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PubMed2003

Can a numerically stable subgrid-scale model for turbulent flow computation be ideally accurate?: a preliminary theoretical study for the Gaussian filtered Navier-Stokes equations.

This paper introduces a candidate for the origin of the numerical instabilities in large eddy simulation repeatedly observed in academic and practical industrial flow computations. Without resorting to any subgrid-scale modeling, but based on a simple assumption regarding the streamwise component of flow velocity, it is shown theoretically that in a channel-flow computation, the application of the Gaussian filtering to the incompressible Navier-Stokes equations yields a numerically unstable term, a cross-derivative term, which is similar to one appearing in the Gaussian filtered Vlasov equation derived by Klimas [J. Comput. Phys. 68, 202 (1987)] and also to one derived recently by Kobayashi and Shimomura [Phys. Fluids 15, L29 (2003)] from the tensor-diffusivity subgrid-scale term in a dynamic mixed model. The present result predicts that not only the numerical methods and the subgrid-scale models employed but also only the applied filtering process can be a seed of this numerical instability. An investigation concerning the relationship between the turbulent energy scattering and the unstable term shows that the instability of the term does not necessarily represent the backscatter of kinetic energy which has been considered a possible origin of numerical instabilities in large eddy simulation. The present findings raise the question whether a numerically stable subgrid-scale model can be ideally accurate.

Journal Article↗

PubMed2006

The multiscale hermite transform for local orientation analysis.

The efficient representation of local differential structure at various resolutions has been a matter of great interest for adaptive image processing and computer vision tasks. In this paper, we derive a multiscale model to represent natural images based on the scale-space representation: a model that has an inspiration in the human visual system. We first derive the one-dimensional case and then extend the results to two and three dimensions. The operators obtained for analysis and synthesis stages are derivatives of the Gaussian smoothing kernel, so that, for the two-dimensional case, we can represent them either in a rotated coordinate system or in terms of directional derivatives. The method to perform the rotation is efficient because it is implemented by means of the application of the so-called generalized binomial filters. Such a family of discrete sequences fulfills a number of properties that allows estimating the local orientation for several image structures. We also define the discrete counterpart in which the coordinate normalization of the continuous case is approximated as a subsampling of the discrete domain.

Algorithms↗

PubMed2006

A fully automated method for lung nodule detection from postero-anterior chest radiographs.

In the past decades, a great deal of research work has been devoted to the development of systems that could improve radiologists' accuracy in detecting lung nodules. Despite the great efforts, the problem is still open. In this paper, we present a fully automated system processing digital postero-anterior (PA) chest radiographs, that starts by producing an accurate segmentation of the lung field area. The segmented lung area includes even those parts of the lungs hidden behind the heart, the spine, and the diaphragm, which are usually excluded from the methods presented in the literature. This decision is motivated by the fact that lung nodules may be found also in these areas. The segmented area is processed with a simple multiscale method that enhances the visibility of the nodules, and an extraction scheme is then applied to select potential nodules. To reduce the high number of false positives extracted, cost-sensitive support vector machines (SVMs) are trained to recognize the true nodules. Different learning experiments were performed on two different data sets, created by means of feature selection, and employing Gaussian and polynomial SVMs trained with different parameters; the results are reported and compared. With the best SVM models, we obtain about 1.5 false positives per image (fp/image) when sensitivity is approximately equal to 0.71; this number increases to about 2.5 and 4 fp/image when sensitivity is = 0.78 and = 0.85, respectively. For the highest sensitivity (= 0.92 and 1.0), we get 7 or 8 fp/image.

Algorithms↗

PubMed2006

Generalization of DNA microarray dispersion properties: microarray equivalent of t-distribution.

BACKGROUND: DNA microarrays are a powerful technology that can provide a wealth of gene expression data for disease studies, drug development, and a wide scope of other investigations. Because of the large volume and inherent variability of DNA microarray data, many new statistical methods have been developed for evaluating the significance of the observed differences in gene expression. However, until now little attention has been given to the characterization of dispersion of DNA microarray data. RESULTS: Here we examine the expression data obtained from 682 Affymetrix GeneChips with 22 different types and we demonstrate that the Gaussian (normal) frequency distribution is characteristic for the variability of gene expression values. However, typically 5 to 15% of the samples deviate from normality. Furthermore, it is shown that the frequency distributions of the difference of expression in subsets of ordered, consecutive pairs of genes (consecutive samples) in pair-wise comparisons of replicate experiments are also normal. We describe a consecutive sampling method, which is employed to calculate the characteristic function approximating standard deviation and show that the standard deviation derived from the consecutive samples is equivalent to the standard deviation obtained from individual genes. Finally, we determine the boundaries of probability intervals and demonstrate that the coefficients defining the intervals are independent of sample characteristics, variability of data, laboratory conditions and type of chips. These coefficients are very closely correlated with Student's t-distribution. CONCLUSION: In this study we ascertained that the non-systematic variations possess Gaussian distribution, determined the probability intervals and demonstrated that the K(alpha) coefficients defining these intervals are invariant; these coefficients offer a convenient universal measure of dispersion of data. The fact that the K(alpha) distributions are so close to t-distribution and independent of conditions and type of arrays suggests that the quantitative data provided by Affymetrix technology give "true" representation of physical processes, involved in measurement of RNA abundance. REVIEWERS: This article was reviewed by Yoav Gilad (nominated by Doron Lancet), Sach Mukherjee (nominated by Sandrine Dudoit) and Amir Niknejad and Shmuel Friedland (nominated by Neil Smalheiser).

Journal Article↗

PubMed2005

Identification of gastroenteric viruses by electron microscopy using higher order spectral features.

BACKGROUND: Many paediatric illnesses are caused by viral agents, for example, acute gastroenteritis. Electron microscopy can provide images of viral particles and can be used to identify the agents. OBJECTIVES: The use of electron microscopy as a diagnostic tool is limited by the need for high level of expertise in interpreting these images and the time required. A semi-automated method is proposed in this paper. STUDY DESIGN: The method is based on bispectal features that capture contour and texture information while providing robustness to shift, rotation, changes in size and noise. The magnification or true size of the viral particles need not be known precisely, but if available can be used additionally for improved classification. Viral particles from one or more images are segmented and analyzed to verify whether they belong to a particular class (such as Adenovirus, Rotavirus, etc.) or not. Two experiments were conducted-depending on the populations from which virus particle images were collected for training and testing, respectively. In the first, disjoint subsets from a pooled population of virus particles obtained from several images were used. In the second, separate populations from separate images were used. The performance of the method on viruses of similar size was separately evaluated using Astrovirus, HAV and Poliovirus. A Gaussian Mixture Model was used for the probability density of the features. A threshold on the log-likelihood is varied to study false alarm and false rejection trade-off. Features from many particles and/or likelihoods from independent tests are averaged to yield better performance. RESULTS: An equal error rate (EER) of 2% is obtained for verification of Rotavirus (tested against three other viruses) when features from 15 viral particle images are averaged. It drops further to less than 0.2% when scores from two tests are averaged to make a decision. For verification of Astrovirus (tested against two others of the same size) the EER was less than 2% when 20 particles and two tests were used. CONCLUSION: Bispectral features and Gaussian mixture modelling of their probability density are shown to be effective in identifying viruses from electron microscope images. With the use of digital imaging in electron microscopes, this method can be fully automated.

Adenoviruses, Human↗

PubMed2003

Noise-induced synchronization and coherence resonance of a Hodgkin-Huxley model of thermally sensitive neurons.

We study nontrivial effects of noise on synchronization and coherence of a chaotic Hodgkin-Huxley model of thermally sensitive neurons. We demonstrate that identical neurons which are not coupled but subjected to a common fluctuating input (Gaussian noise) can achieve complete synchronization when the noise amplitude is larger than a threshold. For nonidentical neurons, noise can induce phase synchronization. Noise enhances synchronization of weakly coupled neurons. We also find that noise enhances the coherence of the spike trains. A saddle point embedded in the chaotic attractor is responsible for these nontrivial noise-induced effects. Relevance of our results to biological information processing is discussed.

Animals↗

PubMed1995

A fast and stable maximum a posteriori conjugate gradient reconstruction algorithm.

We have derived a maximum a posteriori (MAP) approach for iterative reconstruction based on a weighted least-squares conjugate gradient (WLS-CG) algorithm. The WLS-CG algorithm has been shown to have initial convergence rates up to 10x faster than the maximum-likelihood expectation maximization (ML-EM) algorithm, but WLS-CG suffers from rapidly increasing image noise at higher iteration numbers. In our MAP-CG algorithm, the increasing noise is controlled by a Gibbs smoothing prior, resulting in stable, convergent solutions. Our formulation assumes a Gaussian noise model for the likelihood function. When a linear transformation of the pixel space is performed (the "relaxation" acceleration method), the MAP-CG algorithm obtains a low-noise, stable solution (one that does not change with further iterations) in 10-30 iterations, compared to 100-200 iterations for MAP-EM. Each iteration of MAP-CG requires approximately the same amount of processing time as one iteration of ML-EM or MAP-EM. We show that the use of an initial image estimate obtained from a single iteration of the Chang method helps the algorithm to converge faster when acceleration is not used, but does not help when acceleration is applied. While both the WLS-CG and MAP-CG methods suffer from the potential for obtaining negative pixel values in the iterated image estimates, the use of the Gibbs prior substantially reduces the number of pixels with negative values and restricts them to regions of little or no activity. We use SPECT data from simulated hot-sphere phantoms and from patient studies to demonstrate the advantages of the MAP-CG algorithm. We conclude that the MAP-CG algorithm requires 10%-25% of the processing time of EM techniques, and provides images of comparable or superior quality.

Algorithms↗

PubMed2004

An echolocation model for the restoration of an acoustic image from a single-emission echo.

Bats can form a fine acoustic image of an object using frequency-modulated echolocation sound. The acoustic image is an impulse response, known as a reflected-intensity distribution, which is composed of amplitude and phase spectra over a range of frequencies. However, bats detect only the amplitude spectrum due to the low-time resolution of their peripheral auditory system, and the frequency range of emission is restricted. It is therefore necessary to restore the acoustic image from limited information. The amplitude spectrum varies with the changes in the configuration of the reflected-intensity distribution, while the phase spectrum varies with the changes in its configuration and location. Here, by introducing some reasonable constraints, a method is proposed for restoring an acoustic image from the echo. The configuration is extrapolated from the amplitude spectrum of the restricted frequency range by using the continuity condition of the amplitude spectrum at the minimum frequency of the emission and the minimum phase condition. The determination of the location requires extracting the amplitude spectra, which vary with its location. For this purpose, the Gaussian chirplets with a carrier frequency compatible with bat emission sweep rates were used. The location is estimated from the temporal changes of the amplitude spectra.

Animals↗

PubMed2001

Use of historical uranium air sampling data to estimate worker exposure potential to airborne radioactive particulate in a uranium processing facility.

Historical industrial hygiene monitoring records from a uranium processing plant were collected and analyzed to characterize exposure potential to airborne radioactive particulate. More than 2,100 samples were collected during the period of 1954-1968. The data was organized by job title, plant number, and year of measurement. Laboratory analysis of air samples indicated a wide range of potential exposures to the alpha-emitting particulate. Logarithmic transformation of the data was necessary to approximate Gaussian distributions. Geometric Mean (GM) values were used as the measure of central tendency within years. GM values ranged from 23-49 disintegrations per minute per cubic meter of air sampled (dpm/m3) with the years 1963 and 1964 being significantly higher than other years (ANOVA: p < 0.05). When comparing exposure potential across plants, GM ranged from 20-68 dpm/m3, with plants 5 and 8 being significantly higher than the others (ANOVA: p < 0.05). Exposure potential for specific job titles across the plants varied widely. GM for clerks was the lowest (11 dpm/m3) while furnace operators were the highest (235 dpm/m3). Other job titles with potentially high exposures were chemical operators, forklift operators, machine operators, and furnace operators. This analysis indicates the magnitude and distributions of worker exposure to alpha-emitting airborne particulate. Additional analysis and epidemiologic studies are planned for this facility.

Aerosols↗

PubMed2000

Single-file diffusion of colloids in one-dimensional channels

Single-file diffusion, prevalent in many processes, refers to the restricted motion of interacting particles in narrow micropores with the mutual passage excluded. A single-filing system was developed by confining colloidal spheres in one-dimensional circular channels of micrometer scale. Optical video microscopy study shows evidence that the particle self-diffusion is non-Fickian for long periods of time. In particular, the distribution of particle displacement is a Gaussian function.

Journal Article↗

PubMed2000

Complex denoising of MR data via wavelet analysis: application for functional MRI.

A fast post-processing method for noise reduction of MR images, termed complex-denoising, is presented. The method is based on shrinking noisy discrete wavelet transform coefficients via thresholding, and it can be used for any MRI data-set with no need for high power computers. Unlike previous wavelet application to MR images, the denoising algorithm is applied, separately, to the two orthogonal sets of the complex MR image. The norm of the combined data are used to construct the image. With this method, signal-noise decoupling and Gaussian white noise assumptions used in the wavelet noise suppression scheme, are better fulfilled. The performance of the method is tested by carrying out a qualitative and quantitative comparison of a single-average image, complex-denoised image, multiple-average images, and a magnitude-denoised image, of a standard phantom. The comparison shows that the complex-denoising scheme improves the signal-to-noise and contrast-to-noise ratios more than the magnitude-denoising scheme, particularly in low SNR regions. To demonstrate the method strength, it is applied to fMRI data of somatosensory rat stimulation. It is shown that the activation area in a cross-correlation analysis is approximately 63% larger in the complex-denoised versus original data sets when equal threshold value is used. Application of the method of Principal Component Analysis to the complex-denoised, magnitude-denoised, and original data sets results in a similar but higher variance of the first few principal components obtained from the former data set as compared to those obtained from the later two sets.

Algorithms↗

PubMed1999

Some statistical improvements for estimating population size and mutation rate from segregating sites in DNA sequences.

In population genetics, under a neutral Wright-Fisher model, the scaling parameter straight theta=4Nmu represents twice the average number of new mutants per generation. The effective population size is N and mu is the mutation rate per sequence per generation. Watterson proposed a consistent estimator of this parameter based on the number of segregating sites in a sample of nucleotide sequences. We study the distribution of the Watterson estimator. Enlarging the size of the sample, we asymptotically set a Central Limit Theorem for the Watterson estimator. This exhibits asymptotic normality with a slow rate of convergence. We then prove the asymptotic efficiency of this estimator. In the second part, we illustrate the slow rate of convergence found in the Central Limit Theorem. To this end, by studying the confidence intervals, we show that the asymptotic Gaussian distribution is not a good approximation for the Watterson estimator.

Base Sequence↗

PubMedDate not supplied

Assessment and visualization of the curvature of the left ventricle from 3D medical images.

We address the problem of using curvature features to assess the three-dimensional (3D) motion of the left ventricle. The adequacy of this approach depends on the actual characteristics of the curvature of the left ventricle and particularly on the spatial and temporal stability of these features. From experimental data, we compute the distribution of the Gaussian curvature over the surface of the left ventricle by using an iterative procedure. The results are visualized in 3D through a voxel-based surface rendering technique. We show that the Gaussian curvature remains stable along the cardiac cycle. This curvature feature could thus provide a reliable basis for further 3D motion analysis of the left ventricle.

Algorithms↗

PubMed2006

Comparing spectra and coherences for groups of unequal size.

Spectra and coherences are standard measures of association within and between time series. These measures have several advantages over their time-domain counterparts, not the least of which is the ability to derive and estimate confidence intervals. However, comparing spectra and coherences between two groups of observation is a problem that has not received much attention. This problem is important in neuroscience since it is often of great interest to determine whether the estimates differ between distinct experimental/behavioral conditions. Here we propose one approach to this problem. Based on the known distributional properties of spectral and coherence estimates, we derive a test for equality of two spectral or coherence estimates. The test is applicable to unequal sample sizes. We also derive jackknifed estimates of the variance of the proposed test statistic. We suggest that comparing the estimates obtained from the jackknife procedure with the theoretical estimates provides a robust means of determining whether the data in question shows non-Gaussian or non-stationary behavior. Finally, we present applications of the method to simulated and real data.

Computer Simulation↗

PubMed2005

Detection of temporal changes in the spatial distribution of cancer rates using local Moran's I and geostatistically simulated spatial neutral models.

This paper presents the first application of spatially correlated neutral models to the detection of changes in mortality rates across space and time using the local Moran's I statistic. Sequential Gaussian simulation is used to generate realizations of the spatial distribution of mortality rates under increasingly stringent conditions: 1) reproduction of the sample histogram, 2) reproduction of the pattern of spatial autocorrelation modeled from the data, 3) incorporation of regional background obtained by geostatistical smoothing of observed mortality rates, and 4) incorporation of smooth regional background observed at a prior time interval. The simulated neutral models are then processed using two new spatio-temporal variants of the Morany's I statistic, which allow one to identify significant changes in mortality rates above and beyond past spatial patterns. Last, the results are displayed using an original classification of clusters/outliers tailored to the space-time nature of the data. Using this new methodology the space-time distribution of cervix cancer mortality rates recorded over all US State Economic Areas (SEA) is explored for 9 time periods of 5 years each. Incorporation of spatial autocorrelation leads to fewer significant SEA units than obtained under the traditional assumption of spatial independence, confirming earlier claims that Type I errors may increase when tests using the assumption of independence are applied to spatially correlated data. Integration of regional background into the neutral models yields substantially different spatial clusters and outliers, highlighting local patterns which were blurred when local Moran's I was applied under the null hypothesis of constant risk.

Journal Article↗

PubMed2005

Molecular dynamic heterogeneity of confined lipid films by 1H magnetization-exchange nuclear magnetic resonance.

The molecular dynamic heterogeneity of monolayer to submonolayer thin lecithin films confined to submicron cylindrical pores were investigated by 1H magnetization exchange nuclear magnetic resonance. In this experiment a z-magnetization gradient was generated by a double-quantum dipolar filter. The magnetization-exchange decay and buildup curves were interpreted with the help of a theoretical model based on the approximation of a one-dimensional spin-diffusion process in a three-domain morphology. The dynamic heterogeneity of the fatty acid chains and the effects of the surface area per molecule, the diameter of the pores, and the temperature were characterized with the help of local spin-diffusion coefficients. The effect of various parameters on the molecular dynamics of the mobile region of the fatty acid chains was quantified by introducing an ad hoc Gaussian distribution function of the 1H residual dipolar couplings. For the lipid films investigated in this study, the surface induced order and the geometrical confinement affect the chain dynamics of the entire molecule. Therefore, each part of the chain independently reflects the effect of surface coverage, pore size, and temperature.

Aluminum Oxide↗

PubMed2002

Dynamics of wave-pulse penetration into an evanescent region.

The initial problem of plasma wave dynamics in the presence of a sharp density jump that divides the space into transparent and opaque regions is studied. A wave packet is assumed to be initially localized in the transparent region. The transient process of field penetration beyond the density barrier during the wave packet reflection from the density jump is investigated. Signal velocity beyond the barrier is defined as the speed at which some small, but finite, value of the field amplitude appears in the evanescent region. This velocity, which is proved to be always less than the speed of light, is determined analytically for the case of quasi-Gaussian wave packet. Further insight into the field dynamics in opaque region is gained by considering a steplike initial wave packet.

Journal Article↗

PubMed1987

Interlaboratory proficiency-testing programs: a computer model to assess their capability to correctly characterize intralaboratory performance.

We developed a computer model of an interlaboratory survey program to study the ability of proficiency testing (PT) programs to detect intralaboratory errors (total, random, and systematic). It uses a base interlaboratory PT population of 400 laboratories and one test laboratory each with uniquely defined intralaboratory characteristics, i.e., mean, standard deviation (SD), and bias. A gaussian random-number generator uses these parameters to simulate 401 test results analogous to the analysis of one PT sample by each laboratory. The test laboratory's intralaboratory error is expressed as various combinations of bias and coefficient of variation (CV); its simulated survey result is evaluated by a performance criterion derived from the group statistics. To eliminate statistical artifacts, the computer model repeats the complete simulation process 400 times and determines the percentage of the test laboratory's results that fail to meet a specified performance criterion. The computer model can use assigned values or actual intralaboratory data.

Computer Simulation↗