plot. Percentages of positively expressing particles relative to a control sample can also obtained in a similar manner. In addition, multiple histograms can be overlayed on one another to depict qualitative and quantitative differences in two or more samples. Two-parameter data plots are somewhat more complicated than histograms; however, they can yield more information. Two-parameter dot plots of FSC vs SSC allow visualization of both light-scattering parameters that are important for identifying populations of interest. Bivariate fluorescent plots allow discrimination of dual-labeled populations that might remain hidden if histograms were used to display fluorescent data. Two-parameter plots that combine one light-scattering parameter and a fluorescent parameter are useful for analyzing control samples to elucidate the origin of nonspecific binding. Data analysis is very graphically oriented. Experience and pattern recognition become important when using two-parameter data plots for qualitative as well as quantitative analysis. The technique of gating or drawing regions on dual parameter light-scatter plots allows one to exclude information and examine the population of interest by disallowing particles that might confound or interfere with analysis. This is one of the fundamental uses for gating. (ABSTRACT TRUNCATED)

Animals↗