Thresholds of color attribute differences in detecting camouflaged textures

We examined the threshold at which a camouflaged color texture pattern (target) embedded in a surrounding colored texture pattern (background) was discriminated by making the difference between their color distributions serve as a cue. The texture consisted of 900 colored disks. The color applied to the disk was chosen from a normal distribution with the mean and the standard deviation set beforehand. The mean of the background's distribution was a standard achromatic color set at L*=40, u*=0, and v*=0 of CIELUV. In experiment 1, the mean of the target's color distribution was shifted from the background's one. The threshold for the mean of the target's color distribution depended on the standard deviation and increased as the standard deviation became bigger. In experiment 2, the standard deviation of the target's color distribution was shifted. There was the slight dependence of threshold of the standard deviation of the target's distribution on that of the background's distribution. In experiment 3, both of the mean and the standard deviation of the target's color distribution were shifted at the same time. The threshold was not determined by each of the mean and the standard deviation independently. There seemed to be some compensating contribution between them to each other. The threshold could be characterized by Doyle metric or modified Doyle metric.     

Timing of diapause in relation to temporally variable catastrophes

This paper analyses the response of the distribution of diapause switching times in an arthropod population with respect to variation in a catastrophe, which kills nondiapause individuals. For concreteness, the catastrophe will be taken to the onset of winter. The relationship between an individual's switching time and the decision whether to diapause is defined as follows: If she passes through the end of the sensitive period, during which the diapause decision is made, before her switching time, she will complete development and reproduce rather than diapause. If she passes through the sensitive period on or after her switching time, she will diapause. The model follows the evolution of the distribution of switching times for a population over a sequence of years. Random variation in the end of the season is created by sampling from a normal distribution of times at the end of the growing season. The model is for a haploid population in which the distribution of switching times that a female passes to her offspring is normally distributed having her switching time as its mean. This approximates a sexual population with strong positive assortative mating and heritability near 1. This mode of inheritance permits a rapid response to yearly changes in the end of the season as a contrast to earlier models, which incorporated a slow response. Patterns of temporal change in the median switching time are analyzed. The influences of three parameters are considered: the mean and standard deviation of the end of the season, and standard deviation of the offspring distribution. The main conclusion differs from the results of earlier models in that the end of the season must be extremely variable before the median of the distribution of switching times displays conservative behavior, i. e., before it becomes significantly earlier than the median expected when the end of the season is constant and equal to the mean of the normal distribution for the end of the season used in the simulation. Previous models predicted a conservative response even in moderately variable environments.     

A Mixture Model for Quantum Dot Images of Kinesin Motor Assays

Summary We introduce a nearly automatic procedure to locate and count the quantum dots in images of kinesin motor assays. Our procedure employs an approximate likelihood estimator based on a two‐component mixture model for the image data; the first component has a normal distribution, and the other component is distributed as a normal random variable plus an exponential random variable. The normal component has an unknown variance, which we model as a function of the mean. We use B‐splines to estimate the variance function during a training run on a suitable image, and the estimate is used to process subsequent images. Parameter estimates are generated for each image along with estimates of standard errors, and the number of dots in the image is determined using an information criterion and likelihood ratio tests. Realistic simulations show that our procedure is robust and that it leads to accurate estimates, both of parameters and of standard errors.     

Random marginal agreement coefficients: rethinking the adjustment for chance when measuring agreement

Agreement coefficients quantify how well a set of instruments agree in measuring some response on a population of interest. Many standard agreement coefficients (e.g. kappa for nominal, weighted kappa for ordinal, and the concordance correlation coefficient (CCC) for continuous responses) may indicate increasing agreement as the marginal distributions of the two instruments become more different even as the true cost of disagreement stays the same or increases. This problem has been described for the kappa coefficients; here we describe it for the CCC. We propose a solution for all types of responses in the form of random marginal agreement coefficients (RMACs), which use a different adjustment for chance than the standard agreement coefficients. Standard agreement coefficients model chance agreement using expected agreement between two independent random variables each distributed according to the marginal distribution of one of the instruments. RMACs adjust for chance by modeling two independent readings both from the mixture distribution that averages the two marginal distributions. In other words, both independent readings represent first a random choice of instrument, then a random draw from the marginal distribution of the chosen instrument. The advantage of the resulting RMAC is that differences between the two marginal distributions will not induce greater apparent agreement. As with the standard agreement coefficients, the RMACs do not require any assumptions about the bivariate distribution of the random variables associated with the two instruments. We describe the RMAC for nominal, ordinal and continuous data, and show through the delta method how to approximate the variances of some important special cases.     

Variability in mammalian dentitions: size-related bias in the coefficient of variation

The coefficient of variation has been used in many evolutionary studies. However, a strong negative correlation between this index and size may artificially inflate the apparent variability of small traits. This is most pronounced when variables whose size differs by more than an order of magnitude are compared or when the index is applied to variables whose size is within an order of magnitude of their measurement error. When this is likely to affect conclusions, other indexes of variability should be considered. One alternative is to use the standard deviation of log-transformed data; however, this index is sometimes still correlated with variable size so care should be exercised in its use. Another alternative is to regress the standard deviation onto mean variable size; however, this method may also be misleading if variables are not randomly distributed about the regression line. As an example of the effect of bias in the coefficient of variation, previous studies of mammalian dental variability profiles were re-evaluated. It was found that variation among teeth is relatively homogenous, both within and among species. The exception is that the canines of some mammalian species have variability that is considerably higher than would be expected from tooth size. Previous explanations of variability patterns that invoked developmental fields are incompatible with the new data.     

Impact of Random Variables Probability Distribution on Public Health Risk Assessment from Contaminated Soil

Probabilistic methods are now being applied increasingly to public health risk assessment instead of the deterministic, conservative, point estimates. An essential part of the probabilistic methods is the selection of probability distribution functions to represent the uncertainty of the random variables considered. We study the effect of selection of different probability distribution functions on the probabilistic outcome using the first-order reliability method (FORM). An example of cancer risk resulting from dermal contact with benzo(a)pyrene (BaP)-contaminated soil is given. Cancer potency factor, soil concentration, and fraction of skin area exposed were assigned normal, lognormal, and uniform probability distribution functions, and the effect of probability of exceeding a target risk level (termed the probability of failure) and sensitivity measures were studied. We investigated the question: what happens when one assumes different distribution shapes with the same mean and standard deviation? The results indicate that the selection of a probability distribution function for the random variables had a moderate impact on the probability of failure when the target risk is at the 50th percentile level, while the impact was much larger for a 95th target risk percentile. We conclude that the probability distribution will have a large impact because in most cases the regulatory threshold risk is at the tail end of the risk distribution. The impact of the distributions on probabilistic sensitivity, however, showed a reversed trend, where the impact was slightly more appreciable for the 50th percentile than for the 95th percentile. The selection of distribution shape did not, however, alter the order of probabilistic sensitivity of the basic random variables.     

Phytoremediation of palm oil mill secondary effluent (POMSE) by Chrysopogon zizanioides (L.) using artificial neural networks

Artificial neural networks (ANNs) have been widely used to solve the problems because of their reliable, robust, and salient characteristics in capturing the nonlinear relationships between variables in complex systems. In this study, ANN was applied for modeling of Chemical Oxygen Demand (COD) and biodegradable organic matter (BOD) removal from palm oil mill secondary effluent (POMSE) by vetiver system. The independent variable, including POMSE concentration, vetiver slips density, and removal time, has been considered as input parameters to optimize the network, while the removal percentage of COD and BOD were selected as output. To determine the number of hidden layer nodes, the root mean squared error of testing set was minimized, and the topologies of the algorithms were compared by coefficient of determination and absolute average deviation. The comparison indicated that the quick propagation (QP) algorithm had minimum root mean squared error and absolute average deviation, and maximum coefficient of determination. The importance values of the variables was included vetiver slips density with 42.41%, time with 29.8%, and the POMSE concentration with 27.79%, which showed none of them, is negligible. Results show that the ANN has great potential ability in prediction of COD and BOD removal from POMSE with residual standard error (RSE) of less than 0.45%.     

Stochastic disease dynamics of a hospital infection model

A stochastic model for hospital infection incorporating both direct transmission and indirect transmission via free-living bacteria in the environment is investigated. We examine the long term behavior of the model by calculating a stationary distribution and normal approximation of the distribution. The quasi-stationary distribution of the model is studied to investigate the models’ behavior before extinction and the time to extinction. Numerical results show agreement between the calculated distributions and results of event-driven simulations. Hand hygiene of volunteers is more effective in terms of reducing the mean (or standard deviation) of the stationary distribution of colonized patients and the expected time to extinction compared to hand hygiene of health care workers (HCWs), on the basis of our parameter values. However, the indirect (or direct) transmission rate can lead to either increase or decrease in the standard deviation of the stationary distribution, but the impact of the indirect transmission is much greater than that of the direct transmission. The findings suggest that isolation of new admitted colonized patients is most effective in reducing both the mean and standard deviation of the stationary distribution and measures related to indirect transmission are secondary in their effects compared to other interventions.     

The relationship between the Gabor elementary function and a stochastic model of the inter-spike interval distribution in the responses of visual cortex neurons

In a previously reported study (Berger et al. 1990) we analyzed distributions of interspike intervals recorded extracellularly from cat visual cortex under four stimulus conditions. Stimuli were gratings differing in orientation and spatial frequency. The probability density function of first passage time for a random walk with drift process, which is defined by its barrier height and drift coefficient, was used to characterize the generating process of axonal discharge under resting and stimulus conditions. Drift coefficient and barrier height were derived from the sample mean and standard deviation of the measured inter-spike intervals. For cells with simple receptive fields, variations in spatial frequency produced changes only in drift coefficient. Variations in barrier height were produced only by changes in orientation of the stimulus. Currently, the method used to analyze these data was implemented in a simulation which displayed the relationship between the interval distribution of impulses, the random walk which represents the time series characteristic of the spike train model and the Gabor filter function which represents the geometry of the receptive field process.     

Estimation of microbial contamination of food from prevalence and concentration data: application to Listeria monocytogenes in fresh vegetables

A normal distribution and a mixture model of two normal distributions in a Bayesian approach using prevalence and concentration data were used to establish the distribution of contamination of the food-borne pathogenic bacteria Listeria monocytogenes in unprocessed and minimally processed fresh vegetables. A total of 165 prevalence studies, including 15 studies with concentration data, were taken from the scientific literature and from technical reports and used for statistical analysis. The predicted mean of the normal distribution of the logarithms of viable L. monocytogenes per gram of fresh vegetables was -2.63 log viable L. monocytogenes organisms/g, and its standard deviation was 1.48 log viable L. monocytogenes organisms/g. These values were determined by considering one contaminated sample in prevalence studies in which samples are in fact negative. This deliberate overestimation is necessary to complete calculations. With the mixture model, the predicted mean of the distribution of the logarithm of viable L. monocytogenes per gram of fresh vegetables was -3.38 log viable L. monocytogenes organisms/g and its standard deviation was 1.46 log viable L. monocytogenes organisms/g. The probabilities of fresh unprocessed and minimally processed vegetables being contaminated with concentrations higher than 1, 2, and 3 log viable L. monocytogenes organisms/g were 1.44, 0.63, and 0.17%, respectively. Introducing a sensitivity rate of 80 or 95% in the mixture model had a small effect on the estimation of the contamination. In contrast, introducing a low sensitivity rate (40%) resulted in marked differences, especially for high percentiles. There was a significantly lower estimation of contamination in the papers and reports of 2000 to 2005 than in those of 1988 to 1999 and a lower estimation of contamination of leafy salads than that of sprouts and other vegetables. The interest of the mixture model for the estimation of microbial contamination is discussed.     

Feature Selection for Gene Expression Using Model-Based Entropy

Gene expression data usually contain a large number of genes but a small number of samples. Feature selection for gene expression data aims at finding a set of genes that best discriminate biological samples of different types. Using machine learning techniques, traditional gene selection based on empirical mutual information suffers the data sparseness issue due to the small number of samples. To overcome the sparseness issue, we propose a model-based approach to estimate the entropy of class variables on the model, instead of on the data themselves. Here, we use multivariate normal distributions to fit the data, because multivariate normal distributions have maximum entropy among all real-valued distributions with a specified mean and standard deviation and are widely used to approximate various distributions. Given that the data follow a multivariate normal distribution, since the conditional distribution of class variables given the selected features is a normal distribution, its entropy can be computed with the log-determinant of its covariance matrix. Because of the large number of genes, the computation of all possible log-determinants is not efficient. We propose several algorithms to largely reduce the computational cost. The experiments on seven gene data sets and the comparison with other five approaches show the accuracy of the multivariate Gaussian generative model for feature selection, and the efficiency of our algorithms.     

Cell orientation response to cyclically deformed substrates: Experimental validation of a cell model

We have developed a stochastic model that describes the orientation response of bipolar cells grown on a cyclically deformed substrate. The model was based on the following hypotheses regarding the behavior of individual cells: (a) the mechanical signal responsible for cell reorientation is the peak to peak surface strain along the cell's major axis (p-p axial strain); (b) each cell has an axial strain threshold and the threshold is normally distributed in the cell population; (c) the cell will avoid any direction where the p-p axial strain is above its threshold; and (d) the cell will randomly orient within the range of directions where the p-p axial strains are less than the cell's threshold. These hypotheses were tested by comparing model predictions with experimental observations from stretch experiments conducted with human melanocytes. The cells were grown on elastic rectangular culture dishes subjected to unidirectional cyclic (1 Hz) stretching with amplitudes of 0, 4, 8, and 12%. After 24 h of stimulation, the distribution of cell orientations was determined by measuring the orientations of 300–400 randomly selected cells. The 12% stretch experiment was used to determine the mean, 3.5%, and the standard deviation, 1.0%, of the strain threshold for the cell population. The Kolmogorov-Smirnov test was then used to determine if the orientation distributions predicted by the model were different from experimentally measured distributions for the 4 and 8% stretches. No significant differences were found between the predicted and experimental distributions (4%: p = 0.70; and 8%: p = 0.71). These results support the hypothesis that cells randomly orient, but avoid directions where the p-p axial strains are above their thresholds.     

Distribution of age at menopause in two Danish samples

We analyzed the distribution of reported age at natural menopause in two random samples of Danish women (n = 176 and n = 150) to determine the shape of the distribution and to disclose any possible trends in the distribution parameters. It was necessary to correct the frequencies of the reported ages for the effect of differing ages at reporting. The corrected distribution of age at menopause differs from the normal distribution in the same way in both samples. Both distributions could be described by a mixture of two normal distributions. It appears that most of the parameters of the normal distribution mixtures remain unchanged over a 50-year time lag. The position of the distribution, that is, the mean age at menopause, however, increases slightly but significantly.     

On the polydispersity of mitochondria in tissue homogenates and the determination of the average sedimentation coefficients of mixed populations of mitochondria

The sedimentation profile (sediterm) of subcellular particles in homogenous media depends on the average sedimentation coefficient ( value) and the size distribution. The present study has focused on the two common types of polydispersity, i.e., (i) a variable standard deviation in a normal (Gaussian) size distribution, and (ii) two populations of partieles with defined values and size distributions. Theoretical considerations and experimental data indicate that rat liver mitochondria have a normal size distribution, ( ) with much smaller standard deviation than previously assumed (σ = 0.118 μm) based on isokinetic gradient centrifugation and electron microscopy. Sedimentation of a mixture of rat liver and guinea pig ileal mitochondria having the values 17,040 S and 5640 S, respectively, gave the expected profile (sediterm) of two populations of particles. Their values were estimated to be identical to those obtained when the individual mitochondrial populations were sedimented. The ratio between the populations (based on the assay of marker enzyme) was found to be identical to the expected value.     

When will plant morphology affect the shape of a seed dispersal "kernel"?

Most models of dispersal assume that plants are point sources. In reality, the scale in height over which seed sources are distributed is often of the same order as the scale in distance over which most individual seeds are dispersed. But is this sufficient to affect the fundamental shapes of dispersal frequency distributions? Most published conclusions about the effects of canopy structure on dispersal are subjective. A model is developed to explore the consequences of plant canopies for the shapes of whole-plant seed dispersal "kernels". The canopies were described by simple geometric shapes, while an empirical probability density function (PDF) was used for dispersal from a point source. It was found that the resulting whole-plant PDF for dispersal distance was almost invariably peaked, whereas the PDF for the density of seed rain (as would be measured by pitfall traps) could either be peaked or monotonic according to the canopy shape, position of seeds in the canopy, and mean dispersal distance. The shapes of kernels from whole plants (distributed seed sources) can be very different from those derived from a point source under certain circumstances.     

Superstatistics analysis of the ion current distribution function: Met3PbCl influence study

A novel analysis of ion current time series is proposed. It is shown that higher (second, third and fourth) statistical moments of the ion current probability distribution function (PDF) can yield new information about ion channel properties. The method is illustrated on a two-state model where the PDF of the compound states are given by normal distributions. The proposed method was applied to the analysis of the SV cation channels of vacuolar membrane of Beta vulgaris and the influence of trimethyllead chloride (Met₃PbCl) on the ion current probability distribution. Ion currents were measured by patch-clamp technique. It was shown that Met₃PbCl influences the variance of the open-state ion current but does not alter the PDF of the closed-state ion current. Incorporation of higher statistical moments into the standard investigation of ion channel properties is proposed.     

Influence of environmental stress on distributions of times to first division in Escherichia coli populations, as determined by digital-image analysis of individual cells

The distributions of times to first cell division were determined for populations of Escherichia coli stationary-phase cells inoculated onto agar media. This was accomplished by using automated analysis of digital images of individual cells growing on agar and calculation of the "box area ratio." Using approximately 300 cells per experiment, the mean time to first division and standard deviation for cells grown in liquid medium at 37 degrees C and inoculated on agar and incubated at 20 degrees C were determined as 3.0 h and 0.7 h, respectively. Distributions were observed to tail toward the higher values, but no definitive model distribution was identified. Both preinoculation stress by heating cultures at 50 degrees C and postinoculation stress by growth in the presence of higher concentrations of NaCl increased mean times to first division. Both stresses also resulted in an increase in the spread of the distributions that was proportional to the mean division time, the coefficient of variation being constant at approximately 0.2 in all cases. The "relative division time," which is the time to first division for individual cells expressed in terms of the cell size doubling time, was used as measure of the "work to be done" to prepare for cell division. Relative division times were greater for heat-stressed cells than for those growing under osmotic stress.     

Dynamics of the distribution of variables in morphology

This paper discusses examples of exponentially distributed, Poisson-distributed, and binomially distributed random variables from morphology and describes secular and historical processes as well as phenomena of aging as factors of the dynamics of such distributions, the major focus being on tests of morphometric variables for the existence of normal distributions. In those cases where hypotheses of the existence of particular distributions of random morphometric variables are established it is necessary that consideration be given to metrological and stereological factors pertaining to the process of measuring and the geometry of the structures being measured, respectively. Karyometric results are used to demonstrate the splitting of a single statistical population into several populations as a result of the process of aging of the human organism.     

Tooth Size Variation in Pinniped Dentitions

It is contentious whether size variation among mammalian teeth is heterogeneous or homogeneous, whether the coefficient of variation is reliable, and whether the standard deviation of log-transformed data and the residual of standard deviation on mean variable size are useful replacements for the coefficient of variation. Most studies of tooth size variation have been on mammals with complex-crowned teeth, with relatively little attention paid to taxa with simple-crowned teeth, such as Pinnipedia. To fill this gap in knowledge and to resolve the existing controversies, we explored the variation of linear size variables (length and width) for all teeth from complete permanent dentitions of four pinniped species, two phocids (Histriophoca fasciata, Phoca largha) and two otariids (Callorhinus ursinus, Eumetopias jubatus). Size variation among these teeth was mostly heterogeneous both along the toothrow and among species. The incisors, canines, and mesial and distal postcanines were often relatively highly variable. The levels of overall dental size variation ranged from relatively low as in land carnivorans (Phoca largha and both otariids) to high (Histriophoca fasciata). Sexual size dimorphism varied among teeth and among species, with teeth being, on average, larger in males than in females. This dimorphism was more pronounced, and the canines were larger and more dimorphic relative to other teeth in the otariids than in the phocids. The coefficient of variation quantified variation reliably in most cases. The standard deviation of log-transformed data was redundant with the coefficient of variation. The residual of standard deviation on mean variable size was inaccurate when size variation was considerably heterogeneous among the compared variables, and was incomparable between species and between sexes. The existing hypotheses invoking developmental fields, occlusal complexity, and the relative timing of tooth formation and sexually dimorphic hormonal activity do not adequately explain the differential size variation along the pinniped toothrow.     

A semiparametric Bayesian approach for structural equation models

In the development of structural equation models (SEMs), observed variables are usually assumed to be normally distributed. However, this assumption is likely to be violated in many practical researches. As the non‐normality of observed variables in an SEM can be obtained from either non‐normal latent variables or non‐normal residuals or both, semiparametric modeling with unknown distribution of latent variables or unknown distribution of residuals is needed. In this article, we find that an SEM becomes nonidentifiable when both the latent variable distribution and the residual distribution are unknown. Hence, it is impossible to estimate reliably both the latent variable distribution and the residual distribution without parametric assumptions on one or the other. We also find that the residuals in the measurement equation are more sensitive to the normality assumption than the latent variables, and the negative impact on the estimation of parameters and distributions due to the non‐normality of residuals is more serious. Therefore, when there is no prior knowledge about parametric distributions for either the latent variables or the residuals, we recommend making parametric assumption on latent variables, and modeling residuals nonparametrically. We propose a semiparametric Bayesian approach using the truncated Dirichlet process with a stick breaking prior to tackle the non‐normality of residuals in the measurement equation. Simulation studies and a real data analysis demonstrate our findings, and reveal the empirical performance of the proposed methodology. A free WinBUGS code to perform the analysis is available in Supporting Information.