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PubMed1989

The divergence of a polygenic system subject to stabilizing selection, mutation and drift.

Polygenic variation can be maintained by a balance between mutation and stabilizing selection. When the alleles responsible for variation are rare, many classes of equilibria may be stable. The rate at which drift causes shifts between equilibria is investigated by integrating the gene frequency distribution W2N II (pq)4N mu-1. This integral can be found exactly, by numerical integration, or can be approximated by assuming that the full distribution of allele frequencies is approximately Gaussian. These methods are checked against simulations. Over a wide range of population sizes, drift will keep the population near an equilibrium which minimizes the genetic variance and the deviation from the selective optimum. Shifts between equilibria in this class occur at an appreciable rate if the product of population size and selection on each locus is small (Ns alpha 2 less than 10). The Gaussian approximation is accurate even when the underlying distribution is strongly skewed. Reproductive isolation evolves as populations shift to new combinations of alleles: however, this process is slow, approaching the neutral rate (approximately mu) in small populations.

Alleles↗

PubMed1993

Rescaled range analysis of resting respiration.

Fluctuations in resting depth of breathing (tidal volume) at constant breathing rate in the anesthetized adult rat exhibit fractal properties when analyzed by a rescaled range method characterized by a mean (+/-SD) exponent H=0.83+/-0.02 and 0.92+/-0.03 with and without sighs, respectively, for up to 400 breaths. Values of H determined from shuffled tidal volumes and simulated tidal volumes taken randomly from a Gaussian distribution of mean and variance approximating that of the actual data are consistent with the expected value of H=0.5 for an independent random process with finite variances. An empirical description is proposed to predict the change in H with length of time record.

Journal Article↗

PubMed2002

Measurement and data processing approach for detecting anisotropic spatial statistics of the turbulence-induced index of refraction fluctuations in the upper atmosphere.

We discuss a method of data reduction and analysis that has been developed for a novel experiment to detect anisotropic turbulence in the tropopause and to measure the spatial statistics of these flows. The experimental concept is to make measurements of temperature at 15 points on a hexagonal grid for altitudes from 12,000 to 18,000 m while suspended from a balloon performing a controlled descent. From the temperature data, we estimate the index of refraction and study the spatial statistics of the turbulence-induced index of refraction fluctuations. We present and evaluate the performance of a processing approach to estimate the parameters of an anisotropic model for the spatial power spectrum of the turbulence-induced index of refraction fluctuations. A Gaussian correlation model and a least-squares optimization routine are used to estimate the parameters of the model from the measurements. In addition, we implemented a quick-look algorithm to have a computationally nonintensive way of viewing the autocorrelation function of the index fluctuations. The autocorrelation of the index of refraction fluctuations is binned and interpolated onto a uniform grid from the sparse points that exist in our experiment. This allows the autocorrelation to be viewed with a three-dimensional plot to determine whether anisotropy exists in a specific data slab. Simulation results presented here show that, in the presence of the anticipated levels of measurement noise, the least-squares estimation technique allows turbulence parameters to be estimated with low rms error.

Journal Article↗

PubMed2003

"Nonparametric" A' and other modern misconceptions about signal detection theory.

Many modern descriptions of signal detection theory (SDT) are, at best, distorted caricatures of the Gaussian equal-variance model of SDT (G-SDT). The distortions have sometimes led to important, but unwarranted, conclusions about the nature of cognitive processes. Some researchers reject using d' and beta because of concerns about the validity of explicit underlying assumptions (that are shared with most inferential statistics), instead using either the supposedly "nonparametric" measures of A' and B" or measures known to confound ability and bias. The origins, development, and underlying assumptions of SDT are summarized, then contrasted with modern distortions and misconceptions. The nature and interpretation of common descriptive statistics for sensitivity and bias are described along with important pragmatic considerations about use. A deeper understanding of SDT provides researchers with tools that better evaluate both their own findings and the validity of conclusions drawn by others who have utilized SDT measures and analyses.

Decision Making↗

PubMed1998

Statistical Inference (part 1): Basic Concepts.

In the most common research situations, the investigator cannot directly assess the whole population of interest. For this reason, a sample is often studied to infer the actual population measures or parameters. Statistical inference comprises the application of methods to analyze the sample data in order to estimate the population parameters. The basic assumption in statistical inference is that each individual within the population of interest has the same probability of being included in a specific sample. When the sample is not randomly selected. the study findings can still be generalized if the sample can be considered representative of the whole population of interest. A set of statistical methods used to infer the population parameters is performed under the assumption that the sample estimates follow a bell-shaped distribution, called normal distribution. This article presents with the help of examples, the logic used in the sampling distribution theory. The concept of normal (also called gaussian) sampling distribution has an important role in statistical inference, even when the population values are not normally distributed. In fact, in the statistical inference process, the form of the distribution of the sample estimates is more important than the distribution of the individual values.

Journal Article↗

PubMed2004

Cortico-striatal circuits and interval timing: coincidence detection of oscillatory processes.

Humans and other animals demonstrate the ability to perceive and respond to temporally relevant information with characteristic behavioral properties. For example, the response time distributions in peak-interval timing tasks are well described by Gaussian functions, and superimpose when scaled by the criterion duration. This superimposition has been referred to as the scalar property and results from the fact that the standard deviation of a temporal estimate is proportional to the duration being timed. Various psychological models have been proposed to account for such responding. These models vary in their success in predicting the temporal control of behavior as well as in the neurobiological feasibility of the mechanisms they postulate. A review of the major interval timing models reveals that no current model is successful on both counts. The neurobiological properties of the basal ganglia, an area known to be necessary for interval timing and motor control, suggests that this set of structures act as a coincidence detector of cortical and thalamic input. The hypothesized functioning of the basal ganglia is similar to the mechanisms proposed in the beat frequency timing model [R.C. Miall, Neural Computation 1 (1989) 359-371], leading to a reevaluation of its capabilities in terms of behavioral prediction. By implementing a probabilistic firing rule, a dynamic response threshold, and adding variance to a number of its components, simulations of the striatal beat frequency model were able to produce output that is functionally equivalent to the expected behavioral response form of peak-interval timing procedures.

Animals↗

PubMed1988

Evaluation of the frequency of anaemia and iron-deficiency anaemia in a group of Algerian menstruating women by a mixed distribution analysis: contribution of folate deficiency and inflammatory processes in the determination of anaemia.

Frequency of anaemia was estimated by two methods for 254 menstruating women living in South-eastern Algeria. One method defines the frequency of anaemia as the percentage of women with haemoglobin concentrations below the cut-off point defined by WHO (12 g/dl). The second method defines the frequency of anaemia as the percentage of women whose haemoglobin values are shifted downwards relative to a Gaussian distribution of haemoglobin of nonanaemic women. The conventional cut-off point probably tends to overestimate the true frequency of anaemia: 7% of women with haemoglobin concentration less than 12 g/dl were not found as anaemic using the cumulative frequency method. The contribution of iron deficiency folate deficiency and inflammatory process was estimated using the cumulative frequency distribution after excluding respectively women with biological evidence of iron deficiency (serum ferritin of 12 micrograms/l or less, transferrin saturation less than 15% and/or MCV less than 80 fl), of folate deficiency (red blood cell folates less than 100 micrograms/l) and of inflammatory process (C. Reactive Protein more than 12 mg/l, orosomucoid more than 1.4 g/l or white cell counts of more than 10,000/mm3). According to this method iron deficiency represented the most important cause of anaemia in the context of our sample: iron deficiency contributed to 77% of anaemia. Folate deficiency and inflammatory processes do not in themselves appear to contribute to anaemia.

Adult↗

PubMed2000

Automated Gamma Knife dose planning using polygon clipping and adaptive simulated annealing.

The Gamma Knife (Elekta Instruments, Inc., Norcross, GA), a neurosurgical, highly focused radiation delivery device, is used to eradicate deep-seated anomalous tissue within the human brain by delivering a lethal dose of radiation to target tissue. This dose is the accumulated result of delivering sequential "shots" of radiation to the target, where each shot is approximately three-dimensional (3-D) Gaussian in shape. The size and intensity of each shot can be adjusted by varying the time of radiation exposure and by using one of four collimator sizes ranging from 4-18 mm. Current dose planning requires that the dose plan be developed manually to cover the target, and only the target, with a desired minimum radiation intensity using a minimum number of shots. This is a laborious and subjective process that typically leads to suboptimal conformal target coverage by the dose. We have previously presented a forward-direct-method, which, using adaptive simulated annealing and Nelder-Mead simplex optimizers, automates the selection and placement of generic Gaussian-based kernels or "shots" to form a simulated dose plan. In order to make the computation of the problem tractable, the algorithm exploits 2-D contouring and polygon clipping and takes a 2 1/2-D approach to defining the problem. In the current paper we present the results of four experiments on two historical clinical datasets, where the generic kernels have been replaced by patient specific kernels calculated by Elekta's Leksell Gamma Plan software. For these experiments the user only selects the maximum number of shots to use and the optimizers are then given the freedom to vary the number of shots as well as the weight, collimator size, and 3-D location of each shot. Highly conformal and competitive dose plans were generated for these two difficult cases.

Biophysical Phenomena↗

PubMed2002

The time-rescaling theorem and its application to neural spike train data analysis.

Measuring agreement between a statistical model and a spike train data series, that is, evaluating goodness of fit, is crucial for establishing the model's validity prior to using it to make inferences about a particular neural system. Assessing goodness-of-fit is a challenging problem for point process neural spike train models, especially for histogram-based models such as perstimulus time histograms (PSTH) and rate functions estimated by spike train smoothing. The time-rescaling theorem is a well-known result in probability theory, which states that any point process with an integrable conditional intensity function may be transformed into a Poisson process with unit rate. We describe how the theorem may be used to develop goodness-of-fit tests for both parametric and histogram-based point process models of neural spike trains. We apply these tests in two examples: a comparison of PSTH, inhomogeneous Poisson, and inhomogeneous Markov interval models of neural spike trains from the supplementary eye field of a macque monkey and a comparison of temporal and spatial smoothers, inhomogeneous Poisson, inhomogeneous gamma, and inhomogeneous inverse gaussian models of rat hippocampal place cell spiking activity. To help make the logic behind the time-rescaling theorem more accessible to researchers in neuroscience, we present a proof using only elementary probability theory arguments. We also show how the theorem may be used to simulate a general point process model of a spike train. Our paradigm makes it possible to compare parametric and histogram-based neural spike train models directly. These results suggest that the time-rescaling theorem can be a valuable tool for neural spike train data analysis.

Action Potentials↗

PubMed2002

Roughness distributions for 1/f alpha signals.

The probability density function (PDF) of the roughness, i.e., of the temporal variance, of 1/f(alpha) noise signals is studied. Our starting point is the generalization of the model of Gaussian, time periodic, 1/f noise, discussed in our recent Letter [Phys. Rev. Lett. 87, 240601 (2001)], to arbitrary power law. We investigate three main scaling regions (alpha < or = 1/2, 1/2 < alpha < or = 1, and 1< alpha), distinguished by the scaling of the cumulants in terms of the microscopic scale and the total length of the period. Various analytical representations of the PDF allow for a precise numerical evaluation of the scaling function of the PDF for any alpha. A simulation of the periodic process makes it possible to study also nonperiodic, thus experimentally more relevant, signals on relatively short intervals embedded in the full period. We find that for alpha < or = 1/2 the scaled PDFs in both the periodic and the nonperiodic cases are Gaussian, but for alpha > 1/2 they differ from the Gaussian and from each other. Both deviations increase with growing alpha. That conclusion, based on numerics, is reinforced by analytic results for alpha = 2 and alpha-->infinity, in the latter limit the scaling function of the PDF being finite for periodic signals, but developing a singularity for the aperiodic ones. Finally, an overview is given for the scaling of cumulants of the roughness and the various scaling regions in arbitrary dimensions. We suggest that our theoretical and numerical results open a different perspective on the data analysis of 1/f(alpha) processes.

Journal Article↗

PubMed1995

The Rician distribution of noisy MRI data.

The image intensity in magnetic resonance magnitude images in the presence of noise is shown to be governed by a Rician distribution. Low signal intensities (SNR < 2) are therefore biased due to the noise. It is shown how the underlying noise can be estimated from the images and a simple correction scheme is provided to reduce the bias. The noise characteristics in phase images are also studied and shown to be very different from those of the magnitude images. Common to both,however, is that the noise distributions are nearly Gaussian for SNR larger than two.

Artifacts↗

PubMed2000

An adaptive nonlinear diffusion algorithm for filtering medical images.

The nonlinear anisotropic diffusive process has shown the good property of eliminating noise while preserving the accuracy of edges and has been widely used in image processing. However, filtering depends on the threshold of the diffusion process, i.e., the cut-off contrast of edges. The threshold varies from image to image and even from region to region within an image. The problem compounds with intensity distortion and contrast variation. We have developed an adaptive diffusion scheme by applying the Central Limit Theorem to selecting the threshold. Gaussian distribution and Rayleigh distribution are used to estimate the distributions of visual objects in images. Regression under such distributions separates the distribution of the major object from other visual objects in a single-peak histogram. The separation helps to automatically determine the threshold. A fast algorithm is derived for the regression process. The method has been successfully used in filtering various medical images.

Algorithms↗

PubMed2002

DNA separation at a liquid-solid interface.

We demonstrate that it is possible to separate a broad band of DNA on a solid substrate without topological obstacles. The mobility was found to scale with molecular size (N) as N(-0.25), while the resolution scaled as N(0.75) indicating that diffusivity on this substrate was minimal. By varying the buffer concentration we were able to show that the mobility for a given chain length scaled with the persistent length (p) as p(1/2). This could be shown to be related to the Gaussian conformation of the chains adsorbed on the surface. A two-dimensional corrugated surface of nonporous silica beads was produced using a self-assembling process at the air/water interface. Even though the surface corrugations were comparable to persistence length we show that they do not affect the mobility, indicating that surface friction rather than topological constraints are the predominant mechanism of separation on a surface.

Adsorption↗

PubMed1986

A model for the perception of curves in dot figures: the role of local salience of "virtual lines".

In many models of visual information processing the notion of a virtual line or dipole is introduced in order to represent the configurational information, notably length and relative orientation, between identical figure elements in figures with discrete elements. Virtual lines have proven to be very useful in predicting perceptual phenomena (Julesz et al. 1973; Stevens 1978). In the present study, virtual lines are utilized in a model which aims to predict the perception of (dotted) curves in dot figures. Clearly many possible curves, formed by adjacent virtual lines, can be constructed within a set of dots. It is proposed that already at the local level of the virtual lines each line has a perceptual salience which results from the function induced by the global dot figure. It is this local line salience or "connectivity" that directs further processing and determines the curves to be seen in a dot figure. The model presented is an information processing model with a clear modular design. It entails three successive levels of representation. First image functions are derived through a convolution of the input with gaussian distribution functions. Next, a discrete internal representation is extracted from the image function consisting of two primitives; blobs, representing the dots, and virtual lines, representing pairwise relations between blobs. The attributes of the blobs are their positions in the image plane, while those of the virtual lines are length, relative orientation and connectivity. At the third level, the discrete internal representation is used to predict the perceived curves. It is shown that the model has advantages over other approaches, e.g. autocorrelation and network models.

Humans↗

PubMed2005

A possible explanation of the low-level brightness-contrast illusions in the light of an extended classical receptive field model of retinal ganglion cells.

The low-level brightness-contrast illusions constitute a special class within visual illusions. Speculations exist that these illusions may be processed through the filtering action of the retinal ganglion cells without necessitating much intervention from higher order processes of visual perception. Concept of the classical receptive field of the ganglion cell, derived from early physiological studies, prompted the idea that a Difference of Gaussian (DoG) model might explain the low-level illusions. In spite of its many successes, the DoG model fails to explain some of these illusions. It has been shown in this paper that it is possible to simulate those illusions with a model that takes into cognizance the role of the extended classical receptive field.

Animals↗

PubMed2002

Kinetics of growth process controlled by convective fluctuations.

A model of the spherical (compact) growth process controlled by a fluctuating local convective velocity field of the fluid particles is introduced. It is assumed that the particle velocity fluctuations are purely noisy, Gaussian, of zero mean, and of various correlations: Dirac delta, exponential, and algebraic (power law). It is shown that for a large class of the velocity fluctuations, the long-time asymptotics of the growth kinetics is universal (i.e., it does not depend on the details of the statistics of fluctuations) and displays the power-law time dependence with the classical exponent 1/2 resembling the diffusion limited growth. For very slow decay of algebraic correlations of fluctuations asymptotically like t(-gamma), gamma in (0,1]), kinetics is anomalous and depends strongly on the exponent gamma. For the averaged radius of the crystal approximately t(1-gamma/2) for 0 approximately (t ln t)1/2 for gamma=1.

Journal Article↗

PubMed2007

Direct curvature scale space: theory and corner detection.

The Curvature Scale Space (CSS) technique is considered to be a modern tool in image processing and computer vision. Direct Curvature Scale Space (DCSS) is defined as the CSS that results from convolving the curvature of a planar curve with a Gaussian kernel directly. In this paper we present a theoretical analysis of DCSS in detecting corners on planar curves. The scale space behavior of isolated single and double corner models is investigated and a number of model properties are specified which enable us to transform a DCSS image into a tree organization and, so that corners can be detected in a multiscale sense. To overcome the sensitivity of DCSS to noise, a hybrid strategy to apply CSS and DCSS is suggested.

Algorithms↗

PubMed2005

Quantitative characterization of disparity tuning in ventral pathway area V4.

We performed a quantitative characterization of binocular disparity-tuning functions in the ventral (object-processing) pathway of the macaque visual cortex. We measured responses of 452 area V4 neurons to stimuli with disparities ranging from -1.0 to +1.0 degrees. Asymmetric Gaussian functions fit the raw data best (median R = 0.90), capturing both the modal components (local peaks in the -1.0 to +1.0 degrees range) and the monotonic components (linear or sigmoidal dependency on disparity) of the tuning patterns. Values derived from the asymmetric Gaussian fits were used to characterize neurons on a modal x monotonic tuning domain. Points along the modal tuning axis correspond to classic tuned excitatory and inhibitory patterns; points along the monotonic axis correspond to classic near and far patterns. The distribution on this domain was continuous, with the majority of neurons exhibiting a mixed modal/monotonic tuning pattern. The distribution in the modal dimension was shifted toward excitatory patterns, consistent with previous results in other areas. The distribution in the monotonic dimension was shifted toward tuning for crossed disparities (corresponding to stimuli nearer than the fixation plane). This could reflect a perceptual emphasis on objects or object parts closer to the observer. We also found that disparity-tuning strength was positively correlated with orientation-tuning strength and color-tuning strength, and negatively correlated with receptive field eccentricity.

Animals↗