SEARCH · PubMed Health

Results for “Gaussian process”

Explore indexed PubMed citations for clinical trials, systematic reviews and public health research. Read source abstracts and follow each citation to its original PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 325 records · Page 18Linked to original sources

PubMed1998

Effect of noise contrast polarity and temporal asynchrony on visual sensitivity.

We evaluated the effect of substitutive noise on contrast sensitivity within the context of linear (Fourier) and nonlinear (non-Fourier) visual processes. Orientation judgments for D6 (sixth spatial derivative of Gaussian) patterns were obtained from three visually normal subjects when random regions of the target and background were occluded by small (1.7 arc min) pixel arrays that were either all of the same contrast polarity or a mixture of equal percentages of negative and positive contrast. The target was presented either synchronously or asynchronously with the occluding elements. Our results indicate that the manipulation of noise characteristics in this way can bias performance either toward a nonlinear process that is insensitive to noise contrast polarity but sensitive to temporal asynchrony or toward a quasi-linear process that is sensitive to noise contrast polarity but insensitive to temporal asynchrony. These findings have relevance to models of the effect of spatial sampling on the visual performance of persons with retinal disease.

Adult↗

PubMed2001

FDG-PET standardized uptake values in normal anatomical structures using iterative reconstruction segmented attenuation correction and filtered back-projection.

Filtered back-projection (FBP) is the most commonly used reconstruction method for PET images, which are usually noisy. The iterative reconstruction segmented attenuation correction (IRSAC) algorithm improves image quality without reducing image resolution. The standardized uptake value (SUV) is the most clinically utilized quantitative parameter of [fluorine-18]fluoro-2-deoxy-D-glucose (FDG) accumulation. The objective of this study was to obtain a table of SUVs for several normal anatomical structures from both routinely used FBP and IRSAC reconstructed images and to compare the data obtained with both methods. Twenty whole-body PET scans performed in consecutive patients with proven or suspected non-small cell lung cancer were retrospectively analyzed. Images were processed using both IRSAC and FBP algorithms. Nonquantitative or gaussian filters were used to smooth the transmission scan when using FBP or IRSAC algorithms, respectively. A phantom study was performed to evaluate the effect of different filters on SUV. Maximum and average SUVs (SUVmax and SUVavg) were calculated in 28 normal anatomical structures and in one pathological site. The phantom study showed that the use of a nonquantitative smoothing filter in the transmission scan results in a less accurate quantification and in a 20% underestimation of the actual measurement. Most anatomical structures were identified in all patients using the IRSAC images. On average, SUVavg and SUVmax measured on IRSAC images using a gaussian filter in the transmission scan were respectively 20% and 8% higher than the SUVs calculated from conventional FBP images. Scatterplots of the data values showed an overall strong relationship between IRSAC and FBP SUVs. Individual scatterplots of each site demonstrated a weaker relationship for lower SUVs and for SUVmax than for higher SUVs and SUVavg. A set of reference values was obtained for SUVmax and SUVavg of normal anatomical structures, calculated with both IRSAC and FBP image reconstruction algorithms. The use of IRSAC and a gaussian filter for the transmission scan seems to give more accurate SUVs than are obtained from conventional FBP images using a nonquantitative filter for the transmission scan.

Aged↗

PubMed2002

Non-Gaussian nature of the alpha relaxation of glass-forming polyisoprene.

We report quasielastic neutron scattering experiments exploring the alpha relaxation in polyisoprene over an unprecedented range in momentum transfer. Corroborating and validating earlier molecular dynamics simulations, the measurements reveal a crossover from a Gaussian regime of sublinear diffusion to a strongly non-Gaussian regime at short distances. We show that a consistent interpretation in terms of a distribution of finite jumps underlying the alpha process is possible. This model leads to a time-dependent non-Gaussian parameter exhibiting all features revealed so far from various simulations.

Journal Article↗

PubMed1999

The development and maintenance of emmetropia.

The human eye is programmed to achieve emmetropia in youth and to maintain emmetropia with advancing years. This is despite the changes in all eye dimensions during the period of growth and the continuing growth of the lens throughout life. The process of emmetropisation in the child's eye is indicated by a shift from the Gaussian distribution of refractive errors around a hypermetropic mean value at birth to the non-Gaussian leptokurtosis around an emmetropic mean value in the adult. Emmetropisation is the result of both passive and active processes. The passive process is that of proportional enlargement of the eye in the child. The proportional enlargement of the eye reduces the power of the dioptric system in proportion to the increasing axial length. The power of the cornea is reduced by lengthening of the radius of curvature. The power of the lens is reduced by lengthening radii of curvature and the effectivity of the lens is reduced by deepening of the anterior chamber. Ametropia results when these changes are not proportional. The active mechanism involves the feedback of image focus information from the retina and consequent adjustment of the axial length. Defective image formation interferes with this feedback and ametropia then results. Heredity determines the tendency to certain globe proportions and environment plays a part in influencing the action of active emmetropisation. The maintenance of emmetropia in the adult in spite of continuing lens growth with increasing lens thickness and increasing lens curvature, which is known as the lens paradox, is due to the refractive index changes balancing the effect of the increased curvature. These changes may be due to the differences between nucleus and cortex or to gradient changes within the cortex.

Aging↗

PubMed2005

High-temperature unfolding of a trp-cage mini-protein: a molecular dynamics simulation study.

BACKGROUND: Trp cage is a recently-constructed fast-folding miniprotein. It consists of a short helix, a 3,10 helix and a C-terminal poly-proline that packs against a Trp in the alpha helix. It is known to fold within 4 ns. RESULTS: High-temperature unfolding molecular dynamics simulations of the Trp cage miniprotein have been carried out in explicit water using the OPLS-AA force-field incorporated in the program GROMACS. The radius of gyration (Rg) and Root Mean Square Deviation (RMSD) have been used as order parameters to follow the unfolding process. Distributions of Rg were used to identify ensembles. CONCLUSION: Three ensembles could be identified. While the native-state ensemble shows an Rg distribution that is slightly skewed, the second ensemble, which is presumably the Transition State Ensemble (TSE), shows an excellent fit. The denatured ensemble shows large fluctuations, but a Gaussian curve could be fitted. This means that the unfolding process is two-state. Representative structures from each of these ensembles are presented here.

Computer Simulation↗

PubMed2000

The diagnostic utility of the lognormal behavior of PET standardized uptake values in tumors.

UNLABELLED: A meta-analysis of data primarily from PET oncologic investigations using FDG PET was performed. Its purpose was to establish statistical features of the distributions of standardized uptake values (SUVs) as possible aids in the diagnostic process. METHODS: We obtained 1536 values of oncologic markers from patient studies of 40 investigations in the literature. Statistical parameters were tabulated for analysis. RESULTS: A significant observation is that, unlike skewed SUV histograms, log10SUV has Gaussian behavior, which is not uncommon for biologic quantities. This was found for SUVs of FDG and 2 amino acids as well as a few other cancer markers. A possible model for explaining this is proposed. For FDG, the SD sigma of the log10SUVs for an average cancer category was 0.23. Examining data within the framework of the model points to physiologic factors as dominating SUV variability rather than PET protocols. When data for a single cancer category were available from multiple institutions, averages, mean(SUV)s, disagree beyond chance expectations. Diagnostic utility suggestions include a universal linear relationship between sensitivity and severity, defined as SUV/mean(SUV), on semilogarithmic probability paper; a generic receiver-operating-characteristic curve for all cancers; using [log10(mean(SUVmal)/mean(SUVnorm))] divided by (sigma(mal)2 + sigma(norm)2)(1/2) as a simple diagnostic effectiveness measure; and using Gaussian log10SUVs to avoid erroneous P values. CONCLUSION: Using the logarithms of markers, such as SUVs, several advantages stemming from their Gaussian nature can be achieved with benefits ensuing to the diagnostic process.

Biomarkers, Tumor↗

PubMed1980

On transforming biological data to Gaussian form.

Much of the statistical analysis of biological data depends on the assumption that the data are Gaussian (or normal). Some well-known procedures which use this assumption are (i) t-tests (ii) analysis of variance (iii) regression estimation and their attendant tests. If the data are not Gaussian, one can use nonparametric statistical techniques, if they exist, but they often require larger amounts of data to obtain equally precise results (see for example Lumsden and Mullen (7) for a discussion of this with regard to reference value estimation). If the data are not Gaussian a fruitful approach to their analyses lies in trying to find a transformation which will render tham Gaussian. The data thus transformed to a Gaussian form, can be analyzed validly using standard statistical techniques. The process of finding a good transformation of the data has often been an arbitrary and ad hoc one. The purpose of this article is to look at a particular technique for attempting to render nonGaussian data Gaussian, and to illustrate its applicability and breadth of use.

Animals↗

PubMed2006

Hybrid approach of selecting hyperparameters of support vector machine for regression.

To select the hyperparameters of the support vector machine for regression (SVR), a hybrid approach is proposed to determine the kernel parameter of the Gaussian kernel function and the epsilon value of Vapnik's epsilon-insensitive loss function. The proposed hybrid approach includes a competitive agglomeration (CA) clustering algorithm and a repeated SVR (RSVR) approach. Since the CA clustering algorithm is used to find the nearly "optimal" number of clusters and the centers of clusters in the clustering process, the CA clustering algorithm is applied to select the Gaussian kernel parameter. Additionally, an RSVR approach that relies on the standard deviation of a training error is proposed to obtain an epsilon in the loss function. Finally, two functions, one real data set (i.e., a time series of quarterly unemployment rate for West Germany) and an identification of nonlinear plant are used to verify the usefulness of the hybrid approach.

Algorithms↗

PubMed2005

An alternative method for electrophoretic gel image analysis in the GelMaster software.

A novel methodology of electrophoretic gel image analysis has been proposed that is based on two-dimensional image processing methods instead of previously used one-dimensional Gaussian deconvolution. The crucial problem of the analysis of imperfect gels, that consists in band detection, is solved using the algorithms of band boundary detection and intensity homogeneity indication. The template approach represents the core element of the developed algorithms. The GelMaster software system has been developed in which the novel algorithms are implemented. It involves two-stage interaction with the user: detection of the true bands and deleting the false band detections. The main features of the GelMaster system and the most important algorithms are described.

Algorithms↗

PubMed1993

Analyzing and modeling fractal intensity point processes.

Fractal intensity point processes--doubly stochastic point processes with a fractal waveform intensity process--are required to describe the discharge patterns recorded from the auditory and visual systems. The Fano factor--the ratio of the variance of the number of events in an interval to the mean of this number--captures the self-similar characteristics of the intensity via two quantities: fractal dimension and fractal time. The fractal dimension is the exponent of the asymptotic power law behavior of the Fano factor with interval duration. The fractal time delineates long-term fractal behavior from short-term characteristics of the data. The average rate and self-similarity parameter of the intensity process, absolute and relative refractory effects, and serial dependence all modify the fractal time. To generate fractal intensity point processes, stochastic fractal processes are derived by applying memoryless, nonlinear transformations to fractional Gaussian noise. The intensity's amplitude distribution in combination with the Fano factor form criteria to choose the transformation that best describes data.

Auditory Perception↗

PubMed1996

Maximum likelihood analysis of cardiac late potentials.

This study presents a new time-domain method for the detection of late potentials in individual leads. Basic statistical properties of the ECG samples are modeled in order to estimate the amplitude and duration of late potentials. The signal model accounts for correlation in both time and across the ensemble of beats. Late potentials are modeled as a colored process with unknown amplitude which is disturbed by white, Gaussian noise. Maximum likelihood estimation is applied to the model for estimating the amplitude of the late potentials. The resulting estimator consists of an eigenvector-based filter followed by a nonlinear operation. The performance of the maximum likelihood procedure was compared to that obtained by traditional time-domain analysis based on the vector magnitude. It was found that the new technique yielded a substantial improvement of the signal-to-noise ratio in the function used for endpoint determination. This improvement leads to a prolongation of the filtered QRS duration in cases with late potentials.

Action Potentials↗

PubMed2004

Probabilistic independent component analysis for functional magnetic resonance imaging.

We present an integrated approach to probabilistic independent component analysis (ICA) for functional MRI (FMRI) data that allows for nonsquare mixing in the presence of Gaussian noise. In order to avoid overfitting, we employ objective estimation of the amount of Gaussian noise through Bayesian analysis of the true dimensionality of the data, i.e., the number of activation and non-Gaussian noise sources. This enables us to carry out probabilistic modeling and achieves an asymptotically unique decomposition of the data. It reduces problems of interpretation, as each final independent component is now much more likely to be due to only one physical or physiological process. We also describe other improvements to standard ICA, such as temporal prewhitening and variance normalization of timeseries, the latter being particularly useful in the context of dimensionality reduction when weak activation is present. We discuss the use of prior information about the spatiotemporal nature of the source processes, and an alternative-hypothesis testing approach for inference, using Gaussian mixture models. The performance of our approach is illustrated and evaluated on real and artificial FMRI data, and compared to the spatio-temporal accuracy of results obtained from classical ICA and GLM analyses.

Algorithms↗

PubMed1999

Approach to Gaussian stochastic behavior for systems driven by deterministic chaotic forces.

We consider skew-product dynamical systems that describe the stroboscopic dynamics of a damped particle subjected to a chaotic kick force. In a suitable scaling limit the dynamics converges to the Ornstein-Uhlenbeck process. We investigate the deterministic chaotic corrections in the vicinity of this Gaussian limit case for various examples of chaotic forces. We present numerical evidence that, for certain classes of chaotic forces, the deterministic chaotic corrections of the invariant density are universal. We provide analytical results for forces generated by Tchebyscheff maps and sketch a renormalization group theory in the space of probability densities.

Journal Article↗

PubMed2004

Graphical interpretation of confidence curves in rankit plots.

A well-known transformation from the bell-shaped Gaussian (normal) curve to a straight line in the rankit plot is investigated, and a tool for evaluation of the distribution of reference groups is presented. It is based on the confidence intervals for percentiles of the calculated Gaussian distribution and the percentage of cumulative points exceeding these limits. The process is to rank the reference values and plot the cumulative frequency points in a rankit plot with a logarithmic (In=log(e)) transformed abscissa. If the distribution is close to In-Gaussian the cumulative frequency points will fit to the straight line describing the calculated In-Gaussian distribution. The quality of the fit is evaluated by adding confidence intervals (CI) to each point on the line and calculating the percentage of points outside the hyperbola-like CI-curves. The assumption was that the 95% confidence curves for percentiles would show 5% of points outside these limits. However, computer simulations disclosed that approximate 10% of the series would have 5% or more points outside the limits. This is a conservative validation, which is more demanding than the Kolmogorov-Smirnov test. The graphical presentation, however, makes it easy to disclose deviations from In-Gaussianity, and to make other interpretations of the distributions, e.g., comparison to non-Gaussian distributions in the same plot, where the cumulative frequency percentage can be read from the ordinate. A long list of examples of In-Gaussian distributions of subgroups of reference values from healthy individuals is presented. In addition, distributions of values from well-defined diseased individuals may show up as In-Gaussian. It is evident from the examples that the rankit transformation and simple graphical evaluation for non-Gaussianity is a useful tool for the description of sub-groups.

Blood Chemical Analysis↗

PubMed1983

Generation of random sequences with jointly specified probability density and autocorrelation functions.

A new method is presented for the generation of stochastic (random) sequences with an arbitrarily specified first-order probability distribution function (PDF) and an arbitrarily specified first-order auto-correlation function (ACF). A set of numbers with the desired PDF are first generated. These are then given a white (independent) ACF by double stochastic interchange. The desired ACF is then obtained by stochastically shuffling the series to minimize a sum of squares criterion between desired and actual ACFs. The technique is particularly useful for generating experimental stimuli for system identification, sequences for numerical stimulation, and test series for evaluating signal processing algorithms when colored (non-white) non-Gaussian data are required.

Mathematics↗

PubMed1989

Mean and quasideterministic equivalence for linear stochastic dynamics.

In linear, stochastic dynamics it is shown that the quasideterministic population size is equivalent to the mean population size. The quasideterministic dynamics are defined by the conditional infinitesimal mean of the process. The stochastic component of the dynamics includes both Gaussian and Poisson white noise, with amplitude coefficients proportional to the population size. Generalizations are given for nonautonomous coefficients and for distributed Poisson jump amplitudes. A counter example--an exactly integrable nonlinear jump model--shows that the equivalence result does not hold for nonlinear stochastic dynamics.

Linear Models↗

PubMed1987

What causes stereoscopic tilt from spatial frequency disparity.

A controversy still exists concerning whether the tilt created with interocular spatial frequency disparity arises from a computation of spatial frequency differences or from cumulative positional disparity. In a first experiment, we examined the influence of positional disparity on tilt created with frequency disparity, reasoning that if tilt were computed from spatial frequency differences, the perceived angle should remain unaltered since adding a positional disparity does not change the harmonic content of the stimulus. The results indicated that positional disparity weakened perceived tilt. In a second experiment, we tested the idea that tilt results from the calculation of increasing positional disparity across the display, arguing if local matches of features in the two eyes are made in computing tilt, then the solution to binocular correspondence may be less ambiguous if the same number of cycles was displayed for both spatial frequencies. Perceived tilt increased when the number of cycles was equal, although the angle of tilt still decreased with positional disparity. In Experiment 3, we further reduced potential sources of ambiguity for the binocular matching process by employing D10s (the tenth derivative of a Gaussian) instead of grating patterns. Positional disparity exerted essentially no influence on the perceived angle of tilt of the D10s. Taken together, the results of these experiments suggest that tilt from frequency disparity can be explained solely on the basis of positional disparity.

Depth Perception↗

PubMed2002

Controller performance analysis with LQG benchmark obtained under closed loop conditions.

This paper proposes a new method for obtaining a linear quadratic Gaussian (LQG) benchmark in terms of the variances of process input and output from closed-loop data, for assessing the controller performance. LQG benchmark has been proposed in the literature to assess controller performance since the LQG tradeoff curve represents the limit of performance in terms of input and output variances. However, an explicit parametric model is required to calculate the LQG benchmark. In this work, we propose a data driven subspace approach to calculate the LQG benchmark under closed-loop conditions with certain external excitations. The optimal LQG-benchmark variances are obtained directly from the subspace matrices corresponding to the deterministic inputs and the stochastic inputs, which are identified using closed-loop data with setpoint excitation. These variances are used for assessing the controller performance. The method proposed in this paper is applicable to both univariate and multivariate systems. Profit analysis for the implementation of feedforward control to the existing feedback-only control system is also analyzed under the optimal LQG performance framework. The proposed method is illustrated through a simulation example and an application on a pilot scale process.

Benchmarking↗